A two-component Matched Interface and Boundary (MIB) regularization for charge singularity in implicit solvation

NASA Astrophysics Data System (ADS)

Geng, Weihua; Zhao, Shan

2017-12-01

We present a new Matched Interface and Boundary (MIB) regularization method for treating charge singularity in solvated biomolecules whose electrostatics are described by the Poisson-Boltzmann (PB) equation. In a regularization method, by decomposing the potential function into two or three components, the singular component can be analytically represented by the Green's function, while other components possess a higher regularity. Our new regularization combines the efficiency of two-component schemes with the accuracy of the three-component schemes. Based on this regularization, a new MIB finite difference algorithm is developed for solving both linear and nonlinear PB equations, where the nonlinearity is handled by using the inexact-Newton's method. Compared with the existing MIB PB solver based on a three-component regularization, the present algorithm is simpler to implement by circumventing the work to solve a boundary value Poisson equation inside the molecular interface and to compute related interface jump conditions numerically. Moreover, the new MIB algorithm becomes computationally less expensive, while maintains the same second order accuracy. This is numerically verified by calculating the electrostatic potential and solvation energy on the Kirkwood sphere on which the analytical solutions are available and on a series of proteins with various sizes.

A LiDAR data-based camera self-calibration method

NASA Astrophysics Data System (ADS)

Xu, Lijun; Feng, Jing; Li, Xiaolu; Chen, Jianjun

2018-07-01

To find the intrinsic parameters of a camera, a LiDAR data-based camera self-calibration method is presented here. Parameters have been estimated using particle swarm optimization (PSO), enhancing the optimal solution of a multivariate cost function. The main procedure of camera intrinsic parameter estimation has three parts, which include extraction and fine matching of interest points in the images, establishment of cost function, based on Kruppa equations and optimization of PSO using LiDAR data as the initialization input. To improve the precision of matching pairs, a new method of maximal information coefficient (MIC) and maximum asymmetry score (MAS) was used to remove false matching pairs based on the RANSAC algorithm. Highly precise matching pairs were used to calculate the fundamental matrix so that the new cost function (deduced from Kruppa equations in terms of the fundamental matrix) was more accurate. The cost function involving four intrinsic parameters was minimized by PSO for the optimal solution. To overcome the issue of optimization pushed to a local optimum, LiDAR data was used to determine the scope of initialization, based on the solution to the P4P problem for camera focal length. To verify the accuracy and robustness of the proposed method, simulations and experiments were implemented and compared with two typical methods. Simulation results indicated that the intrinsic parameters estimated by the proposed method had absolute errors less than 1.0 pixel and relative errors smaller than 0.01%. Based on ground truth obtained from a meter ruler, the distance inversion accuracy in the experiments was smaller than 1.0 cm. Experimental and simulated results demonstrated that the proposed method was highly accurate and robust.

I-Love-Q to the extreme

NASA Astrophysics Data System (ADS)

Silva, Hector O.; Yunes, Nicolás

2018-01-01

Certain bulk properties of neutron stars, in particular their moment of inertia, rotational quadrupole moment and tidal Love number, when properly normalized, are related to one another in a nearly equation of state independent way. The goal of this paper is to test these relations with extreme equations of state at supranuclear densities constrained to satisfy only a handful of generic, physically sensible conditions. By requiring that the equation of state be (i) barotropic and (ii) its associated speed of sound be real, we construct a piecewise function that matches a tabulated equation of state at low densities, while matching a stiff equation of state parametrized by its sound speed in the high-density region. We show that the I-Love-Q relations hold to 1 percent with this class of equations of state, even in the extreme case where the speed of sound becomes superluminal and independently of the transition density. We also find further support for the interpretation of the I-Love-Q relations as an emergent symmetry due to the nearly constant eccentricity of isodensity contours inside the star. These results reinforce the robustness of the I-Love-Q relations against our current incomplete picture of physics at supranuclear densities, while strengthening our confidence in the applicability of these relations in neutron star astrophysics.

On the tautology of the matching law in consumer behavior analysis.

PubMed

Curry, Bruce; Foxall, Gordon R; Sigurdsson, Valdimar

2010-05-01

Matching analysis has often attracted the criticism that it is formally tautological and hence empirically unfalsifiable, a problem that particularly affects translational attempts to extend behavior analysis into new areas. An example is consumer behavior analysis where application of matching in natural settings requires the inference of ratio-based relationships between amount purchased and amount spent. This gives rise to the argument that matching is an artifact of the way in which the alleged independent and dependent variables are defined and measured. We argue that the amount matching law would be tautological only in extreme circumstances (those in which prices or quantities move strictly in proportion); this is because of the presence of an error term in the matching function which arises from aggregation, particularly aggregation over brands. Cost matching is a viable complement of amount matching which avoids this tautology but a complete explanation of consumer choice requires a viable measure of amount matching also. This necessitates a more general solution to the problem of tautology in matching. In general, the fact that there remain doubts about the functional form of the matching equation itself implies the absence of a tautology. In proposing a general solution to the problem of assumed tautology in matching, the paper notes the experiences of matching researchers in another translation field, sports behavior. Copyright (c) 2009 Elsevier B.V. All rights reserved.

Black Hole and Galaxy Coevolution from Continuity Equation and Abundance Matching

NASA Astrophysics Data System (ADS)

Aversa, R.; Lapi, A.; de Zotti, G.; Shankar, F.; Danese, L.

2015-09-01

We investigate the coevolution of galaxies and hosted supermassive black holes (BHs) throughout the history of the universe by a statistical approach based on the continuity equation and the abundance matching technique. Specifically, we present analytical solutions of the continuity equation without source terms to reconstruct the supermassive BH mass function from the active galactic nucleus (AGN) luminosity functions. Such an approach includes physically motivated AGN light curves tested on independent data sets, which describe the evolution of the Eddington ratio and radiative efficiency from slim- to thin-disk conditions. We nicely reproduce the local estimates of the BH mass function, the AGN duty cycle as a function of mass and redshift, along with the Eddington ratio function and the fraction of galaxies with given stellar mass hosting an AGN with given Eddington ratio. We exploit the same approach to reconstruct the observed stellar mass function at different redshift from the ultraviolet and far-IR luminosity functions associated with star formation in galaxies. These results imply that the build-up of stars and BHs in galaxies occurs via in situ processes, with dry mergers playing a marginal role at least for stellar masses ≲ 3× {10}11 {M}⊙ and BH masses ≲ {10}9 {M}⊙ , where the statistical data are more secure and less biased by systematic errors. In addition, we develop an improved abundance matching technique to link the stellar and BH content of galaxies to the gravitationally dominant dark matter (DM) component. The resulting relationships constitute a testbed for galaxy evolution models, highlighting the complementary role of stellar and AGN feedback in the star formation process. In addition, they may be operationally implemented in numerical simulations to populate DM halos or to gauge subgrid physics. Moreover, they may be exploited to investigate the galaxy/AGN clustering as a function of redshift, mass, and/or luminosity. In fact, the clustering properties of BHs and galaxies are found to be in full agreement with current observations, thus further validating our results from the continuity equation. Finally, our analysis highlights that (i) the fraction of AGNs observed in the slim-disk regime, where most of the BH mass is accreted, increases with redshift; and (ii) already at z≳ 6 a substantial amount of dust must have formed over timescales ≲ {10}8 yr in strongly star-forming galaxies, making these sources well within the reach of ALMA surveys in (sub)millimeter bands.

A new method to simulate the effects of viscous fingering on miscible displacement processes in porous media

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

Vossoughi, S.; Green, D.W.; Smith, J.E.

This paper presents a new method to simulate the effects of viscous fingering on miscible displacement processes in porous media. The method is based on the numerical solution of a general form of the convection-dispersion equation. In this equation the convection term is represented by a fractional flow function. The fractional flow function is derived from Darcy's law using a concentration-dependent, average viscosity and relative flow area to each fluid at any point in the bed. The method was extended to the description of a polymer flood by including retention and inaccessible pore volume. A Langmuir-type model for polymer retentionmore » in the rock was used. The resulting convection-dispersion equation for displacement by polymer was then solved numerically by the use of a finite element method with linear basis functions and Crank-Nicholson derivative approximation. History matches were performed on four sets of laboratory data to verify the model. These were: an unfavorable viscosity ratio displacement, stable displacement of glycerol by polymer solution, unstable displacement of brine by a slug of polymer solution, and a favorable viscosity ratio displacement. In general, computed results from the model matched laboratory data closely. Good agreement of the model with experiments over a significant range of variables lends support to the analysis.« less

Orbital-free extension to Kohn-Sham density functional theory equation of state calculations: Application to silicon dioxide

DOE PAGES

Sjostrom, Travis; Crockett, Scott

2015-09-02

The liquid regime equation of state of silicon dioxide SiO 2 is calculated via quantum molecular dynamics in the density range of 5 to 15 g/cc and with temperatures from 0.5 to 100 eV, including the α-quartz and stishovite phase Hugoniot curves. Below 8 eV calculations are based on Kohn-Sham density functional theory (DFT), and above 8 eV a new orbital-free DFT formulation, presented here, based on matching Kohn-Sham DFT calculations is employed. Recent experimental shock data are found to be in very good agreement with the current results. Finally both experimental and simulation data are used in constructing amore » new liquid regime equation of state table for SiO 2.« less

Curvelet-domain multiple matching method combined with cubic B-spline function

NASA Astrophysics Data System (ADS)

Wang, Tong; Wang, Deli; Tian, Mi; Hu, Bin; Liu, Chengming

2018-05-01

Since the large amount of surface-related multiple existed in the marine data would influence the results of data processing and interpretation seriously, many researchers had attempted to develop effective methods to remove them. The most successful surface-related multiple elimination method was proposed based on data-driven theory. However, the elimination effect was unsatisfactory due to the existence of amplitude and phase errors. Although the subsequent curvelet-domain multiple-primary separation method achieved better results, poor computational efficiency prevented its application. In this paper, we adopt the cubic B-spline function to improve the traditional curvelet multiple matching method. First, select a little number of unknowns as the basis points of the matching coefficient; second, apply the cubic B-spline function on these basis points to reconstruct the matching array; third, build constraint solving equation based on the relationships of predicted multiple, matching coefficients, and actual data; finally, use the BFGS algorithm to iterate and realize the fast-solving sparse constraint of multiple matching algorithm. Moreover, the soft-threshold method is used to make the method perform better. With the cubic B-spline function, the differences between predicted multiple and original data diminish, which results in less processing time to obtain optimal solutions and fewer iterative loops in the solving procedure based on the L1 norm constraint. The applications to synthetic and field-derived data both validate the practicability and validity of the method.

USING MICROSOFT OFFICE EXCEL® 2007 TO CONDUCT GENERALIZED MATCHING ANALYSES

PubMed Central

Reed, Derek D

2009-01-01

The generalized matching equation is a robust and empirically supported means of analyzing relations between reinforcement and behavior. Unfortunately, no simple task analysis is available to behavior analysts interested in using the matching equation to evaluate data in clinical or applied settings. This technical article presents a task analysis for the use of Microsoft Excel to analyze and plot the generalized matching equation. Using a data-based case example and a step-by-step guide for completing the analysis, these instructions are intended to promote the use of quantitative analyses by researchers with little to no experience in quantitative analyses or the matching law. PMID:20514196

Using Microsoft Office Excel 2007 to conduct generalized matching analyses.

PubMed

Reed, Derek D

2009-01-01

The generalized matching equation is a robust and empirically supported means of analyzing relations between reinforcement and behavior. Unfortunately, no simple task analysis is available to behavior analysts interested in using the matching equation to evaluate data in clinical or applied settings. This technical article presents a task analysis for the use of Microsoft Excel to analyze and plot the generalized matching equation. Using a data-based case example and a step-by-step guide for completing the analysis, these instructions are intended to promote the use of quantitative analyses by researchers with little to no experience in quantitative analyses or the matching law.

Predictive equations for lung volumes from computed tomography for size matching in pulmonary transplantation.

PubMed

Konheim, Jeremy A; Kon, Zachary N; Pasrija, Chetan; Luo, Qingyang; Sanchez, Pablo G; Garcia, Jose P; Griffith, Bartley P; Jeudy, Jean

2016-04-01

Size matching for lung transplantation is widely accomplished using height comparisons between donors and recipients. This gross approximation allows for wide variation in lung size and, potentially, size mismatch. Three-dimensional computed tomography (3D-CT) volumetry comparisons could offer more accurate size matching. Although recipient CT scans are universally available, donor CT scans are rarely performed. Therefore, predicted donor lung volumes could be used for comparison to measured recipient lung volumes, but no such predictive equations exist. We aimed to use 3D-CT volumetry measurements from a normal patient population to generate equations for predicted total lung volume (pTLV), predicted right lung volume (pRLV), and predicted left lung volume (pLLV), for size-matching purposes. Chest CT scans of 400 normal patients were retrospectively evaluated. 3D-CT volumetry was performed to measure total lung volume, right lung volume, and left lung volume of each patient, and predictive equations were generated. The fitted model was tested in a separate group of 100 patients. The model was externally validated by comparison of total lung volume with total lung capacity from pulmonary function tests in a subset of those patients. Age, gender, height, and race were independent predictors of lung volume. In the test group, there were strong linear correlations between predicted and actual lung volumes measured by 3D-CT volumetry for pTLV (r = 0.72), pRLV (r = 0.72), and pLLV (r = 0.69). A strong linear correlation was also observed when comparing pTLV and total lung capacity (r = 0.82). We successfully created a predictive model for pTLV, pRLV, and pLLV. These may serve as reference standards and predict donor lung volume for size matching in lung transplantation. Copyright © 2016 The American Association for Thoracic Surgery. Published by Elsevier Inc. All rights reserved.

A new look at photometry of the Moon

USGS Publications Warehouse

Goguen, J.D.; Stone, T.C.; Kieffer, H.H.; Buratti, B.J.

2010-01-01

We use ROLO photometry (Kieffer, H.H., Stone, T.C. [2005]. Astron. J. 129, 2887-2901) to characterize the before and after full Moon radiance variation for a typical highlands site and a typical mare site. Focusing on the phase angle range 45??. ) to calculate the scattering matrix and solve the radiative transfer equation for I/. F. The mean single scattering albedo is ??=0.808, the asymmetry parameter is ???cos. ?????=0.77 and the phase function is very strongly peaked in both the forward and backward scattering directions. The fit to the observations for the highland site is excellent and multiply scattered photons contribute 80% of I/. F. We conclude that either model, roughness or multiple scattering, can match the observations, but that the strongly anisotropic phase functions of realistic particles require rigorous calculation of many orders of scattering or spurious photometric roughness estimates are guaranteed. Our multiple scattering calculation is the first to combine: (1) a regolith model matched to the measured particle size distribution and index of refraction of the lunar soil, (2) a rigorous calculation of the particle phase function and solution of the radiative transfer equation, and (3) application to lunar photometry with absolute radiance calibration. ?? 2010 Elsevier Inc.

Reconstruction of Twist Torque in Main Parachute Risers

NASA Technical Reports Server (NTRS)

Day, Joshua D.

2015-01-01

The reconstruction of twist torque in the Main Parachute Risers of the Capsule Parachute Assembly System (CPAS) has been successfully used to validate CPAS Model Memo conservative twist torque equations. Reconstruction of basic, one degree of freedom drop tests was used to create a functional process for the evaluation of more complex, rigid body simulation. The roll, pitch, and yaw of the body, the fly-out angles of the parachutes, and the relative location of the parachutes to the body are inputs to the torque simulation. The data collected by the Inertial Measurement Unit (IMU) was used to calculate the true torque. The simulation then used photogrammetric and IMU data as inputs into the Model Memo equations. The results were then compared to the true torque results to validate the Model Memo equations. The Model Memo parameters were based off of steel risers and the parameters will need to be re-evaluated for different materials. Photogrammetric data was found to be more accurate than the inertial data in accounting for the relative rotation between payload and cluster. The Model Memo equations were generally a good match and when not matching were generally conservative.

Viability of the matter bounce scenario in F(T) gravity and Loop Quantum Cosmology for general potentials

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

Haro, Jaume; Amorós, Jaume, E-mail: jaime.haro@upc.edu, E-mail: jaume.amoros@upc.edu

2014-12-01

We consider the matter bounce scenario in F(T) gravity and Loop Quantum Cosmology (LQC) for phenomenological potentials that at early times provide a nearly matter dominated Universe in the contracting phase, having a reheating mechanism in the expanding or contracting phase, i.e., being able to release the energy of the scalar field creating particles that thermalize in order to match with the hot Friedmann Universe, and finally at late times leading to the current cosmic acceleration. For these potentials, numerically solving the dynamical perturbation equations we have seen that, for the particular F(T) model that we will name teleparallel versionmore » of LQC, and whose modified Friedmann equation coincides with the corresponding one in holonomy corrected LQC when one deals with the flat Friedmann-Lemaître-Robertson-Walker (FLRW) geometry, the corresponding equations obtained from the well-know perturbed equations in F(T) gravity lead to theoretical results that fit well with current observational data. More precisely, in this teleparallel version of LQC there is a set of solutions which leads to theoretical results that match correctly with last BICEP2 data, and there is another set whose theoretical results fit well with Planck's experimental data. On the other hand, in the standard holonomy corrected LQC, using the perturbed equations obtained replacing the Ashtekar connection by a suitable sinus function and inserting some counter-terms in order to preserve the algebra of constrains, the theoretical value of the tensor/scalar ratio is smaller than in the teleparallel version, which means that there is always a set of solutions that matches with Planck's data, but for some potentials BICEP2 experimental results disfavours holonomy corrected LQC.« less

Smooth function approximation using neural networks.

PubMed

Ferrari, Silvia; Stengel, Robert F

2005-01-01

An algebraic approach for representing multidimensional nonlinear functions by feedforward neural networks is presented. In this paper, the approach is implemented for the approximation of smooth batch data containing the function's input, output, and possibly, gradient information. The training set is associated to the network adjustable parameters by nonlinear weight equations. The cascade structure of these equations reveals that they can be treated as sets of linear systems. Hence, the training process and the network approximation properties can be investigated via linear algebra. Four algorithms are developed to achieve exact or approximate matching of input-output and/or gradient-based training sets. Their application to the design of forward and feedback neurocontrollers shows that algebraic training is characterized by faster execution speeds and better generalization properties than contemporary optimization techniques.

Stellar Mass Function of Active and Quiescent Galaxies via the Continuity Equation

NASA Astrophysics Data System (ADS)

Lapi, A.; Mancuso, C.; Bressan, A.; Danese, L.

2017-09-01

The continuity equation is developed for the stellar mass content of galaxies and exploited to derive the stellar mass function of active and quiescent galaxies over the redshift range z˜ 0{--}8. The continuity equation requires two specific inputs gauged from observations: (I) the star formation rate functions determined on the basis of the latest UV+far-IR/submillimeter/radio measurements and (II) average star formation histories for individual galaxies, with different prescriptions for disks and spheroids. The continuity equation also includes a source term taking into account (dry) mergers, based on recent numerical simulations and consistent with observations. The stellar mass function derived from the continuity equation is coupled with the halo mass function and with the SFR functions to derive the star formation efficiency and the main sequence of star-forming galaxies via the abundance-matching technique. A remarkable agreement of the resulting stellar mass functions for active and quiescent galaxies of the galaxy main sequence, and of the star formation efficiency with current observations is found; the comparison with data also allows the characteristic timescales for star formation and quiescence of massive galaxies, the star formation history of their progenitors, and the amount of stellar mass added by in situ star formation versus that contributed by external merger events to be robustly constrained. The continuity equation is shown to yield quantitative outcomes that detailed physical models must comply with, that can provide a basis for improving the (subgrid) physical recipes implemented in theoretical approaches and numerical simulations, and that can offer a benchmark for forecasts on future observations with multiband coverage, as will become routinely achievable in the era of JWST.

Myocardium tracking via matching distributions.

PubMed

Ben Ayed, Ismail; Li, Shuo; Ross, Ian; Islam, Ali

2009-01-01

The goal of this study is to investigate automatic myocardium tracking in cardiac Magnetic Resonance (MR) sequences using global distribution matching via level-set curve evolution. Rather than relying on the pixelwise information as in existing approaches, distribution matching compares intensity distributions, and consequently, is well-suited to the myocardium tracking problem. Starting from a manual segmentation of the first frame, two curves are evolved in order to recover the endocardium (inner myocardium boundary) and the epicardium (outer myocardium boundary) in all the frames. For each curve, the evolution equation is sought following the maximization of a functional containing two terms: (1) a distribution matching term measuring the similarity between the non-parametric intensity distributions sampled from inside and outside the curve to the model distributions of the corresponding regions estimated from the previous frame; (2) a gradient term for smoothing the curve and biasing it toward high gradient of intensity. The Bhattacharyya coefficient is used as a similarity measure between distributions. The functional maximization is obtained by the Euler-Lagrange ascent equation of curve evolution, and efficiently implemented via level-set. The performance of the proposed distribution matching was quantitatively evaluated by comparisons with independent manual segmentations approved by an experienced cardiologist. The method was applied to ten 2D mid-cavity MR sequences corresponding to ten different subjects. Although neither shape prior knowledge nor curve coupling were used, quantitative evaluation demonstrated that the results were consistent with manual segmentations. The proposed method compares well with existing methods. The algorithm also yields a satisfying reproducibility. Distribution matching leads to a myocardium tracking which is more flexible and applicable than existing methods because the algorithm uses only the current data, i.e., does not require a training, and consequently, the solution is not bounded to some shape/intensity prior information learned from of a finite training set.

The Prediction of Jet Noise Ground Effects Using an Acoustic Analogy and a Tailored Green's Function

NASA Technical Reports Server (NTRS)

Miller, Steven A. E.

2013-01-01

An assessment of an acoustic analogy for the mixing noise component of jet noise in the presence of an infinite surface is presented. The reflection of jet noise by the ground changes the distribution of acoustic energy and is characterized by constructive and destructive interference patterns. The equivalent sources are modeled based on the two-point cross- correlation of the turbulent velocity fluctuations and a steady Reynolds-Averaged Navier-Stokes (RANS) solution. Propagation effects, due to reflection by the surface and refaction by the jet shear layer, are taken into account by calculating the vector Green's function of the linearized Euler equations (LEE). The vector Green's function of the LEE is written in relation to Lilley's equation; that is, approximated with matched asymptotic solutions and the Green's function of the convective Helmholtz equation. The Green's function of the convective Helmholtz equation for an infinite flat plane with impedance is the Weyl-van der Pol equation. Predictions are compared with an unheated Mach 0.95 jet produced by a nozzle with an exit diameter of 0.3302 meters. Microphones are placed at various heights and distances from the nozzle exit in the peak jet noise direction above an acoustically hard and an asphalt surface. The predictions are shown to accurately capture jet noise ground effects that are characterized by constructive and destructive interference patterns in the mid- and far-field and capture overall trends in the near-field.

Spherical space Bessel-Legendre-Fourier localized modes solver for electromagnetic waves.

PubMed

Alzahrani, Mohammed A; Gauthier, Robert C

2015-10-05

Maxwell's vector wave equations are solved for dielectric configurations that match the symmetry of a spherical computational domain. The electric or magnetic field components and the inverse of the dielectric profile are series expansion defined using basis functions composed of the lowest order spherical Bessel function, polar angle single index dependant Legendre polynomials and azimuthal complex exponential (BLF). The series expressions and non-traditional form of the basis functions result in an eigenvalue matrix formulation of Maxwell's equations that are relatively compact and accurately solvable on a desktop PC. The BLF matrix returns the frequencies and field profiles for steady states modes. The key steps leading to the matrix populating expressions are provided. The validity of the numerical technique is confirmed by comparing the results of computations to those published using complementary techniques.

Test verification and design of the bicycle frame parameters

NASA Astrophysics Data System (ADS)

Zhang, Long; Xiang, Zhongxia; Luo, Huan; Tian, Guan

2015-07-01

Research on design of bicycles is concentrated on mechanism and auto appearance design, however few on matches between the bike and the rider. Since unreasonable human-bike relationship leads to both riders' worn-out joints and muscle injuries, the design of bicycles should focus on the matching. In order to find the best position of human-bike system, simulation experiments on riding comfort under different riding postures are done with the lifemode software employed to facilitate the cycling process as well as to obtain the best position and the size function of it. With BP neural network and GA, analyzing simulation data, conducting regression analysis of parameters on different heights and bike frames, the equation of best position of human-bike system is gained at last. In addition, after selecting testers, customized bikes based on testers' height dimensions are produced according to the size function. By analyzing and comparing the experimental data that are collected from testers when riding common bicycles and customized bicycles, it is concluded that customized bicycles are four times even six times as comfortable as common ones. The equation of best position of human-bike system is applied to improve bikes' function, and the new direction on future design of bicycle frame parameters is presented.

A new method to simulate the effects of viscous fingering on miscible displacement processes in porous media

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

Vossoughi, S.; Green, D.W.; Smith, J.E.

Dispersion and viscous fingering are important parameters in miscible displacement. Effects of dispersion on concentration profiles in porous media can be simulated when the viscosity ratio is favorable. The capability to simulate viscous fingering is limited. This paper presents a new method to simulate effects of viscous fingering on miscible displacement processes in porous media. The method is based on the numerical solution of a general form of the convection-dispersion equation. In this equation the convection term is represented by a fractional flow function. The fractional flow function is derived from Darcy's law by using a concentration-dependent average viscosity andmore » relative flow area to each fluid at any point in the bed. The method was extended to the description of a polymer flood by including retention and inaccessible PV. A Langmuir-type model for polymer retention in the rock was used. The resulting convection-dispersion equation for displacement by polymer was solved numerically by the use of a finite-element method with linear basis functions and Crank-Nicholson derivative approximation. History matches were performed on four sets of laboratory data to verify the model: (1) an unfavorable viscosity ratio displacement, (2) stable displacement of glycerol by polymer solution, (3) unstable displacement of brine by a slug of polymer solution, and (4) a favorable viscosity ratio displacement. In general, computed results from the model matched laboratory data closely. Good agreement of the model with experiments over a significant range of variables lends support to the analysis.« less

Unsplit complex frequency shifted perfectly matched layer for second-order wave equation using auxiliary differential equations.

PubMed

Gao, Yingjie; Zhang, Jinhai; Yao, Zhenxing

2015-12-01

The complex frequency shifted perfectly matched layer (CFS-PML) can improve the absorbing performance of PML for nearly grazing incident waves. However, traditional PML and CFS-PML are based on first-order wave equations; thus, they are not suitable for second-order wave equation. In this paper, an implementation of CFS-PML for second-order wave equation is presented using auxiliary differential equations. This method is free of both convolution calculations and third-order temporal derivatives. As an unsplit CFS-PML, it can reduce the nearly grazing incidence. Numerical experiments show that it has better absorption than typical PML implementations based on second-order wave equation.

Optimizing Flight Schedules by an Automated Decision Support System

DTIC Science & Technology

2014-03-01

18 Figure 5-Equation-1 of Grading Pilot-Mission Matches ( Yavuz , 2010) .......................... 22 Figure 6-Equation...2 of Grading Pilot-Mission Matches ( Yavuz , 2010) .......................... 22 Figure 7-Implementation of GRASP ( Yavuz , 2010...23 Figure 8-Overall Process ( Yavuz , 2010

Transformations of Mathematical and Stimulus Functions

PubMed Central

Ninness, Chris; Barnes-Holmes, Dermot; Rumph, Robin; McCuller, Glen; Ford, Angela M; Payne, Robert; Ninness, Sharon K; Smith, Ronald J; Ward, Todd A; Elliott, Marc P

2006-01-01

Following a pretest, 8 participants who were unfamiliar with algebraic and trigonometric functions received a brief presentation on the rectangular coordinate system. Next, they participated in a computer-interactive matching-to-sample procedure that trained formula-to-formula and formula-to-graph relations. Then, they were exposed to 40 novel formula-to-graph tests and 10 novel graph-to-formula tests. Seven of the 8 participants showed substantial improvement in identifying formula-to-graph relations; however, in the test of novel graph-to-formula relations, participants tended to select equations in their factored form. Next, we manipulated contextual cues in the form of rules regarding mathematical preferences. First, we informed participants that standard forms of equations were preferred over factored forms. In a subsequent test of 10 additional novel graph-to-formula relations, participants shifted their selections to favor equations in their standard form. This preference reversed during 10 more tests when financial reward was made contingent on correct identification of formulas in factored form. Formula preferences and transformation of novel mathematical and stimulus functions are discussed. PMID:17020211

Accurate analytical modeling of junctionless DG-MOSFET by green's function approach

NASA Astrophysics Data System (ADS)

Nandi, Ashutosh; Pandey, Nilesh

2017-11-01

An accurate analytical model of Junctionless double gate MOSFET (JL-DG-MOSFET) in the subthreshold regime of operation is developed in this work using green's function approach. The approach considers 2-D mixed boundary conditions and multi-zone techniques to provide an exact analytical solution to 2-D Poisson's equation. The Fourier coefficients are calculated correctly to derive the potential equations that are further used to model the channel current and subthreshold slope of the device. The threshold voltage roll-off is computed from parallel shifts of Ids-Vgs curves between the long channel and short-channel devices. It is observed that the green's function approach of solving 2-D Poisson's equation in both oxide and silicon region can accurately predict channel potential, subthreshold current (Isub), threshold voltage (Vt) roll-off and subthreshold slope (SS) of both long & short channel devices designed with different doping concentrations and higher as well as lower tsi/tox ratio. All the analytical model results are verified through comparisons with TCAD Sentaurus simulation results. It is observed that the model matches quite well with TCAD device simulations.

Macroscopic descriptions of rarefied gases from the elimination of fast variables

NASA Astrophysics Data System (ADS)

Dellar, Paul J.

2007-10-01

The Boltzmann equation describing a dilute monatomic gas is equivalent to an infinite hierarchy of evolution equations for successive moments of the distribution function. The five moments giving the macroscopic mass, momentum, and energy densities are unaffected by collisions between atoms, while all other moments naturally evolve on a fast collisional time scale. We show that the macroscopic equations of Chen, Rao, and Spiegel [Phys. Lett. A 271, 87 (2000)], like the familiar Navier-Stokes-Fourier equations, emerge from using a systematic procedure to eliminate the higher moments, leaving closed evolution equations for the five moments unaffected by collisions. The two equation sets differ through their treatment of contributions from the temperature to the momentum and energy fluxes. Using moment equations offers a definitive treatment of the Prandtl number problem using model collision operators, greatly reduces the labor of deriving equations for different collision operators, and clarifies the role of solvability conditions applied to the distribution function. The original Chen-Rao-Spiegel approach offers greatly improved agreement with experiments for the phase speed of ultrasound, but when corrected to match the Navier-Stokes-Fourier equations at low frequencies, it then underestimates the phase speed at high frequencies. Our introduction of a translational temperature, as in the kinetic theory of polyatomic gases, motivates a distinction in the energy flux between advection of internal energy and the work done by the pressure. Exploiting this distinction yields macroscopic equations that offer further improvement in agreement with experimental data, and arise more naturally as an approximation to the infinite hierarchy of evolution equations for moments.

Falsification of matching theory and confirmation of an evolutionary theory of behavior dynamics in a critical experiment.

PubMed

McDowell, J J; Calvin, Olivia L; Hackett, Ryan; Klapes, Bryan

2017-07-01

Two competing predictions of matching theory and an evolutionary theory of behavior dynamics, and one additional prediction of the evolutionary theory, were tested in a critical experiment in which human participants worked on concurrent schedules for money (Dallery et al., 2005). The three predictions concerned the descriptive adequacy of matching theory equations, and of equations describing emergent equilibria of the evolutionary theory. Tests of the predictions falsified matching theory and supported the evolutionary theory. Copyright © 2017 Elsevier B.V. All rights reserved.

Nonreflective Conditions for Perfectly Matched Layer in Computational Aeroacoustics

NASA Astrophysics Data System (ADS)

Choung, Hanahchim; Jang, Seokjong; Lee, Soogab

2018-05-01

In computational aeroacoustics, boundary conditions such as radiation, outflow, or absorbing boundary conditions are critical issues in that they can affect the entire solution of the computation. Among these types of boundary conditions, the perfectly matched layer boundary condition, which has been widely used in computational fluid dynamics and computational aeroacoustics, is developed by augmenting the additional term in the original governing equations by an absorption function so as to stably absorb the outgoing waves. Even if the perfectly matched layer is analytically a perfectly nonreflective boundary condition, spurious waves occur at the interface, since the analysis is performed in discretized space. Hence, this study is focused on factors that affect numerical errors from perfectly matched layer to find the optimum conditions for nonreflective PML. Through a mathematical approach, a minimum width of perfectly matched layer and an optimum absorption coefficient are suggested. To validate the prediction of the analysis, numerical simulations are performed in a generalized coordinate system, as well as in a Cartesian coordinate system.

Exploring inductive linearization for pharmacokinetic-pharmacodynamic systems of nonlinear ordinary differential equations.

PubMed

Hasegawa, Chihiro; Duffull, Stephen B

2018-02-01

Pharmacokinetic-pharmacodynamic systems are often expressed with nonlinear ordinary differential equations (ODEs). While there are numerous methods to solve such ODEs these methods generally rely on time-stepping solutions (e.g. Runge-Kutta) which need to be matched to the characteristics of the problem at hand. The primary aim of this study was to explore the performance of an inductive approximation which iteratively converts nonlinear ODEs to linear time-varying systems which can then be solved algebraically or numerically. The inductive approximation is applied to three examples, a simple nonlinear pharmacokinetic model with Michaelis-Menten elimination (E1), an integrated glucose-insulin model and an HIV viral load model with recursive feedback systems (E2 and E3, respectively). The secondary aim of this study was to explore the potential advantages of analytically solving linearized ODEs with two examples, again E3 with stiff differential equations and a turnover model of luteinizing hormone with a surge function (E4). The inductive linearization coupled with a matrix exponential solution provided accurate predictions for all examples with comparable solution time to the matched time-stepping solutions for nonlinear ODEs. The time-stepping solutions however did not perform well for E4, particularly when the surge was approximated by a square wave. In circumstances when either a linear ODE is particularly desirable or the uncertainty in matching the integrator to the ODE system is of potential risk, then the inductive approximation method coupled with an analytical integration method would be an appropriate alternative.

A vector matching method for analysing logic Petri nets

NASA Astrophysics Data System (ADS)

Du, YuYue; Qi, Liang; Zhou, MengChu

2011-11-01

Batch processing function and passing value indeterminacy in cooperative systems can be described and analysed by logic Petri nets (LPNs). To directly analyse the properties of LPNs, the concept of transition enabling vector sets is presented and a vector matching method used to judge the enabling transitions is proposed in this article. The incidence matrix of LPNs is defined; an equation about marking change due to a transition's firing is given; and a reachable tree is constructed. The state space explosion is mitigated to a certain extent from directly analysing LPNs. Finally, the validity and reliability of the proposed method are illustrated by an example in electronic commerce.

Kinetic balance and variational bounds failure in the solution of the Dirac equation in a finite Gaussian basis set

NASA Technical Reports Server (NTRS)

Dyall, Kenneth G.; Faegri, Knut, Jr.

1990-01-01

The paper investigates bounds failure in calculations using Gaussian basis sets for the solution of the one-electron Dirac equation for the 2p1/2 state of Hg(79+). It is shown that bounds failure indicates inadequacies in the basis set, both in terms of the exponent range and the number of functions. It is also shown that overrepresentation of the small component space may lead to unphysical results. It is concluded that it is important to use matched large and small component basis sets with an adequate size and exponent range.

Angular quasi-phase-matching experiments and determination of accurate Sellmeier equations for 5%MgO:PPLN.

PubMed

Brand, Pierre; Boulanger, Benoît; Segonds, Patricia; Petit, Yannick; Félix, Corinne; Ménaert, Bertrand; Taira, Takunori; Ishizuki, Hideki

2009-09-01

We validated the theory of angular quasi-phase-matching (AQPM) by performing measurements of second-harmonic generation and difference-frequency generation. A nonlinear least-squares fitting of these experimental data led to refine the Sellmeier equations of 5%MgO:PPLN that are now valid over the complete transparency range of the crystal. We also showed that AQPM exhibits complementary spectral ranges and acceptances compared with birefringence phase matching.

Local-in-Time Adjoint-Based Method for Optimal Control/Design Optimization of Unsteady Compressible Flows

NASA Technical Reports Server (NTRS)

Yamaleev, N. K.; Diskin, B.; Nielsen, E. J.

2009-01-01

.We study local-in-time adjoint-based methods for minimization of ow matching functionals subject to the 2-D unsteady compressible Euler equations. The key idea of the local-in-time method is to construct a very accurate approximation of the global-in-time adjoint equations and the corresponding sensitivity derivative by using only local information available on each time subinterval. In contrast to conventional time-dependent adjoint-based optimization methods which require backward-in-time integration of the adjoint equations over the entire time interval, the local-in-time method solves local adjoint equations sequentially over each time subinterval. Since each subinterval contains relatively few time steps, the storage cost of the local-in-time method is much lower than that of the global adjoint formulation, thus making the time-dependent optimization feasible for practical applications. The paper presents a detailed comparison of the local- and global-in-time adjoint-based methods for minimization of a tracking functional governed by the Euler equations describing the ow around a circular bump. Our numerical results show that the local-in-time method converges to the same optimal solution obtained with the global counterpart, while drastically reducing the memory cost as compared to the global-in-time adjoint formulation.

Longitudinal wave propagation in multi cylindrical viscoelastic matching layers of airborne ultrasonic transducer: new method to consider the matching layer's diameter (frequency <100 kHz).

PubMed

Saffar, Saber; Abdullah, Amir

2013-08-01

Wave propagation in viscoelastic disk layers is encountered in many applications including studies of airborne ultrasonic transducers. For viscoelastic materials, both material and geometric dispersion are possible when the diameter of the matching layer is of the same order as the wavelength. Lateral motions of the matching layer(s) that result from the Poisson effect are accounted by using a new concept called the "effective-density". A new wave equation is derived for both metallic and non-metallic (polymeric) materials, usually employed for the matching layers of airborne ultrasonic transducer. The material properties are modeled by using the Kelvin model for metals and Linear Solid Standard model for non-metallic (polymeric) matching layers. The utilized model of the material of the matching layers has influence on amount and trend of variation in speed ratio. In this regard, 60% reduction in speed ratio is observed for Kelvin model for aluminum with diameter of 80 mm at 100 kHz while for a similar diameter but Standard Linear Model, the speed ratio increase to twice value at 15 kHz, and then reduced until 70% at 67 kHz for Polypropylene. The new wave theory simplifies to the one-dimensional solution for waves in metallic or polymeric matching layers if the Poisson ratio is set to zero. The predictions simplify to Love's equation for stress waves in elastic disks when loss term is removed from equations for both models. Afterwards, the new wave theory is employed to determine the airborne ultrasonic matching layers to maximize the energy transmission to the air. The optimal matching layers are determined by using genetic algorithm theory for 1, 2 and 3 airborne matching layers. It has been shown that 1-D equation is useless at frequencies less than 100 kHz and the effect of diameter of the matching layers must be considered to determine the acoustic impedances (matching layers) to design airborne ultrasonic transducers. Copyright © 2013 Elsevier B.V. All rights reserved.

Pressure and temperature interactions on cellular respiration: a review.

PubMed

Sebert, P; Theron, M; Vettier, A

2004-06-01

Thermodynamic equations show that pressure and temperature can, theoretically, act in synergy or in opposite directions depending on their respective variations. Hence, they interact to establish rates of biological processes (pressure/temperature interactions, PTI). For such studies, it is interesting to use aquatic ectotherms, in particular fish, because it is easy to submit them to temperature and/or pressure changes. This review focuses on the effects of temperature and pressure changes on the energy metabolism of fish, mitochondrial oxygen consumption and functioning, showing that the observed effects do not always match the predictions made by equations or models. Unpublished results concerning the mitochondrial function of eels acclimatised at two temperatures and two pressures show that the mitochondrial targets of pressure and temperature are probably not the same. The possible mechanisms and consequences of PTI are discussed.

Solution of the exact equations for three-dimensional atmospheric entry using directly matched asymptotic expansions

NASA Technical Reports Server (NTRS)

Busemann, A.; Vinh, N. X.; Culp, R. D.

1976-01-01

The problem of determining the trajectories, partially or wholly contained in the atmosphere of a spherical, nonrotating planet, is considered. The exact equations of motion for three-dimensional, aerodynamically affected flight are derived. Modified Chapman variables are introduced and the equations are transformed into a set suitable for analytic integration using asymptotic expansions. The trajectory is solved in two regions: the outer region, where the force may be considered a gravitational field with aerodynamic perturbations, and the inner region, where the force is predominantly aerodynamic, with gravity as a perturbation. The two solutions are matched directly. A composite solution, valid everywhere, is constructed by additive composition. This approach of directly matched asymptotic expansions applied to the exact equations of motion couched in terms of modified Chapman variables yields an analytical solution which should prove to be a powerful tool for aerodynamic orbit calculations.

Student-Teacher Racial Match and Its Association with Black Student Achievement: An Exploration Using Multilevel Structural Equation Modeling

ERIC Educational Resources Information Center

Yarnell, Lisa M.; Bohrnstedt, George W.

2018-01-01

This study examines student-teacher "racial match" for its association with Black student achievement. Multilevel structural equation modeling was used to analyze 2013 National Assessment for Educational Progress (NAEP) Grade 4 Reading Assessment data to examine interactions of teacher race and student race in their associations with…

Dispersive analysis of the scalar form factor of the nucleon

NASA Astrophysics Data System (ADS)

Hoferichter, M.; Ditsche, C.; Kubis, B.; Meißner, U.-G.

2012-06-01

Based on the recently proposed Roy-Steiner equations for pion-nucleon ( πN) scattering [1], we derive a system of coupled integral equations for the π π to overline N N and overline K K to overline N N S-waves. These equations take the form of a two-channel Muskhelishvili-Omnès problem, whose solution in the presence of a finite matching point is discussed. We use these results to update the dispersive analysis of the scalar form factor of the nucleon fully including overline K K intermediate states. In particular, we determine the correction {Δ_{σ }} = σ ( {2M_{π }^2} ) - {σ_{{π N}}} , which is needed for the extraction of the pion-nucleon σ term from πN scattering, as a function of pion-nucleon subthreshold parameters and the πN coupling constant.

A novel unsplit perfectly matched layer for the second-order acoustic wave equation.

PubMed

Ma, Youneng; Yu, Jinhua; Wang, Yuanyuan

2014-08-01

When solving acoustic field equations by using numerical approximation technique, absorbing boundary conditions (ABCs) are widely used to truncate the simulation to a finite space. The perfectly matched layer (PML) technique has exhibited excellent absorbing efficiency as an ABC for the acoustic wave equation formulated as a first-order system. However, as the PML was originally designed for the first-order equation system, it cannot be applied to the second-order equation system directly. In this article, we aim to extend the unsplit PML to the second-order equation system. We developed an efficient unsplit implementation of PML for the second-order acoustic wave equation based on an auxiliary-differential-equation (ADE) scheme. The proposed method can benefit to the use of PML in simulations based on second-order equations. Compared with the existing PMLs, it has simpler implementation and requires less extra storage. Numerical results from finite-difference time-domain models are provided to illustrate the validity of the approach. Copyright © 2014 Elsevier B.V. All rights reserved.

The matching law: a tutorial for practitioners.

PubMed

Reed, Derek D; Kaplan, Brent A

2011-01-01

The application of the matching law has historically been limited to use as a quantitative measurement tool in the experimental analysis of behavior to describe temporally extended patterns of behavior-environment relations. In recent years, however, applications of the matching law have been translated to clinical settings and populations to gain a better understanding of how naturally-occurring events affect socially important behaviors. This tutorial provides a brief background of the conceptual foundations of matching, an overview of the various matching equations that have been used in research, and a description of how to interpret the data derived from these equations in the context of numerous examples of matching analyses conducted with socially important behavior. An appendix of resources is provided to direct readers to primary sources, as well as useful articles and books on the topic.

The Matching Law: A Tutorial for Practitioners

PubMed Central

Kaplan, Brent A

2011-01-01

The application of the matching law has historically been limited to use as a quantitative measurement tool in the experimental analysis of behavior to describe temporally extended patterns of behavior-environment relations. In recent years, however, applications of the matching law have been translated to clinical settings and populations to gain a better understanding of how naturally-occurring events affect socially important behaviors. This tutorial provides a brief background of the conceptual foundations of matching, an overview of the various matching equations that have been used in research, and a description of how to interpret the data derived from these equations in the context of numerous examples of matching analyses conducted with socially important behavior. An appendix of resources is provided to direct readers to primary sources, as well as useful articles and books on the topic. PMID:22649575

Effective field theory approach to trans-TeV supersymmetry: covariant matching, Yukawa unification and Higgs couplings

NASA Astrophysics Data System (ADS)

Wells, James D.; Zhang, Zhengkang

2018-05-01

Dismissing traditional naturalness concerns while embracing the Higgs boson mass measurement and unification motivates careful analysis of trans-TeV supersymmetric theories. We take an effective field theory (EFT) approach, matching the Minimal Supersymmetric Standard Model (MSSM) onto the Standard Model (SM) EFT by integrating out heavy superpartners, and evolving MSSM and SMEFT parameters according to renormalization group equations in each regime. Our matching calculation is facilitated by the recent covariant diagrams formulation of functional matching techniques, with the full one-loop SUSY threshold corrections encoded in just 30 diagrams. Requiring consistent matching onto the SMEFT with its parameters (those in the Higgs potential in particular) measured at low energies, and in addition requiring unification of bottom and tau Yukawa couplings at the scale of gauge coupling unification, we detail the solution space of superpartner masses from the TeV scale to well above. We also provide detailed views of parameter space where Higgs coupling measurements have probing capability at future colliders beyond the reach of direct superpartner searches at the LHC.

Thermal characteristics of second harmonic generation by phase matched calorimetry.

PubMed

Lim, Hwan Hong; Kurimura, Sunao; Noguchi, Keisuke; Shoji, Ichiro

2014-07-28

We analyze a solution of the heat equation for second harmonic generation (SHG) with a focused Gaussian beam and simulate the temperature rise in SHG materials as a function of the second harmonic power and the focusing conditions. We also propose a quantitative value of the heat removal performance of SHG devices, referred to as the effective heat capacity Cα in phase matched calorimetry. We demonstrate the inverse relation between Cα and the focusing parameter ξ, and propose the universal quantity of the product of Cα and ξ for characterizing the thermal property of SHG devices. Finally, we discuss the strategy to manage thermal dephasing in SHG using the results from simulations.

Correlation of embryonic skeletal muscle myotube physical characteristics with contractile force generation on an atomic force microscope-based bio-microelectromechanical systems device

NASA Astrophysics Data System (ADS)

Pirozzi, K. L.; Long, C. J.; McAleer, C. W.; Smith, A. S. T.; Hickman, J. J.

2013-08-01

Rigorous analysis of muscle function in in vitro systems is needed for both acute and chronic biomedical applications. Forces generated by skeletal myotubes on bio-microelectromechanical cantilevers were calculated using a modified version of Stoney's thin-film equation and finite element analysis (FEA), then analyzed for regression to physical parameters. The Stoney's equation results closely matched the more intensive FEA and the force correlated to cross-sectional area (CSA). Normalizing force to measured CSA significantly improved the statistical sensitivity and now allows for close comparison of in vitro data to in vivo measurements for applications in exercise physiology, robotics, and modeling neuromuscular diseases.

Finding an appropriate equation to measure similarity between binary vectors: case studies on Indonesian and Japanese herbal medicines.

PubMed

Wijaya, Sony Hartono; Afendi, Farit Mochamad; Batubara, Irmanida; Darusman, Latifah K; Altaf-Ul-Amin, Md; Kanaya, Shigehiko

2016-12-07

The binary similarity and dissimilarity measures have critical roles in the processing of data consisting of binary vectors in various fields including bioinformatics and chemometrics. These metrics express the similarity and dissimilarity values between two binary vectors in terms of the positive matches, absence mismatches or negative matches. To our knowledge, there is no published work presenting a systematic way of finding an appropriate equation to measure binary similarity that performs well for certain data type or application. A proper method to select a suitable binary similarity or dissimilarity measure is needed to obtain better classification results. In this study, we proposed a novel approach to select binary similarity and dissimilarity measures. We collected 79 binary similarity and dissimilarity equations by extensive literature search and implemented those equations as an R package called bmeasures. We applied these metrics to quantify the similarity and dissimilarity between herbal medicine formulas belonging to the Indonesian Jamu and Japanese Kampo separately. We assessed the capability of binary equations to classify herbal medicine pairs into match and mismatch efficacies based on their similarity or dissimilarity coefficients using the Receiver Operating Characteristic (ROC) curve analysis. According to the area under the ROC curve results, we found Indonesian Jamu and Japanese Kampo datasets obtained different ranking of binary similarity and dissimilarity measures. Out of all the equations, the Forbes-2 similarity and the Variant of Correlation similarity measures are recommended for studying the relationship between Jamu formulas and Kampo formulas, respectively. The selection of binary similarity and dissimilarity measures for multivariate analysis is data dependent. The proposed method can be used to find the most suitable binary similarity and dissimilarity equation wisely for a particular data. Our finding suggests that all four types of matching quantities in the Operational Taxonomic Unit (OTU) table are important to calculate the similarity and dissimilarity coefficients between herbal medicine formulas. Also, the binary similarity and dissimilarity measures that include the negative match quantity d achieve better capability to separate herbal medicine pairs compared to equations that exclude d.

Phase-matching directions, refined Sellmeier equations, and second-order nonlinear coefficient of the infrared Langatate crystal La₃Ga(5.5)Ta(0.5)O₁₄.

PubMed

Boursier, Elodie; Segonds, Patricia; Boulanger, Benoit; Félix, Corinne; Debray, Jérôme; Jegouso, David; Ménaert, Bertrand; Roshchupkin, Dmitry; Shoji, Ichiro

2014-07-01

We directly measured phase-matching directions of second harmonic, sum, and difference frequency generations in the Langatate La₃Ga(5.5)Ta(0.5)O₁₄ (LGT) uniaxial crystal. The simultaneous fit of the data enabled us to refine the Sellmeier equations of the ordinary and extraordinary principal refractive indices over the entire transparency range of the crystal, and to calculate the phase-matching curves and efficiencies of LGT for infrared optical parametric generation.

Introducing a Method for Calculating the Allocation of Attention in a Cognitive “Two-Armed Bandit” Procedure: Probability Matching Gives Way to Maximizing

PubMed Central

Heyman, Gene M.; Grisanzio, Katherine A.; Liang, Victor

2016-01-01

We tested whether principles that describe the allocation of overt behavior, as in choice experiments, also describe the allocation of cognition, as in attention experiments. Our procedure is a cognitive version of the “two-armed bandit choice procedure.” The two-armed bandit procedure has been of interest to psychologistsand economists because it tends to support patterns of responding that are suboptimal. Each of two alternatives provides rewards according to fixed probabilities. The optimal solution is to choose the alternative with the higher probability of reward on each trial. However, subjects often allocate responses so that the probability of a response approximates its probability of reward. Although it is this result which has attracted most interest, probability matching is not always observed. As a function of monetary incentives, practice, and individual differences, subjects tend to deviate from probability matching toward exclusive preference, as predicted by maximizing. In our version of the two-armed bandit procedure, the monitor briefly displayed two, small adjacent stimuli that predicted correct responses according to fixed probabilities, as in a two-armed bandit procedure. We show that in this setting, a simple linear equation describes the relationship between attention and correct responses, and that the equation’s solution is the allocation of attention between the two stimuli. The calculations showed that attention allocation varied as a function of the degree to which the stimuli predicted correct responses. Linear regression revealed a strong correlation (r = 0.99) between the predictiveness of a stimulus and the probability of attending to it. Nevertheless there were deviations from probability matching, and although small, they were systematic and statistically significant. As in choice studies, attention allocation deviated toward maximizing as a function of practice, feedback, and incentives. Our approach also predicts the frequency of correct guesses and the relationship between attention allocation and response latencies. The results were consistent with these two predictions, the assumptions of the equations used to calculate attention allocation, and recent studies which show that predictiveness and reward are important determinants of attention. PMID:27014109

Unsteady fluid flow in a slightly curved pipe: A comparative study of a matched asymptotic expansions solution with a single analytical solution

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

Messaris, Gerasimos A. T., E-mail: messaris@upatras.gr; School of Science and Technology, Hellenic Open University, 11 Sahtouri Street, GR 262 22 Patras; Hadjinicolaou, Maria

The present work is motivated by the fact that blood flow in the aorta and the main arteries is governed by large finite values of the Womersley number α and for such values of α there is not any analytical solution in the literature. The existing numerical solutions, although accurate, give limited information about the factors that affect the flow, whereas an analytical approach has an advantage in that it can provide physical insight to the flow mechanism. Having this in mind, we seek analytical solution to the equations of the fluid flow driven by a sinusoidal pressure gradient inmore » a slightly curved pipe of circular cross section when the Womersley number varies from small finite to infinite values. Initially the equations of motion are expanded in terms of the curvature ratio δ and the resulting linearized equations are solved analytically in two ways. In the first, we match the solution for the main core to that for the Stokes boundary layer. This solution is valid for very large values of α. In the second, we derive a straightforward single solution valid to the entire flow region and for 8 ≤ α < ∞, a range which includes the values of α that refer to the physiological flows. Each solution contains expressions for the axial velocity, the stream function, and the wall stresses and is compared to the analogous forms presented in other studies. The two solutions give identical results to each other regarding the axial flow but differ in the secondary flow and the circumferential wall stress, due to the approximations employed in the matched asymptotic expansion process. The results on the stream function from the second solution are in agreement with analogous results from other numerical solutions. The second solution predicts that the atherosclerotic plaques may develop in any location around the cross section of the aortic wall unlike to the prescribed locations predicted by the first solution. In addition, it gives circumferential wall stresses augmented by approximately 100% with respect to the matched asymptotic expansions, a factor that may contribute jointly with other pathological factors to the faster aging of the arterial system and the possible malfunction of the aorta.« less

Unsteady fluid flow in a slightly curved pipe: A comparative study of a matched asymptotic expansions solution with a single analytical solution

NASA Astrophysics Data System (ADS)

Messaris, Gerasimos A. T.; Hadjinicolaou, Maria; Karahalios, George T.

2016-08-01

The present work is motivated by the fact that blood flow in the aorta and the main arteries is governed by large finite values of the Womersley number α and for such values of α there is not any analytical solution in the literature. The existing numerical solutions, although accurate, give limited information about the factors that affect the flow, whereas an analytical approach has an advantage in that it can provide physical insight to the flow mechanism. Having this in mind, we seek analytical solution to the equations of the fluid flow driven by a sinusoidal pressure gradient in a slightly curved pipe of circular cross section when the Womersley number varies from small finite to infinite values. Initially the equations of motion are expanded in terms of the curvature ratio δ and the resulting linearized equations are solved analytically in two ways. In the first, we match the solution for the main core to that for the Stokes boundary layer. This solution is valid for very large values of α. In the second, we derive a straightforward single solution valid to the entire flow region and for 8 ≤ α < ∞, a range which includes the values of α that refer to the physiological flows. Each solution contains expressions for the axial velocity, the stream function, and the wall stresses and is compared to the analogous forms presented in other studies. The two solutions give identical results to each other regarding the axial flow but differ in the secondary flow and the circumferential wall stress, due to the approximations employed in the matched asymptotic expansion process. The results on the stream function from the second solution are in agreement with analogous results from other numerical solutions. The second solution predicts that the atherosclerotic plaques may develop in any location around the cross section of the aortic wall unlike to the prescribed locations predicted by the first solution. In addition, it gives circumferential wall stresses augmented by approximately 100% with respect to the matched asymptotic expansions, a factor that may contribute jointly with other pathological factors to the faster aging of the arterial system and the possible malfunction of the aorta.

Nonlinear responses of chiral fluids from kinetic theory

NASA Astrophysics Data System (ADS)

Hidaka, Yoshimasa; Pu, Shi; Yang, Di-Lun

2018-01-01

The second-order nonlinear responses of inviscid chiral fluids near local equilibrium are investigated by applying the chiral kinetic theory (CKT) incorporating side-jump effects. It is shown that the local equilibrium distribution function can be nontrivially introduced in a comoving frame with respect to the fluid velocity when the quantum corrections in collisions are involved. For the study of anomalous transport, contributions from both quantum corrections in anomalous hydrodynamic equations of motion and those from the CKT and Wigner functions are considered under the relaxation-time (RT) approximation, which result in anomalous charge Hall currents propagating along the cross product of the background electric field and the temperature (or chemical-potential) gradient and of the temperature and chemical-potential gradients. On the other hand, the nonlinear quantum correction on the charge density vanishes in the classical RT approximation, which in fact satisfies the matching condition given by the anomalous equation obtained from the CKT.

The pointwise estimates of diffusion wave of the compressible micropolar fluids

NASA Astrophysics Data System (ADS)

Wu, Zhigang; Wang, Weike

2018-09-01

The pointwise estimates for the compressible micropolar fluids in dimension three are given, which exhibit generalized Huygens' principle for the fluid density and fluid momentum as the compressible Navier-Stokes equation, while the micro-rational momentum behaves like the fluid momentum of the Euler equation with damping. To circumvent the complexity from 7 × 7 Green's matrix, we use the decomposition of fluid part and electromagnetic part for the momentums to study three smaller Green's matrices. The following from this decomposition is that we have to deal with the new problem that the nonlinear terms contain nonlocal operators. We solve it by using the natural match of these new Green's functions and the nonlinear terms. Moreover, to derive the different pointwise estimates for different unknown variables such that the estimate of each unknown variable is in agreement with its Green's function, we develop some new estimates on the nonlinear interplay between different waves.

Collapsing radiating stars with various equations of state

NASA Astrophysics Data System (ADS)

Brassel, Byron P.; Goswami, Rituparno; Maharaj, Sunil D.

2017-06-01

We study the gravitational collapse of radiating stars in the context of the cosmic censorship conjecture. We consider a generalized Vaidya spacetime with three concentric regions. The local internal atmosphere is a two-component system consisting of standard pressure-free, null radiation and an additional string fluid with energy density and nonzero pressure obeying all physically realistic energy conditions. The middle region is purely radiative which matches to a third region which is the Schwarzschild exterior. We outline the general mathematical framework to study the conditions on the mass function so that future-directed nonspacelike geodesics can terminate at the singularity in the past. Mass functions for several equations of state are analyzed using this framework and it is shown that the collapse in each case terminates at a locally naked central singularity. We calculate the strength of these singularities to show that they are strong curvature singularities which implies that no extension of spacetime through them is possible.

Extensions of the Einstein-Schrodinger non-symmetric theory of gravity

NASA Astrophysics Data System (ADS)

Shifflett, James A.

We modify the Einstein-Schrödinger theory to include a cosmological constant L z which multiplies the symmetric metric. The cosmological constant L z is assumed to be nearly cancelled by Schrödinger's cosmological constant L b which multiplies the nonsymmetric fundamental tensor, such that the total L = L z + L b matches measurement. The resulting theory becomes exactly Einstein-Maxwell theory in the limit as |L z | [arrow right] oo. For |L z | ~ 1/(Planck length) 2 the field equations match the ordinary Einstein and Maxwell equations except for extra terms which are < 10 -16 of the usual terms for worst-case field strengths and rates-of-change accessible to measurement. Additional fields can be included in the Lagrangian, and these fields may couple to the symmetric metric and the electromagnetic vector potential, just as in Einstein-Maxwell theory. The ordinary Lorentz force equation is obtained by taking the divergence of the Einstein equations when sources are included. The Einstein- Infeld-Hoffmann (EIH) equations of motion match the equations of motion for Einstein-Maxwell theory to Newtonian/Coulombian order, which proves the existence of a Lorentz force without requiring sources. An exact charged solution matches the Reissner-Nordström solution except for additional terms which are ~ 10 -66 of the usual terms for worst-case radii accessible to measurement. An exact electromagnetic plane-wave solution is identical to its counterpart in Einstein-Maxwell theory. Peri-center advance, deflection of light and time delay of light have a fractional difference of < 10 -56 compared to Einstein-Maxwell theory for worst-case parameters. When a spin-1/2 field is included in the Lagrangian, the theory gives the ordinary Dirac equation, and the charged solution results in fractional shifts of < 10 -50 in Hydrogen atom energy levels. Newman-Penrose methods are used to derive an exact solution of the connection equations, and to show that the charged solution is Petrov type- D like the Reissner-Nordström solution. The Newman-Penrose asymptotically flat [Special characters omitted.] (1/ r 2 ) expansion of the field equations is shown to match Einstein-Maxwell theory. Finally we generalize the theory to non-Abelian fields, and show that a special case of the resulting theory closely approximates Einstein-Weinberg-Salam theory.

Objective Lightning Probability Forecasting for Kennedy Space Center and Cape Canaveral Air Force Station, Phase II

NASA Technical Reports Server (NTRS)

Lambert, Winifred; Wheeler, Mark

2007-01-01

This report describes the work done by the Applied Meteorology Unit (AMU) to update the lightning probability forecast equations developed in Phase I. In the time since the Phase I equations were developed, new ideas regarding certain predictors were formulated and a desire to make the tool more automated was expressed by 45 WS forecasters. Five modifications were made to the data: 1) increased the period of record from 15 to 17 years, 2) modified the valid area to match the lighting warning areas, 3) added the 1000 UTC CCAFS sounding to the other soundings in determining the flow regime, 4) used a different smoothing function for the daily climatology, and 5) determined the optimal relative humidity (RH) layer to use as a predictor. The new equations outperformed the Phase I equations in several tests, and improved the skill of the forecast over the Phase I equations by 8%. A graphical user interface (GUI) was created in the Meteorological Interactive Data Display System (MIDDS) that gathers the predictor values for the equations automatically. The GUI was transitioned to operations in May 2007 for the 2007 warm season.

Solitons on Noncommutative Torus as Elliptic Calogero-Gaudin Models, Branes and Laughlin Wave Functions

NASA Astrophysics Data System (ADS)

Hou, Bo-Yu; Peng, Dan-Tao; Shi, Kang-Jie; Yue, Rui-Hong

For the noncommutative torus T, in the case of the noncommutative parameter θ = (Z)/(n), we construct the basis of Hilbert space Hn in terms of θ functions of the positions zi of n solitons. The wrapping around the torus generates the algebra An, which is the Zn × Zn Heisenberg group on θ functions. We find the generators g of a local elliptic su(n), which transform covariantly by the global gauge transformation of An. By acting on Hn we establish the isomorphism of An and g. We embed this g into the L-matrix of the elliptic Gaudin and Calogero-Moser models to give the dynamics. The moment map of this twisted cotangent sunT) bundle is matched to the D-equation with the Fayet-Illiopoulos source term, so the dynamics of the noncommutative solitons become that of the brane. The geometric configuration (k, u) of the spectral curve det|L(u) - k| = 0 describes the brane configuration, with the dynamical variables zi of the noncommutative solitons as the moduli T⊗ n/Sn. Furthermore, in the noncommutative Chern-Simons theory for the quantum Hall effect, the constrain equation with quasiparticle source is identified also with the moment map equation of the noncommutative sunT cotangent bundle with marked points. The eigenfunction of the Gaudin differential L-operators as the Laughlin wave function is solved by Bethe ansatz.

Parallel Ellipsoidal Perfectly Matched Layers for Acoustic Helmholtz Problems on Exterior Domains

DOE PAGES

Bunting, Gregory; Prakash, Arun; Walsh, Timothy; ...

2018-01-26

Exterior acoustic problems occur in a wide range of applications, making the finite element analysis of such problems a common practice in the engineering community. Various methods for truncating infinite exterior domains have been developed, including absorbing boundary conditions, infinite elements, and more recently, perfectly matched layers (PML). PML are gaining popularity due to their generality, ease of implementation, and effectiveness as an absorbing boundary condition. PML formulations have been developed in Cartesian, cylindrical, and spherical geometries, but not ellipsoidal. In addition, the parallel solution of PML formulations with iterative solvers for the solution of the Helmholtz equation, and howmore » this compares with more traditional strategies such as infinite elements, has not been adequately investigated. In this study, we present a parallel, ellipsoidal PML formulation for acoustic Helmholtz problems. To faciliate the meshing process, the ellipsoidal PML layer is generated with an on-the-fly mesh extrusion. Though the complex stretching is defined along ellipsoidal contours, we modify the Jacobian to include an additional mapping back to Cartesian coordinates in the weak formulation of the finite element equations. This allows the equations to be solved in Cartesian coordinates, which is more compatible with existing finite element software, but without the necessity of dealing with corners in the PML formulation. Herein we also compare the conditioning and performance of the PML Helmholtz problem with infinite element approach that is based on high order basis functions. On a set of representative exterior acoustic examples, we show that high order infinite element basis functions lead to an increasing number of Helmholtz solver iterations, whereas for PML the number of iterations remains constant for the same level of accuracy. Finally, this provides an additional advantage of PML over the infinite element approach.« less

Parallel Ellipsoidal Perfectly Matched Layers for Acoustic Helmholtz Problems on Exterior Domains

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

Bunting, Gregory; Prakash, Arun; Walsh, Timothy

Exterior acoustic problems occur in a wide range of applications, making the finite element analysis of such problems a common practice in the engineering community. Various methods for truncating infinite exterior domains have been developed, including absorbing boundary conditions, infinite elements, and more recently, perfectly matched layers (PML). PML are gaining popularity due to their generality, ease of implementation, and effectiveness as an absorbing boundary condition. PML formulations have been developed in Cartesian, cylindrical, and spherical geometries, but not ellipsoidal. In addition, the parallel solution of PML formulations with iterative solvers for the solution of the Helmholtz equation, and howmore » this compares with more traditional strategies such as infinite elements, has not been adequately investigated. In this study, we present a parallel, ellipsoidal PML formulation for acoustic Helmholtz problems. To faciliate the meshing process, the ellipsoidal PML layer is generated with an on-the-fly mesh extrusion. Though the complex stretching is defined along ellipsoidal contours, we modify the Jacobian to include an additional mapping back to Cartesian coordinates in the weak formulation of the finite element equations. This allows the equations to be solved in Cartesian coordinates, which is more compatible with existing finite element software, but without the necessity of dealing with corners in the PML formulation. Herein we also compare the conditioning and performance of the PML Helmholtz problem with infinite element approach that is based on high order basis functions. On a set of representative exterior acoustic examples, we show that high order infinite element basis functions lead to an increasing number of Helmholtz solver iterations, whereas for PML the number of iterations remains constant for the same level of accuracy. Finally, this provides an additional advantage of PML over the infinite element approach.« less

Optimization of complex slater-type functions with analytic derivative methods for describing photoionization differential cross sections.

PubMed

Matsuzaki, Rei; Yabushita, Satoshi

2017-05-05

The complex basis function (CBF) method applied to various atomic and molecular photoionization problems can be interpreted as an L2 method to solve the driven-type (inhomogeneous) Schrödinger equation, whose driven term being dipole operator times the initial state wave function. However, efficient basis functions for representing the solution have not fully been studied. Moreover, the relation between their solution and that of the ordinary Schrödinger equation has been unclear. For these reasons, most previous applications have been limited to total cross sections. To examine the applicability of the CBF method to differential cross sections and asymmetry parameters, we show that the complex valued solution to the driven-type Schrödinger equation can be variationally obtained by optimizing the complex trial functions for the frequency dependent polarizability. In the test calculations made for the hydrogen photoionization problem with five or six complex Slater-type orbitals (cSTOs), their complex valued expansion coefficients and the orbital exponents have been optimized with the analytic derivative method. Both the real and imaginary parts of the solution have been obtained accurately in a wide region covering typical molecular regions. Their phase shifts and asymmetry parameters are successfully obtained by extrapolating the CBF solution from the inner matching region to the asymptotic region using WKB method. The distribution of the optimized orbital exponents in the complex plane is explained based on the close connection between the CBF method and the driven-type equation method. The obtained information is essential to constructing the appropriate basis sets in future molecular applications. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

A technique for pole-zero placement for dual-input control systems. [computer simulation of CH-47 helicopter longitudinal dynamics

NASA Technical Reports Server (NTRS)

Reid, G. F.

1976-01-01

A technique is presented for determining state variable feedback gains that will place both the poles and zeros of a selected transfer function of a dual-input control system at pre-determined locations in the s-plane. Leverrier's algorithm is used to determine the numerator and denominator coefficients of the closed-loop transfer function as functions of the feedback gains. The values of gain that match these coefficients to those of a pre-selected model are found by solving two systems of linear simultaneous equations. The algorithm has been used in a computer simulation of the CH-47 helicopter to control longitudinal dynamics.

A modification of Einstein-Schrödinger theory that contains both general relativity and electrodynamics

NASA Astrophysics Data System (ADS)

Shifflett, J. A.

2008-08-01

We modify the Einstein-Schrödinger theory to include a cosmological constant Λ z which multiplies the symmetric metric, and we show how the theory can be easily coupled to additional fields. The cosmological constant Λ z is assumed to be nearly cancelled by Schrödinger’s cosmological constant Λ b which multiplies the nonsymmetric fundamental tensor, such that the total Λ = Λ z + Λ b matches measurement. The resulting theory becomes exactly Einstein-Maxwell theory in the limit as | Λ z | → ∞. For | Λ z | ~ 1/(Planck length)2 the field equations match the ordinary Einstein and Maxwell equations except for extra terms which are < 10-16 of the usual terms for worst-case field strengths and rates-of-change accessible to measurement. Additional fields can be included in the Lagrangian, and these fields may couple to the symmetric metric and the electromagnetic vector potential, just as in Einstein-Maxwell theory. The ordinary Lorentz force equation is obtained by taking the divergence of the Einstein equations when sources are included. The Einstein-Infeld-Hoffmann (EIH) equations of motion match the equations of motion for Einstein-Maxwell theory to Newtonian/Coulombian order, which proves the existence of a Lorentz force without requiring sources. This fixes a problem of the original Einstein-Schrödinger theory, which failed to predict a Lorentz force. An exact charged solution matches the Reissner-Nordström solution except for additional terms which are ~10-66 of the usual terms for worst-case radii accessible to measurement. An exact electromagnetic plane-wave solution is identical to its counterpart in Einstein-Maxwell theory.

AN FDTD ALGORITHM WITH PERFECTLY MATCHED LAYERS FOR CONDUCTIVE MEDIA. (R825225)

EPA Science Inventory

We extend Berenger's perfectly matched layers (PML) to conductive media. A finite-difference-time-domain (FDTD) algorithm with PML as an absorbing boundary condition is developed for solutions of Maxwell's equations in inhomogeneous, conductive media. For a perfectly matched laye...

Development of a golden beam data set for the commissioning of a proton double-scattering system in a pencil-beam dose calculation algorithm

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

Slopsema, R. L., E-mail: rslopsema@floridaproton.org; Flampouri, S.; Yeung, D.

2014-09-15

Purpose: The purpose of this investigation is to determine if a single set of beam data, described by a minimal set of equations and fitting variables, can be used to commission different installations of a proton double-scattering system in a commercial pencil-beam dose calculation algorithm. Methods: The beam model parameters required to commission the pencil-beam dose calculation algorithm (virtual and effective SAD, effective source size, and pristine-peak energy spread) are determined for a commercial double-scattering system. These parameters are measured in a first room and parameterized as function of proton energy and nozzle settings by fitting four analytical equations tomore » the measured data. The combination of these equations and fitting values constitutes the golden beam data (GBD). To determine the variation in dose delivery between installations, the same dosimetric properties are measured in two additional rooms at the same facility, as well as in a single room at another facility. The difference between the room-specific measurements and the GBD is evaluated against tolerances that guarantee the 3D dose distribution in each of the rooms matches the GBD-based dose distribution within clinically reasonable limits. The pencil-beam treatment-planning algorithm is commissioned with the GBD. The three-dimensional dose distribution in water is evaluated in the four treatment rooms and compared to the treatment-planning calculated dose distribution. Results: The virtual and effective SAD measurements fall between 226 and 257 cm. The effective source size varies between 2.4 and 6.2 cm for the large-field options, and 1.0 and 2.0 cm for the small-field options. The pristine-peak energy spread decreases from 1.05% at the lowest range to 0.6% at the highest. The virtual SAD as well as the effective source size can be accurately described by a linear relationship as function of the inverse of the residual energy. An additional linear correction term as function of RM-step thickness is required for accurate parameterization of the effective SAD. The GBD energy spread is given by a linear function of the exponential of the beam energy. Except for a few outliers, the measured parameters match the GBD within the specified tolerances in all of the four rooms investigated. For a SOBP field with a range of 15 g/cm{sup 2} and an air gap of 25 cm, the maximum difference in the 80%–20% lateral penumbra between the GBD-commissioned treatment-planning system and measurements in any of the four rooms is 0.5 mm. Conclusions: The beam model parameters of the double-scattering system can be parameterized with a limited set of equations and parameters. This GBD closely matches the measured dosimetric properties in four different rooms.« less

Similarity solutions of reaction–diffusion equation with space- and time-dependent diffusion and reaction terms

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

Ho, C.-L.; Lee, C.-C., E-mail: chieh.no27@gmail.com

2016-01-15

We consider solvability of the generalized reaction–diffusion equation with both space- and time-dependent diffusion and reaction terms by means of the similarity method. By introducing the similarity variable, the reaction–diffusion equation is reduced to an ordinary differential equation. Matching the resulting ordinary differential equation with known exactly solvable equations, one can obtain corresponding exactly solvable reaction–diffusion systems. Several representative examples of exactly solvable reaction–diffusion equations are presented.

Synesthesia affects verification of simple arithmetic equations.

PubMed

Ghirardelli, Thomas G; Mills, Carol Bergfeld; Zilioli, Monica K C; Bailey, Leah P; Kretschmar, Paige K

2010-01-01

To investigate the effects of color-digit synesthesia on numerical representation, we presented a synesthete, called SE, in the present study, and controls with mathematical equations for verification. In Experiment 1, SE verified addition equations made up of digits that either matched or mismatched her color-digit photisms or were in black. In Experiment 2A, the addends were presented in the different color conditions and the solution was presented in black, whereas in Experiment 2B the addends were presented in black and the solutions were presented in the different color conditions. In Experiment 3, multiplication and division equations were presented in the same color conditions as in Experiment 1. SE responded significantly faster to equations that matched her photisms than to those that did not; controls did not show this effect. These results suggest that photisms influence the processing of digits in arithmetic verification, replicating and extending previous findings.

An Alternative to the Stay/Switch Equation Assessed When Using a Changeover-Delay

PubMed Central

MacDonall, James S.

2015-01-01

An alternative to the generalized matching equation for understanding concurrent performances is the stay/switch model. For the stay/switch model, the important events are the contingencies and behaviors at each alternative. The current experiment compares the descriptions by two stay/switch equations, the original, empirically derived stay/switch equation and a more theoretically derived equation based on ratios of stay to switch responses matching ratios of stay to switch reinforcers. The present experiment compared descriptions by the original stay/switch equation when using and not using a changeover delay. It also compared descriptions by the more theoretical equation with and without a changeover delay. Finally, it compared descriptions of the concurrent performances by these two equations. Rats were trained in 15 conditions on identical concurrent random-interval schedules in each component of a multiple schedule. A COD operated in only one component. There were no consistent differences in the variance accounted for by each equation of concurrent performances whether or not a COD was used. The simpler equation found greater sensitivity to stay than to switch reinforcers. It also found a COD eliminated the influence of switch reinforcers. Because estimates of parameters were more meaningful when using the more theoretical stay/switch equation it is preferred. PMID:26299548

An alternative to the stay/switch equation assessed when using a changeover-delay.

PubMed

MacDonall, James S

2015-11-01

An alternative to the generalized matching equation for understanding concurrent performances is the stay/switch model. For the stay/switch model, the important events are the contingencies and behaviors at each alternative. The current experiment compares the descriptions by two stay/switch equations, the original, empirically derived stay/switch equation and a more theoretically derived equation based on ratios of stay to switch responses matching ratios of stay to switch reinforcers. The present experiment compared descriptions by the original stay/switch equation when using and not using a changeover delay. It also compared descriptions by the more theoretical equation with and without a changeover delay. Finally, it compared descriptions of the concurrent performances by these two equations. Rats were trained in 15 conditions on identical concurrent random-interval schedules in each component of a multiple schedule. A COD operated in only one component. There were no consistent differences in the variance accounted for by each equation of concurrent performances whether or not a COD was used. The simpler equation found greater sensitivity to stay than to switch reinforcers. It also found a COD eliminated the influence of switch reinforcers. Because estimates of parameters were more meaningful when using the more theoretical stay/switch equation it is preferred. Copyright © 2015 Elsevier B.V. All rights reserved.

A series solution for horizontal infiltration in an initially dry aquifer

NASA Astrophysics Data System (ADS)

Furtak-Cole, Eden; Telyakovskiy, Aleksey S.; Cooper, Clay A.

2018-06-01

The porous medium equation (PME) is a generalization of the traditional Boussinesq equation for hydraulic conductivity as a power law function of height. We analyze the horizontal recharge of an initially dry unconfined aquifer of semi-infinite extent, as would be found in an aquifer adjacent a rising river. If the water level can be modeled as a power law function of time, similarity variables can be introduced and the original problem can be reduced to a boundary value problem for a nonlinear ordinary differential equation. The position of the advancing front is not known ahead of time and must be found in the process of solution. We present an analytical solution in the form of a power series, with the coefficients of the series given by a recurrence relation. The analytical solution compares favorably with a highly accurate numerical solution, and only a small number of terms of the series are needed to achieve high accuracy in the scenarios considered here. We also conduct a series of physical experiments in an initially dry wedged Hele-Shaw cell, where flow is modeled by a special form of the PME. Our analytical solution closely matches the hydraulic head profiles in the Hele-Shaw cell experiment.

Evaluating a linearized Euler equations model for strong turbulence effects on sound propagation.

PubMed

Ehrhardt, Loïc; Cheinet, Sylvain; Juvé, Daniel; Blanc-Benon, Philippe

2013-04-01

Sound propagation outdoors is strongly affected by atmospheric turbulence. Under strongly perturbed conditions or long propagation paths, the sound fluctuations reach their asymptotic behavior, e.g., the intensity variance progressively saturates. The present study evaluates the ability of a numerical propagation model based on the finite-difference time-domain solving of the linearized Euler equations in quantitatively reproducing the wave statistics under strong and saturated intensity fluctuations. It is the continuation of a previous study where weak intensity fluctuations were considered. The numerical propagation model is presented and tested with two-dimensional harmonic sound propagation over long paths and strong atmospheric perturbations. The results are compared to quantitative theoretical or numerical predictions available on the wave statistics, including the log-amplitude variance and the probability density functions of the complex acoustic pressure. The match is excellent for the evaluated source frequencies and all sound fluctuations strengths. Hence, this model captures these many aspects of strong atmospheric turbulence effects on sound propagation. Finally, the model results for the intensity probability density function are compared with a standard fit by a generalized gamma function.

A frequency-duty cycle equation for the ACGIH hand activity level.

PubMed

Radwin, Robert G; Azari, David P; Lindstrom, Mary J; Ulin, Sheryl S; Armstrong, Thomas J; Rempel, David

2015-01-01

A new equation for predicting the hand activity level (HAL) used in the American Conference for Government Industrial Hygienists threshold limit value®(TLV®) was based on exertion frequency (F) and percentage duty cycle (D). The TLV® includes a table for estimating HAL from F and D originating from data in Latko et al. (Latko WA, Armstrong TJ, Foulke JA, Herrin GD, Rabourn RA, Ulin SS, Development and evaluation of an observational method for assessing repetition in hand tasks. American Industrial Hygiene Association Journal, 58(4):278-285, 1997) and post hoc adjustments that include extrapolations outside of the data range. Multimedia video task analysis determined D for two additional jobs from Latko's study not in the original data-set, and a new nonlinear regression equation was developed to better fit the data and create a more accurate table. The equation, HAL = 6:56 ln D[F(1:31) /1+3:18 F(1:31), generally matches the TLV® HAL lookup table, and is a substantial improvement over the linear model, particularly for F>1.25 Hz and D>60% jobs. The equation more closely fits the data and applies the TLV® using a continuous function.

A conservative numerical scheme for modeling nonlinear acoustic propagation in thermoviscous homogeneous media

NASA Astrophysics Data System (ADS)

Diaz, Manuel A.; Solovchuk, Maxim A.; Sheu, Tony W. H.

2018-06-01

A nonlinear system of partial differential equations capable of describing the nonlinear propagation and attenuation of finite amplitude perturbations in thermoviscous media is presented. This system constitutes a full nonlinear wave model that has been formulated in the conservation form. Initially, this model is investigated analytically in the inviscid limit where it has been found that the resulting flux function fulfills the Lax-Wendroff theorem, and the scheme can match the solutions of the Westervelt and Burgers equations numerically. Here, high-order numerical descriptions of strongly nonlinear wave propagations become of great interest. For that matter we consider finite difference formulations of the weighted essentially non-oscillatory (WENO) schemes associated with explicit strong stability preserving Runge-Kutta (SSP-RK) time integration methods. Although this strategy is known to be computationally demanding, it is found to be effective when implemented to be solved in graphical processing units (GPUs). As we consider wave propagations in unbounded domains, perfectly matching layers (PML) have been also considered in this work. The proposed system model is validated and illustrated by using one- and two-dimensional benchmark test cases proposed in the literature for nonlinear acoustic propagation in homogeneous thermoviscous media.

Thermo-fluid-dynamics of turbulent boundary layer over a moving continuous flat sheet in a parallel free stream

NASA Astrophysics Data System (ADS)

Afzal, Bushra; Noor Afzal Team; Bushra Afzal Team

2014-11-01

The momentum and thermal turbulent boundary layers over a continuous moving sheet subjected to a free stream have been analyzed in two layers (inner wall and outer wake) theory at large Reynolds number. The present work is based on open Reynolds equations of momentum and heat transfer without any closure model say, like eddy viscosity or mixing length etc. The matching of inner and outer layers has been carried out by Izakson-Millikan-Kolmogorov hypothesis. The matching for velocity and temperature profiles yields the logarithmic laws and power laws in overlap region of inner and outer layers, along with friction factor and heat transfer laws. The uniformly valid solution for velocity, Reynolds shear stress, temperature and thermal Reynolds heat flux have been proposed by introducing the outer wake functions due to momentum and thermal boundary layers. The comparison with experimental data for velocity profile, temperature profile, skin friction and heat transfer are presented. In outer non-linear layers, the lowest order momentum and thermal boundary layer equations have also been analyses by using eddy viscosity closure model, and results are compared with experimental data. Retired Professor, Embassy Hotel, Rasal Ganj, Aligarh 202001 India.

Numerical solution of Boltzmann tranport equation for TEA CO 2 laser having nitrogen-lean gas mixtures to predict laser characteristics and gas lifetime

NASA Astrophysics Data System (ADS)

Kumar, Manoj; Khare, Jai; Nath, A. K.

2007-02-01

Selective laser isotope separation by TEA CO 2 laser often needs short tail-free pulses. Using laser mixtures having very little nitrogen almost tail free laser pulses can be generated. The laser pulse characteristics and its gas lifetime is an important issue for long-term laser operation. Boltzmann transport equation is therefore solved numerically for TEA CO 2 laser gas mixtures having very little nitrogen to predict electron energy distribution function (EEDF). The distribution function is used to calculate various excitation and dissociation rate of CO 2 to predict laser pulse characteristics and laser gas lifetime, respectively. Laser rate equations have been solved with the calculated excitation rates for numerically evaluated discharge current and voltage profiles to calculate laser pulse shape. The calculated laser pulse shape and duration are in good agreement with the measured laser characteristics. The gas lifetime is estimated by integrating the equation governing the dissociation of CO 2. An experimental study of gas lifetime was carried out using quadrapole mass analyzer for such mixtures to estimate the O 2 being produced due to dissociation of CO 2 in the pulse discharge. The theoretically calculated O 2 concentration in the laser gas mixture matches with experimentally observed value. In the present TEA CO 2 laser system, for stable discharge the O 2 concentration should be below 0.2%.

Efficient algorithms for analyzing the singularly perturbed boundary value problems of fractional order

NASA Astrophysics Data System (ADS)

Sayevand, K.; Pichaghchi, K.

2018-04-01

In this paper, we were concerned with the description of the singularly perturbed boundary value problems in the scope of fractional calculus. We should mention that, one of the main methods used to solve these problems in classical calculus is the so-called matched asymptotic expansion method. However we shall note that, this was not achievable via the existing classical definitions of fractional derivative, because they do not obey the chain rule which one of the key elements of the matched asymptotic expansion method. In order to accommodate this method to fractional derivative, we employ a relatively new derivative so-called the local fractional derivative. Using the properties of local fractional derivative, we extend the matched asymptotic expansion method to the scope of fractional calculus and introduce a reliable new algorithm to develop approximate solutions of the singularly perturbed boundary value problems of fractional order. In the new method, the original problem is partitioned into inner and outer solution equations. The reduced equation is solved with suitable boundary conditions which provide the terminal boundary conditions for the boundary layer correction. The inner solution problem is next solved as a solvable boundary value problem. The width of the boundary layer is approximated using appropriate resemblance function. Some theoretical results are established and proved. Some illustrating examples are solved and the results are compared with those of matched asymptotic expansion method and homotopy analysis method to demonstrate the accuracy and efficiency of the method. It can be observed that, the proposed method approximates the exact solution very well not only in the boundary layer, but also away from the layer.

Higher predation risk for insect prey at low latitudes and elevations.

PubMed

Roslin, Tomas; Hardwick, Bess; Novotny, Vojtech; Petry, William K; Andrew, Nigel R; Asmus, Ashley; Barrio, Isabel C; Basset, Yves; Boesing, Andrea Larissa; Bonebrake, Timothy C; Cameron, Erin K; Dáttilo, Wesley; Donoso, David A; Drozd, Pavel; Gray, Claudia L; Hik, David S; Hill, Sarah J; Hopkins, Tapani; Huang, Shuyin; Koane, Bonny; Laird-Hopkins, Benita; Laukkanen, Liisa; Lewis, Owen T; Milne, Sol; Mwesige, Isaiah; Nakamura, Akihiro; Nell, Colleen S; Nichols, Elizabeth; Prokurat, Alena; Sam, Katerina; Schmidt, Niels M; Slade, Alison; Slade, Victor; Suchanková, Alžběta; Teder, Tiit; van Nouhuys, Saskya; Vandvik, Vigdis; Weissflog, Anita; Zhukovich, Vital; Slade, Eleanor M

2017-05-19

Biotic interactions underlie ecosystem structure and function, but predicting interaction outcomes is difficult. We tested the hypothesis that biotic interaction strength increases toward the equator, using a global experiment with model caterpillars to measure predation risk. Across an 11,660-kilometer latitudinal gradient spanning six continents, we found increasing predation toward the equator, with a parallel pattern of increasing predation toward lower elevations. Patterns across both latitude and elevation were driven by arthropod predators, with no systematic trend in attack rates by birds or mammals. These matching gradients at global and regional scales suggest consistent drivers of biotic interaction strength, a finding that needs to be integrated into general theories of herbivory, community organization, and life-history evolution. Copyright © 2017, American Association for the Advancement of Science.

Slowly rotating homogeneous masses revisited

NASA Astrophysics Data System (ADS)

Reina, Borja

2016-02-01

Hartle's model for slowly rotating stars has been extensively used to compute equilibrium configurations of slowly rotating stars to second order in perturbation theory in general relativity, given a barotropic equation of state. A recent study based on the modern theory of perturbed matchings concludes that the functions in the (first and second order) perturbation tensors can always be taken as continuous at the surface of the star, except for the second-order function m0. This function presents a jump at the surface of the star proportional to the discontinuity of the energy density there. This concerns only a particular outcome of the model: the change in mass δM. In this paper, the amended change in mass is calculated for the case of constant density stars.

Full Multigrid Flow Solver

NASA Technical Reports Server (NTRS)

Mineck, Raymond E.; Thomas, James L.; Biedron, Robert T.; Diskin, Boris

2005-01-01

FMG3D (full multigrid 3 dimensions) is a pilot computer program that solves equations of fluid flow using a finite difference representation on a structured grid. Infrastructure exists for three dimensions but the current implementation treats only two dimensions. Written in Fortran 90, FMG3D takes advantage of the recursive subroutine feature, dynamic memory allocation, and structured-programming constructs of that language. FMG3D supports multi-block grids with three types of block-to-block interfaces: periodic, C-zero, and C-infinity. For all three types, grid points must match at interfaces. For periodic and C-infinity types, derivatives of grid metrics must be continuous at interfaces. The available equation sets are as follows: scalar elliptic equations, scalar convection equations, and the pressure-Poisson formulation of the Navier-Stokes equations for an incompressible fluid. All the equation sets are implemented with nonzero forcing functions to enable the use of user-specified solutions to assist in verification and validation. The equations are solved with a full multigrid scheme using a full approximation scheme to converge the solution on each succeeding grid level. Restriction to the next coarser mesh uses direct injection for variables and full weighting for residual quantities; prolongation of the coarse grid correction from the coarse mesh to the fine mesh uses bilinear interpolation; and prolongation of the coarse grid solution uses bicubic interpolation.

The logistics of choice.

PubMed

Killeen, Peter R

2015-07-01

The generalized matching law (GML) is reconstructed as a logistic regression equation that privileges no particular value of the sensitivity parameter, a. That value will often approach 1 due to the feedback that drives switching that is intrinsic to most concurrent schedules. A model of that feedback reproduced some features of concurrent data. The GML is a law only in the strained sense that any equation that maps data is a law. The machine under the hood of matching is in all likelihood the very law that was displaced by the Matching Law. It is now time to return the Law of Effect to centrality in our science. © Society for the Experimental Analysis of Behavior.

Self-consistent adjoint analysis for topology optimization of electromagnetic waves

NASA Astrophysics Data System (ADS)

Deng, Yongbo; Korvink, Jan G.

2018-05-01

In topology optimization of electromagnetic waves, the Gâteaux differentiability of the conjugate operator to the complex field variable results in the complexity of the adjoint sensitivity, which evolves the original real-valued design variable to be complex during the iterative solution procedure. Therefore, the self-inconsistency of the adjoint sensitivity is presented. To enforce the self-consistency, the real part operator has been used to extract the real part of the sensitivity to keep the real-value property of the design variable. However, this enforced self-consistency can cause the problem that the derived structural topology has unreasonable dependence on the phase of the incident wave. To solve this problem, this article focuses on the self-consistent adjoint analysis of the topology optimization problems for electromagnetic waves. This self-consistent adjoint analysis is implemented by splitting the complex variables of the wave equations into the corresponding real parts and imaginary parts, sequentially substituting the split complex variables into the wave equations with deriving the coupled equations equivalent to the original wave equations, where the infinite free space is truncated by the perfectly matched layers. Then, the topology optimization problems of electromagnetic waves are transformed into the forms defined on real functional spaces instead of complex functional spaces; the adjoint analysis of the topology optimization problems is implemented on real functional spaces with removing the variational of the conjugate operator; the self-consistent adjoint sensitivity is derived, and the phase-dependence problem is avoided for the derived structural topology. Several numerical examples are implemented to demonstrate the robustness of the derived self-consistent adjoint analysis.

A General Method for Solving Systems of Non-Linear Equations

NASA Technical Reports Server (NTRS)

Nachtsheim, Philip R.; Deiss, Ron (Technical Monitor)

1995-01-01

The method of steepest descent is modified so that accelerated convergence is achieved near a root. It is assumed that the function of interest can be approximated near a root by a quadratic form. An eigenvector of the quadratic form is found by evaluating the function and its gradient at an arbitrary point and another suitably selected point. The terminal point of the eigenvector is chosen to lie on the line segment joining the two points. The terminal point found lies on an axis of the quadratic form. The selection of a suitable step size at this point leads directly to the root in the direction of steepest descent in a single step. Newton's root finding method not infrequently diverges if the starting point is far from the root. However, the current method in these regions merely reverts to the method of steepest descent with an adaptive step size. The current method's performance should match that of the Levenberg-Marquardt root finding method since they both share the ability to converge from a starting point far from the root and both exhibit quadratic convergence near a root. The Levenberg-Marquardt method requires storage for coefficients of linear equations. The current method which does not require the solution of linear equations requires more time for additional function and gradient evaluations. The classic trade off of time for space separates the two methods.

Digital computer program for generating dynamic turbofan engine models (DIGTEM)

NASA Technical Reports Server (NTRS)

Daniele, C. J.; Krosel, S. M.; Szuch, J. R.; Westerkamp, E. J.

1983-01-01

This report describes DIGTEM, a digital computer program that simulates two spool, two-stream turbofan engines. The turbofan engine model in DIGTEM contains steady-state performance maps for all of the components and has control volumes where continuity and energy balances are maintained. Rotor dynamics and duct momentum dynamics are also included. Altogether there are 16 state variables and state equations. DIGTEM features a backward-differnce integration scheme for integrating stiff systems. It trims the model equations to match a prescribed design point by calculating correction coefficients that balance out the dynamic equations. It uses the same coefficients at off-design points and iterates to a balanced engine condition. Transients can also be run. They are generated by defining controls as a function of time (open-loop control) in a user-written subroutine (TMRSP). DIGTEM has run on the IBM 370/3033 computer using implicit integration with time steps ranging from 1.0 msec to 1.0 sec. DIGTEM is generalized in the aerothermodynamic treatment of components.

[Stimulation parameters for automatic examination of color vision].

PubMed

Sommerhalder, J; Pelizzone, M; Roth, A

1997-05-01

We have developed a polyvalent computer controlled instrument, which uses the "two equation method" (Rayleigh and Moreland equations) to measure human colour vision. This "colorimeter" (or anomaloscope) was used to determine the influence of some important stimulation parameters. The influence of stimulus exposure time, observation field size, absolute stimulus luminance, saturation and luminance mismatches between mixture and reference stimuli were measured on our computer controlled colorimeter. All subjects were normal observers. 1) An exposure time of 2s was found to be optimal for clinical work. 2) The Moreland equation on a 7 degrees observation field yields results in which population variability is comparable to a Rayleigh equation on a 2 degrees field. 3) A retinal illuminance between 40 and 1000 trolands can be used for automated Moreland matches. 4) The saturation of the reference field for the Moreland match can be preset to a fixed value. 5) It is important to vary automatically the radiance of the reference field to provide an approximate luminance match as the ratio of primaries in the mixture field is changed. These measurements allows us to determine optimal conditions for automated colour vision examinations and to make recommendations for an international standard.

A new approach to spherically symmetric junction surfaces and the matching of FLRW regions

NASA Astrophysics Data System (ADS)

Kirchner, U.

2004-08-01

We investigate timelike junctions (with surface layer) between spherically symmetric solutions of the Einstein-field equation. In contrast to previous investigations, this is done in a coordinate system in which the junction surface motion is absorbed in the metric, while all coordinates are continuous at the junction surface. The evolution equations for all relevant quantities are derived. We discuss the no-surface layer case (boundary surface) and study the behaviour for small surface energies. It is shown that one should expect cases in which the speed of light is reached within a finite proper time. We carefully discuss necessary and sufficient conditions for a possible matching of spherically symmetric sections. For timelike junctions between spherically symmetric spacetime sections we show explicitly that the time component of the Lanczos equation always reduces to an identity (independent of the surface equation of state). The results are applied to the matching of Friedmann Lemaître Robertson Walker (FLRW) models. We discuss 'vacuum bubbles' and closed open junctions in detail. As illustrations several numerical integration results are presented, some of them indicate that (observers comoving with) the junction surface can reach the speed of light within a finite time.

A Structural Equation Modeling Analysis of Influences on Juvenile Delinquency

ERIC Educational Resources Information Center

Barrett, David E.; Katsiyannis, Antonis; Zhang, Dalun; Zhang, Dake

2014-01-01

This study examined influences on delinquency and recidivism using structural equation modeling. The sample comprised 199,204 individuals: 99,602 youth whose cases had been processed by the South Carolina Department of Juvenile Justice and a matched control group of 99,602 youth without juvenile records. Structural equation modeling for the…

Perfectly Matched Layer for Linearized Euler Equations in Open and Ducted Domains

NASA Technical Reports Server (NTRS)

Tam, Christopher K. W.; Auriault, Laurent; Cambuli, Francesco

1998-01-01

Recently, perfectly matched layer (PML) as an absorbing boundary condition has widespread applications. The idea was first introduced by Berenger for electromagnetic waves computations. In this paper, it is shown that the PML equations for the linearized Euler equations support unstable solutions when the mean flow has a component normal to the layer. To suppress such unstable solutions so as to render the PML concept useful for this class of problems, it is proposed that artificial selective damping terms be added to the discretized PML equations. It is demonstrated that with a proper choice of artificial mesh Reynolds number, the PML equations can be made stable. Numerical examples are provided to illustrate that the stabilized PML performs well as an absorbing boundary condition. In a ducted environment, the wave mode are dispersive. It will be shown that the group velocity and phase velocity of these modes can have opposite signs. This results in a confined environment, PML may not be suitable as an absorbing boundary condition.

Resonant vibrations of a submerged beam

NASA Astrophysics Data System (ADS)

Achenbach, J. D.; Qu, J.

1986-03-01

Forced vibration of a simply supported submerged beam of circular cross section is investigated by the use of two mathematical methods. In the first approach the problem formulation is reduced to a singular integro-differential equation for the transverse deflection. In the second approach the method of matched asymptotic expansions is employed. The integro-differential equation is solved numerically, to yield an exact solution for the frequency response. Subsequent use of a representation integral yields the radiated far field acoustic pressure. The exact results for the beam deflection are compared with approximate results that are available in the literature. Next, a matched asymptotic expansion is worked out by constructing "inner" and "outer" expansions for frequencies near and not near resonance frequencies, respectively. The two expansions are matched in an appropriate manner to yield a uniformly valid solution. The leading term of the matched asymptotic solution is compared with exact numerical results.

Neoclassical, semi-collisional tearing mode theory in an axisymmetric torus

NASA Astrophysics Data System (ADS)

Connor, J. W.; Hastie, R. J.; Helander, P.

2017-12-01

A set of layer equations for determining the stability of semi-collisional tearing modes in an axisymmetric torus, incorporating neoclassical physics, in the small ion Larmor radius limit, is provided. These can be used as an inner layer module for inclusion in numerical codes that asymptotically match the layer to toroidal calculations of the tearing mode stability index, \\prime $ . They are more complete than in earlier work and comprise equations for the perturbed electron density and temperature, the ion temperature, Ampère's law and the vorticity equation, amounting to a twelvth-order set of radial differential equations. While the toroidal geometry is kept quite general when treating the classical and Pfirsch-Schlüter transport, parallel bootstrap current and semi-collisional physics, it is assumed that the fraction of trapped particles is small for the banana regime contribution. This is to justify the use of a model collision term when acting on the localised (in velocity space) solutions that remain after the Spitzer solutions have been exploited to account for the bulk of the passing distributions. In this respect, unlike standard neoclassical transport theory, the calculation involves the second Spitzer solution connected with a parallel temperature gradient, because this stability problem involves parallel temperature gradients that cannot occur in equilibrium toroidal transport theory. Furthermore, a calculation of the linearised neoclassical radial transport of toroidal momentum for general geometry is required to complete the vorticity equation. The solutions of the resulting set of equations do not match properly to the ideal magnetohydrodynamic (MHD) equations at large distances from the layer, and a further, intermediate layer involving ion corrections to the electrical conductivity and ion parallel thermal transport is invoked to achieve this matching and allow one to correctly calculate the layer \\prime $ .

An economics systems analysis of land mobile radio telephone services

NASA Technical Reports Server (NTRS)

Leroy, B. E.; Stevenson, S. M.

1980-01-01

The economic interaction of the terrestrial and satellite systems is considered. Parametric equations are formulated to allow examination of necessary user thresholds and growth rates as a function of system costs. Conversely, first order allowable systems costs are found as a function of user thresholds and growth rates. Transitions between satellite and terrestrial service systems are examined. User growth rate density (user/year/sq km) is shown to be a key parameter in the analysis of systems compatibility. The concept of system design matching the price/demand curves is introduced and examples are given. The role of satellite systems is critically examined and the economic conditions necessary for the introduction of satellite service are identified.

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.

On-Orbit Line Spread Function Estimation of the SNPP VIIRS Imaging System from Lake Pontchartrain Causeway Bridge Images

NASA Technical Reports Server (NTRS)

Tilton, James C.; Wolfe, Robert E.; Lin, Guoqing

2017-01-01

The visible infrared imaging radiometer suite (VIIRS) instrument was launched 28 October 2011 onboard the Suomi National Polar-orbiting Partnership (SNPP) satellite. The VIIRS instrument is a whiskbroom system with 22 spectral and thermal bands split between 16 moderate resolution bands (M-bands), five imagery resolution bands (I-bands) and a day-night band. In this study we estimate the along-scan line spread function (LSF) of the I-bands and M-bands based on measurements performed on images of the Lake Pontchartrain Causeway Bridge. In doing so we develop a model for the LSF that closely matches the prelaunch laboratory measurements. We utilize VIIRS images co-geolocated with a Landsat TM image to precisely locate the bridge linear feature in the VIIRS images as a linear best fit to a straight line. We then utilize non-linear optimization to compute the best fit equation of the VIIRS image measurements in the vicinity of the bridge to the developed model equation. From the found parameterization of the model equation we derive the full-width at half-maximum (FWHM) as an approximation of the sensor field of view (FOV) for all bands, and compare these on-orbit measured values with prelaunch laboratory results.

Optical antenna gain. I - Transmitting antennas

NASA Technical Reports Server (NTRS)

Klein, B. J.; Degnan, J. J.

1974-01-01

The gain of centrally obscured optical transmitting antennas is analyzed in detail. The calculations, resulting in near- and far-field antenna gain patterns, assume a circular antenna illuminated by a laser operating in the TEM-00 mode. A simple polynomial equation is derived for matching the incident source distribution to a general antenna configuration for maximum on-axis gain. An interpretation of the resultant gain curves allows a number of auxiliary design curves to be drawn that display the losses in antenna gain due to pointing errors and the cone angle of the beam in the far field as a function of antenna aperture size and its central obscuration. The results are presented in a series of graphs that allow the rapid and accurate evaluation of the antenna gain which may then be substituted into the conventional range equation.

Existence conditions for unknown input functional observers

NASA Astrophysics Data System (ADS)

Fernando, T.; MacDougall, S.; Sreeram, V.; Trinh, H.

2013-01-01

This article presents necessary and sufficient conditions for the existence and design of an unknown input Functional observer. The existence of the observer can be verified by computing a nullspace of a known matrix and testing some matrix rank conditions. The existence of the observer does not require the satisfaction of the observer matching condition (i.e. Equation (16) in Hou and Muller 1992, 'Design of Observers for Linear Systems with Unknown Inputs', IEEE Transactions on Automatic Control, 37, 871-875), is not limited to estimating scalar functionals and allows for arbitrary pole placement. The proposed observer always exists when a state observer exists for the unknown input system, and furthermore, the proposed observer can exist even in some instances when an unknown input state observer does not exist.

Nonlinear acoustic wave equations with fractional loss operators.

PubMed

Prieur, Fabrice; Holm, Sverre

2011-09-01

Fractional derivatives are well suited to describe wave propagation in complex media. When introduced in classical wave equations, they allow a modeling of attenuation and dispersion that better describes sound propagation in biological tissues. Traditional constitutive equations from solid mechanics and heat conduction are modified using fractional derivatives. They are used to derive a nonlinear wave equation which describes attenuation and dispersion laws that match observations. This wave equation is a generalization of the Westervelt equation, and also leads to a fractional version of the Khokhlov-Zabolotskaya-Kuznetsov and Burgers' equations. © 2011 Acoustical Society of America

Comparison of Themodynamic and Transport Property Models for Computing Equilibrium High Enthalpy Flows

NASA Astrophysics Data System (ADS)

Ramasahayam, Veda Krishna Vyas; Diwakar, Anant; Bodi, Kowsik

2017-11-01

To study the flow of high temperature air in vibrational and chemical equilibrium, accurate models for thermodynamic state and transport phenomena are required. In the present work, the performance of a state equation model and two mixing rules for determining equilibrium air thermodynamic and transport properties are compared with that of curve fits. The thermodynamic state model considers 11 species which computes flow chemistry by an iterative process and the mixing rules considered for viscosity are Wilke and Armaly-Sutton. The curve fits of Srinivasan, which are based on Grabau type transition functions, are chosen for comparison. A two-dimensional Navier-Stokes solver is developed to simulate high enthalpy flows with numerical fluxes computed by AUSM+-up. The accuracy of state equation model and curve fits for thermodynamic properties is determined using hypersonic inviscid flow over a circular cylinder. The performance of mixing rules and curve fits for viscosity are compared using hypersonic laminar boundary layer prediction on a flat plate. It is observed that steady state solutions from state equation model and curve fits match with each other. Though curve fits are significantly faster the state equation model is more general and can be adapted to any flow composition.

On the Representation of Aquifer Compressibility in General Subsurface Flow Codes: How an Alternate Definition of Aquifer Compressibility Matches Results from the Groundwater Flow Equation

NASA Astrophysics Data System (ADS)

Birdsell, D.; Karra, S.; Rajaram, H.

2016-12-01

The governing equations for subsurface flow codes in deformable porous media are derived from the fluid mass balance equation. One class of these codes, which we call general subsurface flow (GSF) codes, does not explicitly track the motion of the solid porous media but does accept general constitutive relations for porosity, density, and fluid flux. Examples of GSF codes include PFLOTRAN, FEHM, STOMP, and TOUGH2. Meanwhile, analytical and numerical solutions based on the groundwater flow equation have assumed forms for porosity, density, and fluid flux. We review the derivation of the groundwater flow equation, which uses the form of Darcy's equation that accounts for the velocity of fluids with respect to solids and defines the soil matrix compressibility accordingly. We then show how GSF codes have a different governing equation if they use the form of Darcy's equation that is written only in terms of fluid velocity. The difference is seen in the porosity change, which is part of the specific storage term in the groundwater flow equation. We propose an alternative definition of soil matrix compressibility to correct for the untracked solid velocity. Simulation results show significantly less error for our new compressibility definition than the traditional compressibility when compared to analytical solutions from the groundwater literature. For example, the error in one calculation for a pumped sandstone aquifer goes from 940 to <70 Pa when the new compressibility is used. Code users and developers need to be aware of assumptions in the governing equations and constitutive relations in subsurface flow codes, and our newly-proposed compressibility function should be incorporated into GSF codes.

On the Representation of Aquifer Compressibility in General Subsurface Flow Codes: How an Alternate Definition of Aquifer Compressibility Matches Results from the Groundwater Flow Equation

NASA Astrophysics Data System (ADS)

Birdsell, D.; Karra, S.; Rajaram, H.

2017-12-01

The governing equations for subsurface flow codes in deformable porous media are derived from the fluid mass balance equation. One class of these codes, which we call general subsurface flow (GSF) codes, does not explicitly track the motion of the solid porous media but does accept general constitutive relations for porosity, density, and fluid flux. Examples of GSF codes include PFLOTRAN, FEHM, STOMP, and TOUGH2. Meanwhile, analytical and numerical solutions based on the groundwater flow equation have assumed forms for porosity, density, and fluid flux. We review the derivation of the groundwater flow equation, which uses the form of Darcy's equation that accounts for the velocity of fluids with respect to solids and defines the soil matrix compressibility accordingly. We then show how GSF codes have a different governing equation if they use the form of Darcy's equation that is written only in terms of fluid velocity. The difference is seen in the porosity change, which is part of the specific storage term in the groundwater flow equation. We propose an alternative definition of soil matrix compressibility to correct for the untracked solid velocity. Simulation results show significantly less error for our new compressibility definition than the traditional compressibility when compared to analytical solutions from the groundwater literature. For example, the error in one calculation for a pumped sandstone aquifer goes from 940 to <70 Pa when the new compressibility is used. Code users and developers need to be aware of assumptions in the governing equations and constitutive relations in subsurface flow codes, and our newly-proposed compressibility function should be incorporated into GSF codes.

SELECTION DYNAMICS IN JOINT MATCHING TO RATE AND MAGNITUDE OF REINFORCEMENT

PubMed Central

McDowell, J. J; Popa, Andrei; Calvin, Nicholas T

2012-01-01

Virtual organisms animated by a selectionist theory of behavior dynamics worked on concurrent random interval schedules where both the rate and magnitude of reinforcement were varied. The selectionist theory consists of a set of simple rules of selection, recombination, and mutation that act on a population of potential behaviors by means of a genetic algorithm. An extension of the power function matching equation, which expresses behavior allocation as a joint function of exponentiated reinforcement rate and reinforcer magnitude ratios, was fitted to the virtual organisms' data, and over a range of moderate mutation rates was found to provide an excellent description of their behavior without residual trends. The mean exponents in this range of mutation rates were 0.83 for the reinforcement rate ratio and 0.68 for the reinforcer magnitude ratio, which are values that are comparable to those obtained in experiments with live organisms. These findings add to the evidence supporting the selectionist theory, which asserts that the world of behavior we observe and measure is created by evolutionary dynamics. PMID:23008523

Aircraft Range Optimization Using Singular Perturbations

NASA Technical Reports Server (NTRS)

Oconnor, Joseph Taffe

1973-01-01

An approximate analytic solution is developed for the problem of maximizing the range of an aircraft for a fixed end state. The problem is formulated as a singular perturbation and solved by matched inner and outer asymptotic expansions and the minimum principle of Pontryagin. Cruise in the stratosphere, and on transition to and from cruise at constant Mach number are discussed. The state vector includes altitude, flight path angle, and mass. Specific fuel consumption becomes a linear function of power approximating that of the cruise values. Cruise represents the outer solution; altitude and flight path angle are constants, and only mass changes. Transitions between cruise and the specified initial and final conditions correspond to the inner solutions. The mass is constant and altitude and velocity vary. A solution is developed which is valid for cruise but which is not for the initial and final conditions. Transforming of the independent variable near the initial and final conditions result in solutions which are valid for the two inner solutions but not for cruise. The inner solutions can not be obtained without simplifying the state equations. The singular perturbation approach overcomes this difficulty. A quadratic approximation of the state equations is made. The resulting problem is solved analytically, and the two inner solutions are matched to the outer solution.

Upper limit set by causality on the tidal deformability of a neutron star

NASA Astrophysics Data System (ADS)

Van Oeveren, Eric D.; Friedman, John L.

2017-04-01

A principal goal of gravitational-wave astronomy is to constrain the neutron star equation of state (EOS) by measuring the tidal deformability of neutron stars. The tidally induced departure of the waveform from that of a point particle [or a spinless binary black hole (BBH)] increases with the stiffness of the EOS. We show that causality (the requirement that the speed of sound be less than the speed of light for a perfect fluid satisfying a one-parameter equation of state) places an upper bound on tidal deformability as a function of mass. Like the upper mass limit, the limit on deformability is obtained by using an EOS with vsound=c for high densities and matching to a low density (candidate) EOS at a matching density of order nuclear saturation density. We use these results and those of Lackey et al. [Phys. Rev. D 89, 043009 (2014), 10.1103/PhysRevD.89.043009] to estimate the resulting upper limit on the gravitational-wave phase shift of a black hole-neutron star (BHNS) binary relative to a BBH. Even for assumptions weak enough to allow a maximum mass of 4 M⊙ (a match at nuclear saturation density to an unusually stiff low-density candidate EOS), the upper limit on dimensionless tidal deformability is stringent. It leads to a still more stringent estimated upper limit on the maximum tidally induced phase shift prior to merger. We comment in an appendix on the relation among causality, the condition vsound

Switch Hitting in Baseball: Apparent Rule-following, not Matching

PubMed Central

Poling, Alan; Weeden, Marc A; Redner, Ryan; Foster, T. Mary

2011-01-01

Many studies, including some dealing with shot selection in basketball and play selection in football, demonstrate that the generalized matching equation provides a good description of the allocation of time and effort to alternative responses as a function of the consequences of those alternatives. We examined whether it did so with respect to left- and right-handed at bats (alternative responses) and left- and right-handed total bases earned, runs batted in, and home runs (three consequences) for the outstanding baseball switch-hitters Mickey Mantle, Eddie Murray, and Pete Rose. With all hitters, undermatching, suggesting insensitivity to the consequences of behavior (reinforcement), was evident and there was substantial bias towards left-handed at bats. These players apparently chose handedness based on the rule “bat opposite the pitcher,” not on differential consequences obtained in major league games. The present findings are significant in representing a counter-instance of demonstrations of a matching relationship in sports in particular and in human behavior in general and in calling attention to the need for further study of the variables that affect choice. PMID:21909169

Traveling waves in Hall-magnetohydrodynamics and the ion-acoustic shock structure

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

Hagstrom, George I.; Hameiri, Eliezer

Hall-magnetohydrodynamics (HMHD) is a mixed hyperbolic-parabolic partial differential equation that describes the dynamics of an ideal two fluid plasma with massless electrons. We study the only shock wave family that exists in this system (the other discontinuities being contact discontinuities and not shocks). We study planar traveling wave solutions and we find solutions with discontinuities in the hydrodynamic variables, which arise due to the presence of real characteristics in Hall-MHD. We introduce a small viscosity into the equations and use the method of matched asymptotic expansions to show that solutions with a discontinuity satisfying the Rankine-Hugoniot conditions and also anmore » entropy condition have continuous shock structures. The lowest order inner equations reduce to the compressible Navier-Stokes equations, plus an equation which implies the constancy of the magnetic field inside the shock structure. We are able to show that the current is discontinuous across the shock, even as the magnetic field is continuous, and that the lowest order outer equations, which are the equations for traveling waves in inviscid Hall-MHD, are exactly integrable. We show that the inner and outer solutions match, which allows us to construct a family of uniformly valid continuous composite solutions that become discontinuous when the diffusivity vanishes.« less

A Hybrid Ground-Motion Prediction Equation for Earthquakes in Western Alberta

NASA Astrophysics Data System (ADS)

Spriggs, N.; Yenier, E.; Law, A.; Moores, A. O.

2015-12-01

Estimation of ground-motion amplitudes that may be produced by future earthquakes constitutes the foundation of seismic hazard assessment and earthquake-resistant structural design. This is typically done by using a prediction equation that quantifies amplitudes as a function of key seismological variables such as magnitude, distance and site condition. In this study, we develop a hybrid empirical prediction equation for earthquakes in western Alberta, where evaluation of seismic hazard associated with induced seismicity is of particular interest. We use peak ground motions and response spectra from recorded seismic events to model the regional source and attenuation attributes. The available empirical data is limited in the magnitude range of engineering interest (M>4). Therefore, we combine empirical data with a simulation-based model in order to obtain seismologically informed predictions for moderate-to-large magnitude events. The methodology is two-fold. First, we investigate the shape of geometrical spreading in Alberta. We supplement the seismic data with ground motions obtained from mining/quarry blasts, in order to gain insights into the regional attenuation over a wide distance range. A comparison of ground-motion amplitudes for earthquakes and mining/quarry blasts show that both event types decay at similar rates with distance and demonstrate a significant Moho-bounce effect. In the second stage, we calibrate the source and attenuation parameters of a simulation-based prediction equation to match the available amplitude data from seismic events. We model the geometrical spreading using a trilinear function with attenuation rates obtained from the first stage, and calculate coefficients of anelastic attenuation and site amplification via regression analysis. This provides a hybrid ground-motion prediction equation that is calibrated for observed motions in western Alberta and is applicable to moderate-to-large magnitude events.

Closed-loop control of boundary layer streaks induced by free-stream turbulence

NASA Astrophysics Data System (ADS)

Papadakis, George; Lu, Liang; Ricco, Pierre

2016-08-01

The central aim of the paper is to carry out a theoretical and numerical study of active wall transpiration control of streaks generated within an incompressible boundary layer by free-stream turbulence. The disturbance flow model is based on the linearized unsteady boundary-region (LUBR) equations, studied by Leib, Wundrow, and Goldstein [J. Fluid Mech. 380, 169 (1999), 10.1017/S0022112098003504], which are the rigorous asymptotic limit of the Navier-Stokes equations for low-frequency and long-streamwise wavelength. The mathematical formulation of the problem directly incorporates the random forcing into the equations in a consistent way. Due to linearity, this forcing is factored out and appears as a multiplicative factor. It is shown that the cost function (integral of kinetic energy in the domain) is properly defined as the expectation of a random quadratic function only after integration in wave number space. This operation naturally introduces the free-stream turbulence spectral tensor into the cost function. The controller gains for each wave number are independent of the spectral tensor and, in that sense, universal. Asymptotic matching of the LUBR equations with the free-stream conditions results in an additional forcing term in the state-space system whose presence necessitates the reformulation of the control problem and the rederivation of its solution. It is proved that the solution can be obtained analytically using an extension of the sweep method used in control theory to obtain the standard Riccati equation. The control signal consists of two components, a feedback part and a feed-forward part (that depends explicitly on the forcing term). Explicit recursive equations that provide these two components are derived. It is shown that the feed-forward part makes a negligible contribution to the control signal. We also derive an explicit expression that a priori (i.e., before solving the control problem) leads to the minimum of the objective cost function (i.e., the fundamental performance limit), based only on the system matrices and the initial and free-stream boundary conditions. The adjoint equations admit a self-similar solution for large spanwise wave numbers with a scaling which is different from that of the LUBR equations. The controlled flow field also has a self-similar solution if the weighting matrices of the objective function are chosen appropriately. The code developed to implement this algorithm is efficient and has modest memory requirements. Computations show the significant reduction of energy for each wave number. The control of the full spectrum streaks, for conditions corresponding to a realistic experimental case, shows that the root-mean-square of the streamwise velocity is strongly suppressed in the whole domain and for all the frequency ranges examined.

Correlation functions of warped CFT

NASA Astrophysics Data System (ADS)

Song, Wei; Xu, Jianfei

2018-04-01

Warped conformal field theory (WCFT) is a two dimensional quantum field theory whose local symmetry algebra consists of a Virasoro algebra and a U(1) Kac-Moody algebra. In this paper, we study correlation functions for primary operators in WCFT. Similar to conformal symmetry, warped conformal symmetry is very constraining. The form of the two and three point functions are determined by the global warped conformal symmetry while the four point functions can be determined up to an arbitrary function of the cross ratio. The warped conformal bootstrap equation are constructed by formulating the notion of crossing symmetry. In the large central charge limit, four point functions can be decomposed into global warped conformal blocks, which can be solved exactly. Furthermore, we revisit the scattering problem in warped AdS spacetime (WAdS), and give a prescription on how to match the bulk result to a WCFT retarded Green's function. Our result is consistent with the conjectured holographic dualities between WCFT and WAdS.

Matching in an undisturbed natural human environment.

PubMed

McDowell, J J; Caron, Marcia L

2010-05-01

Data from the Oregon Youth Study, consisting of the verbal behavior of 210 adolescent boys determined to be at risk for delinquency (targets) and 210 of their friends (peers), were analyzed for their conformance to the complete family of matching theory equations in light of recent findings from the basic science, and using recently developed analytic techniques. Equations of the classic and modern theories of matching were fitted as ensembles to rates and time allocations of the boys' rule-break and normative talk obtained from conversations between pairs of boys. The verbal behavior of each boy in a conversation was presumed to be reinforced by positive social responses from the other boy. Consistent with recent findings from the basic science, the boys' verbal behavior was accurately described by the modern but not the classic theory of matching. These findings also add support to the assertion that basic principles and processes that are known to govern behavior in laboratory experiments also govern human social behavior in undisturbed natural environments.

Energy transport in the three coupled α-polypeptide chains of collagen molecule with long-range interactions effect

NASA Astrophysics Data System (ADS)

Mvogo, Alain; Ben-Bolie, G. H.; Kofané, T. C.

2015-06-01

The dynamics of three coupled α-polypeptide chains of a collagen molecule is investigated with the influence of power-law long-range exciton-exciton interactions. The continuum limit of the discrete equations reveal that the collagen dynamics is governed by a set of three coupled nonlinear Schrödinger equations, whose dispersive coefficient depends on the LRI parameter r. We construct the analytic symmetric and asymmetric (antisymmetric) soliton solutions, which match with the structural features of collagen related with the acupuncture channels. These solutions are used as initial conditions for the numerical simulations of the discrete equations, which reveal a coherent transport of energy in the molecule for r > 3. The results also indicate that the width of the solitons is a decreasing function of r, which help to stabilize the solitons propagating in the molecule. To confirm further the efficiency of energy transport in the molecule, the modulational instability of the system is performed and the numerical simulations show that the energy can flow from one polypeptide chain to another in the form of nonlinear waves.

Colorimetry and prime colours--a theorem.

PubMed

Hornaes, Hans Petter; Wold, Jan Henrik; Farup, Ivar

2005-08-01

Human colour vision is the result of a complex process involving topics ranging from physics of light to perception. Whereas the diversity of light entering the eye in principle span an infinite-dimensional vector space in terms of the spectral power distributions, the space of human colour perceptions is three dimensional. One important consequence of this is that a variety of colours can be visually matched by a mixture of only three adequately chosen reference lights. It has been observed that there exists one particular set of monochromatic reference lights that, according to a certain definition, is optimal for producing colour matches. These reference lights are commonly denoted prime colours. In the present paper, we intend to rigorously show that the existence of prime colours is not particular to the human visual system as sometimes stated, but rather an algebraic consequence of the manner in which a kind of colorimetric functions called colour-matching functions are defined and transformed. The solution is based on maximisation of a determinant determining the gamut size of the colour space spanned by the prime colours. Cramer's rule for solving a set of linear equations is an essential part of the proof. By means of examples, it is shown that mathematically the optimal set of reference lights is not unique in general, and that the existence of a maximum determinant is not a necessary condition for the existence of prime colours.

Relativistic compact stars with charged anisotropic matter

NASA Astrophysics Data System (ADS)

Maurya, S. K.; Banerjee, Ayan; Channuie, Phongpichit

2018-05-01

In this article, we perform a detailed theoretical analysis of new exact solutions with anisotropic fluid distribution of matter for compact objects subject to hydrostatic equilibrium. We present a family solution to the Einstein-Maxwell equations describing a spherically symmetric, static distribution of a fluid with pressure anisotropy. We implement an embedding class one condition to obtain a relation between the metric functions. We generalize the properties of a spherical star with hydrostatic equilibrium using the generalised Tolman-Oppenheimer-Volkoff (TOV) equation. We match the interior solution to an exterior Reissner-Nordström one, and study the energy conditions, speed of sound, and mass-radius relation of the star. We also show that the obtained solutions are compatible with observational data for the compact object Her X-1. Regarding our results, the physical behaviour of the present model may serve for the modeling of ultra compact objects.

Alterations in Aerobic Exercise Performance and Gait Economy Following High-Intensity Dynamic Stepping Training in Persons With Subacute Stroke.

PubMed

Leddy, Abigail L; Connolly, Mark; Holleran, Carey L; Hennessy, Patrick W; Woodward, Jane; Arena, Ross A; Roth, Elliot J; Hornby, T George

2016-10-01

Impairments in metabolic capacity and economy (O2cost) are hallmark characteristics of locomotor dysfunction following stroke. High-intensity (aerobic) training has been shown to improve peak oxygen consumption in this population, with fewer reports of changes in O2cost. However, particularly in persons with subacute stroke, inconsistent gains in walking function are observed with minimal associations with gains in metabolic parameters. The purpose of this study was to evaluate changes in aerobic exercise performance in participants with subacute stroke following high-intensity variable stepping training as compared with conventional therapy. A secondary analysis was performed on data from a randomized controlled trial comparing high-intensity training with conventional interventions, and from the pilot study that formed the basis for the randomized controlled trial. Participants 1 to 6 months poststroke received 40 or fewer sessions of high-intensity variable stepping training (n = 21) or conventional interventions (n = 12). Assessments were performed at baseline (BSL), posttraining, and 2- to 3-month follow-up and included changes in submaximal (Equation is included in full-text article.)O2 ((Equation is included in full-text article.)O2submax) and O2cost at fastest possible treadmill speeds and peak speeds at BSL testing. Significant improvements were observed in (Equation is included in full-text article.)O2submax with less consistent improvements in O2cost, although individual responses varied substantially. Combined changes in both (Equation is included in full-text article.)O2submax and (Equation is included in full-text article.)O2 at matched peak BSL speeds revealed stronger correlations to improvements in walking function as compared with either measure alone. High-intensity stepping training may elicit significant improvements in (Equation is included in full-text article.)O2submax, whereas changes in both peak capacity and economy better reflect gains in walking function. Providing high-intensity training to improve locomotor and aerobic exercise performance may increase the efficiency of rehabilitation sessions.Video Abstract available for more insights from the authors (see Supplemental Digital Content, http://links.lww.com/JNPT/A142).

Singularity-free solutions for anisotropic charged fluids with Chaplygin equation of state

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

Rahaman, Farook; Ray, Saibal; Jafry, Abdul Kayum

2010-11-15

We extend the Krori-Barua analysis of the static, spherically symmetric, Einstein-Maxwell field equations and consider charged fluid sources with anisotropic stresses. The inclusion of a new variable (tangential pressure) allows the use of a nonlinear, Chaplygin-type equation of state with coefficients fixed by the matching conditions at the boundary of the source. Some physical features are briefly discussed.

Revisiting Wiedemann-Franz law through Boltzmann transport equations and ab-initio density functional theory

NASA Astrophysics Data System (ADS)

Nag, Abhinav; Kumari, Anuja; Kumar, Jagdish

2018-05-01

We have investigated structural, electronic and transport properties of the alkali metals using ab-initio density functional theory. The electron energy dispersions are found parabolic free electron like which is expected for alkali metals. The lattice constants for all the studied metals are also in good agreement within 98% with experiments. We have further computed their transport properties using semi-classical Boltzmann transport equations with special focus on electrical and thermal conductivity. Our objective was to obtain Wiedemann-Franz law and hence Lorenz number. The motivation to do these calculations is to see that how the incorporation of different interactions such as electron-lattice, electron-electron interaction affect the Wiedeman-Franz law. By solving Boltzmann transport equations, we have obtained electrical conductivity (σ/τ) and thermal conductivity (κ0 /τ) at different temperatures and then calculated Lorenz number using L = κ0 /(σT). The obtained value of Lorenz number has been found to match with value derived for free electron Fermi gas 2.44× 10-8 WΩK-2. Our results prove that the Wiedemann-Franz law as derived for free electron gas does not change much for alkali metals, even when one incorporates interaction of electrons with atomic nuclei and other electrons. However, at lower temperatures, the Lorenz number, was found to be deviating from its theoretical value.

Acoustic plane wave diffraction from a truncated semi-infinite cone in axial irradiation

NASA Astrophysics Data System (ADS)

Kuryliak, Dozyslav; Lysechko, Victor

2017-11-01

The diffraction problem of the plane acoustic wave on the semi-infinite truncated soft and rigid cones in the case of axial incidence is solved. The problem is formulated as a boundary-value problem in terms of Helmholtz equation, with Dirichlet and Neumann boundary conditions, for scattered velocity potential. The incident field is taken to be the total field of semi-infinite cone, the expression of which is obtained by solving the auxiliary diffraction problem by the use of Kontorovich-Lebedev integral transformation. The diffracted field is sought via the expansion in series of the eigenfunctions for subdomains of the Helmholtz equation taking into account the edge condition. The corresponding diffraction problem is reduced to infinite system of linear algebraic equations (ISLAE) making use of mode matching technique and orthogonality properties of the Legendre functions. The method of analytical regularization is applied in order to extract the singular part in ISLAE, invert it exactly and reduce the problem to ISLAE of the second kind, which is readily amenable to calculation. The numerical solution of this system relies on the reduction method; and its accuracy depends on the truncation order. The case of degeneration of the truncated semi-infinite cone into an aperture in infinite plane is considered. Characteristic features of diffracted field in near and far fields as functions of cone's parameters are examined.

Self-force calculations with matched expansions and quasinormal mode sums

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

Casals, Marc; Dolan, Sam; Ottewill, Adrian C.

2009-06-15

Accurate modeling of gravitational wave emission by extreme-mass ratio inspirals is essential for their detection by the LISA mission. A leading perturbative approach involves the calculation of the self-force acting upon the smaller orbital body. In this work, we present the first application of the Poisson-Wiseman-Anderson method of 'matched expansions' to compute the self-force acting on a point particle moving in a curved spacetime. The method employs two expansions for the Green function, which are, respectively, valid in the 'quasilocal' and 'distant past' regimes, and which may be matched together within the normal neighborhood. We perform our calculation in amore » static region of the spherically symmetric Nariai spacetime (dS{sub 2}xS{sup 2}), in which scalar-field perturbations are governed by a radial equation with a Poeschl-Teller potential (frequently used as an approximation to the Schwarzschild radial potential) whose solutions are known in closed form. The key new ingredients in our study are (i) very high order quasilocal expansions and (ii) expansion of the distant past Green function in quasinormal modes. In combination, these tools enable a detailed study of the properties of the scalar-field Green function. We demonstrate that the Green function is singular whenever x and x{sup '} are connected by a null geodesic, and apply asymptotic methods to determine the structure of the Green function near the null wave front. We show that the singular part of the Green function undergoes a transition each time the null wave front passes through a caustic point, following a repeating fourfold sequence {delta}({sigma}), 1/{pi}{sigma}, -{delta}({sigma}), -1/{pi}{sigma}, etc., where {sigma} is Synge's world function. The matched-expansion method provides insight into the nonlocal properties of the self-force. We show that the self-force generated by the segment of the worldline lying outside the normal neighborhood is not negligible. We apply the matched-expansion method to compute the scalar self-force acting on a static particle on the Nariai spacetime, and validate against an alternative method, obtaining agreement to six decimal places. We conclude with a discussion of the implications for wave propagation and self-force calculations. On black hole spacetimes, any expansion of the Green function in quasinormal modes must be augmented by a branch-cut integral. Nevertheless, we expect the Green function in Schwarzschild spacetime to inherit certain key features, such as a fourfold singular structure manifesting itself through the asymptotic behavior of quasinormal modes. In this way, the Nariai spacetime provides a fertile testing ground for developing insight into the nonlocal part of the self-force on black hole spacetimes.« less

Microscale Procedure for Inorganic Qualitative Analysis with Emphasis on Writing Equations: Chemical Fingerprinting Applied to the "n"-bottle Problem of Matching Samples with Their Formulas

ERIC Educational Resources Information Center

Sattsangi, Prem D.

2014-01-01

A laboratory method for teaching inorganic qualitative analysis and chemical equations is described. The experiment has been designed to focus attention on cations and anions that react to form products. This leads to a logical approach to understand and write chemical equations. The procedure uses 3 mL plastic micropipettes to store and deliver…

Extended phase matching of second-harmonic generation in periodically poled KTiOPO4 with zero group-velocity mismatch

NASA Astrophysics Data System (ADS)

König, Friedrich; Wong, Franco N. C.

2004-03-01

Under extended phase-matching conditions, the first frequency derivative of the wave-vector mismatch is zero and the phase-matching bandwidth is greatly increased. We present extensive three-wave mixing measurements of the wave-vector mismatch and obtain improved Sellmeier equations for KTiOPO4. We observed a type-II extended phase-matching bandwidth of 100 nm for second-harmonic generation in periodically poled KTiOPO4, centered at the fundamental wavelength of 1584 nm. Applications in quantum entanglement and frequency metrology are discussed.

Thermoelastic analysis of non-uniform pressurized functionally graded cylinder with variable thickness using first order shear deformation theory(FSDT) and perturbation method

NASA Astrophysics Data System (ADS)

Khoshgoftar, M. J.; Mirzaali, M. J.; Rahimi, G. H.

2015-11-01

Recently application of functionally graded materials(FGMs) have attracted a great deal of interest. These materials are composed of various materials with different micro-structures which can vary spatially in FGMs. Such composites with varying thickness and non-uniform pressure can be used in the aerospace engineering. Therefore, analysis of such composite is of high importance in engineering problems. Thermoelastic analysis of functionally graded cylinder with variable thickness under non-uniform pressure is considered. First order shear deformation theory and total potential energy approach is applied to obtain the governing equations of non-homogeneous cylinder. Considering the inner and outer solutions, perturbation series are applied to solve the governing equations. Outer solution for out of boundaries and more sensitive variable in inner solution at the boundaries are considered. Combining of inner and outer solution for near and far points from boundaries leads to high accurate displacement field distribution. The main aim of this paper is to show the capability of matched asymptotic solution for different non-homogeneous cylinders with different shapes and different non-uniform pressures. The results can be used to design the optimum thickness of the cylinder and also some properties such as high temperature residence by applying non-homogeneous material.

Asymptotic matching by the symbolic manipulator MACSYMA

NASA Technical Reports Server (NTRS)

Lo, L. L.

1985-01-01

The delegation of the labor of calculating higher-order terms in singular perturbation (SP) expansions to a computer by the use of MACSYMA is considered. The method of matched asymptotic expansions is studied in detail for two model SP problems: a model resembling the boundary layer equation with a small parameter multiplying the highest derivatives; and a turning-point problem. It is shown that MACSYMA has successfully performed the higher-order matching in both problems.

Combining item response theory with multiple imputation to equate health assessment questionnaires.

PubMed

Gu, Chenyang; Gutman, Roee

2017-09-01

The assessment of patients' functional status across the continuum of care requires a common patient assessment tool. However, assessment tools that are used in various health care settings differ and cannot be easily contrasted. For example, the Functional Independence Measure (FIM) is used to evaluate the functional status of patients who stay in inpatient rehabilitation facilities, the Minimum Data Set (MDS) is collected for all patients who stay in skilled nursing facilities, and the Outcome and Assessment Information Set (OASIS) is collected if they choose home health care provided by home health agencies. All three instruments or questionnaires include functional status items, but the specific items, rating scales, and instructions for scoring different activities vary between the different settings. We consider equating different health assessment questionnaires as a missing data problem, and propose a variant of predictive mean matching method that relies on Item Response Theory (IRT) models to impute unmeasured item responses. Using real data sets, we simulated missing measurements and compared our proposed approach to existing methods for missing data imputation. We show that, for all of the estimands considered, and in most of the experimental conditions that were examined, the proposed approach provides valid inferences, and generally has better coverages, relatively smaller biases, and shorter interval estimates. The proposed method is further illustrated using a real data set. © 2016, The International Biometric Society.

Three-dimensional wave field modeling by a collocated-grid finite-difference method in the anelastic model with surface topography

NASA Astrophysics Data System (ADS)

Wang, N.; Li, J.; Borisov, D.; Gharti, H. N.; Shen, Y.; Zhang, W.; Savage, B. K.

2016-12-01

We incorporate 3D anelastic attenuation into the collocated-grid finite-difference method on curvilinear grids (Zhang et al., 2012), using the rheological model of the generalized Maxwell body (Emmerich and Korn, 1987; Moczo and Kristek, 2005; Käser et al., 2007). We follow a conventional procedure to calculate the anelastic coefficients (Emmerich and Korn, 1987) determined by the Q(ω)-law, with a modification in the choice of frequency band and thus the relaxation frequencies that equidistantly cover the logarithmic frequency range. We show that such an optimization of anelastic coefficients is more accurate when using a fixed number of relaxation mechanisms to fit the frequency independent Q-factors. We use curvilinear grids to represent the surface topography. The velocity-stress form of the 3D isotropic anelastic wave equation is solved with a collocated-grid finite-difference method. Compared with the elastic case, we need to solve additional material-independent anelastic functions (Kristek and Moczo, 2003) for the mechanisms at each relaxation frequency. Based on the stress-strain relation, we calculate the spatial partial derivatives of the anelastic functions indirectly thereby saving computational storage and improving computational efficiency. The complex-frequency-shifted perfectly matched layer (CFS-PML) is used for the absorbing boundary condition based on the auxiliary difference equation (Zhang and Shen, 2010). The traction image method (Zhang and Chen, 2006) is employed for the free-surface boundary condition. We perform several numerical experiments including homogeneous full-space models and layered half-space models, considering both flat and 3D Gaussian-shape hill surfaces. The results match very well with those of the spectral-element method (Komatitisch and Tromp, 2002; Savage et al., 2010), verifying the simulations by our method in the anelastic model with surface topography.

Fast Legendre moment computation for template matching

NASA Astrophysics Data System (ADS)

Li, Bing C.

2017-05-01

Normalized cross correlation (NCC) based template matching is insensitive to intensity changes and it has many applications in image processing, object detection, video tracking and pattern recognition. However, normalized cross correlation implementation is computationally expensive since it involves both correlation computation and normalization implementation. In this paper, we propose Legendre moment approach for fast normalized cross correlation implementation and show that the computational cost of this proposed approach is independent of template mask sizes which is significantly faster than traditional mask size dependent approaches, especially for large mask templates. Legendre polynomials have been widely used in solving Laplace equation in electrodynamics in spherical coordinate systems, and solving Schrodinger equation in quantum mechanics. In this paper, we extend Legendre polynomials from physics to computer vision and pattern recognition fields, and demonstrate that Legendre polynomials can help to reduce the computational cost of NCC based template matching significantly.

Hybrid bandgap engineering for super-hetero-epitaxial semiconductor materials, and products thereof

NASA Technical Reports Server (NTRS)

Park, Yeonjoon (Inventor); Choi, Sang H. (Inventor); King, Glen C. (Inventor); Elliott, James R. (Inventor)

2012-01-01

"Super-hetero-epitaxial" combinations comprise epitaxial growth of one material on a different material with different crystal structure. Compatible crystal structures may be identified using a "Tri-Unity" system. New bandgap engineering diagrams are provided for each class of combination, based on determination of hybrid lattice constants for the constituent materials in accordance with lattice-matching equations. Using known bandgap figures for previously tested materials, new materials with lattice constants that match desired substrates and have the desired bandgap properties may be formulated by reference to the diagrams and lattice matching equations. In one embodiment, this analysis makes it possible to formulate new super-hetero-epitaxial semiconductor systems, such as systems based on group IV alloys on c-plane LaF.sub.3; group IV alloys on c-plane langasite; Group III-V alloys on c-plane langasite; and group II-VI alloys on c-plane sapphire.

Accuracy of AFM force distance curves via direct solution of the Euler-Bernoulli equation

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

Eppell, Steven J., E-mail: steven.eppell@case.edu; Liu, Yehe; Zypman, Fredy R.

2016-03-15

In an effort to improve the accuracy of force-separation curves obtained from atomic force microscope data, we compare force-separation curves computed using two methods to solve the Euler-Bernoulli equation. A recently introduced method using a direct sequential forward solution, Causal Time-Domain Analysis, is compared against a previously introduced Tikhonov Regularization method. Using the direct solution as a benchmark, it is found that the regularization technique is unable to reproduce accurate curve shapes. Using L-curve analysis and adjusting the regularization parameter, λ, to match either the depth or the full width at half maximum of the force curves, the two techniquesmore » are contrasted. Matched depths result in full width at half maxima that are off by an average of 27% and matched full width at half maxima produce depths that are off by an average of 109%.« less

Matched asymptotic expansion of the Hamilton-Jacobi-Bellman equation for aeroassisted plane-change maneuvers

NASA Technical Reports Server (NTRS)

Calise, Anthony J.; Melamed, Nahum

1993-01-01

In this paper we develop a general procedure for constructing a matched asymptotic expansion of the Hamilton-Jacobi-Bellman equation based on the method of characteristics. The development is for a class of perturbation problems whose solution exhibits two-time-scale behavior. A regular expansion for problems of this type is inappropriate since it is not uniformly valid over a narrow range of the independent variable. Of particular interest here is the manner in which matching and boundary conditions are enforced when the expansion is carried out to first order. Two cases are distinguished - one where the left boundary condition coincides with or lies to the right of the singular region and one where the left boundary condition lies to the left of the singular region. A simple example is used to illustrate the procedure, and its potential application to aeroassisted plane change is described.

DSD/WBL-consistent JWL equations of state for EDC35

NASA Astrophysics Data System (ADS)

Hodgson, Alexander N.; Handley, Caroline Angela

2012-03-01

The Detonation Shock Dynamics (DSD) model allows the calculation of curvature-dependent detonation propagation. It is of particular use when applied to insensitive high explosives, such as EDC35, since they have a greater non-ideal behaviour. The DSD model is used in conjunction with experimental cylinder test data to obtain the JWL Equation of State (EOS) for EDC35. Adjustment of parameters in the JWL equation changes the expansion profile of the cylinder wall in hydrocode simulations. The parameters are iterated until the best match can be made between simulation and experiment. Previous DSD models used at AWE have no mechanism to adjust the chemical energy release to match the detonation conditions. Two JWL calibrations are performed using the DSD model, with and without Hetherington's energy release model (these proceedings). Also in use is a newly-calibrated detonation speed-curvature relation.

Motion of a curved vortex filament with decaying vortical core and axial velocity

NASA Technical Reports Server (NTRS)

Callegari, A. J.; Ting, L.

1978-01-01

The motion and decay of a curved vortex filament having large axial and circumferential velocity components in a three-dimensional stream are analyzed by using the method of matched asymptotic expansions of the incompressible Navier-Stokes equations. The small parameter is the square root of the ratio of the kinematic viscosity to the circulation. The outer region is analyzed by the classical Biot-Savart law, and its solution is matched to that of the inner region, where viscous effects are important. Equations describing the coupling between the inner vortex structure and the motion of the vortex filament as well as the time evolution of the inner vortex structure are obtained. Equations are derived for the motion of the vortex filament and for the change and decay in time and space of the leading-order circumferential and axial velocity and vorticity components. Solutions are constructed for these components in terms of initial data.

Spectrum response estimation for deep-water floating platforms via retardation function representation

NASA Astrophysics Data System (ADS)

Liu, Fushun; Liu, Chengcheng; Chen, Jiefeng; Wang, Bin

2017-08-01

The key concept of spectrum response estimation with commercial software, such as the SESAM software tool, typically includes two main steps: finding a suitable loading spectrum and computing the response amplitude operators (RAOs) subjected to a frequency-specified wave component. In this paper, we propose a nontraditional spectrum response estimation method that uses a numerical representation of the retardation functions. Based on estimated added mass and damping matrices of the structure, we decompose and replace the convolution terms with a series of poles and corresponding residues in the Laplace domain. Then, we estimate the power density corresponding to each frequency component using the improved periodogram method. The advantage of this approach is that the frequency-dependent motion equations in the time domain can be transformed into the Laplace domain without requiring Laplace-domain expressions for the added mass and damping. To validate the proposed method, we use a numerical semi-submerged pontoon from the SESAM. The numerical results show that the responses of the proposed method match well with those obtained from the traditional method. Furthermore, the estimated spectrum also matches well, which indicates its potential application to deep-water floating structures.

An economic systems analysis of land mobile radio telephone services

NASA Technical Reports Server (NTRS)

Leroy, B. E.; Stevenson, S. M.

1980-01-01

This paper deals with the economic interaction of the terrestrial and satellite land-mobile radio service systems. The cellular, trunked and satellite land-mobile systems are described. Parametric equations are formulated to allow examination of necessary user thresholds and growth rates as functions of system costs. Conversely, first order allowable systems costs are found as a function of user thresholds and growth rates. Transitions between satellite and terrestrial service systems are examined. User growth rate density (user/year/km squared) is shown to be a key parameter in the analysis of systems compatibility. The concept of system design matching the price demand curves is introduced and examples are given. The role of satellite systems is critically examined and the economic conditions necessary for the introduction of satellite service are identified.

Nonlinear Optical Properties and Applications of Polydiacetylene

NASA Technical Reports Server (NTRS)

Abdeldayem, Hossin; Paley, Mark S.; Witherow, William K.; Frazier, Donald O.

2000-01-01

Recently, we have demonstrated a picosecond all-optical switch, which also functions as a partial all-optical NAND logic gate using a novel polydiacetylene that is synthesized in our laboratory. The nonlinear optical properties of the polydiacetylene material are measured using the Z-scan technique. A theoretical model based on a three level system is investigated and the rate equations of the system are solved. The theoretical calculations are proven to match nicely with the experimental results. The absorption cross-sections for both the first and higher excited states are estimated. The analyses also show that the material suffers a photochemical change beyond a certain level of the laser power and its physical properties suffer radical changes. These changes are the cause for the partial NAND gate function and the switching mechanism.

Rough-to-smooth transition of an equilibrium neutral constant stress layer

NASA Technical Reports Server (NTRS)

Logan, E., Jr.; Fichtl, G. H.

1975-01-01

Purpose of research on rough-to-smooth transition of an equilibrium neutral constant stress layer is to develop a model for low-level atmospheric flow over terrains of abruptly changing roughness, such as those occurring near the windward end of a landing strip, and to use the model to derive functions which define the extent of the region affected by the roughness change and allow adequate prediction of wind and shear stress profiles at all points within the region. A model consisting of two bounding logarithmic layers and an intermediate velocity defect layer is assumed, and dimensionless velocity and stress distribution functions which meet all boundary and matching conditions are hypothesized. The functions are used in an asymptotic form of the equation of motion to derive a relation which governs the growth of the internal boundary layer. The growth relation is used to predict variation of surface shear stress.

Variational methods for direct/inverse problems of atmospheric dynamics and chemistry

NASA Astrophysics Data System (ADS)

Penenko, Vladimir; Penenko, Alexey; Tsvetova, Elena

2013-04-01

We present a variational approach for solving direct and inverse problems of atmospheric hydrodynamics and chemistry. It is important that the accurate matching of numerical schemes has to be provided in the chain of objects: direct/adjoint problems - sensitivity relations - inverse problems, including assimilation of all available measurement data. To solve the problems we have developed a new enhanced set of cost-effective algorithms. The matched description of the multi-scale processes is provided by a specific choice of the variational principle functionals for the whole set of integrated models. Then all functionals of variational principle are approximated in space and time by splitting and decomposition methods. Such approach allows us to separately consider, for example, the space-time problems of atmospheric chemistry in the frames of decomposition schemes for the integral identity sum analogs of the variational principle at each time step and in each of 3D finite-volumes. To enhance the realization efficiency, the set of chemical reactions is divided on the subsets related to the operators of production and destruction. Then the idea of the Euler's integrating factors is applied in the frames of the local adjoint problem technique [1]-[3]. The analytical solutions of such adjoint problems play the role of integrating factors for differential equations describing atmospheric chemistry. With their help, the system of differential equations is transformed to the equivalent system of integral equations. As a result we avoid the construction and inversion of preconditioning operators containing the Jacobi matrixes which arise in traditional implicit schemes for ODE solution. This is the main advantage of our schemes. At the same time step but on the different stages of the "global" splitting scheme, the system of atmospheric dynamic equations is solved. For convection - diffusion equations for all state functions in the integrated models we have developed the monotone and stable discrete-analytical numerical schemes [1]-[3] conserving the positivity of the chemical substance concentrations and possessing the properties of energy and mass balance that are postulated in the general variational principle for integrated models. All algorithms for solution of transport, diffusion and transformation problems are direct (without iterations). The work is partially supported by the Programs No 4 of Presidium RAS and No 3 of Mathematical Department of RAS, by RFBR project 11-01-00187 and Integrating projects of SD RAS No 8 and 35. Our studies are in the line with the goals of COST Action ES1004. References Penenko V., Tsvetova E. Discrete-analytical methods for the implementation of variational principles in environmental applications// Journal of computational and applied mathematics, 2009, v. 226, 319-330. Penenko A.V. Discrete-analytic schemes for solving an inverse coefficient heat conduction problem in a layered medium with gradient methods// Numerical Analysis and Applications, 2012, V. 5, pp 326-341. V. Penenko, E. Tsvetova. Variational methods for constructing the monotone approximations for atmospheric chemistry models //Numerical Analysis and Applications, 2013 (in press).

Bi-Factor MIRT Observed-Score Equating for Mixed-Format Tests

ERIC Educational Resources Information Center

Lee, Guemin; Lee, Won-Chan

2016-01-01

The main purposes of this study were to develop bi-factor multidimensional item response theory (BF-MIRT) observed-score equating procedures for mixed-format tests and to investigate relative appropriateness of the proposed procedures. Using data from a large-scale testing program, three types of pseudo data sets were formulated: matched samples,…

Generalized Bondi-Sachs equations for characteristic formalism of numerical relativity

NASA Astrophysics Data System (ADS)

Cao, Zhoujian; He, Xiaokai

2013-11-01

The Cauchy formalism of numerical relativity has been successfully applied to simulate various dynamical spacetimes without any symmetry assumption. But discovering how to set a mathematically consistent and physically realistic boundary condition is still an open problem for Cauchy formalism. In addition, the numerical truncation error and finite region ambiguity affect the accuracy of gravitational wave form calculation. As to the finite region ambiguity issue, the characteristic extraction method helps much. But it does not solve all of the above issues. Besides the above problems for Cauchy formalism, the computational efficiency is another problem. Although characteristic formalism of numerical relativity suffers the difficulty from caustics in the inner near zone, it has advantages in relation to all of the issues listed above. Cauchy-characteristic matching (CCM) is a possible way to take advantage of characteristic formalism regarding these issues and treat the inner caustics at the same time. CCM has difficulty treating the gauge difference between the Cauchy part and the characteristic part. We propose generalized Bondi-Sachs equations for characteristic formalism for the Cauchy-characteristic matching end. Our proposal gives out a possible same numerical evolution scheme for both the Cauchy part and the characteristic part. And our generalized Bondi-Sachs equations have one adjustable gauge freedom which can be used to relate the gauge used in the Cauchy part. Then these equations can make the Cauchy part and the characteristic part share a consistent gauge condition. So our proposal gives a possible new starting point for Cauchy-characteristic matching.

Age-corrected reference values for the Heidelberg multi-color anomaloscope.

PubMed

Rüfer, Florian; Sauter, Benno; Klettner, Alexa; Göbel, Katja; Flammer, Josef; Erb, Carl

2012-09-01

To determine reference values for the HMC anomaloscope (Heidelberg multi-color anomaloscope) of healthy subjects. One hundred and thirteen healthy subjects were divided into four age groups: <20 years of age (ten female, five male), 20-39 years of age (23 female, 15 male), 40-59 years of age (23 female, ten male) and >60 years of age (nine female, 18 male). Match midpoint, matching range (MR) and anomaly quotient (AQ), according to the Moreland equation [blue (436 nm) + blue-green (490 nm) = cyan (480 nm) + yellow (589 nm)] and according to the Rayleigh equation [green (546 nm) + red (671 nm) = yellow (589 nm)] were determined. The neutral adaptation was done showing white light every 5 seconds in absolute mode and every 15 seconds in relative mode. The mean match midpoint according to the Rayleigh equation was 43.9 ± 2.6 scale units in absolute mode. It was highest between 20-39 years (45.2 ± 2.2) and lowest in subjects >60 years of age (42.2 ± 2.2). The mean MR in absolute mode was 3.1 ± 3.5 scale units with a maximum >60 years (4.4 ± 4.4). The MR in relative mode was between 1.6 ± 1.9 (20-39 years) and 4.4 ± 3.8 (>60 years). The resulting mean AQ was 1.01 ± 0.15 in both modes. The mean match midpoint of the Moreland equation was 51.0 ± 5.2 scale units in absolute mode. It was highest between 20-39 years (52.5 ± 5.7), and lowest in subjects >60 years of age (48.7 ± 3.6). The mean MR according to the Moreland equation was lower in absolute mode (13.4 ± 15.6) than in relative mode (16.2 ± 15.2). The mean resulting AQ was 1.02 ± 0.21 in both modes. The values of this study can be used as references for the diagnosis of red-green and blue perception impairment with the HMC anomaloscope.

Quantum square-well with logarithmic central spike

NASA Astrophysics Data System (ADS)

Znojil, Miloslav; Semorádová, Iveta

2018-01-01

Singular repulsive barrier V (x) = -gln(|x|) inside a square-well is interpreted and studied as a linear analog of the state-dependent interaction ℒeff(x) = -gln[ψ∗(x)ψ(x)] in nonlinear Schrödinger equation. In the linearized case, Rayleigh-Schrödinger perturbation theory is shown to provide a closed-form spectrum at sufficiently small g or after an amendment of the unperturbed Hamiltonian. At any spike strength g, the model remains solvable numerically, by the matching of wave functions. Analytically, the singularity is shown regularized via the change of variables x = expy which interchanges the roles of the asymptotic and central boundary conditions.

Exponential integrators in time-dependent density-functional calculations

NASA Astrophysics Data System (ADS)

Kidd, Daniel; Covington, Cody; Varga, Kálmán

2017-12-01

The integrating factor and exponential time differencing methods are implemented and tested for solving the time-dependent Kohn-Sham equations. Popular time propagation methods used in physics, as well as other robust numerical approaches, are compared to these exponential integrator methods in order to judge the relative merit of the computational schemes. We determine an improvement in accuracy of multiple orders of magnitude when describing dynamics driven primarily by a nonlinear potential. For cases of dynamics driven by a time-dependent external potential, the accuracy of the exponential integrator methods are less enhanced but still match or outperform the best of the conventional methods tested.

The development of a peak-time criterion for designing controlled-release devices.

PubMed

Simon, Laurent; Ospina, Juan

2016-08-25

This work consists of estimating dynamic characteristics for topically-applied drugs when the magnitude of the flux increases to a maximum value, called peak flux, before declining to zero. This situation is typical of controlled-released systems with a finite donor or vehicle volume. Laplace transforms were applied to the governing equations and resulted in an expression for the flux in terms of the physical characteristics of the system. After approximating this function by a second-order model, three parameters of this reduced structure captured the essential features of the original process. Closed-form relationships were then developed for the peak flux and time-to-peak based on the empirical representation. Three case studies that involve mechanisms, such as diffusion, partitioning, dissolution and elimination, were selected to illustrate the procedure. The technique performed successfully as shown by the ability of the second-order flux to match the prediction of the original transport equations. A main advantage of the proposed method is that it does not require a solution of the original partial differential equations. Less accurate results were noted for longer lag times. Copyright © 2016 Elsevier B.V. All rights reserved.

Perfect fluidity of a dissipative system: Analytical solution for the Boltzmann equation in AdS 2 Ⓧ S 2

DOE PAGES

Noronha, Jorge; Denicol, Gabriel S.

2015-12-30

In this paper we obtain an analytical solution of the relativistic Boltzmann equation under the relaxation time approximation that describes the out-of-equilibrium dynamics of a radially expanding massless gas. This solution is found by mapping this expanding system in flat spacetime to a static flow in the curved spacetime AdS 2 Ⓧ S 2. We further derive explicit analytic expressions for the momentum dependence of the single-particle distribution function as well as for the spatial dependence of its moments. We find that this dissipative system has the ability to flow as a perfect fluid even though its entropy density doesmore » not match the equilibrium form. The nonequilibrium contribution to the entropy density is shown to be due to higher-order scalar moments (which possess no hydrodynamical interpretation) of the Boltzmann equation that can remain out of equilibrium but do not couple to the energy-momentum tensor of the system. Furthermore, in this system the slowly moving hydrodynamic degrees of freedom can exhibit true perfect fluidity while being totally decoupled from the fast moving, nonhydrodynamical microscopic degrees of freedom that lead to entropy production.« less

Strong Helioseismic Constraints on Weakly-Coupled Plasmas

NASA Astrophysics Data System (ADS)

Nayfonov, Alan

The extraordinary accuracy of helioseismic data allows detailed theoretical studies of solar plasmas. The necessity to produce solar models matching the experimental results in accuracy imposes strong constrains on the equations of state of solar plasmas. Several discrepancies between the experimental data and models have been successfully identified as the signatures of various non-ideal phenomena. Of a particular interest are questions of the position of the energy levels and the continuum edge and of the effect of the excited states in the solar plasma. Calculations of energy level and continuum shifts, based on the Green function formalism, appeared recently in the literature. These results have been used to examine effects of the shifts on the thermodynamic quantities. A comparison with helioseismic data has shown that the calculations based on lower-level approximations, such as the static screening in the effective two-particle wave equation, agree very well with the experimental data. However, the case of full dynamic screening produces thermodynamic quantities inconsistent with observations. The study of the effect of different internal partition functions on a complete set of thermodynamic quantities has revealed the signature of the excited states in the MHD (Mihalas, Hummer, Dappen) equation of state. The presence of exited states causes a characteristic 'wiggle' in the thermodynamic quantities due to the density-dependent occupation probabilities. This effect is absent if the ACTEX (ACTivity EXpansion) equation of state is used. The wiggle has been found to be most prominent in the quantities sensitive to density. The size of this excited states effect is well within the observational power of helioseismology, and very recent inversion analyses of helioseismic data seem to indicate the presence of the wiggle in the sun. This has a potential importance for the helioseismic determination of the helium abundance of the sun.

A composite velocity procedure for the compressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Khosla, P. K.; Rubin, S. G.

1982-01-01

A new boundary-layer relaxation procedure is presented. In the spirit of the theory of matched asymptotic expansions, a multiplicative composite of the appropriate velocity representations for the inviscid and viscous regions is prescribed. The resulting equations are structured so that far from the surface of the body the momentum equations lead to the Bernoulli relation for the pressure, while the continuity equation reduces to the familiar compressible potential equation. Close to the body surface, the governing equations and solution techniques are characteristic of those describing interacting boundary-layers; although, the full Navier-Stokes equations are considered here. Laminar flow calculations for the subsonic flow over an axisymmetric boattail simulator geometry are presented for a variety of Reynolds and Mach numbers. A strongly implicit solution method is applied for the coupled velocity components.

Asymptotic Standard Errors of Observed-Score Equating with Polytomous IRT Models

ERIC Educational Resources Information Center

Andersson, Björn

2016-01-01

In observed-score equipercentile equating, the goal is to make scores on two scales or tests measuring the same construct comparable by matching the percentiles of the respective score distributions. If the tests consist of different items with multiple categories for each item, a suitable model for the responses is a polytomous item response…

On the falsifiability of matching theory.

PubMed Central

McDowell, J J

1986-01-01

Herrnstein's matching theory requires the parameter, k, which appears in the single-alternative form of the matching equation, to remain invariant with respect to changes in reinforcement parameters like magnitude or immediacy. Recent experiments have disconfirmed matching theory by showing that the invariant-k requirement does not hold. However, the theory can be asserted in a purely algebraic form that does not require an invariant k and that is not disconfirmed by the recent findings. In addition, both the original and the purely algebraic versions of matching theory can be asserted in forms that allow for commonly observed deviations from matching (bias, undermatching, and overmatching). The recent finding of a variable k does not disconfirm these versions of matching theory either. As a consequence, matching remains a viable theory of behavior, the strength of which lies in its general conceptualization of all behavior as choice, and in its unified mathematical treatment of single- and multialternative environments. PMID:3950535

Quantum transport and the Wigner distribution function for Bloch electrons in spatially homogeneous electric and magnetic fields

NASA Astrophysics Data System (ADS)

Iafrate, G. J.; Sokolov, V. N.; Krieger, J. B.

2017-10-01

The theory of Bloch electron dynamics for carriers in homogeneous electric and magnetic fields of arbitrary time dependence is developed in the framework of the Liouville equation. The Wigner distribution function (WDF) is determined from the single-particle density matrix in the ballistic regime, i.e., collision effects are excluded. In the theory, the single-particle transport equation is established with the electric field described in the vector potential gauge, and the magnetic field is treated in the symmetric gauge. No specific assumptions are made concerning the form of the initial distribution in momentum or configuration space. The general approach is to employ the accelerated Bloch state representation (ABR) as a basis so that the dependence upon the electric field, including multiband Zener tunneling, is treated exactly. Further, in the formulation of the WDF, we transform to a new set of variables so that the final WDF is gauge invariant and is expressed explicitly in terms of the position, kinetic momentum, and time. The methodology for developing the WDF is illustrated by deriving the exact WDF equation for free electrons in homogeneous electric and magnetic fields resulting in the same form as given by the collisionless Boltzmann transport equation (BTE). The methodology is then extended to the case of electrons described by an effective Hamiltonian corresponding to an arbitrary energy band function; the exact WDF equation results for the effective Hamiltonian case are shown to approximate the free electron results when taken to second order in the magnetic field. As a corollary, in these cases, it is shown that if the WDF is a wave packet, then the time rate of change of the electron quasimomentum is given by the Lorentz force. In treating the problem of Bloch electrons in a periodic potential in the presence of homogeneous electric and magnetic fields, the methodology for deriving the WDF reveals a multiband character due to the inherent nature of the Bloch states. The K0 representation of the Bloch envelope functions is employed to express the multiband WDF in a useful form. In examining the single-band WDF, it is found that the collisionless WDF equation matches the equivalent BTE to first order in the magnetic field. These results are necessarily extended to second order in the magnetic field by employing a unitary transformation that diagonalizes the Hamiltonian using the ABR to second order. The unitary transformation process includes a discussion of the multiband WDF transport analysis and the identification of the combined Zener-magnetic-field induced tunneling.

Large-aspect-ratio limit of neoclassical transport theory.

PubMed

Wong, S K; Chan, V S

2003-06-01

This paper presents a comprehensive description of neoclassical transport theory in the banana regime for large-aspect-ratio flux surfaces of arbitrary shapes. The method of matched-asymptotic expansions is used to obtain analytical solutions for plasma distribution functions and to compute transport coefficients. The method provides justification for retaining only the part of the Fokker-Planck operator that involves the second derivative with respect to the cosine of the pitch angle for the trapped and barely circulating particles. It leads to a simple equation for the freely circulating particles with boundary conditions that embody a discontinuity separating particles moving in opposite directions. Corrections to the transport coefficients are obtained by generalizing an existing boundary layer analysis. The system of moment and field equations is consistently taken in the cylinder limit, which facilitates the discussion of the treatment of dynamical constraints. It is shown that the nonlocal nature of Ohm's law in neoclassical theory renders the mathematical problem of plasma transport with changing flux surfaces nonstandard.

Vicinal fluorine-fluorine coupling constants: Fourier analysis.

PubMed

San Fabián, J; Westra Hoekzema, A J A

2004-10-01

Stereochemical dependences of vicinal fluorine-fluorine nuclear magnetic resonance coupling constants (3JFF) have been studied with the multiconfigurational self-consistent field in the restricted active space approach, with the second-order polarization propagator approximation (SOPPA), and with density functional theory. The SOPPA results show the best overall agreement with experimental couplings. The relationship with the dihedral angle between the coupled fluorines has been studied by Fourier analysis, the result is very different from that of proton-proton couplings. The Fourier coefficients do not resemble those of a typical Karplus equation. The four nonrelativistic contributions to the coupling constants of 1,2-difluoroethane configurations have been studied separately showing that up to six Fourier coefficients are required to reproduce the calculated values satisfactorily. Comparison with Fourier coefficients for matching hydrogen fluoride dimer configurations suggests that the higher order Fourier coefficients (Cn> or =3) originate mainly from through-space Fermi contact interaction. The through-space interaction is the main reason 3JFF do not follow the Karplus equation. (c) 2004 American Institute of Physics

Vicinal fluorine-fluorine coupling constants: Fourier analysis

NASA Astrophysics Data System (ADS)

San Fabián, J.; Westra Hoekzema, A. J. A.

2004-10-01

Stereochemical dependences of vicinal fluorine-fluorine nuclear magnetic resonance coupling constants (3JFF) have been studied with the multiconfigurational self-consistent field in the restricted active space approach, with the second-order polarization propagator approximation (SOPPA), and with density functional theory. The SOPPA results show the best overall agreement with experimental couplings. The relationship with the dihedral angle between the coupled fluorines has been studied by Fourier analysis, the result is very different from that of proton-proton couplings. The Fourier coefficients do not resemble those of a typical Karplus equation. The four nonrelativistic contributions to the coupling constants of 1,2-difluoroethane configurations have been studied separately showing that up to six Fourier coefficients are required to reproduce the calculated values satisfactorily. Comparison with Fourier coefficients for matching hydrogen fluoride dimer configurations suggests that the higher order Fourier coefficients (Cn⩾3) originate mainly from through-space Fermi contact interaction. The through-space interaction is the main reason 3JFF do not follow the Karplus equation.

A piece of cake: the ground-state energies in γ i -deformed = 4 SYM theory at leading wrapping order

NASA Astrophysics Data System (ADS)

Fokken, Jan; Sieg, Christoph; Wilhelm, Matthias

2014-09-01

In the non-supersymmetric γi-deformed = 4 SYM theory, the scaling dimensions of the operators tr[ Z L ] composed of L scalar fields Z receive finite-size wrapping and prewrapping corrections in the 't Hooft limit. In this paper, we calculate these scaling dimensions to leading wrapping order directly from Feynman diagrams. For L ≥ 3, the result is proportional to the maximally transcendental `cake' integral. It matches with an earlier result obtained from the integrability-based Lüscher corrections, TBA and Y-system equations. At L = 2, where the integrability-based equations yield infinity, we find a finite rational result. This result is renormalization-scheme dependent due to the non-vanishing β-function of an induced quartic scalar double-trace coupling, on which we have reported earlier. This explicitly shows that conformal invariance is broken — even in the 't Hooft limit. [Figure not available: see fulltext.

Properties of a soft-core model of methanol: An integral equation theory and computer simulation study

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

Huš, Matej; Urbic, Tomaz, E-mail: tomaz.urbic@fkkt.uni-lj.si; Munaò, Gianmarco

Thermodynamic and structural properties of a coarse-grained model of methanol are examined by Monte Carlo simulations and reference interaction site model (RISM) integral equation theory. Methanol particles are described as dimers formed from an apolar Lennard-Jones sphere, mimicking the methyl group, and a sphere with a core-softened potential as the hydroxyl group. Different closure approximations of the RISM theory are compared and discussed. The liquid structure of methanol is investigated by calculating site-site radial distribution functions and static structure factors for a wide range of temperatures and densities. Results obtained show a good agreement between RISM and Monte Carlo simulations.more » The phase behavior of methanol is investigated by employing different thermodynamic routes for the calculation of the RISM free energy, drawing gas-liquid coexistence curves that match the simulation data. Preliminary indications for a putative second critical point between two different liquid phases of methanol are also discussed.« less

Relaxation and self-organization in two-dimensional plasma and neutral fluid flow systems

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

Das, Amita

Extensive numerical studies in the framework of a simplified two-dimensional model for neutral and plasma fluid for a variety of initial configurations and for both decaying and driven cases are carried out to illustrate relaxation toward a self-organized state. The dynamical model equation constitutes a simple choice for this purpose, e.g., the vorticity equation of the Navier-Stokes dynamics for the incompressible neutral fluids and the Hasegawa-Mima equation for plasma fluid flow system. Scatter plots are employed to observe a development of functional relationship, if any, amidst the generalized vorticity and its Laplacian. It is seen that they do not satisfymore » a linear relationship as the well known variational approach of enstrophy minimization subject to constancy of the energy integral for the two-dimensional (2D) system suggests. The observed nonlinear functional relationship is understood by separating the contribution to the scatter plot from spatial regions with intense vorticity patches and those of the background flow region where the background vorticity is weak or absent altogether. It is shown that such a separation has close connection with the known exact analytical solutions of the system. The analytical solutions are typically obtained by assuming a finite source of vorticity for the inner core of the localized structure, which is then matched with the solution in the outer region where vorticity is chosen to be zero. The work also demonstrates that the seemingly ad hoc choice of the linear vorticity source function for the inner region is in fact consistent with the self-organization paradigm of the 2D systems.« less

Equation of state and phase diagram of Fe-16Si alloy as a candidate component of Earth's core

NASA Astrophysics Data System (ADS)

Fischer, Rebecca A.; Campbell, Andrew J.; Caracas, Razvan; Reaman, Daniel M.; Dera, Przymyslaw; Prakapenka, Vitali B.

2012-12-01

The outer core of the Earth contains several weight percent of one or more unknown light elements, which may include silicon. Therefore it is critical to understand the high pressure-temperature properties and behavior of an iron-silicon alloy with a geophysically relevant composition (16 wt% silicon). We experimentally determined the melting curve, subsolidus phase diagram, and equations of state of all phases of Fe-16 wt%Si to 140 GPa, finding a conversion from the D03 crystal structure to a B2+hcp mixture at high pressures. The melting curve implies that 3520 K is a minimum temperature for the Earth's outer core, if it consists solely of Fe-Si alloy, and that the eutectic composition in the Fe-Si system is less than 16 wt% silicon at core-mantle boundary conditions. Comparing our new equation of state to that of iron and the density of the core, we find that for an Fe-Ni-Si outer core, 11.3±1.5 wt% silicon would be required to match the core's observed density at the core-mantle boundary. We have also performed first-principles calculations of the equations of state of Fe3Si with the D03 structure, hcp iron, and FeSi with the B2 structure using density-functional theory.

Equation of state and phase diagram of Fe-16Si alloy as a candidate component of Earth's core

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

Fischer, Rebecca A; Campbell, Andrew J; Caracas, Razvan

2016-07-29

The outer core of the Earth contains several weight percent of one or more unknown light elements, which may include silicon. Therefore it is critical to understand the high pressure–temperature properties and behavior of an iron–silicon alloy with a geophysically relevant composition (16 wt% silicon). We experimentally determined the melting curve, subsolidus phase diagram, and equations of state of all phases of Fe–16 wt%Si to 140 GPa, finding a conversion from the D0 3 crystal structure to a B2+hcp mixture at high pressures. The melting curve implies that 3520 K is a minimum temperature for the Earth's outer core, ifmore » it consists solely of Fe–Si alloy, and that the eutectic composition in the Fe–Si system is less than 16 wt% silicon at core–mantle boundary conditions. Comparing our new equation of state to that of iron and the density of the core, we find that for an Fe–Ni–Si outer core, 11.3±1.5 wt% silicon would be required to match the core's observed density at the core–mantle boundary. We have also performed first-principles calculations of the equations of state of Fe 3Si with the D0 3 structure, hcp iron, and FeSi with the B2 structure using density-functional theory.« less

Perceptual learning modules in mathematics: enhancing students' pattern recognition, structure extraction, and fluency.

PubMed

Kellman, Philip J; Massey, Christine M; Son, Ji Y

2010-04-01

Learning in educational settings emphasizes declarative and procedural knowledge. Studies of expertise, however, point to other crucial components of learning, especially improvements produced by experience in the extraction of information: perceptual learning (PL). We suggest that such improvements characterize both simple sensory and complex cognitive, even symbolic, tasks through common processes of discovery and selection. We apply these ideas in the form of perceptual learning modules (PLMs) to mathematics learning. We tested three PLMs, each emphasizing different aspects of complex task performance, in middle and high school mathematics. In the MultiRep PLM, practice in matching function information across multiple representations improved students' abilities to generate correct graphs and equations from word problems. In the Algebraic Transformations PLM, practice in seeing equation structure across transformations (but not solving equations) led to dramatic improvements in the speed of equation solving. In the Linear Measurement PLM, interactive trials involving extraction of information about units and lengths produced successful transfer to novel measurement problems and fraction problem solving. Taken together, these results suggest (a) that PL techniques have the potential to address crucial, neglected dimensions of learning, including discovery and fluent processing of relations; (b) PL effects apply even to complex tasks that involve symbolic processing; and (c) appropriately designed PL technology can produce rapid and enduring advances in learning. Copyright © 2009 Cognitive Science Society, Inc.

TDIGG - TWO-DIMENSIONAL, INTERACTIVE GRID GENERATION CODE

NASA Technical Reports Server (NTRS)

Vu, B. T.

1994-01-01

TDIGG is a fast and versatile program for generating two-dimensional computational grids for use with finite-difference flow-solvers. Both algebraic and elliptic grid generation systems are included. The method for grid generation by algebraic transformation is based on an interpolation algorithm and the elliptic grid generation is established by solving the partial differential equation (PDE). Non-uniform grid distributions are carried out using a hyperbolic tangent stretching function. For algebraic grid systems, interpolations in one direction (univariate) and two directions (bivariate) are considered. These interpolations are associated with linear or cubic Lagrangian/Hermite/Bezier polynomial functions. The algebraic grids can subsequently be smoothed using an elliptic solver. For elliptic grid systems, the PDE can be in the form of Laplace (zero forcing function) or Poisson. The forcing functions in the Poisson equation come from the boundary or the entire domain of the initial algebraic grids. A graphics interface procedure using the Silicon Graphics (GL) Library is included to allow users to visualize the grid variations at each iteration. This will allow users to interactively modify the grid to match their applications. TDIGG is written in FORTRAN 77 for Silicon Graphics IRIS series computers running IRIX. This package requires either MIT's X Window System, Version 11 Revision 4 or SGI (Motif) Window System. A sample executable is provided on the distribution medium. It requires 148K of RAM for execution. The standard distribution medium is a .25 inch streaming magnetic IRIX tape cartridge in UNIX tar format. This program was developed in 1992.

Analysis of the two-point velocity correlations in turbulent boundary layer flows

NASA Technical Reports Server (NTRS)

Oberlack, M.

1995-01-01

The general objective of the present work is to explore the use of Rapid Distortion Theory (RDT) in analysis of the two-point statistics of the log-layer. RDT is applicable only to unsteady flows where the non-linear turbulence-turbulence interaction can be neglected in comparison to linear turbulence-mean interactions. Here we propose to use RDT to examine the structure of the large energy-containing scales and their interaction with the mean flow in the log-region. The contents of the work are twofold: First, two-point analysis methods will be used to derive the law-of-the-wall for the special case of zero mean pressure gradient. The basic assumptions needed are one-dimensionality in the mean flow and homogeneity of the fluctuations. It will be shown that a formal solution of the two-point correlation equation can be obtained as a power series in the von Karman constant, known to be on the order of 0.4. In the second part, a detailed analysis of the two-point correlation function in the log-layer will be given. The fundamental set of equations and a functional relation for the two-point correlation function will be derived. An asymptotic expansion procedure will be used in the log-layer to match Kolmogorov's universal range and the one-point correlations to the inviscid outer region valid for large correlation distances.

Inflation and bubbles in general relativity

NASA Astrophysics Data System (ADS)

Laguna-Castillo, Pablo; Matzner, Richard A.

1986-11-01

Following Israel's study of singular hypersurfaces and thin shells in general relativity, the complete set of Einstein's field equations in the presence of a bubble boundary SIGMA is reviewed for all spherically symmetric embedding four-geometries M+/-. The mapping that identifies points between the boundaries Σ+ and Σ- is obtained explicitly when the regions M+ and M- are described by a de Sitter and a Minkowski metric, respectively. In addition, the evolution of a bubble with vanishing surface energy density is studied in a spatially flat Robertson-Walker space-time, for region M- radiation dominated with a vanishing cosmological constant, and an energy equation in M+ determined by the matching. It is found that this type of bubble leads to a ``worm-hole'' matching; that is, an infinite extent exterior of a sphere is joined across the wall to another infinite extent exterior of a sphere. Interior-interior matches are also possible. Under this model, solutions for a bubble following a Hubble law are analyzed. Numerical solutions for bubbles with constant tension are also obtained.

A Comparison of Grid-based and SPH Binary Mass-transfer and Merger Simulations

DOE PAGES

Motl, Patrick M.; Frank, Juhan; Staff, Jan; ...

2017-03-29

There is currently a great amount of interest in the outcomes and astrophysical implications of mergers of double degenerate binaries. In a commonly adopted approximation, the components of such binaries are represented by polytropes with an index of n = 3/2. We present detailed comparisons of stellar mass-transfer and merger simulations of polytropic binaries that have been carried out using two very different numerical algorithms—a finite-volume "grid" code and a smoothed-particle hydrodynamics (SPH) code. We find that there is agreement in both the ultimate outcomes of the evolutions and the intermediate stages if the initial conditions for each code aremore » chosen to match as closely as possible. We find that even with closely matching initial setups, the time it takes to reach a concordant evolution differs between the two codes because the initial depth of contact cannot be matched exactly. There is a general tendency for SPH to yield higher mass transfer rates and faster evolution to the final outcome. Here, we also present comparisons of simulations calculated from two different energy equations: in one series, we assume a polytropic equation of state and in the other series an ideal gas equation of state. In the latter series of simulations, an atmosphere forms around the accretor, which can exchange angular momentum and cause a more rapid loss of orbital angular momentum. In the simulations presented here, the effect of the ideal equation of state is to de-stabilize the binary in both SPH and grid simulations, but the effect is more pronounced in the grid code.« less

The Analysis and Construction of Perfectly Matched Layers for the Linearized Euler Equations

NASA Technical Reports Server (NTRS)

Hesthaven, J. S.

1997-01-01

We present a detailed analysis of a recently proposed perfectly matched layer (PML) method for the absorption of acoustic waves. The split set of equations is shown to be only weakly well-posed, and ill-posed under small low order perturbations. This analysis provides the explanation for the stability problems associated with the split field formulation and illustrates why applying a filter has a stabilizing effect. Utilizing recent results obtained within the context of electromagnetics, we develop strongly well-posed absorbing layers for the linearized Euler equations. The schemes are shown to be perfectly absorbing independent of frequency and angle of incidence of the wave in the case of a non-convecting mean flow. In the general case of a convecting mean flow, a number of techniques is combined to obtain a absorbing layers exhibiting PML-like behavior. The efficacy of the proposed absorbing layers is illustrated though computation of benchmark problems in aero-acoustics.

System and method for constructing filters for detecting signals whose frequency content varies with time

DOEpatents

Qian, S.; Dunham, M.E.

1996-11-12

A system and method are disclosed for constructing a bank of filters which detect the presence of signals whose frequency content varies with time. The present invention includes a novel system and method for developing one or more time templates designed to match the received signals of interest and the bank of matched filters use the one or more time templates to detect the received signals. Each matched filter compares the received signal x(t) with a respective, unique time template that has been designed to approximate a form of the signals of interest. The robust time domain template is assumed to be of the order of w(t)=A(t)cos(2{pi}{phi}(t)) and the present invention uses the trajectory of a joint time-frequency representation of x(t) as an approximation of the instantaneous frequency function {phi}{prime}(t). First, numerous data samples of the received signal x(t) are collected. A joint time frequency representation is then applied to represent the signal, preferably using the time frequency distribution series. The joint time-frequency transformation represents the analyzed signal energy at time t and frequency f, P(t,f), which is a three-dimensional plot of time vs. frequency vs. signal energy. Then P(t,f) is reduced to a multivalued function f(t), a two dimensional plot of time vs. frequency, using a thresholding process. Curve fitting steps are then performed on the time/frequency plot, preferably using Levenberg-Marquardt curve fitting techniques, to derive a general instantaneous frequency function {phi}{prime}(t) which best fits the multivalued function f(t). Integrating {phi}{prime}(t) along t yields {phi}{prime}(t), which is then inserted into the form of the time template equation. A suitable amplitude A(t) is also preferably determined. Once the time template has been determined, one or more filters are developed which each use a version or form of the time template. 7 figs.

A modified and stable version of a perfectly matched layer technique for the 3-d second order wave equation in time domain with an application to aeroacoustics

PubMed Central

Kaltenbacher, Barbara; Kaltenbacher, Manfred; Sim, Imbo

2013-01-01

We consider the second order wave equation in an unbounded domain and propose an advanced perfectly matched layer (PML) technique for its efficient and reliable simulation. In doing so, we concentrate on the time domain case and use the finite-element (FE) method for the space discretization. Our un-split-PML formulation requires four auxiliary variables within the PML region in three space dimensions. For a reduced version (rPML), we present a long time stability proof based on an energy analysis. The numerical case studies and an application example demonstrate the good performance and long time stability of our formulation for treating open domain problems. PMID:23888085

Multiscale real-space quantum-mechanical tight-binding calculations of electronic structure in crystals with defects using perfectly matched layers

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

Pourmatin, Hossein, E-mail: mpourmat@andrew.cmu.edu; Dayal, Kaushik, E-mail: kaushik@cmu.edu

2016-10-15

Graphical abstract: - Abstract: We consider the scattering of incident plane-wave electrons from a defect in a crystal modeled by the time-harmonic Schrödinger equation. While the defect potential is localized, the far-field potential is periodic, unlike standard free-space scattering problems. Previous work on the Schrödinger equation has been almost entirely in free-space conditions; a few works on crystals have been in one-dimension. We construct absorbing boundary conditions for this problem using perfectly matched layers in a tight-binding formulation. Using the example of a point defect in graphene, we examine the efficiency and convergence of the proposed absorbing boundary condition.

Note: Index of refraction measurement using the Fresnel equations.

PubMed

McClymer, J P

2014-08-01

The real part of the refractive index is measured from 1.30 to above 3.00 without the use of index matching fluids. This approach expands upon the Brewster angle technique as both S and P polarized lights are used and the full Fresnel equations fitted to the data to extract the index of refraction using nonlinear curve fitting.

A hybrid numerical technique for predicting the aerodynamic and acoustic fields of advanced turboprops

NASA Technical Reports Server (NTRS)

Homicz, G. F.; Moselle, J. R.

1985-01-01

A hybrid numerical procedure is presented for the prediction of the aerodynamic and acoustic performance of advanced turboprops. A hybrid scheme is proposed which in principle leads to a consistent simultaneous prediction of both fields. In the inner flow a finite difference method, the Approximate-Factorization Alternating-Direction-Implicit (ADI) scheme, is used to solve the nonlinear Euler equations. In the outer flow the linearized acoustic equations are solved via a Boundary-Integral Equation (BIE) method. The two solutions are iteratively matched across a fictitious interface in the flow so as to maintain continuity. At convergence the resulting aerodynamic load prediction will automatically satisfy the appropriate free-field boundary conditions at the edge of the finite difference grid, while the acoustic predictions will reflect the back-reaction of the radiated field on the magnitude of the loading source terms, as well as refractive effects in the inner flow. The equations and logic needed to match the two solutions are developed and the computer program implementing the procedure is described. Unfortunately, no converged solutions were obtained, due to unexpectedly large running times. The reasons for this are discussed and several means to alleviate the situation are suggested.

MODFLOW-2000, The U.S. Geological Survey Modular Ground-Water Model - User Guide to Modularization Concepts and the Ground-Water Flow Process

USGS Publications Warehouse

Harbaugh, Arlen W.; Banta, Edward R.; Hill, Mary C.; McDonald, Michael G.

2000-01-01

MODFLOW is a computer program that numerically solves the three-dimensional ground-water flow equation for a porous medium by using a finite-difference method. Although MODFLOW was designed to be easily enhanced, the design was oriented toward additions to the ground-water flow equation. Frequently there is a need to solve additional equations; for example, transport equations and equations for estimating parameter values that produce the closest match between model-calculated heads and flows and measured values. This report documents a new version of MODFLOW, called MODFLOW-2000, which is designed to accommodate the solution of equations in addition to the ground-water flow equation. This report is a user's manual. It contains an overview of the old and added design concepts, documents one new package, and contains input instructions for using the model to solve the ground-water flow equation.

Understanding the Psychological Processes of the Racial Match Effect in Asian Americans

PubMed Central

Meyer, Oanh; Zane, Nolan; Cho, Young Il

2014-01-01

Some studies on mental health outcomes research have found that when clients and therapists are ethnically or racially matched, this tends to be related to greater satisfaction and better outcomes. However, the precise underlying mechanism for the match effect has not been extensively examined. In this experimental study, we tested the effect of racial match on critical counseling processes (i.e., therapist credibility and the working alliance) using a sample of 171 Asian American respondents. We also examined Asian ethnic identification as a potential moderator of the racial match effect. Structural equation modeling analyses indicated that racially matched individuals perceived greater experiential similarity with the therapist than nonmatched individuals, and experiential similarity was positively associated with therapist credibility. Although racial match did not predict attitudinal similarity, attitudinal similarity was strongly related to the working alliance and therapist credibility. Counseling implications are discussed. PMID:21574698

Diffusion approximation of the radiative-conductive heat transfer model with Fresnel matching conditions

NASA Astrophysics Data System (ADS)

Chebotarev, Alexander Yu.; Grenkin, Gleb V.; Kovtanyuk, Andrey E.; Botkin, Nikolai D.; Hoffmann, Karl-Heinz

2018-04-01

The paper is concerned with a problem of diffraction type. The study starts with equations of complex (radiative and conductive) heat transfer in a multicomponent domain with Fresnel matching conditions at the interfaces. Applying the diffusion, P1, approximation yields a pair of coupled nonlinear PDEs describing the radiation intensity and temperature for each component of the domain. Matching conditions for these PDEs, imposed at the interfaces between the domain components, are derived. The unique solvability of the obtained problem is proven, and numerical experiments are conducted.

Quasi parton distributions and the gradient flow

DOE PAGES

Monahan, Christopher; Orginos, Kostas

2017-03-22

We propose a new approach to determining quasi parton distribution functions (PDFs) from lattice quantum chromodynamics. By incorporating the gradient flow, this method guarantees that the lattice quasi PDFs are finite in the continuum limit and evades the thorny, and as yet unresolved, issue of the renormalization of quasi PDFs on the lattice. In the limit that the flow time is much smaller than the length scale set by the nucleon momentum, the moments of the smeared quasi PDF are proportional to those of the lightfront PDF. Finally, we use this relation to derive evolution equations for the matching kernelmore » that relates the smeared quasi PDF and the light-front PDF.« less

Quasi parton distributions and the gradient flow

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

Monahan, Christopher; Orginos, Kostas

We propose a new approach to determining quasi parton distribution functions (PDFs) from lattice quantum chromodynamics. By incorporating the gradient flow, this method guarantees that the lattice quasi PDFs are finite in the continuum limit and evades the thorny, and as yet unresolved, issue of the renormalization of quasi PDFs on the lattice. In the limit that the flow time is much smaller than the length scale set by the nucleon momentum, the moments of the smeared quasi PDF are proportional to those of the lightfront PDF. Finally, we use this relation to derive evolution equations for the matching kernelmore » that relates the smeared quasi PDF and the light-front PDF.« less

Demonstration of Detection and Ranging Using Solvable Chaos

NASA Technical Reports Server (NTRS)

Corron, Ned J.; Stahl, Mark T.; Blakely, Jonathan N.

2013-01-01

Acoustic experiments demonstrate a novel approach to ranging and detection that exploits the properties of a solvable chaotic oscillator. This nonlinear oscillator includes an ordinary differential equation and a discrete switching condition. The chaotic waveform generated by this hybrid system is used as the transmitted waveform. The oscillator admits an exact analytic solution that can be written as the linear convolution of binary symbols and a single basis function. This linear representation enables coherent reception using a simple analog matched filter and without need for digital sampling or signal processing. An audio frequency implementation of the transmitter and receiver is described. Successful acoustic ranging measurements are presented to demonstrate the viability of the approach.

Theoretical Investigation of the Process of Steam-Oxygen Gasification of Coke-Ash Particles in a Fluidized Bed Under Pressure

NASA Astrophysics Data System (ADS)

Rokhman, B. B.

2015-03-01

The problem on the evolution of the state of an ensemble of reacting coke-ash particles in a fluidized-bed gas generator is considered. A kinetic equation for the distribution function of particles within small ranges of carbon concentration variation for the stages of surface and bulk reaction has been constructed and integrated. Boundary conditions ("matching" conditions) at the boundaries between these ranges are formulated. The influence of the granulometric composition of the starting coal, height, porosity, and of the bed temperature on the process of steam-oxygen gasification of coke-ash particles of individual sorts of fuel and of a binary coal mixture has been investigated.

Simulation of femtosecond two-dimensional electronic spectra of conical intersections

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

Krčmář, Jindřich; Gelin, Maxim F.; Domcke, Wolfgang

2015-08-21

We have simulated femtosecond two-dimensional (2D) electronic spectra for an excited-state conical intersection using the wave-function version of the equation-of-motion phase-matching approach. We show that 2D spectra at fixed values of the waiting time provide information on the structure of the vibronic eigenstates of the conical intersection, while the evolution of the spectra with the waiting time reveals predominantly ground-state wave-packet dynamics. The results show that 2D spectra of conical intersection systems differ significantly from those obtained for chromophores with well separated excited-state potential-energy surfaces. The spectral signatures which can be attributed to conical intersections are discussed.

Varieties of operator manipulation. [for solving differential equations and calculating finite differences

NASA Technical Reports Server (NTRS)

Doohovskoy, A.

1977-01-01

A change in MACSYMA syntax is proposed to accommodate the operator manipulators necessary to implement direct and indirect methods for the solution of differential equations, calculus of finite differences, and the fractional calculus, as well as their modern counterparts. To illustrate the benefits and convenience of this syntax extension, an example is given to show how MACSYMA's pattern-matching capability can be used to implement a particular set of operator identities which can then be used to obtain exact solutions to nonlinear differential equations.

Theory and simulation of time-fractional fluid diffusion in porous media

NASA Astrophysics Data System (ADS)

Carcione, José M.; Sanchez-Sesma, Francisco J.; Luzón, Francisco; Perez Gavilán, Juan J.

2013-08-01

We simulate a fluid flow in inhomogeneous anisotropic porous media using a time-fractional diffusion equation and the staggered Fourier pseudospectral method to compute the spatial derivatives. A fractional derivative of the order of 0 < ν < 2 replaces the first-order time derivative in the classical diffusion equation. It implies a time-dependent permeability tensor having a power-law time dependence, which describes memory effects and accounts for anomalous diffusion. We provide a complete analysis of the physics based on plane waves. The concepts of phase, group and energy velocities are analyzed to describe the location of the diffusion front, and the attenuation and quality factors are obtained to quantify the amplitude decay. We also obtain the frequency-domain Green function. The time derivative is computed with the Grünwald-Letnikov summation, which is a finite-difference generalization of the standard finite-difference operator to derivatives of fractional order. The results match the analytical solution obtained from the Green function. An example of the pressure field generated by a fluid injection in a heterogeneous sandstone illustrates the performance of the algorithm for different values of ν. The calculation requires storing the whole pressure field in the computer memory since anomalous diffusion ‘recalls the past’.

Initial boundary-value problem for the spherically symmetric Einstein equations with fluids with tangential pressure.

PubMed

Brito, Irene; Mena, Filipe C

2017-08-01

We prove that, for a given spherically symmetric fluid distribution with tangential pressure on an initial space-like hypersurface with a time-like boundary, there exists a unique, local in time solution to the Einstein equations in a neighbourhood of the boundary. As an application, we consider a particular elastic fluid interior matched to a vacuum exterior.

Hypersonic Flight Mechanics. [for atmospheric entry trajectories

NASA Technical Reports Server (NTRS)

Busemann, A.; Vinh, N. X.; Culp, R. D.

1976-01-01

The effects of aerodynamic forces on trajectories at orbital speeds are discussed in terms of atmospheric models. The assumptions for the model are spherical symmetry, nonrotating, and an exponential atmosphere. The equations of flight, and the performance in extra-atmospheric flight are discussed along with the return to the atmosphere, and the entry. Solutions of the exact equations using directly matched asymptotic expansions are presented.

Pure quasi-P wave equation and numerical solution in 3D TTI media

NASA Astrophysics Data System (ADS)

Zhang, Jian-Min; He, Bing-Shou; Tang, Huai-Gu

2017-03-01

Based on the pure quasi-P wave equation in transverse isotropic media with a vertical symmetry axis (VTI media), a quasi-P wave equation is obtained in transverse isotropic media with a tilted symmetry axis (TTI media). This is achieved using projection transformation, which rotates the direction vector in the coordinate system of observation toward the direction vector for the coordinate system in which the z-component is parallel to the symmetry axis of the TTI media. The equation has a simple form, is easily calculated, is not influenced by the pseudo-shear wave, and can be calculated reliably when δ is greater than ɛ. The finite difference method is used to solve the equation. In addition, a perfectly matched layer (PML) absorbing boundary condition is obtained for the equation. Theoretical analysis and numerical simulation results with forward modeling prove that the equation can accurately simulate a quasi-P wave in TTI medium.

Matching Pion-Nucleon Roy-Steiner Equations to Chiral Perturbation Theory.

PubMed

Hoferichter, Martin; Ruiz de Elvira, Jacobo; Kubis, Bastian; Meissner, Ulf-G

2015-11-06

We match the results for the subthreshold parameters of pion-nucleon scattering obtained from a solution of Roy-Steiner equations to chiral perturbation theory up to next-to-next-to-next-to-leading order, to extract the pertinent low-energy constants including a comprehensive analysis of systematic uncertainties and correlations. We study the convergence of the chiral series by investigating the chiral expansion of threshold parameters up to the same order and discuss the role of the Δ(1232) resonance in this context. Results for the low-energy constants are also presented in the counting scheme usually applied in chiral nuclear effective field theory, where they serve as crucial input to determine the long-range part of the nucleon-nucleon potential as well as three-nucleon forces.

Matching Pion-Nucleon Roy-Steiner Equations to Chiral Perturbation Theory

NASA Astrophysics Data System (ADS)

Hoferichter, Martin; Ruiz de Elvira, Jacobo; Kubis, Bastian; Meißner, Ulf-G.

2015-11-01

We match the results for the subthreshold parameters of pion-nucleon scattering obtained from a solution of Roy-Steiner equations to chiral perturbation theory up to next-to-next-to-next-to-leading order, to extract the pertinent low-energy constants including a comprehensive analysis of systematic uncertainties and correlations. We study the convergence of the chiral series by investigating the chiral expansion of threshold parameters up to the same order and discuss the role of the Δ (1232 ) resonance in this context. Results for the low-energy constants are also presented in the counting scheme usually applied in chiral nuclear effective field theory, where they serve as crucial input to determine the long-range part of the nucleon-nucleon potential as well as three-nucleon forces.

Variational stereo imaging of oceanic waves with statistical constraints.

PubMed

Gallego, Guillermo; Yezzi, Anthony; Fedele, Francesco; Benetazzo, Alvise

2013-11-01

An image processing observational technique for the stereoscopic reconstruction of the waveform of oceanic sea states is developed. The technique incorporates the enforcement of any given statistical wave law modeling the quasi-Gaussianity of oceanic waves observed in nature. The problem is posed in a variational optimization framework, where the desired waveform is obtained as the minimizer of a cost functional that combines image observations, smoothness priors and a weak statistical constraint. The minimizer is obtained by combining gradient descent and multigrid methods on the necessary optimality equations of the cost functional. Robust photometric error criteria and a spatial intensity compensation model are also developed to improve the performance of the presented image matching strategy. The weak statistical constraint is thoroughly evaluated in combination with other elements presented to reconstruct and enforce constraints on experimental stereo data, demonstrating the improvement in the estimation of the observed ocean surface.

Investigation of contact pressure and influence function model for soft wheel polishing.

PubMed

Rao, Zhimin; Guo, Bing; Zhao, Qingliang

2015-09-20

The tool influence function (TIF) is critical for calculating the dwell-time map to improve form accuracy. We present the TIF for the process of computer-controlled polishing with a soft polishing wheel. In this paper, the static TIF was developed based on the Preston equation. The pressure distribution was verified by the real removal spot section profiles. According to the experiment measurements, the pressure distribution simulated by Hertz contact theory was much larger than the real contact pressure. The simulated pressure distribution, which was modeled by the Winkler elastic foundation for a soft polishing wheel, matched the real contact pressure. A series of experiments was conducted to obtain the removal spot statistical properties for validating the relationship between material removal and processing time and contact pressure and relative velocity, along with calculating the fitted parameters to establish the TIF. The developed TIF predicted the removal character for the studied soft wheel polishing.

Two-body loss rates for reactive collisions of cold atoms

NASA Astrophysics Data System (ADS)

Cop, C.; Walser, R.

2018-01-01

We present an effective two-channel model for reactive collisions of cold atoms. It augments elastic molecular channels with an irreversible, inelastic loss channel. Scattering is studied with the distorted-wave Born approximation and yields general expressions for angular momentum resolved cross sections as well as two-body loss rates. Explicit expressions are obtained for piecewise constant potentials. A pole expansion reveals simple universal shape functions for cross sections and two-body loss rates in agreement with the Wigner threshold laws. This is applied to collisions of metastable 20Ne and 21Ne atoms, which decay primarily through exothermic Penning or associative ionization processes. From a numerical solution of the multichannel Schrödinger equation using the best currently available molecular potentials, we have obtained synthetic scattering data. Using the two-body loss shape functions derived in this paper, we can match these scattering data very well.

Dyadic Green's function of a cluster of spheres.

PubMed

Moneda, Angela P; Chrissoulidis, Dimitrios P

2007-11-01

The electric dyadic Green's function (dGf) of a cluster of spheres is obtained by application of the superposition principle, dyadic algebra, and the indirect mode-matching method. The analysis results in a set of linear equations for the unknown, vector, wave amplitudes of the dGf; that set is solved by truncation and matrix inversion. The theory is exact in the sense that no simplifying assumptions are made in the analytical steps leading to the dGf, and it is general in the sense that any number, position, size and electrical properties can be considered for the spheres that cluster together. The point source can be anywhere, even within one of the spheres. Energy conservation, reciprocity, and other tests prove that this solution is correct. Numerical results are presented for an electric Hertz dipole radiating in the presence of an array of rexolite spheres, which manifests lensing and beam-forming capabilities.

Using the Kernel Method of Test Equating for Estimating the Standard Errors of Population Invariance Measures

ERIC Educational Resources Information Center

Moses, Tim

2008-01-01

Equating functions are supposed to be population invariant, meaning that the choice of subpopulation used to compute the equating function should not matter. The extent to which equating functions are population invariant is typically assessed in terms of practical difference criteria that do not account for equating functions' sampling…

Partially deuterated potassium dihydrogen phosphate optimized for ultra-broadband optical parametric amplification

NASA Astrophysics Data System (ADS)

Fujioka, K.; Fujimoto, Y.; Tsubakimoto, K.; Kawanaka, J.; Shoji, I.; Miyanaga, N.

2015-03-01

The refractive index of a potassium dihydrogen phosphate (KDP) crystal strongly depends on the deuteration fraction of the crystal. The wavelength dependence of the phase-matching angle in the near-infrared optical parametric process shows convex and concave characteristics for pure KDP and pure deuterated KDP (DKDP), respectively, when pumped by the second harmonic of Nd- or Yb-doped solid state lasers. Using these characteristics, ultra-broadband phase matching can be realized by optimization of the deuteration fraction. The refractive index of DKDP that was grown with a different deuteration fraction (known as partially deuterated KDP or pDKDP) was measured over a wide wavelength range of 0.4-1.5 μm by the minimum deviation method. The wavelength dispersions of the measured refractive indices were fitted using a modified Sellmeier equation, and the deuteration fraction dependence was analyzed using the Lorentz-Lorenz equation. The wavelength-dependent phase-matching angle for an arbitrary deuteration fraction was then calculated for optical parametric amplification with pumping at a wavelength of 526.5 nm. The results revealed that a refractive index database with precision of more than 2 × 10-5 was necessary for exact evaluation of the phase-matching condition. An ultra-broad gain bandwidth of up to 490 nm will be feasible when using the 68% pDKDP crystal.

System and method for constructing filters for detecting signals whose frequency content varies with time

DOEpatents

Qian, Shie; Dunham, Mark E.

1996-01-01

A system and method for constructing a bank of filters which detect the presence of signals whose frequency content varies with time. The present invention includes a novel system and method for developing one or more time templates designed to match the received signals of interest and the bank of matched filters use the one or more time templates to detect the received signals. Each matched filter compares the received signal x(t) with a respective, unique time template that has been designed to approximate a form of the signals of interest. The robust time domain template is assumed to be of the order of w(t)=A(t)cos{2.pi..phi.(t)} and the present invention uses the trajectory of a joint time-frequency representation of x(t) as an approximation of the instantaneous frequency function {.phi.'(t). First, numerous data samples of the received signal x(t) are collected. A joint time frequency representation is then applied to represent the signal, preferably using the time frequency distribution series (also known as the Gabor spectrogram). The joint time-frequency transformation represents the analyzed signal energy at time t and frequency .function., P(t,f), which is a three-dimensional plot of time vs. frequency vs. signal energy. Then P(t,f) is reduced to a multivalued function f(t), a two dimensional plot of time vs. frequency, using a thresholding process. Curve fitting steps are then performed on the time/frequency plot, preferably using Levenberg-Marquardt curve fitting techniques, to derive a general instantaneous frequency function .phi.'(t) which best fits the multivalued function f(t), a trajectory of the joint time-frequency domain representation of x(t). Integrating .phi.'(t) along t yields .phi.(t), which is then inserted into the form of the time template equation. A suitable amplitude A(t) is also preferably determined. Once the time template has been determined, one or more filters are developed which each use a version or form of the time template.

Energy/dissipation-preserving Birkhoffian multi-symplectic methods for Maxwell's equations with dissipation terms

DOE PAGES

Su, Hongling; Li, Shengtai

2016-02-03

In this study, we propose two new energy/dissipation-preserving Birkhoffian multi-symplectic methods (Birkhoffian and Birkhoffian box) for Maxwell's equations with dissipation terms. After investigating the non-autonomous and autonomous Birkhoffian formalism for Maxwell's equations with dissipation terms, we first apply a novel generating functional theory to the non-autonomous Birkhoffian formalism to propose our Birkhoffian scheme, and then implement a central box method to the autonomous Birkhoffian formalism to derive the Birkhoffian box scheme. We have obtained four formal local conservation laws and three formal energy global conservation laws. We have also proved that both of our derived schemes preserve the discrete versionmore » of the global/local conservation laws. Furthermore, the stability, dissipation and dispersion relations are also investigated for the schemes. Theoretical analysis shows that the schemes are unconditionally stable, dissipation-preserving for Maxwell's equations in a perfectly matched layer (PML) medium and have second order accuracy in both time and space. Numerical experiments for problems with exact theoretical results are given to demonstrate that the Birkhoffian multi-symplectic schemes are much more accurate in preserving energy than both the exponential finite-difference time-domain (FDTD) method and traditional Hamiltonian scheme. Finally, we also solve the electromagnetic pulse (EMP) propagation problem and the numerical results show that the Birkhoffian scheme recovers the magnitude of the current source and reaction history very well even after long time propagation.« less

Energy/dissipation-preserving Birkhoffian multi-symplectic methods for Maxwell's equations with dissipation terms

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

Su, Hongling; Li, Shengtai

In this study, we propose two new energy/dissipation-preserving Birkhoffian multi-symplectic methods (Birkhoffian and Birkhoffian box) for Maxwell's equations with dissipation terms. After investigating the non-autonomous and autonomous Birkhoffian formalism for Maxwell's equations with dissipation terms, we first apply a novel generating functional theory to the non-autonomous Birkhoffian formalism to propose our Birkhoffian scheme, and then implement a central box method to the autonomous Birkhoffian formalism to derive the Birkhoffian box scheme. We have obtained four formal local conservation laws and three formal energy global conservation laws. We have also proved that both of our derived schemes preserve the discrete versionmore » of the global/local conservation laws. Furthermore, the stability, dissipation and dispersion relations are also investigated for the schemes. Theoretical analysis shows that the schemes are unconditionally stable, dissipation-preserving for Maxwell's equations in a perfectly matched layer (PML) medium and have second order accuracy in both time and space. Numerical experiments for problems with exact theoretical results are given to demonstrate that the Birkhoffian multi-symplectic schemes are much more accurate in preserving energy than both the exponential finite-difference time-domain (FDTD) method and traditional Hamiltonian scheme. Finally, we also solve the electromagnetic pulse (EMP) propagation problem and the numerical results show that the Birkhoffian scheme recovers the magnitude of the current source and reaction history very well even after long time propagation.« less

Valve Repair Is Superior to Replacement in Most Patients With Coexisting Degenerative Mitral Valve and Coronary Artery Diseases.

PubMed

Javadikasgari, Hoda; Gillinov, A Marc; Idrees, Jay J; Mihaljevic, Tomislav; Suri, Rakesh M; Raza, Sajjad; Houghtaling, Penny L; Svensson, Lars G; Navia, José L; Mick, Stephanie L; Desai, Milind Y; Sabik, Joseph F; Blackstone, Eugene H

2017-06-01

For mitral regurgitation (MR) from degenerative mitral disease in patients with coexisting coronary artery disease, the appropriate surgical strategy remains controversial. From 1985 to 2011, 1,071 adults (age 70 ± 9.3 years, 77% men) underwent combined coronary artery bypass grafting and either mitral valve repair (n = 872, 81%) or replacement (n=199, 19%) for degenerative MR. Propensity matching (177 patient pairs, 89% of possible matches) was used to compare early outcomes and time-related recurrence of MR after mitral valve repair, mitral valve reoperation, and mortality. Risk factors for death were identified with multivariable, multiphase hazard-function analysis. Patients undergoing valve replacement were older, with more valve calcification and a higher prevalence of preoperative atrial fibrillation and heart failure (all p < .0001). Among matched pairs, mitral replacement versus repair was associated with higher hospital mortality (5.0% vs 1.0%, p = .0001) and more postoperative renal failure (7.0% vs 3.2%, p = .01), reexplorations for bleeding (6.0% vs 3.1%, p = .05), and respiratory failure (14% vs 4.7%, p < .0001). Of matched patients undergoing repair, 18% had MR above 3+ by 5 years. Mitral valve durability was similar between matched groups, but survival at 15 years was 18% after replacement versus 52% after repair. Nomograms from the multivariable equation revealed that in 94% of cases, 10-year survival was calculated to be higher after repair than after replacement. In patients with coexisting degenerative mitral valve and coronary artery diseases, mitral valve repair is expected to confer a long-term survival advantage over replacement despite some recurrence of MR. When feasible, it is the procedure of choice for these patients. Copyright © 2017 The Society of Thoracic Surgeons. Published by Elsevier Inc. All rights reserved.

Changes in Sympathetic Nervous System Activity are Associated with Changes in Sexual Wellbeing in Women with a History of Childhood Sexual Abuse

PubMed Central

Lorenz, Tierney K.; Harte, Christopher B.; Meston, Cindy M.

2015-01-01

Introduction Women with histories of childhood sexual abuse (CSA) have higher rates of sexual difficulties, as well as high sympathetic nervous system (SNS) response to sexual stimuli. Aim To examine whether treatment-related changes in autonomic balance, as indexed by heart rate variability (HRV), were associated with changes in sexual arousal and orgasm function. Methods In Study 1, we measured HRV while writing a sexual essay in 42 healthy, sexually functional women without any history of sexual trauma. These data, along with demographics, were used to develop HRV norms equations. In Study 2, 136 women with a history of CSA were randomized to one of three active expressive writing treatments that focused on their trauma, sexuality, or daily life (control condition). We recorded HRV while writing a sexual essay at pre-treatment, post-treatment, and 2 week, 1 month, and 6 month follow-ups; we also calculated the expected HRV for each participant based on the norms equations from Study 1. Main Outcome Measures Heart rate variability, Female Sexual Function Index (FSFI), Sexual Satisfaction Scale – Women (SSS-W) Results The difference between expected and observed HRV decreased over time, indicating that, post-treatment, CSA survivors displayed HRV closer to the expected HRV of a demographics-matched woman with no history of sexual trauma. Also, over time, participants whose HRV became less dysregulated showed the biggest gains in sexual arousal and orgasm function. These effects were consistent across condition. Conclusions Treatments that reduce autonomic imbalance may improve sexual wellbeing among CSA populations. PMID:25963394

Search algorithm complexity modeling with application to image alignment and matching

NASA Astrophysics Data System (ADS)

DelMarco, Stephen

2014-05-01

Search algorithm complexity modeling, in the form of penetration rate estimation, provides a useful way to estimate search efficiency in application domains which involve searching over a hypothesis space of reference templates or models, as in model-based object recognition, automatic target recognition, and biometric recognition. The penetration rate quantifies the expected portion of the database that must be searched, and is useful for estimating search algorithm computational requirements. In this paper we perform mathematical modeling to derive general equations for penetration rate estimates that are applicable to a wide range of recognition problems. We extend previous penetration rate analyses to use more general probabilistic modeling assumptions. In particular we provide penetration rate equations within the framework of a model-based image alignment application domain in which a prioritized hierarchical grid search is used to rank subspace bins based on matching probability. We derive general equations, and provide special cases based on simplifying assumptions. We show how previously-derived penetration rate equations are special cases of the general formulation. We apply the analysis to model-based logo image alignment in which a hierarchical grid search is used over a geometric misalignment transform hypothesis space. We present numerical results validating the modeling assumptions and derived formulation.

On the Effects of Artificial Feeding on Bee Colony Dynamics: A Mathematical Model

PubMed Central

Paiva, Juliana Pereira Lisboa Mohallem; Paiva, Henrique Mohallem; Esposito, Elisa; Morais, Michelle Manfrini

2016-01-01

This paper proposes a new mathematical model to evaluate the effects of artificial feeding on bee colony population dynamics. The proposed model is based on a classical framework and contains differential equations that describe the changes in the number of hive bees, forager bees, and brood cells, as a function of amounts of natural and artificial food. The model includes the following elements to characterize the artificial feeding scenario: a function to model the preference of the bees for natural food over artificial food; parameters to quantify the quality and palatability of artificial diets; a function to account for the efficiency of the foragers in gathering food under different environmental conditions; and a function to represent different approaches used by the beekeeper to feed the hive with artificial food. Simulated results are presented to illustrate the main characteristics of the model and its behavior under different scenarios. The model results are validated with experimental data from the literature involving four different artificial diets. A good match between simulated and experimental results was achieved. PMID:27875589

The exact rogue wave recurrence in the NLS periodic setting via matched asymptotic expansions, for 1 and 2 unstable modes

NASA Astrophysics Data System (ADS)

Grinevich, P. G.; Santini, P. M.

2018-04-01

The focusing Nonlinear Schrödinger (NLS) equation is the simplest universal model describing the modulation instability (MI) of quasi monochromatic waves in weakly nonlinear media, the main physical mechanism for the generation of rogue (anomalous) waves (RWs) in Nature. In this paper we investigate the x-periodic Cauchy problem for NLS for a generic periodic initial perturbation of the unstable constant background solution, in the case of N = 1 , 2 unstable modes. We use matched asymptotic expansion techniques to show that the solution of this problem describes an exact deterministic alternate recurrence of linear and nonlinear stages of MI, and that the nonlinear RW stages are described by the N-breather solution of Akhmediev type, whose parameters, different at each RW appearance, are always given in terms of the initial data through elementary functions. This paper is motivated by a preceding work of the authors in which a different approach, the finite gap method, was used to investigate periodic Cauchy problems giving rise to RW recurrence.

Solution of Volterra and Fredholm Classes of Equations via Triangular Orthogonal Function (A Combination of Right Hand Triangular Function and Left Hand Triangular Function) and Hybrid Orthogonal Function (A Combination of Sample Hold Function and Right Hand Triangular Function)

NASA Astrophysics Data System (ADS)

Mukhopadhyay, Anirban; Ganguly, Anindita; Chatterjee, Saumya Deep

2018-04-01

In this paper the authors have dealt with seven kinds of non-linear Volterra and Fredholm classes of equations. The authors have formulated an algorithm for solving the aforementioned equation types via Hybrid Function (HF) and Triangular Function (TF) piecewise-linear orthogonal approach. In this approach the authors have reduced integral equation or integro-differential equation into equivalent system of simultaneous non-linear equation and have employed either Newton's method or Broyden's method to solve the simultaneous non-linear equations. The authors have calculated the L2-norm error and the max-norm error for both HF and TF method for each kind of equations. Through the illustrated examples, the authors have shown that the HF based algorithm produces stable result, on the contrary TF-computational method yields either stable, anomalous or unstable results.

Guidance law development for aeroassisted transfer vehicles using matched asymptotic expansions

NASA Technical Reports Server (NTRS)

Calise, Anthony J.; Melamed, Nahum

1993-01-01

This report addresses and clarifies a number of issues related to the Matched Asymptotic Expansion (MAE) analysis of skip trajectories, or any class of problems that give rise to inner layers that are not associated directly with satisfying boundary conditions. The procedure for matching inner and outer solutions, and using the composite solution to satisfy boundary conditions is developed and rigorously followed to obtain a set of algebraic equations for the problem of inclination change with minimum energy loss. A detailed evaluation of the zeroth order guidance algorithm for aeroassisted orbit transfer is performed. It is shown that by exploiting the structure of the MAE solution procedure, the original problem, which requires the solution of a set of 20 implicit algebraic equations, can be reduced to a problem of 6 implicit equations in 6 unknowns. A solution that is near optimal, requires a minimum of computation, and thus can be implemented in real time and on-board the vehicle, has been obtained. Guidance law implementation entails treating the current state as a new initial state and repetitively solving the zeroth order MAE problem to obtain the feedback controls. Finally, a general procedure is developed for constructing a MAE solution up to first order, of the Hamilton-Jacobi-Bellman equation based on the method of characteristics. The development is valid for a class of perturbation problems whose solution exhibits two-time-scale behavior. A regular expansion for problems of this type is shown to be inappropriate since it is not valid over a narrow range of the independent variable. That is, it is not uniformly valid. Of particular interest here is the manner in which matching and boundary conditions are enforced when the expansion is carried out to first order. Two cases are distinguished-one where the left boundary condition coincides with, or lies to the right of, the singular region, and another one where the left boundary condition lies to the left of the singular region. A simple example is used to illustrate the procedure where the obtained solution is uniformly valid to O(Epsilon(exp 2)). The potential application of this procedure to aeroassisted plane change is also described and partially evaluated.

Incorporation of an Energy Equation into a Pulsed Inductive Thruster Performance Model

NASA Technical Reports Server (NTRS)

Polzin, Kurt A.; Reneau, Jarred P.; Sankaran, Kameshwaran

2011-01-01

A model for pulsed inductive plasma acceleration containing an energy equation to account for the various sources and sinks in such devices is presented. The model consists of a set of circuit equations coupled to an equation of motion and energy equation for the plasma. The latter two equations are obtained for the plasma current sheet by treating it as a one-element finite volume, integrating the equations over that volume, and then matching known terms or quantities already calculated in the model to the resulting current sheet-averaged terms in the equations. Calculations showing the time-evolution of the various sources and sinks in the system are presented to demonstrate the efficacy of the model, with two separate resistivity models employed to show an example of how the plasma transport properties can affect the calculation. While neither resistivity model is fully accurate, the demonstration shows that it is possible within this modeling framework to time-accurately update various plasma parameters.

DSD-Consistent JWL Equations of State for EDC35

NASA Astrophysics Data System (ADS)

Hodgson, Alexander

2011-06-01

The Detonation Shock Dynamics model (DSD) allows the calculation of curvature-dependent detonation propagation. It is of particular use when applied to insensitive high explosives, such as EDC35, since they have a greater non-ideal behaviour. The DSD model has been used in conjunction with an experimental cylinder test to obtain the JWL Equation of State (EoS) for EDC35. Adjustment of parameters in the JWL equation changes the expansion profile of the simulated wall expansion. The parameters are iterated until the best match can be made between simulation and experiment. Previous DSD models used at AWE have no energy release mechanism to adjust the release of chemical energy to match the detonation conditions. Two JWL calibrations are performed using the DSD model, with and without Hetherington's energy release model (these proceedings). Also in use is a newly-calibrated detonation speed-curvature relation that is much closer, compared to previous calibrations, to Bdzil's equivalent for PBX9502. This paper discusses the possible improvements that this approach makes to the EDC35 JWL EoS.

Aerosol correction for remotely sensed sea surface temperatures from the National Oceanic and Atmospheric Administration advanced very high resolution radiometer

NASA Astrophysics Data System (ADS)

Nalli, Nicholas R.; Stowe, Larry L.

2002-10-01

This research presents the first-phase derivation and implementation of daytime aerosol correction algorithms for remotely sensed sea surface temperature (SST) from the advanced very high resolution radiometer (AVHRR) instrument flown onboard NOAA polar orbiting satellites. To accomplish this, a long-term (1990-1998), global AVHRR-buoy match-up database was created by merging the NOAA/NASA Pathfinder Atmospheres and Pathfinder Oceans data sets. The merged data set is unique in that it includes daytime estimates of aerosol optical depth (AOD) derived from AVHRR channel 1 (0.63 μm) under global conditions of significant aerosol loading. Histograms of retrieved AOD reveal monomodal, lognormal distributions for both tropospheric and stratospheric aerosol modes. It is then shown empirically that the SST depression caused under each aerosol mode can be expressed as a linear function in two predictors, these being the slant path AOD retrieved from AVHRR channel 1 along with the ratio of channels 1 and 2 normalized reflectances. On the basis of these relationships, parametric equations are derived to provide an aerosol correction for retrievals from the daytime NOAA operational multichannel and nonlinear SST algorithms. Separate sets of coefficients are utilized for two aerosol modes: tropospheric (i.e., dust, smoke, haze) and stratospheric/tropospheric (i.e., following a major volcanic eruption). The equations are shown to significantly reduce retrieved SST bias using an independent set of match-ups. Eliminating aerosol-induced bias in both real-time and retrospective processing will enhance the utility of the AVHRR SST for the general user community and in climate research.

Brain Correlates of Mathematical Competence in Processing Mathematical Representations

PubMed Central

Grabner, Roland H.; Reishofer, Gernot; Koschutnig, Karl; Ebner, Franz

2011-01-01

The ability to extract numerical information from different representation formats (e.g., equations, tables, or diagrams) is a key component of mathematical competence but little is known about its neural correlate. Previous studies comparing mathematically less and more competent adults have focused on mental arithmetic and reported differences in left angular gyrus (AG) activity which were interpreted to reflect differential reliance on arithmetic fact retrieval during problem solving. The aim of the present functional magnetic resonance imaging study was to investigate the brain correlates of mathematical competence in a task requiring the processing of typical mathematical representations. Twenty-eight adults of lower and higher mathematical competence worked on a representation matching task in which they had to evaluate whether the numerical information of a symbolic equation matches that of a bar chart. Two task conditions without and one condition with arithmetic demands were administered. Both competence groups performed equally well in the non-arithmetic conditions and only differed in accuracy in the condition requiring calculation. Activation contrasts between the groups revealed consistently stronger left AG activation in the more competent individuals across all three task conditions. The finding of competence-related activation differences independently of arithmetic demands suggests that more and less competent individuals differ in a cognitive process other than arithmetic fact retrieval. Specifically, it is argued that the stronger left AG activity in the more competent adults may reflect their higher proficiency in processing mathematical symbols. Moreover, the study demonstrates competence-related parietal activation differences that were not accompanied by differential experimental performance. PMID:22069387

Diffraction of a plane wave on two-dimensional conductive structures and a surface wave

NASA Astrophysics Data System (ADS)

Davidovich, Mikhael V.

2018-04-01

We consider the structures type of two-dimensional electron gas in the form of a thin conductive, in particular, graphene films described by tensor conductivity, which are isolated or located on the dielectric layers. The dispersion equation for hybrid modes, as well as scattering parameters. We show that free wave (eigenwaves) problem follow from the problem of diffraction when linking the amplitude of the current of the linear equations are unsolvable, i.e., the determinant of this system is zero. As a particular case the dispersion equation follow from the conditions of matching (with zero reflection coefficient).

Mathematical modeling of PDC bit drilling process based on a single-cutter mechanics

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

Wojtanowicz, A.K.; Kuru, E.

1993-12-01

An analytical development of a new mechanistic drilling model for polycrystalline diamond compact (PDC) bits is presented. The derivation accounts for static balance of forces acting on a single PDC cutter and is based on assumed similarity between bit and cutter. The model is fully explicit with physical meanings given to all constants and functions. Three equations constitute the mathematical model: torque, drilling rate, and bit life. The equations comprise cutter`s geometry, rock properties drilling parameters, and four empirical constants. The constants are used to match the model to a PDC drilling process. Also presented are qualitative and predictive verificationsmore » of the model. Qualitative verification shows that the model`s response to drilling process variables is similar to the behavior of full-size PDC bits. However, accuracy of the model`s predictions of PDC bit performance is limited primarily by imprecision of bit-dull evaluation. The verification study is based upon the reported laboratory drilling and field drilling tests as well as field data collected by the authors.« less

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

Noronha, Jorge; Denicol, Gabriel S.

In this paper we obtain an analytical solution of the relativistic Boltzmann equation under the relaxation time approximation that describes the out-of-equilibrium dynamics of a radially expanding massless gas. This solution is found by mapping this expanding system in flat spacetime to a static flow in the curved spacetime AdS 2 Ⓧ S 2. We further derive explicit analytic expressions for the momentum dependence of the single-particle distribution function as well as for the spatial dependence of its moments. We find that this dissipative system has the ability to flow as a perfect fluid even though its entropy density doesmore » not match the equilibrium form. The nonequilibrium contribution to the entropy density is shown to be due to higher-order scalar moments (which possess no hydrodynamical interpretation) of the Boltzmann equation that can remain out of equilibrium but do not couple to the energy-momentum tensor of the system. Furthermore, in this system the slowly moving hydrodynamic degrees of freedom can exhibit true perfect fluidity while being totally decoupled from the fast moving, nonhydrodynamical microscopic degrees of freedom that lead to entropy production.« less

A generalized computer code for developing dynamic gas turbine engine models (DIGTEM)

NASA Technical Reports Server (NTRS)

Daniele, C. J.

1984-01-01

This paper describes DIGTEM (digital turbofan engine model), a computer program that simulates two spool, two stream (turbofan) engines. DIGTEM was developed to support the development of a real time multiprocessor based engine simulator being designed at the Lewis Research Center. The turbofan engine model in DIGTEM contains steady state performance maps for all the components and has control volumes where continuity and energy balances are maintained. Rotor dynamics and duct momentum dynamics are also included. DIGTEM features an implicit integration scheme for integrating stiff systems and trims the model equations to match a prescribed design point by calculating correction coefficients that balance out the dynamic equations. It uses the same coefficients at off design points and iterates to a balanced engine condition. Transients are generated by defining the engine inputs as functions of time in a user written subroutine (TMRSP). Closed loop controls can also be simulated. DIGTEM is generalized in the aerothermodynamic treatment of components. This feature, along with DIGTEM's trimming at a design point, make it a very useful tool for developing a model of a specific turbofan engine.

A generalized computer code for developing dynamic gas turbine engine models (DIGTEM)

NASA Technical Reports Server (NTRS)

Daniele, C. J.

1983-01-01

This paper describes DIGTEM (digital turbofan engine model), a computer program that simulates two spool, two stream (turbofan) engines. DIGTEM was developed to support the development of a real time multiprocessor based engine simulator being designed at the Lewis Research Center. The turbofan engine model in DIGTEM contains steady state performance maps for all the components and has control volumes where continuity and energy balances are maintained. Rotor dynamics and duct momentum dynamics are also included. DIGTEM features an implicit integration scheme for integrating stiff systems and trims the model equations to match a prescribed design point by calculating correction coefficients that balance out the dynamic equations. It uses the same coefficients at off design points and iterates to a balanced engine condition. Transients are generated by defining the engine inputs as functions of time in a user written subroutine (TMRSP). Closed loop controls can also be simulated. DIGTEM is generalized in the aerothermodynamic treatment of components. This feature, along with DIGTEM's trimming at a design point, make it a very useful tool for developing a model of a specific turbofan engine.

A computer program for automated flutter solution and matched point determination

NASA Technical Reports Server (NTRS)

Bhatia, K. G.

1973-01-01

The use of a digital computer program (MATCH) for automated determination of the flutter velocity and the matched-point flutter density is described. The program is based on the use of the modified Laguerre iteration formula to converge to a flutter crossing or a matched-point density. A general description of the computer program is included and the purpose of all subroutines used is stated. The input required by the program and various input options are detailed, and the output description is presented. The program can solve flutter equations formulated with up to 12 vibration modes and obtain flutter solutions for up to 10 air densities. The program usage is illustrated by a sample run, and the FORTRAN program listing is included.

Closed-loop spontaneous baroreflex transfer function is inappropriate for system identification of neural arc but partly accurate for peripheral arc: predictability analysis

PubMed Central

Kamiya, Atsunori; Kawada, Toru; Shimizu, Shuji; Sugimachi, Masaru

2011-01-01

Abstract Although the dynamic characteristics of the baroreflex system have been described by baroreflex transfer functions obtained from open-loop analysis, the predictability of time-series output dynamics from input signals, which should confirm the accuracy of system identification, remains to be elucidated. Moreover, despite theoretical concerns over closed-loop system identification, the accuracy and the predictability of the closed-loop spontaneous baroreflex transfer function have not been evaluated compared with the open-loop transfer function. Using urethane and α-chloralose anaesthetized, vagotomized and aortic-denervated rabbits (n = 10), we identified open-loop baroreflex transfer functions by recording renal sympathetic nerve activity (SNA) while varying the vascularly isolated intracarotid sinus pressure (CSP) according to a binary random (white-noise) sequence (operating pressure ± 20 mmHg), and using a simplified equation to calculate closed-loop-spontaneous baroreflex transfer function while matching CSP with systemic arterial pressure (AP). Our results showed that the open-loop baroreflex transfer functions for the neural and peripheral arcs predicted the time-series SNA and AP outputs from measured CSP and SNA inputs, with r2 of 0.8 ± 0.1 and 0.8 ± 0.1, respectively. In contrast, the closed-loop-spontaneous baroreflex transfer function for the neural arc was markedly different from the open-loop transfer function (enhanced gain increase and a phase lead), and did not predict the time-series SNA dynamics (r2; 0.1 ± 0.1). However, the closed-loop-spontaneous baroreflex transfer function of the peripheral arc partially matched the open-loop transfer function in gain and phase functions, and had limited but reasonable predictability of the time-series AP dynamics (r2, 0.7 ± 0.1). A numerical simulation suggested that a noise predominantly in the neural arc under resting conditions might be a possible mechanism responsible for our findings. Furthermore, the predictabilities of the neural arc transfer functions obtained in open-loop and closed-loop conditions were validated by closed-loop pharmacological (phenylephrine and nitroprusside infusions) pressure interventions. Time-series SNA responses to drug-induced AP changes predicted by the open-loop transfer function matched closely the measured responses (r2, 0.9 ± 0.1), whereas SNA responses predicted by closed-loop-spontaneous transfer function deviated greatly and were the inverse of measured responses (r, −0.8 ± 0.2). These results indicate that although the spontaneous baroreflex transfer function obtained by closed-loop analysis has been believed to represent the neural arc function, it is inappropriate for system identification of the neural arc but is essentially appropriate for the peripheral arc under resting conditions, when compared with open-loop analysis. PMID:21486839

Influence of acoustic impedance of multilayer acoustic systems on the transfer function of ultrasonic airborne transducers.

PubMed

Gudra, Tadeusz; Opieliński, Krzysztof J

2002-05-01

In different solutions of ultrasonic transducers radiating acoustic energy into the air there occurs the problem of the proper selection of the acoustic impedance of one or more matching layers. The goal of this work was a computer analysis of the influence of acoustic impedance on the transfer function of piezoceramic transducers equipped with matching layers. Cases of resonance and non-resonance matching impedance in relation to the transfer function and the energy transmission coefficient for solid state-air systems were analysed. With stable thickness of matching layers the required shape of the transfer function can be obtained through proper choice of acoustic impedance were built (e.g. maximal flat function). The proper choice of acoustic impedance requires an elaboration of precise methods of synthesis of matching systems. Using the known matching criteria (Chebyshev's, DeSilets', Souquet's), the transfer function characteristics of transducers equipped with one, two, and three matching layers as well as the optimisation methods of the energy transmission coefficient were presented. The influence of the backside load of the transducer on the shape of transfer function was also analysed. The calculation results of this function for different loads of the transducer backside without and with the different matching layers were presented. The proper load selection allows us to obtain the desired shape of the transfer function, which determines the pulse shape generated by the transducer.

Cauchy-Jost function and hierarchy of integrable equations

NASA Astrophysics Data System (ADS)

Boiti, M.; Pempinelli, F.; Pogrebkov, A. K.

2015-11-01

We describe the properties of the Cauchy-Jost (also known as Cauchy-Baker-Akhiezer) function of the Kadomtsev-Petviashvili-II equation. Using the bar partial -method, we show that for this function, all equations of the Kadomtsev-Petviashvili-II hierarchy are given in a compact and explicit form, including equations for the Cauchy-Jost function itself, time evolutions of the Jost solutions, and evolutions of the potential of the heat equation.

Standard Errors of Equating Differences: Prior Developments, Extensions, and Simulations

ERIC Educational Resources Information Center

Moses, Tim; Zhang, Wenmin

2011-01-01

The purpose of this article was to extend the use of standard errors for equated score differences (SEEDs) to traditional equating functions. The SEEDs are described in terms of their original proposal for kernel equating functions and extended so that SEEDs for traditional linear and traditional equipercentile equating functions can be computed.…

Gravitoelectromagnetic analogy based on tidal tensors

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

Costa, L. Filipe O.; Herdeiro, Carlos A. R.

2008-07-15

We propose a new approach to a physical analogy between general relativity and electromagnetism, based on tidal tensors of both theories. Using this approach we write a covariant form for the gravitational analogues of the Maxwell equations, which makes transparent both the similarities and key differences between the two interactions. The following realizations of the analogy are given. The first one matches linearized gravitational tidal tensors to exact electromagnetic tidal tensors in Minkowski spacetime. The second one matches exact magnetic gravitational tidal tensors for ultrastationary metrics to exact magnetic tidal tensors of electromagnetism in curved spaces. In the third wemore » show that our approach leads to a two-step exact derivation of Papapetrou's equation describing the force exerted on a spinning test particle. Analogous scalar invariants built from tidal tensors of both theories are also discussed.« less

Self-consistent Maxwell-Bloch model of quantum-dot photonic-crystal-cavity lasers

NASA Astrophysics Data System (ADS)

Cartar, William; Mørk, Jesper; Hughes, Stephen

2017-08-01

We present a powerful computational approach to simulate the threshold behavior of photonic-crystal quantum-dot (QD) lasers. Using a finite-difference time-domain (FDTD) technique, Maxwell-Bloch equations representing a system of thousands of statistically independent and randomly positioned two-level emitters are solved numerically. Phenomenological pure dephasing and incoherent pumping is added to the optical Bloch equations to allow for a dynamical lasing regime, but the cavity-mediated radiative dynamics and gain coupling of each QD dipole (artificial atom) is contained self-consistently within the model. These Maxwell-Bloch equations are implemented by using Lumerical's flexible material plug-in tool, which allows a user to define additional equations of motion for the nonlinear polarization. We implement the gain ensemble within triangular-lattice photonic-crystal cavities of various length N (where N refers to the number of missing holes), and investigate the cavity mode characteristics and the threshold regime as a function of cavity length. We develop effective two-dimensional model simulations which are derived after studying the full three-dimensional passive material structures by matching the cavity quality factors and resonance properties. We also demonstrate how to obtain the correct point-dipole radiative decay rate from Fermi's golden rule, which is captured naturally by the FDTD method. Our numerical simulations predict that the pump threshold plateaus around cavity lengths greater than N =9 , which we identify as a consequence of the complex spatial dynamics and gain coupling from the inhomogeneous QD ensemble. This behavior is not expected from simple rate-equation analysis commonly adopted in the literature, but is in qualitative agreement with recent experiments. Single-mode to multimode lasing is also observed, depending on the spectral peak frequency of the QD ensemble. Using a statistical modal analysis of the average decay rates, we also show how the average radiative decay rate decreases as a function of cavity size. In addition, we investigate the role of structural disorder on both the passive cavity and active lasers, where the latter show a general increase in the pump threshold for cavity lengths greater than N =7 , and a reduction in the nominal cavity mode volume for increasing amounts of disorder.

Do Pigeons Prefer Information in the Absence of Differential Reinforcement?

PubMed Central

Zentall, Thomas R.; Stagner, Jessica P.

2012-01-01

Prior research indicates that pigeons do not prefer an alternative that provides a sample (for matching-to-sample) over an alternative that does not provide a sample (i.e., there is no indication of which comparison stimulus is correct). However, Zentall and Stagner (2010) showed that when delay of reinforcement was controlled, pigeons had a strong preference for matching over pseudo-matching (there was a sample but it did not indicate which comparison stimulus was correct). Experiment 1 of the present study replicated and extended the results of the Zentall and Stagner study by including an identity relation between the sample and one of the comparison stimuli in both the matching and pseudo-matching tasks. In Experiment 2, when we asked if the pigeons would still prefer matching if we equated the two tasks for probability of reinforcement, we found no systematic preference for matching over pseudo-matching. Thus, it appears that in the absence of differential reinforcement, the information provided by a sample that signals which of the two comparison stimuli is correct is insufficient to produce a preference for that alternative. PMID:22367755

Infinite product expansion of the Fokker-Planck equation with steady-state solution.

PubMed

Martin, R J; Craster, R V; Kearney, M J

2015-07-08

We present an analytical technique for solving Fokker-Planck equations that have a steady-state solution by representing the solution as an infinite product rather than, as usual, an infinite sum. This method has many advantages: automatically ensuring positivity of the resulting approximation, and by design exactly matching both the short- and long-term behaviour. The efficacy of the technique is demonstrated via comparisons with computations of typical examples.

Millimeter Wave Generation by Relativistic Electron Beams.

DTIC Science & Technology

1984-12-01

frequency and wave vector matching relations for influence of various nonlinear effects on this instability is this four-wave interaction require...following coupled mode equations _ 6 = 6 _ (14)-- v vx (14) ." .’ for the lower hybrid sidebands: v - V 2 - The x component of the resultant vector equation...involves a purely growing modte, a four-wave interaction plitoces is analysed, including a u ap ti wave- vector up-shifted and ilown-shiftes upper

Infinite product expansion of the Fokker–Planck equation with steady-state solution

PubMed Central

Martin, R. J.; Craster, R. V.; Kearney, M. J.

2015-01-01

We present an analytical technique for solving Fokker–Planck equations that have a steady-state solution by representing the solution as an infinite product rather than, as usual, an infinite sum. This method has many advantages: automatically ensuring positivity of the resulting approximation, and by design exactly matching both the short- and long-term behaviour. The efficacy of the technique is demonstrated via comparisons with computations of typical examples. PMID:26346100

An efficient way of layout processing based on calibre DRC and pattern matching for defects inspection application

NASA Astrophysics Data System (ADS)

Li, Helen; Lee, Robben; Lee, Tyzy; Xue, Teddy; Liu, Hermes; Wu, Hall; Wan, Qijian; Du, Chunshan; Hu, Xinyi; Liu, Zhengfang

2018-03-01

As technology advances, escalating layout design complexity and chip size make defect inspection becomes more challenging than ever before. The YE (Yield Enhancement) engineers are seeking for an efficient strategy to ensure accuracy without suffering running time. A smart way is to set different resolutions for different pattern structures, for examples, logic pattern areas have a higher scan resolution while the dummy areas have a lower resolution, SRAM area may have another different resolution. This can significantly reduce the scan processing time meanwhile the accuracy does not suffer. Due to the limitation of the inspection equipment, the layout must be processed in order to output the Care Area marker in line with the requirement of the equipment, for instance, the marker shapes must be rectangle and the number of the rectangle shapes should be as small as possible. The challenge is how to select the different Care Areas by pattern structures, merge the areas efficiently and then partition them into pieces of rectangle shapes. This paper presents a solution based on Calibre DRC and Pattern Matching. Calibre equation-based DRC is a powerful layout processing engine and Calibre Pattern Matching's automated visual capture capability enables designers to define these geometries as layout patterns and store them in libraries which can be re-used in multiple design layouts. Pattern Matching simplifies the description of very complex relationships between pattern shapes efficiently and accurately. Pattern matching's true power is on display when it is integrated with normal DRC deck. In this application of defects inspection, we first run Calibre DRC to get rule based Care Area then use Calibre Pattern Matching's automated pattern capture capability to capture Care Area shapes which need a higher scan resolution with a tune able pattern halo. In the pattern matching step, when the patterns are matched, a bounding box marker will be output to identify the high resolution area. The equation-based DRC and Pattern Matching effectively work together for different scan phases.

Theoretical and computational analyses of LNG evaporator

NASA Astrophysics Data System (ADS)

Chidambaram, Palani Kumar; Jo, Yang Myung; Kim, Heuy Dong

2017-04-01

Theoretical and numerical analysis on the fluid flow and heat transfer inside a LNG evaporator is conducted in this work. Methane is used instead of LNG as the operating fluid. This is because; methane constitutes over 80% of natural gas. The analytical calculations are performed using simple mass and energy balance equations. The analytical calculations are made to assess the pressure and temperature variations in the steam tube. Multiphase numerical simulations are performed by solving the governing equations (basic flow equations of continuity, momentum and energy equations) in a portion of the evaporator domain consisting of a single steam pipe. The flow equations are solved along with equations of species transport. Multiphase modeling is incorporated using VOF method. Liquid methane is the primary phase. It vaporizes into the secondary phase gaseous methane. Steam is another secondary phase which flows through the heating coils. Turbulence is modeled by a two equation turbulence model. Both the theoretical and numerical predictions are seen to match well with each other. Further parametric studies are planned based on the current research.

Derivation of a Provisional, Age-dependent, AIS2+ Thoracic Risk Curve for the THOR50 Test Dummy via Integration of NASS Cases, PMHS Tests, and Simulation Data.

PubMed

Laituri, Tony R; Henry, Scott; El-Jawahri, Raed; Muralidharan, Nirmal; Li, Guosong; Nutt, Marvin

2015-11-01

A provisional, age-dependent thoracic risk equation (or, "risk curve") was derived to estimate moderate-to-fatal injury potential (AIS2+), pertaining to men with responses gaged by the advanced mid-sized male test dummy (THOR50). The derivation involved two distinct data sources: cases from real-world crashes (e.g., the National Automotive Sampling System, NASS) and cases involving post-mortem human subjects (PMHS). The derivation was therefore more comprehensive, as NASS datasets generally skew towards younger occupants, and PMHS datasets generally skew towards older occupants. However, known deficiencies had to be addressed (e.g., the NASS cases had unknown stimuli, and the PMHS tests required transformation of known stimuli into THOR50 stimuli). For the NASS portion of the analysis, chest-injury outcomes for adult male drivers about the size of the THOR50 were collected from real-world, 11-1 o'clock, full-engagement frontal crashes (NASS, 1995-2012 calendar years, 1985-2012 model-year light passenger vehicles). The screening for THOR50-sized men involved application of a set of newly-derived "correction" equations for self-reported height and weight data in NASS. Finally, THOR50 stimuli were estimated via field simulations involving attendant representative restraint systems, and those stimuli were then assigned to corresponding NASS cases (n=508). For the PMHS portion of the analysis, simulation-based closure equations were developed to convert PMHS stimuli into THOR50 stimuli. Specifically, closure equations were derived for the four measurement locations on the THOR50 chest by cross-correlating the results of matched-loading simulations between the test dummy and the age-dependent, Ford Human Body Model. The resulting closure equations demonstrated acceptable fidelity (n=75 matched simulations, R2≥0.99). These equations were applied to the THOR50-sized men in the PMHS dataset (n=20). The NASS and PMHS datasets were combined and subjected to survival analysis with event-frequency weighting and arbitrary censoring. The resulting risk curve--a function of peak THOR50 chest compression and age--demonstrated acceptable fidelity for recovering the AIS2+ chest injury rate of the combined dataset (i.e., IR_dataset=1.97% vs. curve-based IR_dataset=1.98%). Additional sensitivity analyses showed that (a) binary logistic regression yielded a risk curve with nearly-identical fidelity, (b) there was only a slight advantage of combining the small-sample PMHS dataset with the large-sample NASS dataset, (c) use of the PMHS-based risk curve for risk estimation of the combined dataset yielded relatively poor performance (194% difference), and (d) when controlling for the type of contact (lab-consistent or not), the resulting risk curves were similar.

Modeling Interactions Between Flexible Flapping Wing Spars, Mechanisms, and Drive Motors

DTIC Science & Technology

2011-09-01

of dynamical equations is presented that allow micro air vehicle (MAV) or- nithopter designers to match drive motors to loads produced by flexible...aeroelastic systems is presented. One potential use for such a model is to serve as the basis for a vehicle design tool that matches drive motors to loads...friction. ∗Senior Aerospace Engineer, Control Design and Analysis Branch, 2210 Eighth Street, Ste. 21, Air Force Research Labora- tory, WPAFB, OH 45433

Adiabatic release measurements in aluminum between 400 and 1200 GPa: Characterization of aluminum as a shock standard in the multimegabar regime

DOE PAGES

Knudson, Marcus D.; Desjarlais, Michael P.; Pribram-Jones, Aurora

2015-06-15

Aluminum has been used prolifically as an impedance matching standard in the multimegabar regime (1 Mbar = 100 GPa), particularly in nuclear driven, early laser driven, and early magnetically driven flyer plate experiments. The accuracy of these impedance matching measurements depends upon the knowledge of both the Hugoniot and release or reshock response of aluminum. Here, we present the results of several adiabatic release measurements of aluminum from ~400–1200 GPa states along the principal Hugoniot using full density polymethylpentene (commonly known as TPX), and both ~190 and ~110 mg/cc silica aerogel standards. Additionally, these data were analyzed within the frameworkmore » of a simple, analytical model that was motivated by a first-principles molecular dynamics investigation into the release response of aluminum, as well as by a survey of the release response determined from several tabular equations of state for aluminum. Combined, this theoretical and experimental study provides a method to perform impedance matching calculations without the need to appeal to any tabular equation of state for aluminum. Furthermore, as an analytical model, this method allows for propagation of all uncertainty, including the random measurement uncertainties and the systematic uncertainties of the Hugoniot and release response of aluminum. This work establishes aluminum for use as a high-precision standard for impedance matching in the multimegabar regime.« less

The convergence of the order sequence and the solution function sequence on fractional partial differential equation

NASA Astrophysics Data System (ADS)

Rusyaman, E.; Parmikanti, K.; Chaerani, D.; Asefan; Irianingsih, I.

2018-03-01

One of the application of fractional ordinary differential equation is related to the viscoelasticity, i.e., a correlation between the viscosity of fluids and the elasticity of solids. If the solution function develops into function with two or more variables, then its differential equation must be changed into fractional partial differential equation. As the preliminary study for two variables viscoelasticity problem, this paper discusses about convergence analysis of function sequence which is the solution of the homogenous fractional partial differential equation. The method used to solve the problem is Homotopy Analysis Method. The results show that if given two real number sequences (αn) and (βn) which converge to α and β respectively, then the solution function sequences of fractional partial differential equation with order (αn, βn) will also converge to the solution function of fractional partial differential equation with order (α, β).

First-principles modeling of quantum nuclear effects and atomic interactions in solid 4He at high pressure

NASA Astrophysics Data System (ADS)

Cazorla, Claudio; Boronat, Jordi

2015-01-01

We present a first-principles computational study of solid 4He at T =0 K and pressures up to ˜160 GPa. Our computational strategy consists in using van der Waals density functional theory (DFT-vdW) to describe the electronic degrees of freedom in this material, and the diffusion Monte Carlo (DMC) method to solve the Schrödinger equation describing the behavior of the quantum nuclei. For this, we construct an analytical interaction function based on the pairwise Aziz potential that closely matches the volume variation of the cohesive energy calculated with DFT-vdW in dense helium. Interestingly, we find that the kinetic energy of solid 4He does not increase appreciably with compression for P ≥85 GPa. Also, we show that the Lindemann ratio in dense solid 4He amounts to 0.10 almost independently of pressure. The reliability of customary quasiharmonic DFT (QH DFT) approaches in describing quantum nuclear effects in solids is also studied. We find that QH DFT simulations, although provide a reasonable equation of state in agreement with experiments, are not able to reproduce correctly these critical effects in compressed 4He. In particular, we disclose huge discrepancies of at least ˜50 % in the calculated 4He kinetic energies using both the QH DFT and present DFT-DMC methods.

Analytical Formulation of Equatorial Standing Wave Phenomena: Application to QBO and ENSO

NASA Astrophysics Data System (ADS)

Pukite, P. R.

2016-12-01

Key equatorial climate phenomena such as QBO and ENSO have never been adequately explained as deterministic processes. This in spite of recent research showing growing evidence of predictable behavior. This study applies the fundamental Laplace tidal equations with simplifying assumptions along the equator — i.e. no Coriolis force and a small angle approximation. To connect the analytical Sturm-Liouville results to observations, a first-order forcing consistent with a seasonally aliased Draconic or nodal lunar period (27.21d aliased into 2.36y) is applied. This has a plausible rationale as it ties a latitudinal forcing cycle via a cross-product to the longitudinal terms in the Laplace formulation. The fitted results match the features of QBO both qualitatively and quantitatively; adding second-order terms due to other seasonally aliased lunar periods provides finer detail while remaining consistent with the physical model. Further, running symbolic regression machine learning experiments on the data provided a validation to the approach, as it discovered the same analytical form and fitted values as the first principles Laplace model. These results conflict with Lindzen's QBO model, in that his original formulation fell short of making the lunar connection, even though Lindzen himself asserted "it is unlikely that lunar periods could be produced by anything other than the lunar tidal potential".By applying a similar analytical approach to ENSO, we find that the tidal equations need to be replaced with a Mathieu-equation formulation consistent with describing a sloshing process in the thermocline depth. Adapting the hydrodynamic math of sloshing, we find a biennial modulation coupled with angular momentum forcing variations matching the Chandler wobble gives an impressive match over the measured ENSO range of 1880 until the present. Lunar tidal periods and an additional triaxial nutation of 14 year period provide additional fidelity. The caveat is a phase inversion of the biennial mode lasting from 1980 to 1996. The parsimony of these analytical models arises from applying only known cyclic forcing terms to fundamental wave equation formulations. This raises the possibility that both QBO and ENSO can be predicted years in advance, apart from a metastable biennial phase inversion in ENSO.

Automated analysis of biological oscillator models using mode decomposition.

PubMed

Konopka, Tomasz

2011-04-01

Oscillating signals produced by biological systems have shapes, described by their Fourier spectra, that can potentially reveal the mechanisms that generate them. Extracting this information from measured signals is interesting for the validation of theoretical models, discovery and classification of interaction types, and for optimal experiment design. An automated workflow is described for the analysis of oscillating signals. A software package is developed to match signal shapes to hundreds of a priori viable model structures defined by a class of first-order differential equations. The package computes parameter values for each model by exploiting the mode decomposition of oscillating signals and formulating the matching problem in terms of systems of simultaneous polynomial equations. On the basis of the computed parameter values, the software returns a list of models consistent with the data. In validation tests with synthetic datasets, it not only shortlists those model structures used to generate the data but also shows that excellent fits can sometimes be achieved with alternative equations. The listing of all consistent equations is indicative of how further invalidation might be achieved with additional information. When applied to data from a microarray experiment on mice, the procedure finds several candidate model structures to describe interactions related to the circadian rhythm. This shows that experimental data on oscillators is indeed rich in information about gene regulation mechanisms. The software package is available at http://babylone.ulb.ac.be/autoosc/.

Integrating different tracking systems in football: multiple camera semi-automatic system, local position measurement and GPS technologies.

PubMed

Buchheit, Martin; Allen, Adam; Poon, Tsz Kit; Modonutti, Mattia; Gregson, Warren; Di Salvo, Valter

2014-12-01

Abstract During the past decade substantial development of computer-aided tracking technology has occurred. Therefore, we aimed to provide calibration equations to allow the interchangeability of different tracking technologies used in soccer. Eighty-two highly trained soccer players (U14-U17) were monitored during training and one match. Player activity was collected simultaneously with a semi-automatic multiple-camera (Prozone), local position measurement (LPM) technology (Inmotio) and two global positioning systems (GPSports and VX). Data were analysed with respect to three different field dimensions (small, <30 m 2 to full-pitch, match). Variables provided by the systems were compared, and calibration equations (linear regression models) between each system were calculated for each field dimension. Most metrics differed between the 4 systems with the magnitude of the differences dependant on both pitch size and the variable of interest. Trivial-to-small between-system differences in total distance were noted. However, high-intensity running distance (>14.4 km · h -1 ) was slightly-to-moderately greater when tracked with Prozone, and accelerations, small-to-very largely greater with LPM. For most of the equations, the typical error of the estimate was of a moderate magnitude. Interchangeability of the different tracking systems is possible with the provided equations, but care is required given their moderate typical error of the estimate.

A human auditory tuning curves matched wavelet function.

PubMed

Abolhassani, Mohammad D; Salimpour, Yousef

2008-01-01

This paper proposes a new quantitative approach to the problem of matching a wavelet function to a human auditory tuning curves. The auditory filter shapes were derived from the psychophysical measurements in normal-hearing listeners using the variant of the notched-noise method for brief signals in forward and simultaneous masking. These filters were used as templates for the designing a wavelet function that has the maximum matching to a tuning curve. The scaling function was calculated from the matched wavelet function and by using these functions, low pass and high pass filters were derived for the implementation of a filter bank. Therefore, new wavelet families were derived.

Quasi-Newton methods for parameter estimation in functional differential equations

NASA Technical Reports Server (NTRS)

Brewer, Dennis W.

1988-01-01

A state-space approach to parameter estimation in linear functional differential equations is developed using the theory of linear evolution equations. A locally convergent quasi-Newton type algorithm is applied to distributed systems with particular emphasis on parameters that induce unbounded perturbations of the state. The algorithm is computationally implemented on several functional differential equations, including coefficient and delay estimation in linear delay-differential equations.

Using the Kernel Method of Test Equating for Estimating the Standard Errors of Population Invariance Measures. Research Report. ETS RR-06-20

ERIC Educational Resources Information Center

Moses, Tim

2006-01-01

Population invariance is an important requirement of test equating. An equating function is said to be population invariant when the choice of (sub)population used to compute the equating function does not matter. In recent studies, the extent to which equating functions are population invariant is typically addressed in terms of practical…

Emotion perception after moderate-severe traumatic brain injury: The valence effect and the role of working memory, processing speed, and nonverbal reasoning.

PubMed

Rosenberg, Hannah; Dethier, Marie; Kessels, Roy P C; Westbrook, R Frederick; McDonald, Skye

2015-07-01

Traumatic brain injury (TBI) impairs emotion perception. Perception of negative emotions (sadness, disgust, fear, and anger) is reportedly affected more than positive (happiness and surprise) ones. It has been argued that this reflects a specialized neural network underpinning negative emotions that is vulnerable to brain injury. However, studies typically do not equate for differential difficulty between emotions. We aimed to examine whether emotion recognition deficits in people with TBI were specific to negative emotions, while equating task difficulty, and to determine whether perception deficits might be accounted for by other cognitive processes. Twenty-seven people with TBI and 28 matched control participants identified 6 basic emotions at 2 levels of intensity (a) the conventional 100% intensity and (b) "equated intensity"-that is, an intensity that yielded comparable accuracy rates across emotions in controls. (a) At 100% intensity, the TBI group was impaired in recognizing anger, fear, and disgust but not happiness, surprise, or sadness and performed worse on negative than positive emotions. (b) At equated intensity, the TBI group was poorer than controls overall but not differentially poorer in recognizing negative emotions. Although processing speed and nonverbal reasoning were associated with emotion accuracy, injury severity by itself was a unique predictor. When task difficulty is taken into account, individuals with TBI show impairment in recognizing all facial emotions. There was no evidence for a specific impairment for negative emotions or any particular emotion. Impairment was accounted for by injury severity rather than being a secondary effect of reduced neuropsychological functioning. (c) 2015 APA, all rights reserved).

Transmutation of a trans-series: the Gross-Witten-Wadia phase transition

NASA Astrophysics Data System (ADS)

Ahmed, Anees; Dunne, Gerald V.

2017-11-01

We study the change in the resurgent asymptotic properties of a trans-series in two parameters, a coupling g 2 and a gauge index N, as a system passes through a large N phase transition, using the universal example of the Gross-Witten-Wadia third-order phase transition in the unitary matrix model. This transition is well-studied in the immediate vicinity of the transition point, where it is characterized by a double-scaling limit Painlevé II equation, and also away from the transition point using the pre-string difference equation. Here we present a complementary analysis of the transition at all coupling and all finite N, in terms of a differential equation, using the explicit Tracy-Widom mapping of the Gross-Witten-Wadia partition function to a solution of a Painlevé III equation. This mapping provides a simple method to generate trans-series expansions in all parameter regimes, and to study their transmutation as the parameters are varied. For example, at any finite N the weak coupling expansion is divergent, with a non-perturbative trans-series completion; on the other hand, the strong coupling expansion is convergent, and yet there is still a non-perturbative trans-series completion. We show how the different instanton terms `condense' at the transition point to match with the double-scaling limit trans-series. We also define a uniform large N strong-coupling expansion (a non-linear analogue of uniform WKB), which is much more precise than the conventional large N expansion through the transition region, and apply it to the evaluation of Wilson loops.

Similarity Laws for the Lines of Ideal Free Energy and Chemical Potential in Supercritical Fluids.

PubMed

Apfelbaum, E M; Vorob'ev, V S

2017-09-21

We have found the curves on the density-temperature plane, along which the values of free energy and chemical potential correspond to ideal gas quantities. At first, we have applied the van der Waals equation to construct them and to derive their equations. Then we have shown that the same lines for real substances (Ar, N 2 , CH 4 , SF 6 , H 2 , H 2 O) and for the model Lennard-Jones system constructed on the basis of the measurements data and calculations are well matched with the derived equations. The validity and deviations from the obtained similarity laws are discussed.

High-order FDTD methods for transverse electromagnetic systems in dispersive inhomogeneous media.

PubMed

Zhao, Shan

2011-08-15

This Letter introduces a novel finite-difference time-domain (FDTD) formulation for solving transverse electromagnetic systems in dispersive media. Based on the auxiliary differential equation approach, the Debye dispersion model is coupled with Maxwell's equations to derive a supplementary ordinary differential equation for describing the regularity changes in electromagnetic fields at the dispersive interface. The resulting time-dependent jump conditions are rigorously enforced in the FDTD discretization by means of the matched interface and boundary scheme. High-order convergences are numerically achieved for the first time in the literature in the FDTD simulations of dispersive inhomogeneous media. © 2011 Optical Society of America

Transfer Alignment Error Compensator Design Based on Robust State Estimation

NASA Astrophysics Data System (ADS)

Lyou, Joon; Lim, You-Chol

This paper examines the transfer alignment problem of the StrapDown Inertial Navigation System (SDINS), which is subject to the ship’s roll and pitch. Major error sources for velocity and attitude matching are lever arm effect, measurement time delay and ship-body flexure. To reduce these alignment errors, an error compensation method based on state augmentation and robust state estimation is devised. A linearized error model for the velocity and attitude matching transfer alignment system is derived first by linearizing the nonlinear measurement equation with respect to its time delay and dominant Y-axis flexure, and by augmenting the delay state and flexure state into conventional linear state equations. Then an H∞ filter is introduced to account for modeling uncertainties of time delay and the ship-body flexure. The simulation results show that this method considerably decreases azimuth alignment errors considerably.

Efficiency of perfectly matched layers for seismic wave modeling in second-order viscoelastic equations

NASA Astrophysics Data System (ADS)

Ping, Ping; Zhang, Yu; Xu, Yixian; Chu, Risheng

2016-12-01

In order to improve the perfectly matched layer (PML) efficiency in viscoelastic media, we first propose a split multi-axial PML (M-PML) and an unsplit convolutional PML (C-PML) in the second-order viscoelastic wave equations with the displacement as the only unknown. The advantage of these formulations is that it is easy and efficient to revise the existing codes of the second-order spectral element method (SEM) or finite-element method (FEM) with absorbing boundaries in a uniform equation, as well as more economical than the auxiliary differential equations PML. Three models which are easily suffered from late time instabilities are considered to validate our approaches. Through comparison the M-PML with C-PML efficiency of absorption and stability for long time simulation, it can be concluded that: (1) for an isotropic viscoelastic medium with high Poisson's ratio, the C-PML will be a sufficient choice for long time simulation because of its weak reflections and superior stability; (2) unlike the M-PML with high-order damping profile, the M-PML with second-order damping profile loses its stability in long time simulation for an isotropic viscoelastic medium; (3) in an anisotropic viscoelastic medium, the C-PML suffers from instabilities, while the M-PML with second-order damping profile can be a better choice for its superior stability and more acceptable weak reflections than the M-PML with high-order damping profile. The comparative analysis of the developed methods offers meaningful significance for long time seismic wave modeling in second-order viscoelastic wave equations.

The classical D-type expansion of spherical H II regions

NASA Astrophysics Data System (ADS)

Williams, Robin J. R.; Bibas, Thomas G.; Haworth, Thomas J.; Mackey, Jonathan

2018-06-01

Recent numerical and analytic work has highlighted some shortcomings in our understanding of the dynamics of H II region expansion, especially at late times, when the H II region approaches pressure equilibrium with the ambient medium. Here we reconsider the idealized case of a constant radiation source in a uniform and spherically symmetric ambient medium, with an isothermal equation of state. A thick-shell solution is developed which captures the stalling of the ionization front and the decay of the leading shock to a weak compression wave as it escapes to large radii. An acoustic approximation is introduced to capture the late-time damped oscillations of the H II region about the stagnation radius. Putting these together, a matched asymptotic equation is derived for the radius of the ionization front which accounts for both the inertia of the expanding shell and the finite temperature of the ambient medium. The solution to this equation is shown to agree very well with the numerical solution at all times, and is superior to all previously published solutions. The matched asymptotic solution can also accurately model the variation of H II region radius for a time-varying radiation source.

A boundary condition to the Khokhlov-Zabolotskaya equation for modeling strongly focused nonlinear ultrasound fields

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

Rosnitskiy, P., E-mail: pavrosni@yandex.ru; Yuldashev, P., E-mail: petr@acs366.phys.msu.ru; Khokhlova, V., E-mail: vera@acs366.phys.msu.ru

2015-10-28

An equivalent source model was proposed as a boundary condition to the nonlinear parabolic Khokhlov-Zabolotskaya (KZ) equation to simulate high intensity focused ultrasound (HIFU) fields generated by medical ultrasound transducers with the shape of a spherical shell. The boundary condition was set in the initial plane; the aperture, the focal distance, and the initial pressure of the source were chosen based on the best match of the axial pressure amplitude and phase distributions in the Rayleigh integral analytic solution for a spherical transducer and the linear parabolic approximation solution for the equivalent source. Analytic expressions for the equivalent source parametersmore » were derived. It was shown that the proposed approach allowed us to transfer the boundary condition from the spherical surface to the plane and to achieve a very good match between the linear field solutions of the parabolic and full diffraction models even for highly focused sources with F-number less than unity. The proposed method can be further used to expand the capabilities of the KZ nonlinear parabolic equation for efficient modeling of HIFU fields generated by strongly focused sources.« less

Nonlinear self-reflection of intense ultra-wideband femtosecond pulses in optical fiber

NASA Astrophysics Data System (ADS)

Konev, Leonid S.; Shpolyanskiy, Yuri A.

2013-05-01

We simulated propagation of few-cycle femtosecond pulses in fused silica fiber based on the set of first-order equations for forward and backward waves that generalizes widely used equation of unidirectional approximation. Appearance of a weak reflected field in conditions default to the unidirectional approach is observed numerically. It arises from nonmatched initial field distribution with the nonlinear medium response. Besides additional field propagating forward along with the input pulse is revealed. The analytical solution of a simplified set of equations valid over distances of a few wavelengths confirms generation of reflected and forward-propagating parts of the backward wave. It allowed us to find matched conditions when the reflected field is eliminated and estimate the amplitude of backward wave via medium properties. The amplitude has the order of the nonlinear contribution to the refractive index divided by the linear refractive index. It is small for the fused silica so the conclusions obtained in the unidirectional approach are valid. The backward wave should be proportionally higher in media with stronger nonlinear response. We did not observe in simulations additional self-reflection not related to non-matched boundary conditions.

Multiscale modelling for tokamak pedestals

NASA Astrophysics Data System (ADS)

Abel, I. G.

2018-04-01

Pedestal modelling is crucial to predict the performance of future fusion devices. Current modelling efforts suffer either from a lack of kinetic physics, or an excess of computational complexity. To ameliorate these problems, we take a first-principles multiscale approach to the pedestal. We will present three separate sets of equations, covering the dynamics of edge localised modes (ELMs), the inter-ELM pedestal and pedestal turbulence, respectively. Precisely how these equations should be coupled to each other is covered in detail. This framework is completely self-consistent; it is derived from first principles by means of an asymptotic expansion of the fundamental Vlasov-Landau-Maxwell system in appropriate small parameters. The derivation exploits the narrowness of the pedestal region, the smallness of the thermal gyroradius and the low plasma (the ratio of thermal to magnetic pressures) typical of current pedestal operation to achieve its simplifications. The relationship between this framework and gyrokinetics is analysed, and possibilities to directly match our systems of equations onto multiscale gyrokinetics are explored. A detailed comparison between our model and other models in the literature is performed. Finally, the potential for matching this framework onto an open-field-line region is briefly discussed.

Impedance Matched Absorptive Thermal Blocking Filters

NASA Technical Reports Server (NTRS)

Wollack, E. J.; Chuss, D. T.; U-Yen, K.; Rostem, K.

2014-01-01

We have designed, fabricated and characterized absorptive thermal blocking filters for cryogenic microwave applications. The transmission line filter's input characteristic impedance is designed to match 50 Omega and its response has been validated from 0-to-50GHz. The observed return loss in the 0-to-20GHz design band is greater than 20 dB and shows graceful degradation with frequency. Design considerations and equations are provided that enable this approach to be scaled and modified for use in other applications.

Impedance Matched Absorptive Thermal Blocking Filters

NASA Technical Reports Server (NTRS)

Wollack, E. J.; Chuss, D. T.; Rostem, K.; U-Yen, K.

2014-01-01

We have designed, fabricated and characterized absorptive thermal blocking filters for cryogenic microwave applications. The transmission line filter's input characteristic impedance is designed to match 50O and its response has been validated from 0-to-50GHz. The observed return loss in the 0-to-20GHz design band is greater than 20 dB and shows graceful degradation with frequency. Design considerations and equations are provided that enable this approach to be scaled and modified for use in other applications.

Fragmentation functions beyond fixed order accuracy

NASA Astrophysics Data System (ADS)

Anderle, Daniele P.; Kaufmann, Tom; Stratmann, Marco; Ringer, Felix

2017-03-01

We give a detailed account of the phenomenology of all-order resummations of logarithmically enhanced contributions at small momentum fraction of the observed hadron in semi-inclusive electron-positron annihilation and the timelike scale evolution of parton-to-hadron fragmentation functions. The formalism to perform resummations in Mellin moment space is briefly reviewed, and all relevant expressions up to next-to-next-to-leading logarithmic order are derived, including their explicit dependence on the factorization and renormalization scales. We discuss the details pertinent to a proper numerical implementation of the resummed results comprising an iterative solution to the timelike evolution equations, the matching to known fixed-order expressions, and the choice of the contour in the Mellin inverse transformation. First extractions of parton-to-pion fragmentation functions from semi-inclusive annihilation data are performed at different logarithmic orders of the resummations in order to estimate their phenomenological relevance. To this end, we compare our results to corresponding fits up to fixed, next-to-next-to-leading order accuracy and study the residual dependence on the factorization scale in each case.

Time dependent turbulence modeling and analytical theories of turbulence

NASA Technical Reports Server (NTRS)

Rubinstein, R.

1993-01-01

By simplifying the direct interaction approximation (DIA) for turbulent shear flow, time dependent formulas are derived for the Reynolds stresses which can be included in two equation models. The Green's function is treated phenomenologically, however, following Smith and Yakhot, we insist on the short and long time limits required by DIA. For small strain rates, perturbative evaluation of the correlation function yields a time dependent theory which includes normal stress effects in simple shear flows. From this standpoint, the phenomenological Launder-Reece-Rodi model is obtained by replacing the Green's function by its long time limit. Eddy damping corrections to short time behavior initiate too quickly in this model; in contrast, the present theory exhibits strong suppression of eddy damping at short times. A time dependent theory for large strain rates is proposed in which large scales are governed by rapid distortion theory while small scales are governed by Kolmogorov inertial range dynamics. At short times and large strain rates, the theory closely matches rapid distortion theory, but at long times it relaxes to an eddy damping model.

Algebro-geometric Solutions for the Derivative Burgers Hierarchy

NASA Astrophysics Data System (ADS)

Hou, Yu; Fan, Engui; Qiao, Zhijun; Wang, Zhong

2015-02-01

Though completely integrable Camassa-Holm (CH) equation and Degasperis-Procesi (DP) equation are cast in the same peakon family, they possess the second- and third-order Lax operators, respectively. From the viewpoint of algebro-geometrical study, this difference lies in hyper-elliptic and non-hyper-elliptic curves. The non-hyperelliptic curves lead to great difficulty in the construction of algebro-geometric solutions of the DP equation. In this paper, we study algebro-geometric solutions for the derivative Burgers (DB) equation, which is derived by Qiao and Li (2004) as a short wave model of the DP equation with the help of functional gradient and a pair of Lenard operators. Based on the characteristic polynomial of a Lax matrix for the DB equation, we introduce a third order algebraic curve with genus , from which the associated Baker-Akhiezer functions, meromorphic function, and Dubrovin-type equations are constructed. Furthermore, the theory of algebraic curve is applied to derive explicit representations of the theta function for the Baker-Akhiezer functions and the meromorphic function. In particular, the algebro-geometric solutions are obtained for all equations in the whole DB hierarchy.

Wave equations in conformal gravity

NASA Astrophysics Data System (ADS)

Du, Juan-Juan; Wang, Xue-Jing; He, You-Biao; Yang, Si-Jiang; Li, Zhong-Heng

2018-05-01

We study the wave equation governing massless fields of all spins (s = 0, 1 2, 1, 3 2 and 2) in the most general spherical symmetric metric of conformal gravity. The equation is separable, the solution of the angular part is a spin-weighted spherical harmonic, and the radial wave function may be expressed in terms of solutions of the Heun equation which has four regular singular points. We also consider various special cases of the metric and find that the angular wave functions are the same for all cases, the actual shape of the metric functions affects only the radial wave function. It is interesting to note that each radial equation can be transformed into a known ordinary differential equation (i.e. Heun equation, or confluent Heun equation, or hypergeometric equation). The results show that there are analytic solutions for all the wave equations of massless spin fields in the spacetimes of conformal gravity. This is amazing because exact solutions are few and far between for other spacetimes.

Multiscale modeling and computation of nano-electronic transistors and transmembrane proton channels

NASA Astrophysics Data System (ADS)

Chen, Duan

The miniaturization of nano-scale electronic transistors, such as metal oxide semiconductor field effect transistors (MOSFETs), has given rise to a pressing demand in the new theoretical understanding and practical tactic for dealing with quantum mechanical effects in integrated circuits. In biology, proton dynamics and transport across membrane proteins are of paramount importance to the normal function of living cells. Similar physical characteristics are behind the two subjects, and model simulations share common mathematical interests/challenges. In this thesis work, multiscale and multiphysical models are proposed to study the mechanisms of nanotransistors and proton transport in transmembrane at the atomic level. For nano-electronic transistors, we introduce a unified two-scale energy functional to describe the electrons and the continuum electrostatic potential. This framework enables us to put microscopic and macroscopic descriptions on an equal footing at nano-scale. Additionally, this model includes layered structures and random doping effect of nano-transistors. For transmembrane proton channels, we describe proton dynamics quantum mechanically via a density functional approach while implicitly treat numerous solvent molecules as a dielectric continuum. The densities of all other ions in the solvent are assumed to obey the Boltzmann distribution. The impact of protein molecular structure and its charge polarization on the proton transport is considered in atomic details. We formulate a total free energy functional to include kinetic and potential energies of protons, as well as electrostatic energy of all other ions on an equal footing. For both nano-transistors and proton channels systems, the variational principle is employed to derive nonlinear governing equations. The Poisson-Kohn-Sham equations are derived for nano-transistors while the generalized Poisson-Boltzmann equation and Kohn-Sham equation are obtained for proton channels. Related numerical challenges in simulations are addressed: the matched interface and boundary (MIB) method, the Dirichlet-to-Neumann mapping (DNM) technique, and the Krylov subspace and preconditioner theory are introduced to improve the computational efficiency of the Poisson-type equation. The quantum transport theory is employed to solve the Kohn-Sham equation. The Gummel iteration and relaxation technique are utilized for overall self-consistent iterations. Finally, applications are considered and model validations are verified by realistic nano-transistors and transmembrane proteins. Two distinct device configurations, a double-gate MOSFET and a four-gate MOSFET, are considered in our threedimensional numerical simulations. For these devices, the current uctuation and voltage threshold lowering effect induced by discrete dopants are explored. For proton transport, a realistic channel protein, the Gramicidin A (GA) is used to demonstrate the performance of the proposed proton channel model and validate the efficiency of the proposed mathematical algorithms. The electrostatic characteristics of the GA channel is analyzed with a wide range of model parameters. Proton channel conductances are studied over a number of applied voltages and reference concentrations. Comparisons with experimental data are utilized to verify our model predictions.

General equations for the motions of ice crystals and water drops in gravitational and electric fields

NASA Technical Reports Server (NTRS)

Nisbet, John S.

1988-01-01

General equations for the Reynolds number of a variety of types of ice crystals and water drops are given in terms of the Davies, Bond, and Knudsen numbers. The equations are in terms of the basic physical parameters of the system and are valid for calculating velocities in gravitational and electric fields over a very wide range of sizes and atmospheric conditions. The equations are asymptotically matched at the bottom and top of the size spectrum, useful when checking large computer codes. A numerical system for specifying the dimensional properties of ice crystals is introduced. Within the limits imposed by such variables as particle density, which have large deviations, the accuracy of velocities appears to be within 10 percent over the entire range of sizes of interest.

Wigner distribution functions for complex dynamical systems: the emergence of the Wigner-Boltzmann equation.

PubMed

Sels, Dries; Brosens, Fons

2013-10-01

The equation of motion for the reduced Wigner function of a system coupled to an external quantum system is presented for the specific case when the external quantum system can be modeled as a set of harmonic oscillators. The result is derived from the Wigner function formulation of the Feynman-Vernon influence functional theory. It is shown how the true self-energy for the equation of motion is connected with the influence functional for the path integral. Explicit expressions are derived in terms of the bare Wigner propagator. Finally, we show under which approximations the resulting equation of motion reduces to the Wigner-Boltzmann equation.

Double absorbing boundaries for finite-difference time-domain electromagnetics

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

LaGrone, John, E-mail: jlagrone@smu.edu; Hagstrom, Thomas, E-mail: thagstrom@smu.edu

We describe the implementation of optimal local radiation boundary condition sequences for second order finite difference approximations to Maxwell's equations and the scalar wave equation using the double absorbing boundary formulation. Numerical experiments are presented which demonstrate that the design accuracy of the boundary conditions is achieved and, for comparable effort, exceeds that of a convolution perfectly matched layer with reasonably chosen parameters. An advantage of the proposed approach is that parameters can be chosen using an accurate a priori error bound.

The Role Of Neuropeptide Y (Npy) in Uncontrolled Alcohol Drinking and Relapse Behavior Resulting from Exposure to Stressful Events

DTIC Science & Technology

2009-01-01

as the pair-feeding procedure equated the volume of diet consumption between CD and ED groups, and because the CD and ED were calorically equated...there were no differences in caloric intake between groups given access to liquid diet . These observations reinforce the con- clusion the differences...group that received the CD versus the groups that received ED, and because caloric intake between diet groups were matched, reductions of a-MSH

Quality of life, activity impairment, and healthcare resource utilization associated with atrial fibrillation in the US National Health and Wellness Survey.

PubMed

Goren, Amir; Liu, Xianchen; Gupta, Shaloo; Simon, Teresa A; Phatak, Hemant

2013-01-01

This study builds upon current studies of atrial fibrillation (AF) and health outcomes by examining more comprehensively the humanistic burden of illness (quality of life, activity impairment, and healthcare resource utilization) among adult patients with AF, using a large, nationally representative sample and matched controls. Data were analyzed from the Internet-based 2009 US National Health and Wellness Survey. Outcomes were Mental and Physical Component Summary (MCS and PCS) and health utility scores from the SF-12, activity impairment, hospitalizations, and healthcare provider and emergency room (ER) visits. Patients with self-reported diagnosis of AF were matched randomly on age and gender with an equal number of respondents without AF. Generalized linear models examined outcomes as a function of AF vs. non-AF status, controlling for CHADS2 score, comorbidity counts, demographics, and clinical variables. Exploratory structural equation modeling assessed the above in an integrated model of humanistic burden. Mean age of AF patients (1,296 from a total sample of 75,000) was 64.9 years and 65.1% were male. Adjusting for covariates, compared with non-AF patients, AF patients had lower MCS, PCS, and utility scores, greater activity impairment (rate ratio = 1.26), more traditional provider visits (rate ratio = 1.43), and increased odds of ER visits (OR = 2.53) and hospitalizations (OR = 2.71). Exploratory structural equation modeling analyses revealed that persons with AF experienced a significantly higher overall humanistic burden. This study highlights and clarifies the substantial burden of AF and its implications for preparing efficacious AF management plans to address the imminent rise in prevalence.

Curved Displacement Transfer Functions for Geometric Nonlinear Large Deformation Structure Shape Predictions

NASA Technical Reports Server (NTRS)

Ko, William L.; Fleischer, Van Tran; Lung, Shun-Fat

2017-01-01

For shape predictions of structures under large geometrically nonlinear deformations, Curved Displacement Transfer Functions were formulated based on a curved displacement, traced by a material point from the undeformed position to deformed position. The embedded beam (depth-wise cross section of a structure along a surface strain-sensing line) was discretized into multiple small domains, with domain junctures matching the strain-sensing stations. Thus, the surface strain distribution could be described with a piecewise linear or a piecewise nonlinear function. The discretization approach enabled piecewise integrations of the embedded-beam curvature equations to yield the Curved Displacement Transfer Functions, expressed in terms of embedded beam geometrical parameters and surface strains. By entering the surface strain data into the Displacement Transfer Functions, deflections along each embedded beam can be calculated at multiple points for mapping the overall structural deformed shapes. Finite-element linear and nonlinear analyses of a tapered cantilever tubular beam were performed to generate linear and nonlinear surface strains and the associated deflections to be used for validation. The shape prediction accuracies were then determined by comparing the theoretical deflections with the finiteelement- generated deflections. The results show that the newly developed Curved Displacement Transfer Functions are very accurate for shape predictions of structures under large geometrically nonlinear deformations.

Variational Methods in Sensitivity Analysis and Optimization for Aerodynamic Applications

NASA Technical Reports Server (NTRS)

Ibrahim, A. H.; Hou, G. J.-W.; Tiwari, S. N. (Principal Investigator)

1996-01-01

Variational methods (VM) sensitivity analysis, which is the continuous alternative to the discrete sensitivity analysis, is employed to derive the costate (adjoint) equations, the transversality conditions, and the functional sensitivity derivatives. In the derivation of the sensitivity equations, the variational methods use the generalized calculus of variations, in which the variable boundary is considered as the design function. The converged solution of the state equations together with the converged solution of the costate equations are integrated along the domain boundary to uniquely determine the functional sensitivity derivatives with respect to the design function. The determination of the sensitivity derivatives of the performance index or functional entails the coupled solutions of the state and costate equations. As the stable and converged numerical solution of the costate equations with their boundary conditions are a priori unknown, numerical stability analysis is performed on both the state and costate equations. Thereafter, based on the amplification factors obtained by solving the generalized eigenvalue equations, the stability behavior of the costate equations is discussed and compared with the state (Euler) equations. The stability analysis of the costate equations suggests that the converged and stable solution of the costate equation is possible only if the computational domain of the costate equations is transformed to take into account the reverse flow nature of the costate equations. The application of the variational methods to aerodynamic shape optimization problems is demonstrated for internal flow problems at supersonic Mach number range. The study shows, that while maintaining the accuracy of the functional sensitivity derivatives within the reasonable range for engineering prediction purposes, the variational methods show a substantial gain in computational efficiency, i.e., computer time and memory, when compared with the finite difference sensitivity analysis.

Substrate-induced reduction of graphene thermal conductivity

NASA Astrophysics Data System (ADS)

Koniakhin, S. V.; Utesov, O. I.; Terterov, I. N.; Nalitov, A. V.

2017-01-01

We develop a theory of heat conductivity in supported graphene, accounting for coherent phonon scattering on disorder induced by an amorphous substrate. We derive spectra for in-plane and out-of-plane phonons in the framework of Green's function approach. The energy parameters of the theory are obtained using molecular dynamics simulations for graphene on a SiO2 substrate. The heat conductivity is calculated by the Boltzmann transport equation. We find that the interaction with the substrate drastically reduces the phonon lifetime and completely suppresses the contribution of flexural (ZA) phonons to the heat conductivity. As a result, the total heat conductivity is reduced by several times, which matches with the tendency observed in the available experimental data. The considered effect is important for managing the thermal properties of graphene-based electronic devices.

Statistical properties of Charney-Hasegawa-Mima zonal flows

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

Anderson, Johan, E-mail: anderson.johan@gmail.com; Botha, G. J. J.

2015-05-15

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

Stochastic thermodynamics of fluctuating density fields: Non-equilibrium free energy differences under coarse-graining

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

Leonard, T.; Lander, B.; Seifert, U.

2013-11-28

We discuss the stochastic thermodynamics of systems that are described by a time-dependent density field, for example, simple liquids and colloidal suspensions. For a time-dependent change of external parameters, we show that the Jarzynski relation connecting work with the change of free energy holds if the time evolution of the density follows the Kawasaki-Dean equation. Specifically, we study the work distributions for the compression and expansion of a two-dimensional colloidal model suspension implementing a practical coarse-graining scheme of the microscopic particle positions. We demonstrate that even if coarse-grained dynamics and density functional do not match, the fluctuation relations for themore » work still hold albeit for a different, apparent, change of free energy.« less

Error Control with Perfectly Matched Layer or Damping Layer Treatments for Computational Aeroacoustics with Jet Flows

NASA Technical Reports Server (NTRS)

Goodrich, John W.

2009-01-01

In this paper we show by means of numerical experiments that the error introduced in a numerical domain because of a Perfectly Matched Layer or Damping Layer boundary treatment can be controlled. These experimental demonstrations are for acoustic propagation with the Linearized Euler Equations with both uniform and steady jet flows. The propagating signal is driven by a time harmonic pressure source. Combinations of Perfectly Matched and Damping Layers are used with different damping profiles. These layer and profile combinations allow the relative error introduced by a layer to be kept as small as desired, in principle. Tradeoffs between error and cost are explored.

Easy method of matching fighter engine to airframe for use in aircraft engine design courses

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

Mattingly, J.D.

1989-01-01

The proper match of the engine(s) to the airframe affects both aircraft size and life cycle cost. A fast and straightforward method is developed and used for the matching of fighter engine(s) to airframes during conceptual design. A thrust-lapse equation is developed for the dual-spool, mixed-flow, afterburning turbofan type of engine based on the installation losses of 'Aircraft Engine Design' and the performance predictions of the cycle analysis programs ONX and OFFX. Using system performance requirements, the effects of aircraft thrust-to-weight, wing loading, and engine cycle on takeoff weight are analyzed and example design course results presented. 5 refs.

Fractional Poisson-Nernst-Planck Model for Ion Channels I: Basic Formulations and Algorithms.

PubMed

Chen, Duan

2017-11-01

In this work, we propose a fractional Poisson-Nernst-Planck model to describe ion permeation in gated ion channels. Due to the intrinsic conformational changes, crowdedness in narrow channel pores, binding and trapping introduced by functioning units of channel proteins, ionic transport in the channel exhibits a power-law-like anomalous diffusion dynamics. We start from continuous-time random walk model for a single ion and use a long-tailed density distribution function for the particle jump waiting time, to derive the fractional Fokker-Planck equation. Then, it is generalized to the macroscopic fractional Poisson-Nernst-Planck model for ionic concentrations. Necessary computational algorithms are designed to implement numerical simulations for the proposed model, and the dynamics of gating current is investigated. Numerical simulations show that the fractional PNP model provides a more qualitatively reasonable match to the profile of gating currents from experimental observations. Meanwhile, the proposed model motivates new challenges in terms of mathematical modeling and computations.

A reduced-order model from high-dimensional frictional hysteresis

PubMed Central

Biswas, Saurabh; Chatterjee, Anindya

2014-01-01

Hysteresis in material behaviour includes both signum nonlinearities as well as high dimensionality. Available models for component-level hysteretic behaviour are empirical. Here, we derive a low-order model for rate-independent hysteresis from a high-dimensional massless frictional system. The original system, being given in terms of signs of velocities, is first solved incrementally using a linear complementarity problem formulation. From this numerical solution, to develop a reduced-order model, basis vectors are chosen using the singular value decomposition. The slip direction in generalized coordinates is identified as the minimizer of a dissipation-related function. That function includes terms for frictional dissipation through signum nonlinearities at many friction sites. Luckily, it allows a convenient analytical approximation. Upon solution of the approximated minimization problem, the slip direction is found. A final evolution equation for a few states is then obtained that gives a good match with the full solution. The model obtained here may lead to new insights into hysteresis as well as better empirical modelling thereof. PMID:24910522

A simple low-computation-intensity model for approximating the distribution function of a sum of non-identical lognormals for financial applications

NASA Astrophysics Data System (ADS)

Messica, A.

2016-10-01

The probability distribution function of a weighted sum of non-identical lognormal random variables is required in various fields of science and engineering and specifically in finance for portfolio management as well as exotic options valuation. Unfortunately, it has no known closed form and therefore has to be approximated. Most of the approximations presented to date are complex as well as complicated for implementation. This paper presents a simple, and easy to implement, approximation method via modified moments matching and a polynomial asymptotic series expansion correction for a central limit theorem of a finite sum. The method results in an intuitively-appealing and computation-efficient approximation for a finite sum of lognormals of at least ten summands and naturally improves as the number of summands increases. The accuracy of the method is tested against the results of Monte Carlo simulationsand also compared against the standard central limit theorem andthe commonly practiced Markowitz' portfolio equations.

Integrable dissipative exclusion process: Correlation functions and physical properties

NASA Astrophysics Data System (ADS)

Crampe, N.; Ragoucy, E.; Rittenberg, V.; Vanicat, M.

2016-09-01

We study a one-parameter generalization of the symmetric simple exclusion process on a one-dimensional lattice. In addition to the usual dynamics (where particles can hop with equal rates to the left or to the right with an exclusion constraint), annihilation and creation of pairs can occur. The system is driven out of equilibrium by two reservoirs at the boundaries. In this setting the model is still integrable: it is related to the open XXZ spin chain through a gauge transformation. This allows us to compute the full spectrum of the Markov matrix using Bethe equations. We also show that the stationary state can be expressed in a matrix product form permitting to compute the multipoints correlation functions as well as the mean value of the lattice and the creation-annihilation currents. Finally, the variance of the lattice current is computed for a finite-size system. In the thermodynamic limit, it matches the value obtained from the associated macroscopic fluctuation theory.

Quantum-Inspired Maximizer

NASA Technical Reports Server (NTRS)

Zak, Michail

2008-01-01

A report discusses an algorithm for a new kind of dynamics based on a quantum- classical hybrid-quantum-inspired maximizer. The model is represented by a modified Madelung equation in which the quantum potential is replaced by different, specially chosen 'computational' potential. As a result, the dynamics attains both quantum and classical properties: it preserves superposition and entanglement of random solutions, while allowing one to measure its state variables, using classical methods. Such optimal combination of characteristics is a perfect match for quantum-inspired computing. As an application, an algorithm for global maximum of an arbitrary integrable function is proposed. The idea of the proposed algorithm is very simple: based upon the Quantum-inspired Maximizer (QIM), introduce a positive function to be maximized as the probability density to which the solution is attracted. Then the larger value of this function will have the higher probability to appear. Special attention is paid to simulation of integer programming and NP-complete problems. It is demonstrated that the problem of global maximum of an integrable function can be found in polynomial time by using the proposed quantum- classical hybrid. The result is extended to a constrained maximum with applications to integer programming and TSP (Traveling Salesman Problem).

Diffusion with Varying Drag; the Runaway Problem.

NASA Astrophysics Data System (ADS)

Rollins, David Kenneth

We study the motion of electrons in an ionized plasma of electrons and ions in an external electric field. A probability distribution function describes the electron motion and is a solution of a Fokker-Planck equation. In zero field, the solution approaches an equilibrium Maxwellian. For arbitrarily small field, electrons overcome the diffusive effects and are freely accelerated by the field. This is the electron runaway phenomenon. We treat the electric field as a small perturbation. We consider various diffusion coefficients for the one dimensional problem and determine the runaway current as a function of the field strength. Diffusion coefficients, non-zero on a finite interval are examined. Some non-trivial cases of these can be solved exactly in terms of known special functions. The more realistic case where the diffusion coefficient decays with velocity are then considered. To determine the runaway current, the equivalent Schrodinger eigenvalue problem is analysed. The smallest eigenvalue is shown to be equal to the runaway current. Using asymptotic matching a solution can be constructed which is then used to evaluate the runaway current. The runaway current is exponentially small as a function of field strength. This method is used to extract results from the three dimensional problem.

Enhancing the calculation accuracy of performance characteristics of power-generating units by correcting general measurands based on matching energy balances

NASA Astrophysics Data System (ADS)

Shchinnikov, P. A.; Safronov, A. V.

2014-12-01

General principles of a procedure for matching energy balances of thermal power plants (TPPs), whose use enhances the accuracy of information-measuring systems (IMSs) during calculations of performance characteristics (PCs), are stated. To do this, there is the possibility for changing values of measured and calculated variables within intervals determined by measurement errors and regulations. An example of matching energy balances of the thermal power plants with a T-180 turbine is made. The proposed procedure allows one to reduce the divergence of balance equations by 3-4 times. It is shown also that the equipment operation mode affects the profit deficiency. Dependences for the divergence of energy balances on the deviation of input parameters and calculated data for the fuel economy before and after matching energy balances are represented.

Computation of shear-induced collective-diffusivity in emulsions

NASA Astrophysics Data System (ADS)

Malipeddi, Abhilash Reddy; Sarkar, Kausik

2017-11-01

The shear-induced collective-diffusivity of drops in an emulsion is calculated through simulation. A front-tracking finite difference method is used to integrate the Navier-Stokes equations. When a cloud of drops is subjected to shear flow, after a certain time, the width of the cloud increases with the 1/3 power of time. This scaling of drop-cloud-width with time is characteristic of (sub-)diffusion that arises from irreversible two-drop interactions. The collective diffusivity is calculated from this relationship. A feature of the procedure adopted here is the modest computational requirement, wherein, a few drops ( 70) in shear for short time ( 70 strain) is found to be sufficient to get a good estimate. As far as we know, collective-diffusivity has not been calculated for drops through simulation till now. The computed values match with experimental measurements reported in the literature. The diffusivity in emulsions is calculated for a range of Capillary (Ca) and Reynolds (Re) numbers. It is found to be a unimodal function of Ca , similar to self-diffusivity. A sub-linear increase of the diffusivity with Re is seen for Re < 5 . This work has been limited to a viscosity matched case.

Hypergeometric Equation in Modeling Relativistic Isotropic Sphere

NASA Astrophysics Data System (ADS)

Thirukkanesh, S.; Ragel, F. C.

2014-04-01

We study the Einstein system of equations in static spherically symmetric spacetimes. We obtained classes of exact solutions to the Einstein system by transforming the condition for pressure isotropy to a hypergeometric equation choosing a rational form for one of the gravitational potentials. The solutions are given in simple form that is a desirable requisite to study the behavior of relativistic compact objects in detail. A physical analysis indicate that our models satisfy all the fundamental requirements of realistic star and match smoothly with the exterior Schwarzschild metric. The derived masses and densities are consistent with the previously reported experimental and theoretical studies describing strange stars. The models satisfy the standard energy conditions required by normal matter.

A Zonal Approach for Prediction of Jet Noise

NASA Technical Reports Server (NTRS)

Shih, S. H.; Hixon, D. R.; Mankbadi, Reda R.

1995-01-01

A zonal approach for direct computation of sound generation and propagation from a supersonic jet is investigated. The present work splits the computational domain into a nonlinear, acoustic-source regime and a linear acoustic wave propagation regime. In the nonlinear regime, the unsteady flow is governed by the large-scale equations, which are the filtered compressible Navier-Stokes equations. In the linear acoustic regime, the sound wave propagation is described by the linearized Euler equations. Computational results are presented for a supersonic jet at M = 2. 1. It is demonstrated that no spurious modes are generated in the matching region and the computational expense is reduced substantially as opposed to fully large-scale simulation.

Lump solutions to nonlinear partial differential equations via Hirota bilinear forms

NASA Astrophysics Data System (ADS)

Ma, Wen-Xiu; Zhou, Yuan

2018-02-01

Lump solutions are analytical rational function solutions localized in all directions in space. We analyze a class of lump solutions, generated from quadratic functions, to nonlinear partial differential equations. The basis of success is the Hirota bilinear formulation and the primary object is the class of positive multivariate quadratic functions. A complete determination of quadratic functions positive in space and time is given, and positive quadratic functions are characterized as sums of squares of linear functions. Necessary and sufficient conditions for positive quadratic functions to solve Hirota bilinear equations are presented, and such polynomial solutions yield lump solutions to nonlinear partial differential equations under the dependent variable transformations u = 2(ln ⁡ f) x and u = 2(ln ⁡ f) xx, where x is one spatial variable. Applications are made for a few generalized KP and BKP equations.

Smoothing and Equating Methods Applied to Different Types of Test Score Distributions and Evaluated with Respect to Multiple Equating Criteria. Research Report. ETS RR-11-20

ERIC Educational Resources Information Center

Moses, Tim; Liu, Jinghua

2011-01-01

In equating research and practice, equating functions that are smooth are typically assumed to be more accurate than equating functions with irregularities. This assumption presumes that population test score distributions are relatively smooth. In this study, two examples were used to reconsider common beliefs about smoothing and equating. The…

Numerical Modeling of Coupled Water Flow and Heat Transport in Soil and Snow

NASA Astrophysics Data System (ADS)

Kelleners, T.

2015-12-01

A numerical model is developed to calculate coupled water flow and heat transport in seasonally frozen soil and snow. Both liquid water flow and water vapor flow are included. The effect of dissolved ions on soil water freezing point depression is included by combining an expression for osmotic head with the Clapeyron equation and the van Genuchten soil water retention function. The coupled water flow and heat transport equations are solved using the Thomas algorithm and Picard iteration. Ice pressure is always assumed zero and frost heave is neglected. The new model is tested using data from a high-elevation rangeland soil that is subject to significant soil freezing and a mountainous forest soil that is snow-covered for about 8 months of the year. Soil hydraulic parameters are mostly based on measurements and only vegetation parameters are fine-tuned to match measured and calculated soil water content, soil & snow temperature, and snow height. Modeling statistics for both systems show good performance for temperature, intermediate performance for snow height, and relatively low performance for soil water content, in accordance with earlier results with an older version of the model.

A first-order k-space model for elastic wave propagation in heterogeneous media.

PubMed

Firouzi, K; Cox, B T; Treeby, B E; Saffari, N

2012-09-01

A pseudospectral model of linear elastic wave propagation is described based on the first order stress-velocity equations of elastodynamics. k-space adjustments to the spectral gradient calculations are derived from the dyadic Green's function solution to the second-order elastic wave equation and used to (a) ensure the solution is exact for homogeneous wave propagation for timesteps of arbitrarily large size, and (b) also allows larger time steps without loss of accuracy in heterogeneous media. The formulation in k-space allows the wavefield to be split easily into compressional and shear parts. A perfectly matched layer (PML) absorbing boundary condition was developed to effectively impose a radiation condition on the wavefield. The staggered grid, which is essential for accurate simulations, is described, along with other practical details of the implementation. The model is verified through comparison with exact solutions for canonical examples and further examples are given to show the efficiency of the method for practical problems. The efficiency of the model is by virtue of the reduced point-per-wavelength requirement, the use of the fast Fourier transform (FFT) to calculate the gradients in k space, and larger time steps made possible by the k-space adjustments.

Transmitter and receiver antenna gain analysis for laser radar and communication systems

NASA Technical Reports Server (NTRS)

Klein, B. J.; Degnan, J. J.

1973-01-01

A comprehensive and fairly self-contained study of centrally obscured optical transmitting and receiving antennas is presented and is intended for use by the laser radar and communication systems designer. The material is presented in a format which allows the rapid and accurate evaluation of antenna gain. The Fresnel approximation to scalar wave theory is reviewed and the antenna analysis proceeds in terms of the power gain. Conventional range equations may then be used to calculate the power budget. The transmitter calculations, resulting in near and far field antenna gain patterns, assumes the antenna is illuminated by a laser operating in the fundamental cavity mode. A simple equation is derived for matching the incident source distribution to a general antenna configuration for maximum on-axis gain. An interpretation of the resultant gain curves allows a number of auxiliary design curves to be drawn which display the losses in antenna gain due to pointing errors and the cone angle of the outgoing beam as a function of antenna size and central obscuration. The use of telescope defocusing as an approach to spreading the beam for target acquisition is compared to some alternate methods.

Coupled double-distribution-function lattice Boltzmann method for the compressible Navier-Stokes equations.

PubMed

Li, Q; He, Y L; Wang, Y; Tao, W Q

2007-11-01

A coupled double-distribution-function lattice Boltzmann method is developed for the compressible Navier-Stokes equations. Different from existing thermal lattice Boltzmann methods, this method can recover the compressible Navier-Stokes equations with a flexible specific-heat ratio and Prandtl number. In the method, a density distribution function based on a multispeed lattice is used to recover the compressible continuity and momentum equations, while the compressible energy equation is recovered by an energy distribution function. The energy distribution function is then coupled to the density distribution function via the thermal equation of state. In order to obtain an adjustable specific-heat ratio, a constant related to the specific-heat ratio is introduced into the equilibrium energy distribution function. Two different coupled double-distribution-function lattice Boltzmann models are also proposed in the paper. Numerical simulations are performed for the Riemann problem, the double-Mach-reflection problem, and the Couette flow with a range of specific-heat ratios and Prandtl numbers. The numerical results are found to be in excellent agreement with analytical and/or other solutions.

Estimating Soil Hydraulic Parameters using Gradient Based Approach

NASA Astrophysics Data System (ADS)

Rai, P. K.; Tripathi, S.

2017-12-01

The conventional way of estimating parameters of a differential equation is to minimize the error between the observations and their estimates. The estimates are produced from forward solution (numerical or analytical) of differential equation assuming a set of parameters. Parameter estimation using the conventional approach requires high computational cost, setting-up of initial and boundary conditions, and formation of difference equations in case the forward solution is obtained numerically. Gaussian process based approaches like Gaussian Process Ordinary Differential Equation (GPODE) and Adaptive Gradient Matching (AGM) have been developed to estimate the parameters of Ordinary Differential Equations without explicitly solving them. Claims have been made that these approaches can straightforwardly be extended to Partial Differential Equations; however, it has been never demonstrated. This study extends AGM approach to PDEs and applies it for estimating parameters of Richards equation. Unlike the conventional approach, the AGM approach does not require setting-up of initial and boundary conditions explicitly, which is often difficult in real world application of Richards equation. The developed methodology was applied to synthetic soil moisture data. It was seen that the proposed methodology can estimate the soil hydraulic parameters correctly and can be a potential alternative to the conventional method.

A procedure to construct exact solutions of nonlinear fractional differential equations.

PubMed

Güner, Özkan; Cevikel, Adem C

2014-01-01

We use the fractional transformation to convert the nonlinear partial fractional differential equations with the nonlinear ordinary differential equations. The Exp-function method is extended to solve fractional partial differential equations in the sense of the modified Riemann-Liouville derivative. We apply the Exp-function method to the time fractional Sharma-Tasso-Olver equation, the space fractional Burgers equation, and the time fractional fmKdV equation. As a result, we obtain some new exact solutions.

Increased Cortical Activity in Binge Drinkers during Working Memory Task: A Preliminary Assessment through a Functional Magnetic Resonance Imaging Study

PubMed Central

Campanella, Salvatore; Peigneux, Philippe; Petit, Géraldine; Lallemand, Frédéric; Saeremans, Mélanie; Noël, Xavier; Metens, Thierry; Nouali, Mustapha; De Tiège, Xavier; De Witte, Philippe; Ward, Roberta; Verbanck, Paul

2013-01-01

Background Cerebral dysfunction is a common feature of both chronic alcohol abusers and binge drinkers. Here, we aimed to study whether, at equated behavioral performance levels, binge drinkers exhibited increased neural activity while performing simple cognitive tasks. Methods Thirty-two participants (16 binge drinkers and 16 matched controls) were scanned using functional magnetic resonance imaging (fMRI) while performing an n-back working memory task. In the control zero-back (N0) condition, subjects were required to press a button with the right hand when the number “2″ was displayed. In the two-back (N2) condition, subjects had to press a button when the displayed number was identical to the number shown two trials before. Results fMRI analyses revealed higher bilateral activity in the pre-supplementary motor area in binge drinkers than matched controls, even though behavioral performances were similar. Moreover, binge drinkers showed specific positive correlations between the number of alcohol doses consumed per occasion and higher activity in the dorsomedial prefrontal cortex, as well as between the number of drinking occasions per week and higher activity in cerebellum, thalamus and insula while performing the N2 memory task. Conclusions Binge alcohol consumption leads to possible compensatory cerebral changes in binge drinkers that facilitate normal behavioral performance. These changes in cerebral responses may be considered as vulnerability factors for developing adult substance use disorders. PMID:23638017

Iohexol clearance is superior to creatinine-based renal function estimating equations in detecting short-term renal function decline in chronic heart failure.

PubMed

Cvan Trobec, Katja; Kerec Kos, Mojca; von Haehling, Stephan; Anker, Stefan D; Macdougall, Iain C; Ponikowski, Piotr; Lainscak, Mitja

2015-12-01

To compare the performance of iohexol plasma clearance and creatinine-based renal function estimating equations in monitoring longitudinal renal function changes in chronic heart failure (CHF) patients, and to assess the effects of body composition on the equation performance. Iohexol plasma clearance was measured in 43 CHF patients at baseline and after at least 6 months. Simultaneously, renal function was estimated with five creatinine-based equations (four- and six-variable Modification of Diet in Renal Disease, Cockcroft-Gault, Cockcroft-Gault adjusted for lean body mass, Chronic Kidney Disease Epidemiology Collaboration equation) and body composition was assessed using bioimpedance and dual-energy x-ray absorptiometry. Over a median follow-up of 7.5 months (range 6-17 months), iohexol clearance significantly declined (52.8 vs 44.4 mL/[min ×1.73 m2], P=0.001). This decline was significantly higher in patients receiving mineralocorticoid receptor antagonists at baseline (mean decline -22% of baseline value vs -3%, P=0.037). Mean serum creatinine concentration did not change significantly during follow-up and no creatinine-based renal function estimating equation was able to detect the significant longitudinal decline of renal function determined by iohexol clearance. After accounting for body composition, the accuracy of the equations improved, but not their ability to detect renal function decline. Renal function measured with iohexol plasma clearance showed relevant decline in CHF patients, particularly in those treated with mineralocorticoid receptor antagonists. None of the equations for renal function estimation was able to detect these changes. ClinicalTrials.gov registration number: NCT01829880.

The Matching Law

ERIC Educational Resources Information Center

Poling, Alan; Edwards, Timothy L.; Weeden, Marc; Foster, T. Mary

2011-01-01

This article introduces the quantitative analysis of choice behavior by describing a number of equations developed over the years to describe the relation between the allocation of behavior under concurrent schedules of reinforcement and the consequences received for alternative responses. Direct proportionality between rate of responding and rate…

Admitting the Inadmissible: Adjoint Formulation for Incomplete Cost Functionals in Aerodynamic Optimization

NASA Technical Reports Server (NTRS)

Arian, Eyal; Salas, Manuel D.

1997-01-01

We derive the adjoint equations for problems in aerodynamic optimization which are improperly considered as "inadmissible." For example, a cost functional which depends on the density, rather than on the pressure, is considered "inadmissible" for an optimization problem governed by the Euler equations. We show that for such problems additional terms should be included in the Lagrangian functional when deriving the adjoint equations. These terms are obtained from the restriction of the interior PDE to the control surface. Demonstrations of the explicit derivation of the adjoint equations for "inadmissible" cost functionals are given for the potential, Euler, and Navier-Stokes equations.

A Computer Aided Broad Band Impedance Matching Technique Using a Comparison Reflectometer. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Gordy, R. S.

1972-01-01

An improved broadband impedance matching technique was developed. The technique is capable of resolving points in the waveguide which generate reflected energy. A version of the comparison reflectometer was developed and fabricated to determine the mean amplitude of the reflection coefficient excited at points in the guide as a function of distance, and the complex reflection coefficient of a specific discontinuity in the guide as a function of frequency. An impedance matching computer program was developed which is capable of impedance matching the characteristics of each disturbance independent of other reflections in the guide. The characteristics of four standard matching elements were compiled, and their associated curves of reflection coefficient and shunt susceptance as a function of frequency are presented. It is concluded that an economical, fast, and reliable impedance matching technique has been established which can provide broadband impedance matches.

Second order Method for Solving 3D Elasticity Equations with Complex Interfaces

PubMed Central

Wang, Bao; Xia, Kelin; Wei, Guo-Wei

2015-01-01

Elastic materials are ubiquitous in nature and indispensable components in man-made devices and equipments. When a device or equipment involves composite or multiple elastic materials, elasticity interface problems come into play. The solution of three dimensional (3D) elasticity interface problems is significantly more difficult than that of elliptic counterparts due to the coupled vector components and cross derivatives in the governing elasticity equation. This work introduces the matched interface and boundary (MIB) method for solving 3D elasticity interface problems. The proposed MIB elasticity interface scheme utilizes fictitious values on irregular grid points near the material interface to replace function values in the discretization so that the elasticity equation can be discretized using the standard finite difference schemes as if there were no material interface. The interface jump conditions are rigorously enforced on the intersecting points between the interface and the mesh lines. Such an enforcement determines the fictitious values. A number of new techniques has been developed to construct efficient MIB elasticity interface schemes for dealing with cross derivative in coupled governing equations. The proposed method is extensively validated over both weak and strong discontinuity of the solution, both piecewise constant and position-dependent material parameters, both smooth and nonsmooth interface geometries, and both small and large contrasts in the Poisson’s ratio and shear modulus across the interface. Numerical experiments indicate that the present MIB method is of second order convergence in both L∞ and L2 error norms for handling arbitrarily complex interfaces, including biomolecular surfaces. To our best knowledge, this is the first elasticity interface method that is able to deliver the second convergence for the molecular surfaces of proteins.. PMID:25914422

A Procedure to Construct Exact Solutions of Nonlinear Fractional Differential Equations

PubMed Central

Güner, Özkan; Cevikel, Adem C.

2014-01-01

We use the fractional transformation to convert the nonlinear partial fractional differential equations with the nonlinear ordinary differential equations. The Exp-function method is extended to solve fractional partial differential equations in the sense of the modified Riemann-Liouville derivative. We apply the Exp-function method to the time fractional Sharma-Tasso-Olver equation, the space fractional Burgers equation, and the time fractional fmKdV equation. As a result, we obtain some new exact solutions. PMID:24737972

Effect of casing yield stress on bomb blast impulse

NASA Astrophysics Data System (ADS)

Hutchinson, M. D.

2012-08-01

An equation to predict blast effects from cased charges was first proposed by U. Fano in 1944 and revised by E.M. Fisher in 1953 [1]. Fisher's revision provides much better matches to available blast impulse data, but still requires empirical parameter adjustments. A new derivation [2], based on the work of R.W. Gurney [3] and G.I. Taylor [4], has resulted in an equation which nearly matches experimental data. This new analytical model is also capable of being extended, through the incorporation of additional physics, such as the effects of early case fracture, finite casing thickness, casing metal strain energy dissipation, explosive gas escape through casing fractures and the comparative dynamics of blast wave and metal fragment impacts. This paper will focus on the choice of relevant case fracture strain criterion, as it will be shown that this allows the explicit inclusion of the dynamic properties of the explosive and casing metal. It will include a review and critique of the most significant earlier work on this topic, contained in a paper by Hoggatt and Recht [5]. Using this extended analytical model, good matches can readily be made to available free-field blast impulse data, without any empirical adjustments being needed. Further work will be required to apply this model to aluminised and other highly oxygen-deficient explosives.

Liquid film drag out in the presence of molecular forces

NASA Astrophysics Data System (ADS)

Schmidhalter, I.; Cerro, R. L.; Giavedoni, M. D.; Saita, F. A.

2013-03-01

From a practical as well as a conceptual point of view, one of the most interesting problems of physicochemical hydrodynamics is the drag out of a liquid film by a moving solid out of a pool of liquid. The basic problem, sometimes denoted the Landau-Levich problem [L. Landau and B. Levich, "Dragging of a liquid by a moving plate," Acta Physicochim. USSR 17, 42-54 (1942)], involves an interesting blend of capillary and viscous forces plus a matching of the static solution for capillary rise with a numerical solution of the film evolution equation, neglecting gravity, on the downstream region of the flow field. The original solution describes experimental data for a wide range of Capillary numbers but fails to match results for large and very small Capillary numbers. Molecular level forces are introduced to create an augmented version of the film evolution equation to show the effect of van der Waals forces at the lower range of Capillary numbers. A closed form solution for static capillary rise, including molecular forces, was matched with a numerical solution of the augmented film evolution equation in the dynamic meniscus region. Molecular forces do not sensibly modify the static capillary rise region, since film thicknesses are larger than the range of influence of van der Waals forces, but are determinant in shaping the downstream dynamic meniscus of the very thin liquid films. As expected, a quantitatively different level of disjoining pressure for different values of molecular constants remains in the very thin liquid film far downstream. Computational results for a wide range of Capillary numbers and Hamaker constants show a clear transition towards a region where the film thickness becomes independent of the coating speed.

Quantum Dynamics with Short-Time Trajectories and Minimal Adaptive Basis Sets.

PubMed

Saller, Maximilian A C; Habershon, Scott

2017-07-11

Methods for solving the time-dependent Schrödinger equation via basis set expansion of the wave function can generally be categorized as having either static (time-independent) or dynamic (time-dependent) basis functions. We have recently introduced an alternative simulation approach which represents a middle road between these two extremes, employing dynamic (classical-like) trajectories to create a static basis set of Gaussian wavepackets in regions of phase-space relevant to future propagation of the wave function [J. Chem. Theory Comput., 11, 8 (2015)]. Here, we propose and test a modification of our methodology which aims to reduce the size of basis sets generated in our original scheme. In particular, we employ short-time classical trajectories to continuously generate new basis functions for short-time quantum propagation of the wave function; to avoid the continued growth of the basis set describing the time-dependent wave function, we employ Matching Pursuit to periodically minimize the number of basis functions required to accurately describe the wave function. Overall, this approach generates a basis set which is adapted to evolution of the wave function while also being as small as possible. In applications to challenging benchmark problems, namely a 4-dimensional model of photoexcited pyrazine and three different double-well tunnelling problems, we find that our new scheme enables accurate wave function propagation with basis sets which are around an order-of-magnitude smaller than our original trajectory-guided basis set methodology, highlighting the benefits of adaptive strategies for wave function propagation.

A computer program to obtain time-correlated gust loads for nonlinear aircraft using the matched-filter-based method

NASA Technical Reports Server (NTRS)

Scott, Robert C.; Pototzky, Anthony S.; Perry, Boyd, III

1994-01-01

NASA Langley Research Center has, for several years, conducted research in the area of time-correlated gust loads for linear and nonlinear aircraft. The results of this work led NASA to recommend that the Matched-Filter-Based One-Dimensional Search Method be used for gust load analyses of nonlinear aircraft. This manual describes this method, describes a FORTRAN code which performs this method, and presents example calculations for a sample nonlinear aircraft model. The name of the code is MFD1DS (Matched-Filter-Based One-Dimensional Search). The program source code, the example aircraft equations of motion, a sample input file, and a sample program output are all listed in the appendices.

Psychophysical correspondence between vibrotactile intensity and intracortical microstimulation for tactile neuroprostheses in rats

NASA Astrophysics Data System (ADS)

Devecioğlu, İsmail; Güçlü, Burak

2017-02-01

Objective. Recent studies showed that intracortical microstimulation (ICMS) generates artificial sensations which can be utilized as somatosensory feedback in cortical neuroprostheses. To mimic the natural psychophysical response, ICMS parameters are modulated according to psychometric equivalence functions (PEFs). PEFs match the intensity levels of ICMS and mechanical stimuli, which elicit equal detection probabilities, but they typically do not include the frequency as a control variable. We aimed to establish frequency-dependent PEFs for vibrotactile stimulation of the glabrous skin and ICMS in the primary somatosensory cortex of awake freely behaving rats. Approach. We collected psychometric data for vibrotactile and ICMS detection at three stimulation frequencies (40, 60 and 80 Hz). The psychometric data were fitted with a model equation of two independent variables (stimulus intensity and frequency) and four subject-dependent parameters. For each rat, we constructed a separate PEF which was used to estimate the ICMS current amplitude for a given displacement amplitude and frequency. The ICMS frequency was set equal to the vibrotactile frequency. We validated the PEFs in a modified task which included randomly selected probe trials presented either with a vibrotactile or an ICMS stimulus, and also at frequencies and intensity levels not tested before. Main results. The PEFs were generally successful in estimating the ICMS current intensities (no significant differences between vibrotactile and ICMS trials in Kolmogorov-Smirnov tests). Specifically, hit rates from both trial conditions were significantly correlated in 86% of the cases, and 52% of all data had perfect match in linear regression. Significance. The psychometric correspondence model presented in this study was constructed based on surface functions which define psychophysical detection probability as a function of stimulus intensity and frequency. Therefore, it may be used for the real-time modulation of the frequency and intensity of ICMS pulses in somatosensory neuroprostheses.

Psychophysical correspondence between vibrotactile intensity and intracortical microstimulation for tactile neuroprostheses in rats.

PubMed

Devecioğlu, İsmail; Güçlü, Burak

2017-02-01

Recent studies showed that intracortical microstimulation (ICMS) generates artificial sensations which can be utilized as somatosensory feedback in cortical neuroprostheses. To mimic the natural psychophysical response, ICMS parameters are modulated according to psychometric equivalence functions (PEFs). PEFs match the intensity levels of ICMS and mechanical stimuli, which elicit equal detection probabilities, but they typically do not include the frequency as a control variable. We aimed to establish frequency-dependent PEFs for vibrotactile stimulation of the glabrous skin and ICMS in the primary somatosensory cortex of awake freely behaving rats. We collected psychometric data for vibrotactile and ICMS detection at three stimulation frequencies (40, 60 and 80 Hz). The psychometric data were fitted with a model equation of two independent variables (stimulus intensity and frequency) and four subject-dependent parameters. For each rat, we constructed a separate PEF which was used to estimate the ICMS current amplitude for a given displacement amplitude and frequency. The ICMS frequency was set equal to the vibrotactile frequency. We validated the PEFs in a modified task which included randomly selected probe trials presented either with a vibrotactile or an ICMS stimulus, and also at frequencies and intensity levels not tested before. The PEFs were generally successful in estimating the ICMS current intensities (no significant differences between vibrotactile and ICMS trials in Kolmogorov-Smirnov tests). Specifically, hit rates from both trial conditions were significantly correlated in 86% of the cases, and 52% of all data had perfect match in linear regression. The psychometric correspondence model presented in this study was constructed based on surface functions which define psychophysical detection probability as a function of stimulus intensity and frequency. Therefore, it may be used for the real-time modulation of the frequency and intensity of ICMS pulses in somatosensory neuroprostheses.

Nonlinear inhomogeneous Fokker-Planck equations: Entropy and free-energy time evolution.

PubMed

Sicuro, Gabriele; Rapčan, Peter; Tsallis, Constantino

2016-12-01

We extend a recently introduced free-energy formalism for homogeneous Fokker-Planck equations to a wide, and physically appealing, class of inhomogeneous nonlinear Fokker-Planck equations. In our approach, the free-energy functional is expressed in terms of an entropic functional and an auxiliary potential, both derived from the coefficients of the equation. With reference to the introduced entropic functional, we discuss the entropy production in a relaxation process towards equilibrium. The properties of the stationary solutions of the considered Fokker-Planck equations are also discussed.

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.

Some Theoretical Aspects of Nonzero Sum Differential Games and Applications to Combat Problems

DTIC Science & Technology

1971-06-01

the Equilibrium Solution . 7 Hamilton-Jacobi-Bellman Partial Differential Equations ............. .............. 9 Influence Function Differential...Linearly .......... ............ 18 Problem Statement .......... ............ 18 Formulation of LJB Equations, Influence Function Equations and the TPBVP...19 Control Lawe . . .. ...... ........... 21 Conditions for Influence Function Continuity along Singular Surfaces

Quantum dynamics in continuum for proton transport II: Variational solvent-solute interface.

PubMed

Chen, Duan; Chen, Zhan; Wei, Guo-Wei

2012-01-01

Proton transport plays an important role in biological energy transduction and sensory systems. Therefore, it has attracted much attention in biological science and biomedical engineering in the past few decades. The present work proposes a multiscale/multiphysics model for the understanding of the molecular mechanism of proton transport in transmembrane proteins involving continuum, atomic, and quantum descriptions, assisted with the evolution, formation, and visualization of membrane channel surfaces. We describe proton dynamics quantum mechanically via a new density functional theory based on the Boltzmann statistics, while implicitly model numerous solvent molecules as a dielectric continuum to reduce the number of degrees of freedom. The density of all other ions in the solvent is assumed to obey the Boltzmann distribution in a dynamic manner. The impact of protein molecular structure and its charge polarization on the proton transport is considered explicitly at the atomic scale. A variational solute-solvent interface is designed to separate the explicit molecule and implicit solvent regions. We formulate a total free-energy functional to put proton kinetic and potential energies, the free energy of all other ions, and the polar and nonpolar energies of the whole system on an equal footing. The variational principle is employed to derive coupled governing equations for the proton transport system. Generalized Laplace-Beltrami equation, generalized Poisson-Boltzmann equation, and generalized Kohn-Sham equation are obtained from the present variational framework. The variational solvent-solute interface is generated and visualized to facilitate the multiscale discrete/continuum/quantum descriptions. Theoretical formulations for the proton density and conductance are constructed based on fundamental laws of physics. A number of mathematical algorithms, including the Dirichlet-to-Neumann mapping, matched interface and boundary method, Gummel iteration, and Krylov space techniques are utilized to implement the proposed model in a computationally efficient manner. The gramicidin A channel is used to validate the performance of the proposed proton transport model and demonstrate the efficiency of the proposed mathematical algorithms. The proton channel conductances are studied over a number of applied voltages and reference concentrations. A comparison with experimental data verifies the present model predictions and confirms the proposed model. Copyright © 2011 John Wiley & Sons, Ltd.

Radiation Boundary Conditions for Maxwell’s Equations: A Review of Accurate Time-Domain Formulations

DTIC Science & Technology

2007-01-01

conditions have only been constructed for the case ne = 0. Lastly we note that exact reflection formulas have recently been derived by Diaz and Joly [20, 21...SIAM J. Numer. Anal. 41 (2003), 287–305. 6. E. Bécache and P. Joly , On the analysis of Bérenger’s perfectly matched layers for Maxwell’s equations...Computational Wave Propagation (M. Ainsworth, P. Davies, D. Duncan, P. Martin , and B. Rynne, eds.), Springer-Verlag, 2003, pp. 43–82. 13. O. Bruno and D. Hoch

Resonance fluorescence in the resolvent-operator formalism

NASA Astrophysics Data System (ADS)

Debierre, V.; Harman, Z.

2017-10-01

The Mollow spectrum for the light scattered by a driven two-level atom is derived in the resolvent operator formalism. The derivation is based on the construction of a master equation from the resolvent operator of the atom-field system. We show that the natural linewidth of the excited atomic level remains essentially unmodified, to a very good level of approximation, even in the strong-field regime, where Rabi flopping becomes relevant inside the self-energy loop that yields the linewidth. This ensures that the obtained master equation and the spectrum derived matches that of Mollow.

On numerical solution of the Schrödinger equation: the shooting method revisited

NASA Astrophysics Data System (ADS)

Indjin, D.; Todorović, G.; Milanović, V.; Ikonić, Z.

1995-09-01

An alternative formulation of the "shooting" method for a numerical solution of the Schrödinger equation is described for cases of general asymmetric one-dimensional potential (planar geometry), and spherically symmetric potential. The method relies on matching the asymptotic wavefunctions and the potential core region wavefunctions, in course of finding bound states energies. It is demonstrated in the examples of Morse and Kratzer potentials, where a high accuracy of the calculated eigenvalues is found, together with a considerable saving of the computation time.

Tunnelling from non-localised initial states

NASA Technical Reports Server (NTRS)

Bowcock, Peter; Gregory, Ruth

1991-01-01

An approach for calculating tunneling amplitudes from a nonlocalized initial state is presented. Generalizing the matching conditions and equations of motion to allow for complex momentum permits a description of tunneling in the presence of so-called classical motion. Possible applications of the method are presented.

A counter-rotating vortex pair in inviscid fluid

NASA Astrophysics Data System (ADS)

Habibah, Ummu; Fukumoto, Yasuhide

2017-12-01

We study the motion of a counter-rotating vortex pair with the circulations ±Γ move in incompressible fluid. The assumption is made that the core is very thin, that is the core radius σ is much smaller than the vortex radius d such that ɛ = σ/d ≪ 1. With this condition, the method of matched asymptotic expansion is employed. The solutions of the Navier-Stokes equations and the Biot-Savart law, regarding the inner and outer solutions respectively, are constructed in the form of a small parameter. An asymptotic expansion of the Biot-Savart law near the vortex core provides with the matching condition for an asymptotic expansion for limiting the Navier-Stokes equations for large radius r. The general formula of an anti-parallel vortex pair is established. At leading order O(ɛ0), we apply the special case in inviscid fluid, the Rankine vortex, a circular vortex of uniform vorticity. Furthermore at leading order O(ɛ5) we show the traveling speed of a vortex pair.

Efficient parallel resolution of the simplified transport equations in mixed-dual formulation

NASA Astrophysics Data System (ADS)

Barrault, M.; Lathuilière, B.; Ramet, P.; Roman, J.

2011-03-01

A reactivity computation consists of computing the highest eigenvalue of a generalized eigenvalue problem, for which an inverse power algorithm is commonly used. Very fine modelizations are difficult to treat for our sequential solver, based on the simplified transport equations, in terms of memory consumption and computational time. A first implementation of a Lagrangian based domain decomposition method brings to a poor parallel efficiency because of an increase in the power iterations [1]. In order to obtain a high parallel efficiency, we improve the parallelization scheme by changing the location of the loop over the subdomains in the overall algorithm and by benefiting from the characteristics of the Raviart-Thomas finite element. The new parallel algorithm still allows us to locally adapt the numerical scheme (mesh, finite element order). However, it can be significantly optimized for the matching grid case. The good behavior of the new parallelization scheme is demonstrated for the matching grid case on several hundreds of nodes for computations based on a pin-by-pin discretization.

H-mode transitions and limit cycle oscillations from mean field transport equations

DOE PAGES

Staebler, Gary M.; Groebner, Richard J.

2014-11-28

The mean field toroidal and parallel momentum transport equations will be shown to admit both onestep transitions to suppressed transport (L/H) and limit cycle oscillations (LCO). Both types of transitions are driven by the suppression of turbulence by the mean field ExB velocity shear. Using experimental data to evaluate the coefficients of a reduced transport model, the observed frequency of the LCO can be matched. The increase in the H-mode power threshold above and below a minimum density agrees with the trends in the model. Both leading and lagging phase relations between the turbulent density fluctuation amplitude and the ExBmore » velocity shear can occur depending on the evolution of the linear growth rate of the turbulence. As a result, the transport solutions match the initial phase of the L/H transition where the poloidal and ExB velocities are observed to change, and the density fluctuations drop, faster than the diamagnetic velocity.« less

The Matching Relation and Situation-Specific Bias Modulation in Professional Football Play Selection

PubMed Central

Stilling, Stephanie T; Critchfield, Thomas S

2010-01-01

The utility of a quantitative model depends on the extent to which its fitted parameters vary systematically with environmental events of interest. Professional football statistics were analyzed to determine whether play selection (passing versus rushing plays) could be accounted for with the generalized matching equation, and in particular whether variations in play selection across game situations would manifest as changes in the equation's fitted parameters. Statistically significant changes in bias were found for each of five types of game situations; no systematic changes in sensitivity were observed. Further analyses suggested relationships between play selection bias and both turnover probability (which can be described in terms of punishment) and yards-gained variance (which can be described in terms of variable-magnitude reinforcement schedules). The present investigation provides a useful demonstration of association between face-valid, situation-specific effects in a domain of everyday interest, and a theoretically important term of a quantitative model of behavior. Such associations, we argue, are an essential focus in translational extensions of quantitative models. PMID:21119855

Field analysis of the Cerenkov doubling of infrared coherent radiation utilizing an organic crystal core bounded by a glass capillary

NASA Astrophysics Data System (ADS)

Hayata, K.; Yanagawa, K.; Koshiba, M.

1990-12-01

A mode field analysis is presented of the second-harmonic electromagnetic wave that radiates from a nonlinear core bounded by a dielectric cladding. With this analysis the ultimate performance of the organic crystal-cored single-mode optical fiber waveguide as a guided-wave frequency doubler is evaluated through the solution of nonlinear parametric equations derived from Maxwell's equations under some assumptions. As a phase-matching scheme, a Cerenkov approach is considered because of advantages in actual device applications, in which the phase matching is achievable between the fundamental guided LP01 mode and the second-harmonic radiation (leaky) mode. Calculated results for organic cores made of benzil, 4-(N,N-dimethyl-amino)-3-acetamidonitrobenzen, 2-methyl-4-nitroaniline, and 4'-nitrobenzilidene-3-acetoamino-4-metxianiline provide useful data for designing an efficient fiber-optic wavelength converter utilizing nonlinear parametric processes. A detailed comparison is made between results for infinite and finite cladding thicknesses.

Iohexol clearance is superior to creatinine-based renal function estimating equations in detecting short-term renal function decline in chronic heart failure

PubMed Central

Cvan Trobec, Katja; Kerec Kos, Mojca; von Haehling, Stephan; Anker, Stefan D.; Macdougall, Iain C.; Ponikowski, Piotr; Lainscak, Mitja

2015-01-01

Aim To compare the performance of iohexol plasma clearance and creatinine-based renal function estimating equations in monitoring longitudinal renal function changes in chronic heart failure (CHF) patients, and to assess the effects of body composition on the equation performance. Methods Iohexol plasma clearance was measured in 43 CHF patients at baseline and after at least 6 months. Simultaneously, renal function was estimated with five creatinine-based equations (four- and six-variable Modification of Diet in Renal Disease, Cockcroft-Gault, Cockcroft-Gault adjusted for lean body mass, Chronic Kidney Disease Epidemiology Collaboration equation) and body composition was assessed using bioimpedance and dual-energy x-ray absorptiometry. Results Over a median follow-up of 7.5 months (range 6-17 months), iohexol clearance significantly declined (52.8 vs 44.4 mL/[min ×1.73 m2], P = 0.001). This decline was significantly higher in patients receiving mineralocorticoid receptor antagonists at baseline (mean decline -22% of baseline value vs -3%, P = 0.037). Mean serum creatinine concentration did not change significantly during follow-up and no creatinine-based renal function estimating equation was able to detect the significant longitudinal decline of renal function determined by iohexol clearance. After accounting for body composition, the accuracy of the equations improved, but not their ability to detect renal function decline. Conclusions Renal function measured with iohexol plasma clearance showed relevant decline in CHF patients, particularly in those treated with mineralocorticoid receptor antagonists. None of the equations for renal function estimation was able to detect these changes. ClinicalTrials.gov registration number NCT01829880 PMID:26718759

A multiscale approach to modelling electrochemical processes occurring across the cell membrane with application to transmission of action potentials.

PubMed

Richardson, G

2009-09-01

By application of matched asymptotic expansions, a simplified partial differential equation (PDE) model for the dynamic electrochemical processes occurring in the vicinity of a membrane, as ions selectively permeate across it, is formally derived from the Poisson-Nernst-Planck equations of electrochemistry. It is demonstrated that this simplified model reduces itself, in the limit of a long thin axon, to the cable equation used by Hodgkin and Huxley to describe the propagation of action potentials in the unmyelinated squid giant axon. The asymptotic reduction from the simplified PDE model to the cable equation leads to insights that are not otherwise apparent; these include an explanation of why the squid giant axon attains a diameter in the region of 1 mm. The simplified PDE model has more general application than the Hodgkin-Huxley cable equation and can, e.g. be used to describe action potential propagation in myelinated axons and neuronal cell bodies.

Preservice Mathematics Teachers' Experiences about Function and Equation Concepts

ERIC Educational Resources Information Center

Dede, Yuksel; Soybas, Danyal

2011-01-01

The purpose of this study is to determine the experience of mathematics preservice teachers related to function and equation concepts and the relations between them. Determining preservice mathematics teachers' understanding of function and equation concepts has great importance since it directly affects their future teaching careers. Data were…

Solution of the nonlinear mixed Volterra-Fredholm integral equations by hybrid of block-pulse functions and Bernoulli polynomials.

PubMed

Mashayekhi, S; Razzaghi, M; Tripak, O

2014-01-01

A new numerical method for solving the nonlinear mixed Volterra-Fredholm integral equations is presented. This method is based upon hybrid functions approximation. The properties of hybrid functions consisting of block-pulse functions and Bernoulli polynomials are presented. The operational matrices of integration and product are given. These matrices are then utilized to reduce the nonlinear mixed Volterra-Fredholm integral equations to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.

Solution of the Nonlinear Mixed Volterra-Fredholm Integral Equations by Hybrid of Block-Pulse Functions and Bernoulli Polynomials

PubMed Central

Mashayekhi, S.; Razzaghi, M.; Tripak, O.

2014-01-01

A new numerical method for solving the nonlinear mixed Volterra-Fredholm integral equations is presented. This method is based upon hybrid functions approximation. The properties of hybrid functions consisting of block-pulse functions and Bernoulli polynomials are presented. The operational matrices of integration and product are given. These matrices are then utilized to reduce the nonlinear mixed Volterra-Fredholm integral equations to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique. PMID:24523638

Extension of the KLI approximation toward the exact optimized effective potential.

PubMed

Iafrate, G J; Krieger, J B

2013-03-07

The integral equation for the optimized effective potential (OEP) is utilized in a compact form from which an accurate OEP solution for the spin-unrestricted exchange-correlation potential, Vxcσ, is obtained for any assumed orbital-dependent exchange-correlation energy functional. The method extends beyond the Krieger-Li-Iafrate (KLI) approximation toward the exact OEP result. The compact nature of the OEP equation arises by replacing the integrals involving the Green's function terms in the traditional OEP equation by an equivalent first-order perturbation theory wavefunction often referred to as the "orbital shift" function. Significant progress is then obtained by solving the equation for the first order perturbation theory wavefunction by use of Dalgarno functions which are determined from well known methods of partial differential equations. The use of Dalgarno functions circumvents the need to explicitly address the Green's functions and the associated problems with "sum over states" numerics; as well, the Dalgarno functions provide ease in dealing with inherent singularities arising from the origin and the zeros of the occupied orbital wavefunctions. The Dalgarno approach for finding a solution to the OEP equation is described herein, and a detailed illustrative example is presented for the special case of a spherically symmetric exchange-correlation potential. For the case of spherical symmetry, the relevant Dalgarno function is derived by direct integration of the appropriate radial equation while utilizing a user friendly method which explicitly treats the singular behavior at the origin and at the nodal singularities arising from the zeros of the occupied states. The derived Dalgarno function is shown to be an explicit integral functional of the exact OEP Vxcσ, thus allowing for the reduction of the OEP equation to a self-consistent integral equation for the exact exchange-correlation potential; the exact solution to this integral equation can be determined by iteration with the natural zeroth order correction given by the KLI exchange-correlation potential. Explicit analytic results are provided to illustrate the first order iterative correction beyond the KLI approximation. The derived correction term to the KLI potential explicitly involves spatially weighted products of occupied orbital densities in any assumed orbital-dependent exchange-correlation energy functional; as well, the correction term is obtained with no adjustable parameters. Moreover, if the equation for the exact optimized effective potential is further iterated, one can obtain the OEP as accurately as desired.

Extension of the KLI approximation toward the exact optimized effective potential

NASA Astrophysics Data System (ADS)

Iafrate, G. J.; Krieger, J. B.

2013-03-01

The integral equation for the optimized effective potential (OEP) is utilized in a compact form from which an accurate OEP solution for the spin-unrestricted exchange-correlation potential, Vxcσ, is obtained for any assumed orbital-dependent exchange-correlation energy functional. The method extends beyond the Krieger-Li-Iafrate (KLI) approximation toward the exact OEP result. The compact nature of the OEP equation arises by replacing the integrals involving the Green's function terms in the traditional OEP equation by an equivalent first-order perturbation theory wavefunction often referred to as the "orbital shift" function. Significant progress is then obtained by solving the equation for the first order perturbation theory wavefunction by use of Dalgarno functions which are determined from well known methods of partial differential equations. The use of Dalgarno functions circumvents the need to explicitly address the Green's functions and the associated problems with "sum over states" numerics; as well, the Dalgarno functions provide ease in dealing with inherent singularities arising from the origin and the zeros of the occupied orbital wavefunctions. The Dalgarno approach for finding a solution to the OEP equation is described herein, and a detailed illustrative example is presented for the special case of a spherically symmetric exchange-correlation potential. For the case of spherical symmetry, the relevant Dalgarno function is derived by direct integration of the appropriate radial equation while utilizing a user friendly method which explicitly treats the singular behavior at the origin and at the nodal singularities arising from the zeros of the occupied states. The derived Dalgarno function is shown to be an explicit integral functional of the exact OEP Vxcσ, thus allowing for the reduction of the OEP equation to a self-consistent integral equation for the exact exchange-correlation potential; the exact solution to this integral equation can be determined by iteration with the natural zeroth order correction given by the KLI exchange-correlation potential. Explicit analytic results are provided to illustrate the first order iterative correction beyond the KLI approximation. The derived correction term to the KLI potential explicitly involves spatially weighted products of occupied orbital densities in any assumed orbital-dependent exchange-correlation energy functional; as well, the correction term is obtained with no adjustable parameters. Moreover, if the equation for the exact optimized effective potential is further iterated, one can obtain the OEP as accurately as desired.

Poisson-Boltzmann-Nernst-Planck model

NASA Astrophysics Data System (ADS)

Zheng, Qiong; Wei, Guo-Wei

2011-05-01

The Poisson-Nernst-Planck (PNP) model is based on a mean-field approximation of ion interactions and continuum descriptions of concentration and electrostatic potential. It provides qualitative explanation and increasingly quantitative predictions of experimental measurements for the ion transport problems in many areas such as semiconductor devices, nanofluidic systems, and biological systems, despite many limitations. While the PNP model gives a good prediction of the ion transport phenomenon for chemical, physical, and biological systems, the number of equations to be solved and the number of diffusion coefficient profiles to be determined for the calculation directly depend on the number of ion species in the system, since each ion species corresponds to one Nernst-Planck equation and one position-dependent diffusion coefficient profile. In a complex system with multiple ion species, the PNP can be computationally expensive and parameter demanding, as experimental measurements of diffusion coefficient profiles are generally quite limited for most confined regions such as ion channels, nanostructures and nanopores. We propose an alternative model to reduce number of Nernst-Planck equations to be solved in complex chemical and biological systems with multiple ion species by substituting Nernst-Planck equations with Boltzmann distributions of ion concentrations. As such, we solve the coupled Poisson-Boltzmann and Nernst-Planck (PBNP) equations, instead of the PNP equations. The proposed PBNP equations are derived from a total energy functional by using the variational principle. We design a number of computational techniques, including the Dirichlet to Neumann mapping, the matched interface and boundary, and relaxation based iterative procedure, to ensure efficient solution of the proposed PBNP equations. Two protein molecules, cytochrome c551 and Gramicidin A, are employed to validate the proposed model under a wide range of bulk ion concentrations and external voltages. Extensive numerical experiments show that there is an excellent consistency between the results predicted from the present PBNP model and those obtained from the PNP model in terms of the electrostatic potentials, ion concentration profiles, and current-voltage (I-V) curves. The present PBNP model is further validated by a comparison with experimental measurements of I-V curves under various ion bulk concentrations. Numerical experiments indicate that the proposed PBNP model is more efficient than the original PNP model in terms of simulation time.

Poisson-Boltzmann-Nernst-Planck model

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

Zheng Qiong; Wei Guowei; Department of Electrical and Computer Engineering, Michigan State University, East Lansing, Michigan 48824

2011-05-21

The Poisson-Nernst-Planck (PNP) model is based on a mean-field approximation of ion interactions and continuum descriptions of concentration and electrostatic potential. It provides qualitative explanation and increasingly quantitative predictions of experimental measurements for the ion transport problems in many areas such as semiconductor devices, nanofluidic systems, and biological systems, despite many limitations. While the PNP model gives a good prediction of the ion transport phenomenon for chemical, physical, and biological systems, the number of equations to be solved and the number of diffusion coefficient profiles to be determined for the calculation directly depend on the number of ion species inmore » the system, since each ion species corresponds to one Nernst-Planck equation and one position-dependent diffusion coefficient profile. In a complex system with multiple ion species, the PNP can be computationally expensive and parameter demanding, as experimental measurements of diffusion coefficient profiles are generally quite limited for most confined regions such as ion channels, nanostructures and nanopores. We propose an alternative model to reduce number of Nernst-Planck equations to be solved in complex chemical and biological systems with multiple ion species by substituting Nernst-Planck equations with Boltzmann distributions of ion concentrations. As such, we solve the coupled Poisson-Boltzmann and Nernst-Planck (PBNP) equations, instead of the PNP equations. The proposed PBNP equations are derived from a total energy functional by using the variational principle. We design a number of computational techniques, including the Dirichlet to Neumann mapping, the matched interface and boundary, and relaxation based iterative procedure, to ensure efficient solution of the proposed PBNP equations. Two protein molecules, cytochrome c551 and Gramicidin A, are employed to validate the proposed model under a wide range of bulk ion concentrations and external voltages. Extensive numerical experiments show that there is an excellent consistency between the results predicted from the present PBNP model and those obtained from the PNP model in terms of the electrostatic potentials, ion concentration profiles, and current-voltage (I-V) curves. The present PBNP model is further validated by a comparison with experimental measurements of I-V curves under various ion bulk concentrations. Numerical experiments indicate that the proposed PBNP model is more efficient than the original PNP model in terms of simulation time.« less

Poisson–Boltzmann–Nernst–Planck model

PubMed Central

Zheng, Qiong; Wei, Guo-Wei

2011-01-01

The Poisson–Nernst–Planck (PNP) model is based on a mean-field approximation of ion interactions and continuum descriptions of concentration and electrostatic potential. It provides qualitative explanation and increasingly quantitative predictions of experimental measurements for the ion transport problems in many areas such as semiconductor devices, nanofluidic systems, and biological systems, despite many limitations. While the PNP model gives a good prediction of the ion transport phenomenon for chemical, physical, and biological systems, the number of equations to be solved and the number of diffusion coefficient profiles to be determined for the calculation directly depend on the number of ion species in the system, since each ion species corresponds to one Nernst–Planck equation and one position-dependent diffusion coefficient profile. In a complex system with multiple ion species, the PNP can be computationally expensive and parameter demanding, as experimental measurements of diffusion coefficient profiles are generally quite limited for most confined regions such as ion channels, nanostructures and nanopores. We propose an alternative model to reduce number of Nernst–Planck equations to be solved in complex chemical and biological systems with multiple ion species by substituting Nernst–Planck equations with Boltzmann distributions of ion concentrations. As such, we solve the coupled Poisson–Boltzmann and Nernst–Planck (PBNP) equations, instead of the PNP equations. The proposed PBNP equations are derived from a total energy functional by using the variational principle. We design a number of computational techniques, including the Dirichlet to Neumann mapping, the matched interface and boundary, and relaxation based iterative procedure, to ensure efficient solution of the proposed PBNP equations. Two protein molecules, cytochrome c551 and Gramicidin A, are employed to validate the proposed model under a wide range of bulk ion concentrations and external voltages. Extensive numerical experiments show that there is an excellent consistency between the results predicted from the present PBNP model and those obtained from the PNP model in terms of the electrostatic potentials, ion concentration profiles, and current–voltage (I–V) curves. The present PBNP model is further validated by a comparison with experimental measurements of I–V curves under various ion bulk concentrations. Numerical experiments indicate that the proposed PBNP model is more efficient than the original PNP model in terms of simulation time. PMID:21599038

Poisson-Boltzmann-Nernst-Planck model.

PubMed

Zheng, Qiong; Wei, Guo-Wei

2011-05-21

The Poisson-Nernst-Planck (PNP) model is based on a mean-field approximation of ion interactions and continuum descriptions of concentration and electrostatic potential. It provides qualitative explanation and increasingly quantitative predictions of experimental measurements for the ion transport problems in many areas such as semiconductor devices, nanofluidic systems, and biological systems, despite many limitations. While the PNP model gives a good prediction of the ion transport phenomenon for chemical, physical, and biological systems, the number of equations to be solved and the number of diffusion coefficient profiles to be determined for the calculation directly depend on the number of ion species in the system, since each ion species corresponds to one Nernst-Planck equation and one position-dependent diffusion coefficient profile. In a complex system with multiple ion species, the PNP can be computationally expensive and parameter demanding, as experimental measurements of diffusion coefficient profiles are generally quite limited for most confined regions such as ion channels, nanostructures and nanopores. We propose an alternative model to reduce number of Nernst-Planck equations to be solved in complex chemical and biological systems with multiple ion species by substituting Nernst-Planck equations with Boltzmann distributions of ion concentrations. As such, we solve the coupled Poisson-Boltzmann and Nernst-Planck (PBNP) equations, instead of the PNP equations. The proposed PBNP equations are derived from a total energy functional by using the variational principle. We design a number of computational techniques, including the Dirichlet to Neumann mapping, the matched interface and boundary, and relaxation based iterative procedure, to ensure efficient solution of the proposed PBNP equations. Two protein molecules, cytochrome c551 and Gramicidin A, are employed to validate the proposed model under a wide range of bulk ion concentrations and external voltages. Extensive numerical experiments show that there is an excellent consistency between the results predicted from the present PBNP model and those obtained from the PNP model in terms of the electrostatic potentials, ion concentration profiles, and current-voltage (I-V) curves. The present PBNP model is further validated by a comparison with experimental measurements of I-V curves under various ion bulk concentrations. Numerical experiments indicate that the proposed PBNP model is more efficient than the original PNP model in terms of simulation time. © 2011 American Institute of Physics.

Squared eigenfunctions for the Sasa-Satsuma equation

NASA Astrophysics Data System (ADS)

Yang, Jianke; Kaup, D. J.

2009-02-01

Squared eigenfunctions are quadratic combinations of Jost functions and adjoint Jost functions which satisfy the linearized equation of an integrable equation. They are needed for various studies related to integrable equations, such as the development of its soliton perturbation theory. In this article, squared eigenfunctions are derived for the Sasa-Satsuma equation whose spectral operator is a 3×3 system, while its linearized operator is a 2×2 system. It is shown that these squared eigenfunctions are sums of two terms, where each term is a product of a Jost function and an adjoint Jost function. The procedure of this derivation consists of two steps: First is to calculate the variations of the potentials via variations of the scattering data by the Riemann-Hilbert method. The second one is to calculate the variations of the scattering data via the variations of the potentials through elementary calculations. While this procedure has been used before on other integrable equations, it is shown here, for the first time, that for a general integrable equation, the functions appearing in these variation relations are precisely the squared eigenfunctions and adjoint squared eigenfunctions satisfying, respectively, the linearized equation and the adjoint linearized equation of the integrable system. This proof clarifies this procedure and provides a unified explanation for previous results of squared eigenfunctions on individual integrable equations. This procedure uses primarily the spectral operator of the Lax pair. Thus two equations in the same integrable hierarchy will share the same squared eigenfunctions (except for a time-dependent factor). In the Appendix, the squared eigenfunctions are presented for the Manakov equations whose spectral operator is closely related to that of the Sasa-Satsuma equation.

Boundary-driven anomalous spirals in oscillatory media

NASA Astrophysics Data System (ADS)

Kessler, David A.; Levine, Herbert

2017-06-01

We study a heretofore ignored class of spiral patterns in oscillatory media as characterized by the complex Landau-Ginzburg model. These spirals emerge from modulating the growth rate as a function of r, thereby turning off the instability at large r. They are uniquely determined by matching to this outer condition, lifting a degeneracy in the set of steady-state solutions of the original equations. Unlike the well-studied spiral which acts as a wave source, has a simple core structure and is insensitive to the details of the boundary on which no-flux conditions are imposed, these new spirals are wave sinks, have non-monotonic wavefront curvature near the core, and can be patterned by the form of the spatial boundary. We predict that these anomalous spirals could be produced in nonlinear optics experiments via spatially modulating the gain of the medium.

Solid lubrication design methodology

NASA Technical Reports Server (NTRS)

Aggarwal, B. B.; Yonushonis, T. M.; Bovenkerk, R. L.

1984-01-01

A single element traction rig was used to measure the traction forces at the contact of a ball against a flat disc at room temperature under combined rolling and sliding. The load and speed conditions were selected to match those anticipated for bearing applications in adiabatic diesel engines. The test program showed that the magnitude of traction forces were almost the same for all the lubricants tested; a lubricant should, therefore, be selected on the basis of its ability to prevent wear of the contact surfaces. Traction vs. slide/roll ratio curves were similar to those for liquid lubricants but the traction forces were an order of magnitude higher. The test data was used to derive equations to predict traction force as a function of contact stress and rolling speed. Qualitative design guidelines for solid lubricated concentrated contacts are proposed.

Lepton-rich cold QCD matter in protoneutron stars

NASA Astrophysics Data System (ADS)

Jiménez, J. C.; Fraga, E. S.

2018-05-01

We investigate protoneutron star matter using the state-of-the-art perturbative equation of state for cold and dense QCD in the presence of a fixed lepton fraction in which both electrons and neutrinos are included. Besides computing the modifications in the equation of state due to the presence of trapped neutrinos, we show that stable strange quark matter has a more restricted parameter space. We also study the possibility of nucleation of unpaired quark matter in the core of protoneutron stars by matching the lepton-rich QCD pressure onto a hadronic equation of state, namely TM1 with trapped neutrinos. Using the inherent dependence of perturbative QCD on the renormalization scale parameter, we provide a measure of the uncertainty in the observables we compute.

Study of travelling wave solutions for some special-type nonlinear evolution equations

NASA Astrophysics Data System (ADS)

Song, Junquan; Hu, Lan; Shen, Shoufeng; Ma, Wen-Xiu

2018-07-01

The tanh-function expansion method has been improved and used to construct travelling wave solutions of the form U={\\sum }j=0n{a}j{\\tanh }jξ for some special-type nonlinear evolution equations, which have a variety of physical applications. The positive integer n can be determined by balancing the highest order linear term with the nonlinear term in the evolution equations. We improve the tanh-function expansion method with n = 0 by introducing a new transform U=-W\\prime (ξ )/{W}2. A nonlinear wave equation with source terms, and mKdV-type equations, are considered in order to show the effectiveness of the improved scheme. We also propose the tanh-function expansion method of implicit function form, and apply it to a Harry Dym-type equation as an example.

The probability density function (PDF) of Lagrangian Turbulence

NASA Astrophysics Data System (ADS)

Birnir, B.

2012-12-01

The statistical theory of Lagrangian turbulence is derived from the stochastic Navier-Stokes equation. Assuming that the noise in fully-developed turbulence is a generic noise determined by the general theorems in probability, the central limit theorem and the large deviation principle, we are able to formulate and solve the Kolmogorov-Hopf equation for the invariant measure of the stochastic Navier-Stokes equations. The intermittency corrections to the scaling exponents of the structure functions require a multiplicative (multipling the fluid velocity) noise in the stochastic Navier-Stokes equation. We let this multiplicative noise, in the equation, consists of a simple (Poisson) jump process and then show how the Feynmann-Kac formula produces the log-Poissonian processes, found by She and Leveque, Waymire and Dubrulle. These log-Poissonian processes give the intermittency corrections that agree with modern direct Navier-Stokes simulations (DNS) and experiments. The probability density function (PDF) plays a key role when direct Navier-Stokes simulations or experimental results are compared to theory. The statistical theory of turbulence is determined, including the scaling of the structure functions of turbulence, by the invariant measure of the Navier-Stokes equation and the PDFs for the various statistics (one-point, two-point, N-point) can be obtained by taking the trace of the corresponding invariant measures. Hopf derived in 1952 a functional equation for the characteristic function (Fourier transform) of the invariant measure. In distinction to the nonlinear Navier-Stokes equation, this is a linear functional differential equation. The PDFs obtained from the invariant measures for the velocity differences (two-point statistics) are shown to be the four parameter generalized hyperbolic distributions, found by Barndorff-Nilsen. These PDF have heavy tails and a convex peak at the origin. A suitable projection of the Kolmogorov-Hopf equations is the differential equation determining the generalized hyperbolic distributions. Then we compare these PDFs with DNS results and experimental data.

Radiative transfer equation accounting for rotational Raman scattering and its solution by the discrete-ordinates method

NASA Astrophysics Data System (ADS)

Rozanov, Vladimir V.; Vountas, Marco

2014-01-01

Rotational Raman scattering of solar light in Earth's atmosphere leads to the filling-in of Fraunhofer and telluric lines observed in the reflected spectrum. The phenomenological derivation of the inelastic radiative transfer equation including rotational Raman scattering is presented. The different forms of the approximate radiative transfer equation with first-order rotational Raman scattering terms are obtained employing the Cabannes, Rayleigh, and Cabannes-Rayleigh scattering models. The solution of these equations is considered in the framework of the discrete-ordinates method using rigorous and approximate approaches to derive particular integrals. An alternative forward-adjoint technique is suggested as well. A detailed description of the model including the exact spectral matching and a binning scheme that significantly speeds up the calculations is given. The considered solution techniques are implemented in the radiative transfer software package SCIATRAN and a specified benchmark setup is presented to enable readers to compare with own results transparently.

Derivation of Continuum Models from An Agent-based Cancer Model: Optimization and Sensitivity Analysis.

PubMed

Voulgarelis, Dimitrios; Velayudhan, Ajoy; Smith, Frank

2017-01-01

Agent-based models provide a formidable tool for exploring complex and emergent behaviour of biological systems as well as accurate results but with the drawback of needing a lot of computational power and time for subsequent analysis. On the other hand, equation-based models can more easily be used for complex analysis in a much shorter timescale. This paper formulates an ordinary differential equations and stochastic differential equations model to capture the behaviour of an existing agent-based model of tumour cell reprogramming and applies it to optimization of possible treatment as well as dosage sensitivity analysis. For certain values of the parameter space a close match between the equation-based and agent-based models is achieved. The need for division of labour between the two approaches is explored. Copyright© Bentham Science Publishers; For any queries, please email at epub@benthamscience.org.

Discrete sensitivity derivatives of the Navier-Stokes equations with a parallel Krylov solver

NASA Technical Reports Server (NTRS)

Ajmani, Kumud; Taylor, Arthur C., III

1994-01-01

This paper solves an 'incremental' form of the sensitivity equations derived by differentiating the discretized thin-layer Navier Stokes equations with respect to certain design variables of interest. The equations are solved with a parallel, preconditioned Generalized Minimal RESidual (GMRES) solver on a distributed-memory architecture. The 'serial' sensitivity analysis code is parallelized by using the Single Program Multiple Data (SPMD) programming model, domain decomposition techniques, and message-passing tools. Sensitivity derivatives are computed for low and high Reynolds number flows over a NACA 1406 airfoil on a 32-processor Intel Hypercube, and found to be identical to those computed on a single-processor Cray Y-MP. It is estimated that the parallel sensitivity analysis code has to be run on 40-50 processors of the Intel Hypercube in order to match the single-processor processing time of a Cray Y-MP.

Asymptotic analysis of the Boltzmann equation for dark matter relics in the presence of a running dilaton and space-time defects

NASA Astrophysics Data System (ADS)

Bender, Carl M.; Mavromatos, Nick E.; Sarkar, Sarben

2013-03-01

The interplay of dilatonic effects in dilaton cosmology and stochastic quantum space-time defects within the framework of string/brane cosmologies is examined. The Boltzmann equation describes the physics of thermal dark-matter-relic abundances in the presence of rolling dilatons. These dilatons affect the coupling of stringy matter to D-particle defects, which are generic in string theory. This coupling leads to an additional source term in the Boltzmann equation. The techniques of asymptotic matching and boundary-layer theory, which were recently applied by two of the authors (Bender and Sarkar) to a Boltzmann equation, are used here to find the detailed asymptotic relic abundances for all ranges of the expectation value of the dilaton field. The phenomenological implications for the search for supersymmetric dark matter in current colliders, such as the LHC, are discussed.

Macroscopic dielectric function within time-dependent density functional theory—Real time evolution versus the Casida approach

NASA Astrophysics Data System (ADS)

Sander, Tobias; Kresse, Georg

2017-02-01

Linear optical properties can be calculated by solving the time-dependent density functional theory equations. Linearization of the equation of motion around the ground state orbitals results in the so-called Casida equation, which is formally very similar to the Bethe-Salpeter equation. Alternatively one can determine the spectral functions by applying an infinitely short electric field in time and then following the evolution of the electron orbitals and the evolution of the dipole moments. The long wavelength response function is then given by the Fourier transformation of the evolution of the dipole moments in time. In this work, we compare the results and performance of these two approaches for the projector augmented wave method. To allow for large time steps and still rely on a simple difference scheme to solve the differential equation, we correct for the errors in the frequency domain, using a simple analytic equation. In general, we find that both approaches yield virtually indistinguishable results. For standard density functionals, the time evolution approach is, with respect to the computational performance, clearly superior compared to the solution of the Casida equation. However, for functionals including nonlocal exchange, the direct solution of the Casida equation is usually much more efficient, even though it scales less beneficial with the system size. We relate this to the large computational prefactors in evaluating the nonlocal exchange, which renders the time evolution algorithm fairly inefficient.

Research on Standard Errors of Equating Differences. Research Report. ETS RR-10-25

ERIC Educational Resources Information Center

Moses, Tim; Zhang, Wenmin

2010-01-01

In this paper, the "standard error of equating difference" (SEED) is described in terms of originally proposed kernel equating functions (von Davier, Holland, & Thayer, 2004) and extended to incorporate traditional linear and equipercentile functions. These derivations expand on prior developments of SEEDs and standard errors of equating and…

Modeling of High-Frequency Acoustic Propagation in Shallow Water

DTIC Science & Technology

2007-06-01

is a product of a phase function, called the eikonal equation, and an amplitude function, called the transport equation. To solve the eikonal ... eikonal equation in the ray coordinate system. Expanding Equation (2.6), 2 1 c =∇⋅∇ ττ , (2.14) so that substituting the value of τ∇ from

Fokker-Planck equation of the reduced Wigner function associated to an Ohmic quantum Langevin dynamics

NASA Astrophysics Data System (ADS)

Colmenares, Pedro J.

2018-05-01

This article has to do with the derivation and solution of the Fokker-Planck equation associated to the momentum-integrated Wigner function of a particle subjected to a harmonic external field in contact with an ohmic thermal bath of quantum harmonic oscillators. The strategy employed is a simplified version of the phenomenological approach of Schramm, Jung, and Grabert of interpreting the operators as c numbers to derive the quantum master equation arising from a twofold transformation of the Wigner function of the entire phase space. The statistical properties of the random noise comes from the integral functional theory of Grabert, Schramm, and Ingold. By means of a single Wigner transformation, a simpler equation than that mentioned before is found. The Wigner function reproduces the known results of the classical limit. This allowed us to rewrite the underdamped classical Langevin equation as a first-order stochastic differential equation with time-dependent drift and diffusion terms.

Painlevé equations, elliptic integrals and elementary functions

NASA Astrophysics Data System (ADS)

Żołądek, Henryk; Filipuk, Galina

2015-02-01

The six Painlevé equations can be written in the Hamiltonian form, with time dependent Hamilton functions. We present a rather new approach to this result, leading to rational Hamilton functions. By a natural extension of the phase space one gets corresponding autonomous Hamiltonian systems with two degrees of freedom. We realize the Bäcklund transformations of the Painlevé equations as symplectic birational transformations in C4 and we interpret the cases with classical solutions as the cases of partial integrability of the extended Hamiltonian systems. We prove that the extended Hamiltonian systems do not have any additional algebraic first integral besides the known special cases of the third and fifth Painlevé equations. We also show that the original Painlevé equations admit the first integrals expressed in terms of the elementary functions only in the special cases mentioned above. In the proofs we use equations in variations with respect to a parameter and Liouville's theory of elementary functions.

The Boundary Function Method. Fundamentals

NASA Astrophysics Data System (ADS)

Kot, V. A.

2017-03-01

The boundary function method is proposed for solving applied problems of mathematical physics in the region defined by a partial differential equation of the general form involving constant or variable coefficients with a Dirichlet, Neumann, or Robin boundary condition. In this method, the desired function is defined by a power polynomial, and a boundary function represented in the form of the desired function or its derivative at one of the boundary points is introduced. Different sequences of boundary equations have been set up with the use of differential operators. Systems of linear algebraic equations constructed on the basis of these sequences allow one to determine the coefficients of a power polynomial. Constitutive equations have been derived for initial boundary-value problems of all the main types. With these equations, an initial boundary-value problem is transformed into the Cauchy problem for the boundary function. The determination of the boundary function by its derivative with respect to the time coordinate completes the solution of the problem.

Comparison of Eight Equations That Predict Percent Body Fat Using Skinfolds in American Youth

PubMed Central

Roberts, Amy; Cai, Jianwen; Berge, Jerica M.; Stevens, June

2016-01-01

Abstract Background: Skinfolds are often used in equations to predict percent body fat (PBF) in youth. Although there are numerous such equations published, there is limited information to help researchers determine which equation to use for their sample. Methods: Using data from the 1999–2006 National Health and Nutrition Examination Surveys (NHANES), we compared eight published equations for prediction of PBF. These published equations all included triceps and/or subscapular skinfold measurements. We examined the PBF equations in a nationally representative sample of American youth that was matched by age, sex, and race/ethnicity to the original equation development population and a full sample of 8- to 18-year-olds. We compared the equation-predicted PBF to the dual-emission X-ray absorptiometry (DXA)-measured PBF. The adjusted R2, root mean square error (RMSE), and mean signed difference (MSD) were compared. The MSDs were used to examine accuracy and differential bias by age, sex, and race/ethnicity. Results: When applied to the full range of 8- 18-year-old youth, the R2 values ranged from 0.495 to 0.738. The MSD between predicted and DXA-measured PBF indicated high average accuracy (MSD between −1.0 and 1.0) for only three equations (Bray subscapular equation and Dezenberg equations [with and without race/ethnicity]). The majority of the equations showed differential bias by sex, race/ethnicity, weight status, or age. Conclusions: These findings indicate that investigators should use caution in the selection of an equation to predict PBF in youth given that results may vary systematically in important subgroups. PMID:27045618

Comparison of Eight Equations That Predict Percent Body Fat Using Skinfolds in American Youth.

PubMed

Truesdale, Kimberly P; Roberts, Amy; Cai, Jianwen; Berge, Jerica M; Stevens, June

2016-08-01

Skinfolds are often used in equations to predict percent body fat (PBF) in youth. Although there are numerous such equations published, there is limited information to help researchers determine which equation to use for their sample. Using data from the 1999-2006 National Health and Nutrition Examination Surveys (NHANES), we compared eight published equations for prediction of PBF. These published equations all included triceps and/or subscapular skinfold measurements. We examined the PBF equations in a nationally representative sample of American youth that was matched by age, sex, and race/ethnicity to the original equation development population and a full sample of 8- to 18-year-olds. We compared the equation-predicted PBF to the dual-emission X-ray absorptiometry (DXA)-measured PBF. The adjusted R(2), root mean square error (RMSE), and mean signed difference (MSD) were compared. The MSDs were used to examine accuracy and differential bias by age, sex, and race/ethnicity. When applied to the full range of 8- 18-year-old youth, the R(2) values ranged from 0.495 to 0.738. The MSD between predicted and DXA-measured PBF indicated high average accuracy (MSD between -1.0 and 1.0) for only three equations (Bray subscapular equation and Dezenberg equations [with and without race/ethnicity]). The majority of the equations showed differential bias by sex, race/ethnicity, weight status, or age. These findings indicate that investigators should use caution in the selection of an equation to predict PBF in youth given that results may vary systematically in important subgroups.

Low-degree Structure in Mercury's Planetary Magnetic Field

NASA Technical Reports Server (NTRS)

Anderson, Brian J.; Johnson, Catherine L.; Korth, Haje; Winslow, Reka M.; Borovsky, Joseph E.; Purucker, Michael E.; Slavin, James A.; Solomon, Sean C.; Zuber, Maria T.; McNutt, Ralph L. Jr.

2012-01-01

The structure of Mercury's internal magnetic field has been determined from analysis of orbital Magnetometer measurements by the MESSENGER spacecraft. We identified the magnetic equator on 531 low-altitude and 120 high-altitude equator crossings from the zero in the radial cylindrical magnetic field component, Beta (sub rho). The low-altitude crossings are offset 479 +/- 6 km northward, indicating an offset of the planetary dipole. The tilt of the magnetic pole relative to the planetary spin axis is less than 0.8 deg.. The high-altitude crossings yield a northward offset of the magnetic equator of 486 +/- 74 km. A field with only nonzero dipole and octupole coefficients also matches the low-altitude observations but cannot yield off-equatorial Beta (sub rho) = 0 at radial distances greater than 3520 km. We compared offset dipole and other descriptions of the field with vector field observations below 600 km for 13 longitudinally distributed, magnetically quiet orbits. An offset dipole with southward directed moment of 190 nT-R-cube (sub M) yields root-mean-square (RMS) residuals below 14 nT, whereas a field with only dipole and octupole terms tuned to match the polar field and the low-altitude magnetic equator crossings yields RMS residuals up to 68 nT. Attributing the residuals from the offset-dipole field to axial degree 3 and 4 contributions we estimate that the Gauss coefficient magnitudes for the additional terms are less than 4% and 7%, respectively, relative to the dipole. The axial alignment and prominent quadrupole are consistent with a non-convecting layer above a deep dynamo in Mercury's fluid outer core.

Combining existing numerical models with data assimilation using weighted least-squares finite element methods.

PubMed

Rajaraman, Prathish K; Manteuffel, T A; Belohlavek, M; Heys, Jeffrey J

2017-01-01

A new approach has been developed for combining and enhancing the results from an existing computational fluid dynamics model with experimental data using the weighted least-squares finite element method (WLSFEM). Development of the approach was motivated by the existence of both limited experimental blood velocity in the left ventricle and inexact numerical models of the same flow. Limitations of the experimental data include measurement noise and having data only along a two-dimensional plane. Most numerical modeling approaches do not provide the flexibility to assimilate noisy experimental data. We previously developed an approach that could assimilate experimental data into the process of numerically solving the Navier-Stokes equations, but the approach was limited because it required the use of specific finite element methods for solving all model equations and did not support alternative numerical approximation methods. The new approach presented here allows virtually any numerical method to be used for approximately solving the Navier-Stokes equations, and then the WLSFEM is used to combine the experimental data with the numerical solution of the model equations in a final step. The approach dynamically adjusts the influence of the experimental data on the numerical solution so that more accurate data are more closely matched by the final solution and less accurate data are not closely matched. The new approach is demonstrated on different test problems and provides significantly reduced computational costs compared with many previous methods for data assimilation. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

Hypersonic three-dimensional nonequilibrium boundary-layer equations in generalized curvilinear coordinates

NASA Technical Reports Server (NTRS)

Lee, Jong-Hun

1993-01-01

The basic governing equations for the second-order three-dimensional hypersonic thermal and chemical nonequilibrium boundary layer are derived by means of an order-of-magnitude analysis. A two-temperature concept is implemented into the system of boundary-layer equations by simplifying the rather complicated general three-temperature thermal gas model. The equations are written in a surface-oriented non-orthogonal curvilinear coordinate system, where two curvilinear coordinates are non-orthogonial and a third coordinate is normal to the surface. The equations are described with minimum use of tensor expressions arising from the coordinate transformation, to avoid unnecessary confusion for readers. The set of equations obtained will be suitable for the development of a three-dimensional nonequilibrium boundary-layer code. Such a code could be used to determine economically the aerodynamic/aerothermodynamic loads to the surfaces of hypersonic vehicles with general configurations. In addition, the basic equations for three-dimensional stagnation flow, of which solution is required as an initial value for space-marching integration of the boundary-layer equations, are given along with the boundary conditions, the boundary-layer parameters, and the inner-outer layer matching procedure. Expressions for the chemical reaction rates and the thermodynamic and transport properties in the thermal nonequilibrium environment are explicitly given.

Weierstrass traveling wave solutions for dissipative Benjamin, Bona, and Mahony (BBM) equation

NASA Astrophysics Data System (ADS)

Mancas, Stefan C.; Spradlin, Greg; Khanal, Harihar

2013-08-01

In this paper the effect of a small dissipation on waves is included to find exact solutions to the modified Benjamin, Bona, and Mahony (BBM) equation by viscosity. Using Lyapunov functions and dynamical systems theory, we prove that when viscosity is added to the BBM equation, in certain regions there still exist bounded traveling wave solutions in the form of solitary waves, periodic, and elliptic functions. By using the canonical form of Abel equation, the polynomial Appell invariant makes the equation integrable in terms of Weierstrass ℘ functions. We will use a general formalism based on Ince's transformation to write the general solution of dissipative BBM in terms of ℘ functions, from which all the other known solutions can be obtained via simplifying assumptions. Using ODE (ordinary differential equations) analysis we show that the traveling wave speed is a bifurcation parameter that makes transition between different classes of waves.

Numerical solution of the nonlinear Schrodinger equation by feedforward neural networks

NASA Astrophysics Data System (ADS)

Shirvany, Yazdan; Hayati, Mohsen; Moradian, Rostam

2008-12-01

We present a method to solve boundary value problems using artificial neural networks (ANN). A trial solution of the differential equation is written as a feed-forward neural network containing adjustable parameters (the weights and biases). From the differential equation and its boundary conditions we prepare the energy function which is used in the back-propagation method with momentum term to update the network parameters. We improved energy function of ANN which is derived from Schrodinger equation and the boundary conditions. With this improvement of energy function we can use unsupervised training method in the ANN for solving the equation. Unsupervised training aims to minimize a non-negative energy function. We used the ANN method to solve Schrodinger equation for few quantum systems. Eigenfunctions and energy eigenvalues are calculated. Our numerical results are in agreement with their corresponding analytical solution and show the efficiency of ANN method for solving eigenvalue problems.

Solution of D dimensional Dirac equation for hyperbolic tangent potential using NU method and its application in material properties

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

Suparmi, A., E-mail: soeparmi@staff.uns.ac.id; Cari, C., E-mail: cari@staff.uns.ac.id; Pratiwi, B. N., E-mail: namakubetanurpratiwi@gmail.com

2016-02-08

The analytical solution of D-dimensional Dirac equation for hyperbolic tangent potential is investigated using Nikiforov-Uvarov method. In the case of spin symmetry the D dimensional Dirac equation reduces to the D dimensional Schrodinger equation. The D dimensional relativistic energy spectra are obtained from D dimensional relativistic energy eigen value equation by using Mat Lab software. The corresponding D dimensional radial wave functions are formulated in the form of generalized Jacobi polynomials. The thermodynamically properties of materials are generated from the non-relativistic energy eigen-values in the classical limit. In the non-relativistic limit, the relativistic energy equation reduces to the non-relativistic energy.more » The thermal quantities of the system, partition function and specific heat, are expressed in terms of error function and imaginary error function which are numerically calculated using Mat Lab software.« less

Siewert solutions of transcendental equations, generalized Lambert functions and physical applications

NASA Astrophysics Data System (ADS)

Barsan, Victor

2018-05-01

Several classes of transcendental equations, mainly eigenvalue equations associated to non-relativistic quantum mechanical problems, are analyzed. Siewert's systematic approach of such equations is discussed from the perspective of the new results recently obtained in the theory of generalized Lambert functions and of algebraic approximations of various special or elementary functions. Combining exact and approximate analytical methods, quite precise analytical outputs are obtained for apparently untractable problems. The results can be applied in quantum and classical mechanics, magnetism, elasticity, solar energy conversion, etc.

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.

Impact of an entertainment-education television drama on health knowledge and behavior in Bangladesh: an application of propensity score matching.

PubMed

Do, Mai P; Kincaid, D Lawrence

2006-01-01

Shabuj Chaya is a weekly television drama broadcast during a 13-week period in Bangladesh in 2000. It used an entertainment-education format to increase health knowledge and to promote visits to health clinic and modern contraceptive use. The purpose of this article is to demonstrate how a relatively new statistical technique, propensity score matching in conjunction with structural equation modeling, can be used to obtain an unbiased estimate of changes in health outcomes that can be attributed to exposure to the drama. The analysis is conducted with data from an after-only, cross-sectional survey of 4,492 men and women from the intended audience. The results from propensity score matching approximate what would be expected from a randomized control group design.

Quantum Dynamics in Continuum for Proton Transport I: Basic Formulation.

PubMed

Chen, Duan; Wei, Guo-Wei

2013-01-01

Proton transport is one of the most important and interesting phenomena in living cells. The present work proposes a multiscale/multiphysics model for the understanding of the molecular mechanism of proton transport in transmembrane proteins. We describe proton dynamics quantum mechanically via a density functional approach while implicitly model other solvent ions as a dielectric continuum to reduce the number of degrees of freedom. The densities of all other ions in the solvent are assumed to obey the Boltzmann distribution. The impact of protein molecular structure and its charge polarization on the proton transport is considered explicitly at the atomic level. We formulate a total free energy functional to put proton kinetic and potential energies as well as electrostatic energy of all ions on an equal footing. The variational principle is employed to derive nonlinear governing equations for the proton transport system. Generalized Poisson-Boltzmann equation and Kohn-Sham equation are obtained from the variational framework. Theoretical formulations for the proton density and proton conductance are constructed based on fundamental principles. The molecular surface of the channel protein is utilized to split the discrete protein domain and the continuum solvent domain, and facilitate the multiscale discrete/continuum/quantum descriptions. A number of mathematical algorithms, including the Dirichlet to Neumann mapping, matched interface and boundary method, Gummel iteration, and Krylov space techniques are utilized to implement the proposed model in a computationally efficient manner. The Gramicidin A (GA) channel is used to demonstrate the performance of the proposed proton transport model and validate the efficiency of proposed mathematical algorithms. The electrostatic characteristics of the GA channel is analyzed with a wide range of model parameters. The proton conductances are studied over a number of applied voltages and reference concentrations. A comparison with experimental data verifies the present model predictions and validates the proposed model.

Green function of the double-fractional Fokker-Planck equation: path integral and stochastic differential equations.

PubMed

Kleinert, H; Zatloukal, V

2013-11-01

The statistics of rare events, the so-called black-swan events, is governed by non-Gaussian distributions with heavy power-like tails. We calculate the Green functions of the associated Fokker-Planck equations and solve the related stochastic differential equations. We also discuss the subject in the framework of path integration.

General existence principles for Stieltjes differential equations with applications to mathematical biology

NASA Astrophysics Data System (ADS)

López Pouso, Rodrigo; Márquez Albés, Ignacio

2018-04-01

Stieltjes differential equations, which contain equations with impulses and equations on time scales as particular cases, simply consist on replacing usual derivatives by derivatives with respect to a nondecreasing function. In this paper we prove new existence results for functional and discontinuous Stieltjes differential equations and we show that such general results have real world applications. Specifically, we show that Stieltjes differential equations are specially suitable to study populations which exhibit dormant states and/or very short (impulsive) periods of reproduction. In particular, we construct two mathematical models for the evolution of a silkworm population. Our first model can be explicitly solved, as it consists on a linear Stieltjes equation. Our second model, more realistic, is nonlinear, discontinuous and functional, and we deduce the existence of solutions by means of a result proven in this paper.

More on a Functional Equation

ERIC Educational Resources Information Center

Deakin, Michael A. B.

2006-01-01

This classroom note presents a final solution for the functional equation: f(xy)=xf(y) + yf(x). The functional equation if formally similar to the familiar product rule of elementary calculus and this similarity prompted its study by Ren et al., who derived some results concerning it. The purpose of this present note is to extend these results and…

Regional height-diameter equations for major tree species of southwest Oregon.

Treesearch

H. Temesgen; D.W. Hann; V.J. Monleon

2006-01-01

Selected tree height and diameter functions were evaluated for their predictive abilities for major tree species of southwest Oregon. The equations included tree diameter alone, or diameter plus alternative measures of stand density and relative position. Two of the base equations were asymptotic functions, and two were exponential functional forms. The inclusion of...

New Results on the Linear Equating Methods for the Non-Equivalent-Groups Design

ERIC Educational Resources Information Center

von Davier, Alina A.

2008-01-01

The two most common observed-score equating functions are the linear and equipercentile functions. These are often seen as different methods, but von Davier, Holland, and Thayer showed that any equipercentile equating function can be decomposed into linear and nonlinear parts. They emphasized the dominant role of the linear part of the nonlinear…

Multiscale moment-based technique for object matching and recognition

NASA Astrophysics Data System (ADS)

Thio, HweeLi; Chen, Liya; Teoh, Eam-Khwang

2000-03-01

A new method is proposed to extract features from an object for matching and recognition. The features proposed are a combination of local and global characteristics -- local characteristics from the 1-D signature function that is defined to each pixel on the object boundary, global characteristics from the moments that are generated from the signature function. The boundary of the object is first extracted, then the signature function is generated by computing the angle between two lines from every point on the boundary as a function of position along the boundary. This signature function is position, scale and rotation invariant (PSRI). The shape of the signature function is then described quantitatively by using moments. The moments of the signature function are the global characters of a local feature set. Using moments as the eventual features instead of the signature function reduces the time and complexity of an object matching application. Multiscale moments are implemented to produce several sets of moments that will generate more accurate matching. Basically multiscale technique is a coarse to fine procedure and makes the proposed method more robust to noise. This method is proposed to match and recognize objects under simple transformation, such as translation, scale changes, rotation and skewing. A simple logo indexing system is implemented to illustrate the performance of the proposed method.

Baseline Experiments on Coulomb Damping due to Rotational Slip

DTIC Science & Technology

1992-12-01

by Griffe121 . As expected Equation (2-39) matches the result given by Griffel . 2.2.2. Euler-Bernoulli Beam versus Timeshenko Beam. Omitted from Euler...McGraw-Hill, Inc., 1983. 20. Clark, S. K., Dynamics of Continuous Elements, New Jersey, Prentice-Hall, Inc., 1972. 21. Griffel , W., Beam Formulas

Efficiency of laser beam utilization in gas laser cutting of materials

NASA Astrophysics Data System (ADS)

Galushkin, M. G.; Grishaev, R. V.

2018-02-01

Relying on the condition of dynamic matching of the process parameters in gas laser cutting, the dependence of the beam utilization factor on the cutting speed and the beam power has been determined. An energy balance equation has been derived for a wide range of cutting speed values.

Stationary axisymmetric exteriors for perturbations of isolated bodies in general relativity, to second order

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

MacCallum, Malcolm A. H.; Mars, Marc; Vera, Rauel

Perturbed stationary axisymmetric isolated bodies, e.g. stars, represented by a matter-filled interior and an asymptotically flat vacuum exterior joined at a surface where the Darmois matching conditions are satisfied, are considered. The initial state is assumed to be static. The perturbations of the matching conditions are derived and used as boundary conditions for the perturbed Ernst equations in the exterior region. The perturbations are calculated to second order. The boundary conditions are overdetermined: necessary and sufficient conditions for their compatibility are derived. The special case of perturbations of spherical bodies is given in detail.

Variational Methods in Design Optimization and Sensitivity Analysis for Two-Dimensional Euler Equations

NASA Technical Reports Server (NTRS)

Ibrahim, A. H.; Tiwari, S. N.; Smith, R. E.

1997-01-01

Variational methods (VM) sensitivity analysis employed to derive the costate (adjoint) equations, the transversality conditions, and the functional sensitivity derivatives. In the derivation of the sensitivity equations, the variational methods use the generalized calculus of variations, in which the variable boundary is considered as the design function. The converged solution of the state equations together with the converged solution of the costate equations are integrated along the domain boundary to uniquely determine the functional sensitivity derivatives with respect to the design function. The application of the variational methods to aerodynamic shape optimization problems is demonstrated for internal flow problems at supersonic Mach number range. The study shows, that while maintaining the accuracy of the functional sensitivity derivatives within the reasonable range for engineering prediction purposes, the variational methods show a substantial gain in computational efficiency, i.e., computer time and memory, when compared with the finite difference sensitivity analysis.

Acute fatigue impairs neuromuscular activity of anterior cruciate ligament-agonist muscles in female team handball players.

PubMed

Zebis, M K; Bencke, J; Andersen, L L; Alkjaer, T; Suetta, C; Mortensen, P; Kjaer, M; Aagaard, P

2011-12-01

In sports, like team handball, fatigue has been associated with an increased risk of anterior cruciate ligament (ACL) injury. While effects of fatigue on muscle function are commonly assessed during maximal isometric voluntary contraction (MVC), such measurements may not relate to the muscle function during match play. The purpose of this study was to investigate the effect of muscle fatigue induced by a simulated handball match on neuromuscular strategy during a functional sidecutting movement, associated with the incidence of ACL injury. Fourteen female team handball players were tested for neuromuscular activity [electromyography (EMG)] during a sidecutting maneuver on a force plate, pre and post a simulated handball match. MVC was obtained during maximal isometric quadriceps and hamstring contraction. The simulated handball match consisted of exercises mimicking handball match activity. Whereas the simulated handball match induced a decrease in MVC strength for both the quadriceps and hamstring muscles (P<0.05), a selective decrease in hamstring neuromuscular activity was seen during sidecutting (P<0.05). This study shows impaired ACL-agonist muscle (i.e. hamstring) activity during sidecutting in response to acute fatigue induced by handball match play. Thus, screening procedures should involve functional movements to reveal specific fatigue-induced deficits in ACL-agonist muscle activation during high-risk phases of match play. © 2010 John Wiley & Sons A/S.

Gauge-free cluster variational method by maximal messages and moment matching.

PubMed

Domínguez, Eduardo; Lage-Castellanos, Alejandro; Mulet, Roberto; Ricci-Tersenghi, Federico

2017-04-01

We present an implementation of the cluster variational method (CVM) as a message passing algorithm. The kind of message passing algorithm used for CVM, usually named generalized belief propagation (GBP), is a generalization of the belief propagation algorithm in the same way that CVM is a generalization of the Bethe approximation for estimating the partition function. However, the connection between fixed points of GBP and the extremal points of the CVM free energy is usually not a one-to-one correspondence because of the existence of a gauge transformation involving the GBP messages. Our contribution is twofold. First, we propose a way of defining messages (fields) in a generic CVM approximation, such that messages arrive on a given region from all its ancestors, and not only from its direct parents, as in the standard parent-to-child GBP. We call this approach maximal messages. Second, we focus on the case of binary variables, reinterpreting the messages as fields enforcing the consistency between the moments of the local (marginal) probability distributions. We provide a precise rule to enforce all consistencies, avoiding any redundancy, that would otherwise lead to a gauge transformation on the messages. This moment matching method is gauge free, i.e., it guarantees that the resulting GBP is not gauge invariant. We apply our maximal messages and moment matching GBP to obtain an analytical expression for the critical temperature of the Ising model in general dimensions at the level of plaquette CVM. The values obtained outperform Bethe estimates, and are comparable with loop corrected belief propagation equations. The method allows for a straightforward generalization to disordered systems.

Gauge-free cluster variational method by maximal messages and moment matching

NASA Astrophysics Data System (ADS)

Domínguez, Eduardo; Lage-Castellanos, Alejandro; Mulet, Roberto; Ricci-Tersenghi, Federico

2017-04-01

We present an implementation of the cluster variational method (CVM) as a message passing algorithm. The kind of message passing algorithm used for CVM, usually named generalized belief propagation (GBP), is a generalization of the belief propagation algorithm in the same way that CVM is a generalization of the Bethe approximation for estimating the partition function. However, the connection between fixed points of GBP and the extremal points of the CVM free energy is usually not a one-to-one correspondence because of the existence of a gauge transformation involving the GBP messages. Our contribution is twofold. First, we propose a way of defining messages (fields) in a generic CVM approximation, such that messages arrive on a given region from all its ancestors, and not only from its direct parents, as in the standard parent-to-child GBP. We call this approach maximal messages. Second, we focus on the case of binary variables, reinterpreting the messages as fields enforcing the consistency between the moments of the local (marginal) probability distributions. We provide a precise rule to enforce all consistencies, avoiding any redundancy, that would otherwise lead to a gauge transformation on the messages. This moment matching method is gauge free, i.e., it guarantees that the resulting GBP is not gauge invariant. We apply our maximal messages and moment matching GBP to obtain an analytical expression for the critical temperature of the Ising model in general dimensions at the level of plaquette CVM. The values obtained outperform Bethe estimates, and are comparable with loop corrected belief propagation equations. The method allows for a straightforward generalization to disordered systems.

Evaluation of pier-scour equations for coarse-bed streams

USGS Publications Warehouse

Chase, Katherine J.; Holnbeck, Stephen R.

2004-01-01

Streambed scour at bridge piers is among the leading causes of bridge failure in the United States. Several pier-scour equations have been developed to calculate potential scour depths at existing and proposed bridges. Because many pier-scour equations are based on data from laboratory flumes and from cohesionless silt- and sand-bottomed streams, they tend to overestimate scour for piers in coarse-bed materials. Several equations have been developed to incorporate the mitigating effects of large particle sizes on pier scour, but further investigations are needed to evaluate how accurately pier-scour depths calculated by these equations match measured field data. This report, prepared in cooperation with the Montana Department of Transportation, describes the evaluation of five pier-scour equations for coarse-bed streams. Pier-scour and associated bridge-geometry, bed-material, and streamflow-measurement data at bridges over coarse-bed streams in Montana, Alaska, Maryland, Ohio, and Virginia were selected from the Bridge Scour Data Management System. Pier scour calculated using the Simplified Chinese equation, the Froehlich equation, the Froehlich design equation, the HEC-18/Jones equation and the HEC-18/Mueller equation for flood events with approximate recurrence intervals of less than 2 to 100 years were compared to 42 pier-scour measurements. Comparison of results showed that pier-scour depths calculated with the HEC-18/Mueller equation were seldom smaller than measured pier-scour depths. In addition, pier-scour depths calculated using the HEC-18/Mueller equation were closer to measured scour than for the other equations that did not underestimate pier scour. However, more data are needed from coarse-bed streams and from less frequent flood events to further evaluate pier-scour equations.

Algebraic Construction of Exact Difference Equations from Symmetry of Equations

NASA Astrophysics Data System (ADS)

Itoh, Toshiaki

2009-09-01

Difference equations or exact numerical integrations, which have general solutions, are treated algebraically. Eliminating the symmetries of the equation, we can construct difference equations (DCE) or numerical integrations equivalent to some ODEs or PDEs that means both have the same solution functions. When arbitrary functions are given, whether we can construct numerical integrations that have solution functions equal to given function or not are treated in this work. Nowadays, Lie's symmetries solver for ODE and PDE has been implemented in many symbolic software. Using this solver we can construct algebraic DCEs or numerical integrations which are correspond to some ODEs or PDEs. In this work, we treated exact correspondence between ODE or PDE and DCE or numerical integration with Gröbner base and Janet base from the view of Lie's symmetries.

Kicking the rugby ball: perturbations of 6D gauged chiral supergravity

NASA Astrophysics Data System (ADS)

Burgess, C. P.; de Rham, C.; Hoover, D.; Mason, D.; Tolley, A. J.

2007-02-01

We analyse the axially symmetric scalar perturbations of 6D chiral gauged supergravity compactified on the general warped geometries in the presence of two source branes. We find that all of the conical geometries are marginally stable for normalizable perturbations (in disagreement with some recent calculations) and the non-conical ones for regular perturbations, even though none of them are supersymmetric (apart from the trivial Salam Sezgin solution, for which there are no source branes). The marginal direction is the one whose presence is required by the classical scaling property of the field equations, and all other modes have positive squared mass. In the special case of the conical solutions, including (but not restricted to) the unwarped 'rugby-ball' solutions, we find closed-form expressions for the mode functions in terms of Legendre and hypergeometric functions. In so doing we show how to match the asymptotic near-brane form for the solution to the physics of the source branes, and thereby how to physically interpret perturbations which can be singular at the brane positions.

Modeling and simulation of electronic structure, material interface and random doping in nano electronic devices

PubMed Central

Chen, Duan; Wei, Guo-Wei

2010-01-01

The miniaturization of nano-scale electronic devices, such as metal oxide semiconductor field effect transistors (MOSFETs), has given rise to a pressing demand in the new theoretical understanding and practical tactic for dealing with quantum mechanical effects in integrated circuits. Modeling and simulation of this class of problems have emerged as an important topic in applied and computational mathematics. This work presents mathematical models and computational algorithms for the simulation of nano-scale MOSFETs. We introduce a unified two-scale energy functional to describe the electrons and the continuum electrostatic potential of the nano-electronic device. This framework enables us to put microscopic and macroscopic descriptions in an equal footing at nano scale. By optimization of the energy functional, we derive consistently-coupled Poisson-Kohn-Sham equations. Additionally, layered structures are crucial to the electrostatic and transport properties of nano transistors. A material interface model is proposed for more accurate description of the electrostatics governed by the Poisson equation. Finally, a new individual dopant model that utilizes the Dirac delta function is proposed to understand the random doping effect in nano electronic devices. Two mathematical algorithms, the matched interface and boundary (MIB) method and the Dirichlet-to-Neumann mapping (DNM) technique, are introduced to improve the computational efficiency of nano-device simulations. Electronic structures are computed via subband decomposition and the transport properties, such as the I-V curves and electron density, are evaluated via the non-equilibrium Green's functions (NEGF) formalism. Two distinct device configurations, a double-gate MOSFET and a four-gate MOSFET, are considered in our three-dimensional numerical simulations. For these devices, the current fluctuation and voltage threshold lowering effect induced by the discrete dopant model are explored. Numerical convergence and model well-posedness are also investigated in the present work. PMID:20396650

F-Expansion Method and New Exact Solutions of the Schrödinger-KdV Equation

PubMed Central

Filiz, Ali; Ekici, Mehmet; Sonmezoglu, Abdullah

2014-01-01

F-expansion method is proposed to seek exact solutions of nonlinear evolution equations. With the aid of symbolic computation, we choose the Schrödinger-KdV equation with a source to illustrate the validity and advantages of the proposed method. A number of Jacobi-elliptic function solutions are obtained including the Weierstrass-elliptic function solutions. When the modulus m of Jacobi-elliptic function approaches to 1 and 0, soliton-like solutions and trigonometric-function solutions are also obtained, respectively. The proposed method is a straightforward, short, promising, and powerful method for the nonlinear evolution equations in mathematical physics. PMID:24672327

F-expansion method and new exact solutions of the Schrödinger-KdV equation.

PubMed

Filiz, Ali; Ekici, Mehmet; Sonmezoglu, Abdullah

2014-01-01

F-expansion method is proposed to seek exact solutions of nonlinear evolution equations. With the aid of symbolic computation, we choose the Schrödinger-KdV equation with a source to illustrate the validity and advantages of the proposed method. A number of Jacobi-elliptic function solutions are obtained including the Weierstrass-elliptic function solutions. When the modulus m of Jacobi-elliptic function approaches to 1 and 0, soliton-like solutions and trigonometric-function solutions are also obtained, respectively. The proposed method is a straightforward, short, promising, and powerful method for the nonlinear evolution equations in mathematical physics.

Analytical expressions for the correlation function of a hard sphere dimer fluid

NASA Astrophysics Data System (ADS)

Kim, Soonho; Chang, Jaeeon; Kim, Hwayong

A closed form expression is given for the correlation function of a hard sphere dimer fluid. A set of integral equations is obtained from Wertheim's multidensity Ornstein-Zernike integral equation theory with Percus-Yevick approximation. Applying the Laplace transformation method to the integral equations and then solving the resulting equations algebraically, the Laplace transforms of the individual correlation functions are obtained. By the inverse Laplace transformation, the radial distribution function (RDF) is obtained in closed form out to 3D (D is the segment diameter). The analytical expression for the RDF of the hard dimer should be useful in developing the perturbation theory of dimer fluids.

Analytical expression for the correlation function of a hard sphere chain fluid

NASA Astrophysics Data System (ADS)

Chang, Jaeeon; Kim, Hwayong

A closed form expression is given for the correlation function of flexible hard sphere chain fluid. A set of integral equations obtained from Wertheim's multidensity Ornstein-Zernike integral equation theory with the polymer Percus-Yevick ideal chain approximation is considered. Applying the Laplace transformation method to the integral equations and then solving the resulting equations algebraically, the Laplace transforms of individual correlation functions are obtained. By inverse Laplace transformation the inter- and intramolecular radial distribution functions (RDFs) are obtained in closed forms up to 3D(D is segment diameter). These analytical expressions for the RDFs would be useful in developing the perturbation theory of chain fluids.

Modeling of dispersed-drug delivery from planar polymeric systems: optimizing analytical solutions.

PubMed

Helbling, Ignacio M; Ibarra, Juan C D; Luna, Julio A; Cabrera, María I; Grau, Ricardo J A

2010-11-15

Analytical solutions for the case of controlled dispersed-drug release from planar non-erodible polymeric matrices, based on Refined Integral Method, are presented. A new adjusting equation is used for the dissolved drug concentration profile in the depletion zone. The set of equations match the available exact solution. In order to illustrate the usefulness of this model, comparisons with experimental profiles reported in the literature are presented. The obtained results show that the model can be employed in a broad range of applicability. Copyright © 2010 Elsevier B.V. All rights reserved.

Holographic Quark Matter and Neutron Stars.

PubMed

Hoyos, Carlos; Jokela, Niko; Rodríguez Fernández, David; Vuorinen, Aleksi

2016-07-15

We use a top-down holographic model for strongly interacting quark matter to study the properties of neutron stars. When the corresponding equation of state (EOS) is matched with state-of-the-art results for dense nuclear matter, we consistently observe a first-order phase transition at densities between 2 and 7 times the nuclear saturation density. Solving the Tolman-Oppenheimer-Volkov equations with the resulting hybrid EOSs, we find maximal stellar masses in excess of two solar masses, albeit somewhat smaller than those obtained with simple extrapolations of the nuclear matter EOSs. Our calculation predicts that no quark matter exists inside neutron stars.

Laplace-transform-based method to calculate back-reflected radiance from an isotropically scattering half-space

NASA Astrophysics Data System (ADS)

Rinzema, K.; Hoenders, B. J.; Ferwerda, H. A.

1997-07-01

We present a method to determine the back-reflected radiance from an isotropically scattering half-space with matched boundary. This method has the advantage that it leads very quickly to the relevant equations, the numerical solution of which is also quite easy. Essentially, the method is derived from a mathematical criterion that effectively forbids the existence of solutions to the transport equation which grow exponentially as one moves away from the surface and deeper into the medium. Preliminary calculations for infinitely wide beams yield results which agree very well with what is found in the literature.

Solidification of a binary mixture

NASA Technical Reports Server (NTRS)

Antar, B. N.

1982-01-01

The time dependent concentration and temperature profiles of a finite layer of a binary mixture are investigated during solidification. The coupled time dependent Stefan problem is solved numerically using an implicit finite differencing algorithm with the method of lines. Specifically, the temporal operator is approximated via an implicit finite difference operator resulting in a coupled set of ordinary differential equations for the spatial distribution of the temperature and concentration for each time. Since the resulting differential equations set form a boundary value problem with matching conditions at an unknown spatial point, the method of invariant imbedding is used for its solution.

Brane world in non-Riemannian geometry

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

Maier, R.; Falciano, F. T.

2011-03-15

We carefully investigate the modified Einstein's field equation in a 4-dimensional (3-brane) arbitrary manifold embedded in a 5-dimensional non-Riemannian bulk spacetime with a noncompact extra dimension. In this context the Israel-Darmois matching conditions are extended assuming that the torsion in the bulk is continuous. The discontinuity in the torsion first derivatives are related to the matter distribution through the field equation. In addition, we develop a model that describes a flat FLRW model embedded in a 5-dimensional de Sitter or anti-de Sitter, where a 5-dimensional cosmological constant emerges from the torsion.

Predictive equation of state method for heavy materials based on the Dirac equation and density functional theory

NASA Astrophysics Data System (ADS)

Wills, John M.; Mattsson, Ann E.

2012-02-01

Density functional theory (DFT) provides a formally predictive base for equation of state properties. Available approximations to the exchange/correlation functional provide accurate predictions for many materials in the periodic table. For heavy materials however, DFT calculations, using available functionals, fail to provide quantitative predictions, and often fail to be even qualitative. This deficiency is due both to the lack of the appropriate confinement physics in the exchange/correlation functional and to approximations used to evaluate the underlying equations. In order to assess and develop accurate functionals, it is essential to eliminate all other sources of error. In this talk we describe an efficient first-principles electronic structure method based on the Dirac equation and compare the results obtained with this method with other methods generally used. Implications for high-pressure equation of state of relativistic materials are demonstrated in application to Ce and the light actinides. Sandia National Laboratories is a multi-program laboratory managed andoperated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

Greedy algorithms for diffuse optical tomography reconstruction

NASA Astrophysics Data System (ADS)

Dileep, B. P. V.; Das, Tapan; Dutta, Pranab K.

2018-03-01

Diffuse optical tomography (DOT) is a noninvasive imaging modality that reconstructs the optical parameters of a highly scattering medium. However, the inverse problem of DOT is ill-posed and highly nonlinear due to the zig-zag propagation of photons that diffuses through the cross section of tissue. The conventional DOT imaging methods iteratively compute the solution of forward diffusion equation solver which makes the problem computationally expensive. Also, these methods fail when the geometry is complex. Recently, the theory of compressive sensing (CS) has received considerable attention because of its efficient use in biomedical imaging applications. The objective of this paper is to solve a given DOT inverse problem by using compressive sensing framework and various Greedy algorithms such as orthogonal matching pursuit (OMP), compressive sampling matching pursuit (CoSaMP), and stagewise orthogonal matching pursuit (StOMP), regularized orthogonal matching pursuit (ROMP) and simultaneous orthogonal matching pursuit (S-OMP) have been studied to reconstruct the change in the absorption parameter i.e, Δα from the boundary data. Also, the Greedy algorithms have been validated experimentally on a paraffin wax rectangular phantom through a well designed experimental set up. We also have studied the conventional DOT methods like least square method and truncated singular value decomposition (TSVD) for comparison. One of the main features of this work is the usage of less number of source-detector pairs, which can facilitate the use of DOT in routine applications of screening. The performance metrics such as mean square error (MSE), normalized mean square error (NMSE), structural similarity index (SSIM), and peak signal to noise ratio (PSNR) have been used to evaluate the performance of the algorithms mentioned in this paper. Extensive simulation results confirm that CS based DOT reconstruction outperforms the conventional DOT imaging methods in terms of computational efficiency. The main advantage of this study is that the forward diffusion equation solver need not be repeatedly solved.

Optical systolic solutions of linear algebraic equations

NASA Technical Reports Server (NTRS)

Neuman, C. P.; Casasent, D.

1984-01-01

The philosophy and data encoding possible in systolic array optical processor (SAOP) were reviewed. The multitude of linear algebraic operations achievable on this architecture is examined. These operations include such linear algebraic algorithms as: matrix-decomposition, direct and indirect solutions, implicit and explicit methods for partial differential equations, eigenvalue and eigenvector calculations, and singular value decomposition. This architecture can be utilized to realize general techniques for solving matrix linear and nonlinear algebraic equations, least mean square error solutions, FIR filters, and nested-loop algorithms for control engineering applications. The data flow and pipelining of operations, design of parallel algorithms and flexible architectures, application of these architectures to computationally intensive physical problems, error source modeling of optical processors, and matching of the computational needs of practical engineering problems to the capabilities of optical processors are emphasized.

Matrix approaches to assess terrestrial nitrogen scheme in CLM4.5

NASA Astrophysics Data System (ADS)

Du, Z.

2017-12-01

Terrestrial carbon (C) and nitrogen (N) cycles have been commonly represented by a series of balance equations to track their influxes into and effluxes out of individual pools in earth system models (ESMs). This representation matches our understanding of C and N cycle processes well but makes it difficult to track model behaviors. To overcome these challenges, we developed a matrix approach, which reorganizes the series of terrestrial C and N balance equations in the CLM4.5 into two matrix equations based on original representation of C and N cycle processes and mechanisms. The matrix approach would consequently help improve the comparability of models and data, evaluate impacts of additional model components, facilitate benchmark analyses, model intercomparisons, and data-model fusion, and improve model predictive power.

Quantum integrability and functional equations

NASA Astrophysics Data System (ADS)

Volin, Dmytro

2010-03-01

In this thesis a general procedure to represent the integral Bethe Ansatz equations in the form of the Reimann-Hilbert problem is given. This allows us to study in simple way integrable spin chains in the thermodynamic limit. Based on the functional equations we give the procedure that allows finding the subleading orders in the solution of various integral equations solved to the leading order by the Wiener-Hopf technics. The integral equations are studied in the context of the AdS/CFT correspondence, where their solution allows verification of the integrability conjecture up to two loops of the strong coupling expansion. In the context of the two-dimensional sigma models we analyze the large-order behavior of the asymptotic perturbative expansion. Obtained experience with the functional representation of the integral equations allowed us also to solve explicitly the crossing equations that appear in the AdS/CFT spectral problem.

Dispersion relations of elastic waves in one-dimensional piezoelectric/piezomagnetic phononic crystal with functionally graded interlayers.

PubMed

Guo, Xiao; Wei, Peijun; Lan, Man; Li, Li

2016-08-01

The effects of functionally graded interlayers on dispersion relations of elastic waves in a one-dimensional piezoelectric/piezomagnetic phononic crystal are studied in this paper. First, the state transfer equation of the functionally graded interlayer is derived from the motion equation by the reduction of order (from second order to first order). The transfer matrix of the functionally graded interlayer is obtained by solving the state transfer equation with the spatial-varying coefficient. Based on the transfer matrixes of the piezoelectric slab, the piezomagnetic slab and the functionally graded interlayers, the total transfer matrix of a single cell is obtained. Further, the Bloch theorem is used to obtain the resultant dispersion equations of in-plane and anti-plane Bloch waves. The dispersion equations are solved numerically and the numerical results are shown graphically. Five kinds of profiles of functionally graded interlayers between a piezoelectric slab and a piezomagnetic slab are considered. It is shown that the functionally graded interlayers have evident influences on the dispersion curves and the band gaps. Copyright © 2016 Elsevier B.V. All rights reserved.

The structure of a three-dimensional turbulent boundary layer

NASA Technical Reports Server (NTRS)

Degani, A. T.; Smith, F. T.; Walker, J. D. A.

1993-01-01

The three-dimensional turbulent boundary layer is shown to have a self-consistent two-layer asymptotic structure in the limit of large Reynolds number. In a streamline coordinate system, the streamwise velocity distribution is similar to that in two-dimensional flows, having a defect-function form in the outer layer which is adjusted to zero at the wall through an inner wall layer. An asymptotic expansion accurate to two orders is required for the cross-stream velocity which is shown to exhibit a logarithmic form in the overlap region. The inner wall-layer flow is collateral to leading order but the influence of the pressure gradient, at large but finite Reynolds numbers, is not negligible and can cause substantial skewing of the velocity profile near the wall. Conditions under which the boundary layer achieves self-similarity and the governing set of ordinary differential equations for the outer layer are derived. The calculated solution of these equations is matched asymptotically to an inner wall-layer solution and the composite profiles so formed describe the flow throughout the entire boundary layer. The effects of Reynolds number and cross-stream pressure gradient on the crossstream velocity profile are discussed and it is shown that the location of the maximum cross-stream velocity is within the overlap region.

Modeling and predicting the biofilm formation of Salmonella Virchow with respect to temperature and pH.

PubMed

Ariafar, M Nima; Buzrul, Sencer; Akçelik, Nefise

2016-03-01

Biofilm formation of Salmonella Virchow was monitored with respect to time at three different temperature (20, 25 and 27.5 °C) and pH (5.2, 5.9 and 6.6) values. As the temperature increased at a constant pH level, biofilm formation decreased while as the pH level increased at a constant temperature, biofilm formation increased. Modified Gompertz equation with high adjusted determination coefficient (Radj(2)) and low mean square error (MSE) values produced reasonable fits for the biofilm formation under all conditions. Parameters of the modified Gompertz equation could be described in terms of temperature and pH by use of a second order polynomial function. In general, as temperature increased maximum biofilm quantity, maximum biofilm formation rate and time of acceleration of biofilm formation decreased; whereas, as pH increased; maximum biofilm quantity, maximum biofilm formation rate and time of acceleration of biofilm formation increased. Two temperature (23 and 26 °C) and pH (5.3 and 6.3) values were used up to 24 h to predict the biofilm formation of S. Virchow. Although the predictions did not perfectly match with the data, reasonable estimates were obtained. In principle, modeling and predicting the biofilm formation of different microorganisms on different surfaces under various conditions could be possible.

Barometric fluctuations in wells tapping deep unconfined aquifers

USGS Publications Warehouse

Weeks, Edwin P.

1979-01-01

Water levels in wells screened only below the water table in unconfined aquifers fluctuate in response to atmospheric pressure changes. These fluctuations occur because the materials composing the unsaturated zone resist air movement and have capacity to store air with a change in pressure. Consequently, the translation of any pressure change at land surface is slowed as it moves through the unsaturated zone to the water table, but it reaches the water surface in the well instantaneously. Thus a pressure imbalance is created that results in a water level fluctuation. Barometric effects on water levels in unconfined aquifers can be computed by solution of the differential equation governing the flow of gas in the unsaturated zone subject to the appropriate boundary conditions. Solutions to this equation for two sets of boundary conditions were applied to compute water level response in a well tapping the Ogallala Formation near Lubbock, Texas from simultaneous microbarograph records. One set of computations, based on the step function unit response solution and convolution, resulted in a very good match between computed and measured water levels. A second set of computations, based on analysis of the amplitude ratios of simultaneous cyclic microbarograph and water level fluctuations, gave inconsistent results in terms of the unsaturated zone pneumatic properties but provided useful insights on the nature of unconfined-aquifer water level fluctuations.

Intrusion detection using secure signatures

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

Nelson, Trent Darnel; Haile, Jedediah

A method and device for intrusion detection using secure signatures comprising capturing network data. A search hash value, value employing at least one one-way function, is generated from the captured network data using a first hash function. The presence of a search hash value match in a secure signature table comprising search hash values and an encrypted rule is determined. After determining a search hash value match, a decryption key is generated from the captured network data using a second hash function, a hash function different form the first hash function. One or more of the encrypted rules of themore » secure signatures table having a hash value equal to the generated search hash value are then decrypted using the generated decryption key. The one or more decrypted secure signature rules are then processed for a match and one or more user notifications are deployed if a match is identified.« less

Multiscale functions, scale dynamics, and applications to partial differential equations

NASA Astrophysics Data System (ADS)

Cresson, Jacky; Pierret, Frédéric

2016-05-01

Modeling phenomena from experimental data always begins with a choice of hypothesis on the observed dynamics such as determinism, randomness, and differentiability. Depending on these choices, different behaviors can be observed. The natural question associated to the modeling problem is the following: "With a finite set of data concerning a phenomenon, can we recover its underlying nature? From this problem, we introduce in this paper the definition of multi-scale functions, scale calculus, and scale dynamics based on the time scale calculus [see Bohner, M. and Peterson, A., Dynamic Equations on Time Scales: An Introduction with Applications (Springer Science & Business Media, 2001)] which is used to introduce the notion of scale equations. These definitions will be illustrated on the multi-scale Okamoto's functions. Scale equations are analysed using scale regimes and the notion of asymptotic model for a scale equation under a particular scale regime. The introduced formalism explains why a single scale equation can produce distinct continuous models even if the equation is scale invariant. Typical examples of such equations are given by the scale Euler-Lagrange equation. We illustrate our results using the scale Newton's equation which gives rise to a non-linear diffusion equation or a non-linear Schrödinger equation as asymptotic continuous models depending on the particular fractional scale regime which is considered.

A System of Poisson Equations for a Nonconstant Varadhan Functional on a Finite State Space

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

Cavazos-Cadena, Rolando; Hernandez-Hernandez, Daniel

2006-01-15

Given a discrete-time Markov chain with finite state space and a stationary transition matrix, a system of 'local' Poisson equations characterizing the (exponential) Varadhan's functional J(.) is given. The main results, which are derived for an arbitrary transition structure so that J(.) may be nonconstant, are as follows: (i) Any solution to the local Poisson equations immediately renders Varadhan's functional, and (ii) a solution of the system always exist. The proof of this latter result is constructive and suggests a method to solve the local Poisson equations.

The Analytical Solution of the Transient Radial Diffusion Equation with a Nonuniform Loss Term.

NASA Astrophysics Data System (ADS)

Loridan, V.; Ripoll, J. F.; De Vuyst, F.

2017-12-01

Many works have been done during the past 40 years to perform the analytical solution of the radial diffusion equation that models the transport and loss of electrons in the magnetosphere, considering a diffusion coefficient proportional to a power law in shell and a constant loss term. Here, we propose an original analytical method to address this challenge with a nonuniform loss term. The strategy is to match any L-dependent electron losses with a piecewise constant function on M subintervals, i.e., dealing with a constant lifetime on each subinterval. Applying an eigenfunction expansion method, the eigenvalue problem becomes presently a Sturm-Liouville problem with M interfaces. Assuming the continuity of both the distribution function and its first spatial derivatives, we are able to deal with a well-posed problem and to find the full analytical solution. We further show an excellent agreement between both the analytical solutions and the solutions obtained directly from numerical simulations for different loss terms of various shapes and with a diffusion coefficient DLL L6. We also give two expressions for the required number of eigenmodes N to get an accurate snapshot of the analytical solution, highlighting that N is proportional to 1/√t0, where t0 is a time of interest, and that N increases with the diffusion power. Finally, the equilibrium time, defined as the time to nearly reach the steady solution, is estimated by a closed-form expression and discussed. Applications to Earth and also Jupiter and Saturn are discussed.

Treatment of charge singularities in implicit solvent models.

PubMed

Geng, Weihua; Yu, Sining; Wei, Guowei

2007-09-21

This paper presents a novel method for solving the Poisson-Boltzmann (PB) equation based on a rigorous treatment of geometric singularities of the dielectric interface and a Green's function formulation of charge singularities. Geometric singularities, such as cusps and self-intersecting surfaces, in the dielectric interfaces are bottleneck in developing highly accurate PB solvers. Based on an advanced mathematical technique, the matched interface and boundary (MIB) method, we have recently developed a PB solver by rigorously enforcing the flux continuity conditions at the solvent-molecule interface where geometric singularities may occur. The resulting PB solver, denoted as MIBPB-II, is able to deliver second order accuracy for the molecular surfaces of proteins. However, when the mesh size approaches half of the van der Waals radius, the MIBPB-II cannot maintain its accuracy because the grid points that carry the interface information overlap with those that carry distributed singular charges. In the present Green's function formalism, the charge singularities are transformed into interface flux jump conditions, which are treated on an equal footing as the geometric singularities in our MIB framework. The resulting method, denoted as MIBPB-III, is able to provide highly accurate electrostatic potentials at a mesh as coarse as 1.2 A for proteins. Consequently, at a given level of accuracy, the MIBPB-III is about three times faster than the APBS, a recent multigrid PB solver. The MIBPB-III has been extensively validated by using analytically solvable problems, molecular surfaces of polyatomic systems, and 24 proteins. It provides reliable benchmark numerical solutions for the PB equation.

Treatment of charge singularities in implicit solvent models

NASA Astrophysics Data System (ADS)

Geng, Weihua; Yu, Sining; Wei, Guowei

2007-09-01

This paper presents a novel method for solving the Poisson-Boltzmann (PB) equation based on a rigorous treatment of geometric singularities of the dielectric interface and a Green's function formulation of charge singularities. Geometric singularities, such as cusps and self-intersecting surfaces, in the dielectric interfaces are bottleneck in developing highly accurate PB solvers. Based on an advanced mathematical technique, the matched interface and boundary (MIB) method, we have recently developed a PB solver by rigorously enforcing the flux continuity conditions at the solvent-molecule interface where geometric singularities may occur. The resulting PB solver, denoted as MIBPB-II, is able to deliver second order accuracy for the molecular surfaces of proteins. However, when the mesh size approaches half of the van der Waals radius, the MIBPB-II cannot maintain its accuracy because the grid points that carry the interface information overlap with those that carry distributed singular charges. In the present Green's function formalism, the charge singularities are transformed into interface flux jump conditions, which are treated on an equal footing as the geometric singularities in our MIB framework. The resulting method, denoted as MIBPB-III, is able to provide highly accurate electrostatic potentials at a mesh as coarse as 1.2Å for proteins. Consequently, at a given level of accuracy, the MIBPB-III is about three times faster than the APBS, a recent multigrid PB solver. The MIBPB-III has been extensively validated by using analytically solvable problems, molecular surfaces of polyatomic systems, and 24 proteins. It provides reliable benchmark numerical solutions for the PB equation.

Models for microtubule cargo transport coupling the Langevin equation to stochastic stepping motor dynamics: Caring about fluctuations.

PubMed

Bouzat, Sebastián

2016-01-01

One-dimensional models coupling a Langevin equation for the cargo position to stochastic stepping dynamics for the motors constitute a relevant framework for analyzing multiple-motor microtubule transport. In this work we explore the consistence of these models focusing on the effects of the thermal noise. We study how to define consistent stepping and detachment rates for the motors as functions of the local forces acting on them in such a way that the cargo velocity and run-time match previously specified functions of the external load, which are set on the base of experimental results. We show that due to the influence of the thermal fluctuations this is not a trivial problem, even for the single-motor case. As a solution, we propose a motor stepping dynamics which considers memory on the motor force. This model leads to better results for single-motor transport than the approaches previously considered in the literature. Moreover, it gives a much better prediction for the stall force of the two-motor case, highly compatible with the experimental findings. We also analyze the fast fluctuations of the cargo position and the influence of the viscosity, comparing the proposed model to the standard one, and we show how the differences on the single-motor dynamics propagate to the multiple motor situations. Finally, we find that the one-dimensional character of the models impede an appropriate description of the fast fluctuations of the cargo position at small loads. We show how this problem can be solved by considering two-dimensional models.

Far-from-equilibrium attractors and nonlinear dynamical systems approach to the Gubser flow

NASA Astrophysics Data System (ADS)

Behtash, Alireza; Cruz-Camacho, C. N.; Martinez, M.

2018-02-01

The nonequilibrium attractors of systems undergoing Gubser flow within relativistic kinetic theory are studied. In doing so we employ well-established methods of nonlinear dynamical systems which rely on finding the fixed points, investigating the structure of the flow diagrams of the evolution equations, and characterizing the basin of attraction using a Lyapunov function near the stable fixed points. We obtain the attractors of anisotropic hydrodynamics, Israel-Stewart (IS) and transient fluid (DNMR) theories and show that they are indeed nonplanar and the basin of attraction is essentially three dimensional. The attractors of each hydrodynamical model are compared with the one obtained from the exact Gubser solution of the Boltzmann equation within the relaxation time approximation. We observe that the anisotropic hydrodynamics is able to match up to high numerical accuracy the attractor of the exact solution while the second-order hydrodynamical theories fail to describe it. We show that the IS and DNMR asymptotic series expansions diverge and use resurgence techniques to perform the resummation of these divergences. We also comment on a possible link between the manifold of steepest descent paths in path integrals and the basin of attraction for the attractors via Lyapunov functions that opens a new horizon toward an effective field theory description of hydrodynamics. Our findings indicate that the reorganization of the expansion series carried out by anisotropic hydrodynamics resums the Knudsen and inverse Reynolds numbers to all orders and thus, it can be understood as an effective theory for the far-from-equilibrium fluid dynamics.

Mapping surrogate gasoline compositions into RON/MON space

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

Morgan, Neal; Kraft, Markus; Smallbone, Andrew

2010-06-15

In this paper, new experimentally determined octane numbers (RON and MON) of blends of a tri-component surrogate consisting of toluene, n-heptane, i-octane (called toluene reference fuel TRF) arranged in an augmented simplex design are used to derive a simple response surface model for the octane number of any arbitrary TRF mixture. The model is second-order in its complexity and is shown to be more accurate to the standard ''linear-by-volume'' (LbV) model which is often used when no other information is available. Such observations are due to the existence of both synergistic and antagonistic blending of the octane numbers between themore » three components. In particular, antagonistic blending of toluene and iso-octane leads to a maximum in sensitivity that lies on the toluene/iso-octane line. The model equations are inverted so as to map from RON/MON space back into composition space. Enabling one to use two simple formulae to determine, for a given fuel with known RON and MON, the volume fractions of toluene, n-heptane and iso-octane to be blended in order to emulate that fuel. HCCI engine simulations using gasoline with a RON of 98.5 and a MON of 88 were simulated using a TRF fuel, blended according to the derived equations to match the RON and MON. The simulations matched the experimentally obtained pressure profiles well, especially when compared to simulations using only PRF fuels which matched the RON or MON. This suggested that the mapping is accurate and that to emulate a refinery gasoline, it is necessary to match not only the RON but also the MON of the fuel. (author)« less

Determination of lateral-stability derivatives and transfer-function coefficients from frequency-response data for lateral motions

NASA Technical Reports Server (NTRS)

Donegan, James J; Robinson, Samuel W , Jr; Gates, Ordway, B , jr

1955-01-01

A method is presented for determining the lateral-stability derivatives, transfer-function coefficients, and the modes for lateral motion from frequency-response data for a rigid aircraft. The method is based on the application of the vector technique to the equations of lateral motion, so that the three equations of lateral motion can be separated into six equations. The method of least squares is then applied to the data for each of these equations to yield the coefficients of the equations of lateral motion from which the lateral-stability derivatives and lateral transfer-function coefficients are computed. Two numerical examples are given to demonstrate the use of the method.

Artery buckling analysis using a two-layered wall model with collagen dispersion.

PubMed

Mottahedi, Mohammad; Han, Hai-Chao

2016-07-01

Artery buckling has been proposed as a possible cause for artery tortuosity associated with various vascular diseases. Since microstructure of arterial wall changes with aging and diseases, it is essential to establish the relationship between microscopic wall structure and artery buckling behavior. The objective of this study was to developed arterial buckling equations to incorporate the two-layered wall structure with dispersed collagen fiber distribution. Seven porcine carotid arteries were tested for buckling to determine their critical buckling pressures at different axial stretch ratios. The mechanical properties of these intact arteries and their intima-media layer were determined via pressurized inflation test. Collagen alignment was measured from histological sections and modeled by a modified von-Mises distribution. Buckling equations were developed accordingly using microstructure-motivated strain energy function. Our results demonstrated that collagen fibers disperse around two mean orientations symmetrically to the circumferential direction (39.02°±3.04°) in the adventitia layer; while aligning closely in the circumferential direction (2.06°±3.88°) in the media layer. The microstructure based two-layered model with collagen fiber dispersion described the buckling behavior of arteries well with the model predicted critical pressures match well with the experimental measurement. Parametric studies showed that with increasing fiber dispersion parameter, the predicted critical buckling pressure increases. These results validate the microstructure-based model equations for artery buckling and set a base for further studies to predict the stability of arteries due to microstructural changes associated with vascular diseases and aging. Copyright © 2016 Elsevier Ltd. All rights reserved.

Models of collective cell spreading with variable cell aspect ratio: a motivation for degenerate diffusion models.

PubMed

Simpson, Matthew J; Baker, Ruth E; McCue, Scott W

2011-02-01

Continuum diffusion models are often used to represent the collective motion of cell populations. Most previous studies have simply used linear diffusion to represent collective cell spreading, while others found that degenerate nonlinear diffusion provides a better match to experimental cell density profiles. In the cell modeling literature there is no guidance available with regard to which approach is more appropriate for representing the spreading of cell populations. Furthermore, there is no knowledge of particular experimental measurements that can be made to distinguish between situations where these two models are appropriate. Here we provide a link between individual-based and continuum models using a multiscale approach in which we analyze the collective motion of a population of interacting agents in a generalized lattice-based exclusion process. For round agents that occupy a single lattice site, we find that the relevant continuum description of the system is a linear diffusion equation, whereas for elongated rod-shaped agents that occupy L adjacent lattice sites we find that the relevant continuum description is connected to the porous media equation (PME). The exponent in the nonlinear diffusivity function is related to the aspect ratio of the agents. Our work provides a physical connection between modeling collective cell spreading and the use of either the linear diffusion equation or the PME to represent cell density profiles. Results suggest that when using continuum models to represent cell population spreading, we should take care to account for variations in the cell aspect ratio because different aspect ratios lead to different continuum models.

Control of functional differential equations with function space boundary conditions

NASA Technical Reports Server (NTRS)

Banks, H. T.

1972-01-01

Problems involving functional differential equations with terminal conditions in function space are considered. Their application to mechanical and electrical systems is discussed. Investigations of controllability, existence of optimal controls, and necessary and sufficient conditions for optimality are reported.

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

Baer, M.R.; Hobbs, M.L.; McGee, B.C.

Exponential-13,6 (EXP-13,6) potential pammeters for 750 gases composed of 48 elements were determined and assembled in a database, referred to as the JCZS database, for use with the Jacobs Cowperthwaite Zwisler equation of state (JCZ3-EOS)~l) The EXP- 13,6 force constants were obtained by using literature values of Lennard-Jones (LJ) potential functions, by using corresponding states (CS) theory, by matching pure liquid shock Hugoniot data, and by using molecular volume to determine the approach radii with the well depth estimated from high-pressure isen- tropes. The JCZS database was used to accurately predict detonation velocity, pressure, and temperature for 50 dif- 3more » Accurate predictions were also ferent explosives with initial densities ranging from 0.25 glcm3 to 1.97 g/cm . obtained for pure liquid shock Hugoniots, static properties of nitrogen, and gas detonations at high initial pressures.« less

Space-Time Characteristic Functions in Multivariate Logic and Possible Interpretation of Entanglement

NASA Astrophysics Data System (ADS)

Gaudeau de Gerlicz, Claude; Sechpine, Pierre; Bobola, Philippe; Antoine, Mathias

The knowledge about hidden variables in physics, (Bohr's-Schrödinger theories) and their developments, boundaries seem more and more fuzzy at physical scales. Also some other new theories give to both time and space as much fuzziness. The classical theory, (school of Copenhagen's) and also Heisenberg and Louis de Broglie give us the idea of a dual wave and particle parts such the way we observe. Thus, the Pondichery interpretation recently developed by Cramer and al. gives to the time part this duality. According Cramer, there could be a little more to this duality, some late or advanced waves of time that have been confirmed and admitted as possible solutions with the Maxwell's equations. We developed here a possible pattern that could matched in the sequence between Space and both retarded and advanced time wave in the "Cramer handshake" in locality of the present when the observation is made everything become local.

Anomalous dimensions of spinning operators from conformal symmetry

NASA Astrophysics Data System (ADS)

Gliozzi, Ferdinando

2018-01-01

We compute, to the first non-trivial order in the ɛ-expansion of a perturbed scalar field theory, the anomalous dimensions of an infinite class of primary operators with arbitrary spin ℓ = 0, 1, . . . , including as a particular case the weakly broken higher-spin currents, using only constraints from conformal symmetry. Following the bootstrap philosophy, no reference is made to any Lagrangian, equations of motion or coupling constants. Even the space dimensions d are left free. The interaction is implicitly turned on through the local operators by letting them acquire anomalous dimensions. When matching certain four-point and five-point functions with the corresponding quantities of the free field theory in the ɛ → 0 limit, no free parameter remains. It turns out that only the expected discrete d values are permitted and the ensuing anomalous dimensions reproduce known results for the weakly broken higher-spin currents and provide new results for the other spinning operators.

Coloured Logic Petri Nets and analysis of their reachable trees

NASA Astrophysics Data System (ADS)

Wang, Jing; Du, YuYue; Yu, ShuXia

2015-11-01

Logic Petri nets (LPNs) can describe and analyse the batch processing function and passing value indeterminacy in cooperative systems, and alleviate the state space explosion problem. However, the indeterminate data of logical output transitions cannot be described explicitly in LPNs. Therefore, Coloured Logic Petri nets (CLPNs) are defined in this paper. It can determine the indeterminate data of logic output transitions in LPNs, i.e., the indeterminate data can be represented definitely in CLPNs. A vector matching method is proposed to judge the enabling transitions and analyse CLPNs. From the marking equation and the proposed reachable tree generation algorithm of CLPNs, a reachable tree can be built, and reachable markings are calculated. The advantage of CLPNs can be shown based on the number of leaf nodes of the reachability tree, and CLPNs can solve the indeterminate data of logical output transitions. Finally, an example shows that CLPNs can further reduce the dimensionality of reachable markings.

On an example of a system of differential equations that are integrated in Abelian functions

NASA Astrophysics Data System (ADS)

Malykh, M. D.; Sevastianov, L. A.

2017-12-01

The short review of the theory of Abelian functions and its applications in mechanics and analytical theory of differential equations is given. We think that Abelian functions are the natural generalization of commonly used functions because if the general solution of the 2nd order differential equation depends algebraically on the constants of integration, then integrating this equation does not lead out of the realm of commonly used functions complemented by the Abelian functions (Painlevé theorem). We present a relatively simple example of a dynamical system that is integrated in Abelian integrals by “pairing” two copies of a hyperelliptic curve. Unfortunately, initially simple formulas unfold into very long ones. Apparently the theory of Abelian functions hasn’t been finished in the last century because without computer algebra systems it was impossible to complete the calculations to the end. All calculations presented in our report are performed in Sage.

Application of the principal fractional meta-trigonometric functions for the solution of linear commensurate-order time-invariant fractional differential equations.

PubMed

Lorenzo, C F; Hartley, T T; Malti, R

2013-05-13

A new and simplified method for the solution of linear constant coefficient fractional differential equations of any commensurate order is presented. The solutions are based on the R-function and on specialized Laplace transform pairs derived from the principal fractional meta-trigonometric functions. The new method simplifies the solution of such fractional differential equations and presents the solutions in the form of real functions as opposed to fractional complex exponential functions, and thus is directly applicable to real-world physics.

Exp-function method for solving fractional partial differential equations.

PubMed

Zheng, Bin

2013-01-01

We extend the Exp-function method to fractional partial differential equations in the sense of modified Riemann-Liouville derivative based on nonlinear fractional complex transformation. For illustrating the validity of this method, we apply it to the space-time fractional Fokas equation and the nonlinear fractional Sharma-Tasso-Olver (STO) equation. As a result, some new exact solutions for them are successfully established.

Coincidence degree and periodic solutions of neutral equations

NASA Technical Reports Server (NTRS)

Hale, J. K.; Mawhin, J.

1973-01-01

The problem of existence of periodic solutions for some nonautonomous neutral functional differential equations is examined. It is an application of a basic theorem on the Fredholm alternative for periodic solutions of some linear neutral equations and of a generalized Leray-Schauder theory. Although proofs are simple, the results are nontrivial extensions to the neutral case of existence theorems for periodic solutions of functional differential equations.

Orbital stability and energy estimate of ground states of saturable nonlinear Schrödinger equations with intensity functions in R2

NASA Astrophysics Data System (ADS)

Lin, Tai-Chia; Wang, Xiaoming; Wang, Zhi-Qiang

2017-10-01

Conventionally, the existence and orbital stability of ground states of nonlinear Schrödinger (NLS) equations with power-law nonlinearity (subcritical case) can be proved by an argument using strict subadditivity of the ground state energy and the concentration compactness method of Cazenave and Lions [4]. However, for saturable nonlinearity, such an argument is not applicable because strict subadditivity of the ground state energy fails in this case. Here we use a convexity argument to prove the existence and orbital stability of ground states of NLS equations with saturable nonlinearity and intensity functions in R2. Besides, we derive the energy estimate of ground states of saturable NLS equations with intensity functions using the eigenvalue estimate of saturable NLS equations without intensity function.

The general relativistic thin disc evolution equation

NASA Astrophysics Data System (ADS)

Balbus, Steven A.

2017-11-01

In the classical theory of thin disc accretion discs, the constraints of mass and angular momentum conservation lead to a diffusion-like equation for the turbulent evolution of the surface density. Here, we revisit this problem, extending the Newtonian analysis to the regime of Kerr geometry relevant to black holes. A diffusion-like equation once again emerges, but now with a singularity at the radius at which the effective angular momentum gradient passes through zero. The equation may be analysed using a combination of Wentzel-Kramers-Brillouin techniques, local techniques and matched asymptotic expansions. It is shown that imposing the boundary condition of a vanishing stress tensor (more precisely the radial-azimuthal component thereof) allows smooth stable modes to exist external to the angular momentum singularity, the innermost stable circular orbit, while smoothly vanishing inside this location. The extension of the disc diffusion equation to the domain of general relativity introduces a new tool for numerical and phenomenological studies of accretion discs, and may prove to be a useful technique for understanding black hole X-ray transients.

Low-Storage, Explicit Runge-Kutta Schemes for the Compressible Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Kennedy, Chistopher A.; Carpenter, Mark H.; Lewis, R. Michael

1999-01-01

The derivation of storage explicit Runge-Kutta (ERK) schemes has been performed in the context of integrating the compressible Navier-Stokes equations via direct numerical simulation. Optimization of ERK methods is done across the broad range of properties, such as stability and accuracy efficiency, linear and nonlinear stability, error control reliability, step change stability, and dissipation/dispersion accuracy, subject to varying degrees of memory economization. Following van der Houwen and Wray, 16 ERK pairs are presented using from two to five registers of memory per equation, per grid point and having accuracies from third- to fifth-order. Methods have been assessed using the differential equation testing code DETEST, and with the 1D wave equation. Two of the methods have been applied to the DNS of a compressible jet as well as methane-air and hydrogen-air flames. Derived 3(2) and 4(3) pairs are competitive with existing full-storage methods. Although a substantial efficiency penalty accompanies use of two- and three-register, fifth-order methods, the best contemporary full-storage methods can be pearl), matched while still saving two to three registers of memory.

A complete equation of state for non-ideal condensed phase explosives

NASA Astrophysics Data System (ADS)

Wilkinson, S. D.; Braithwaite, M.; Nikiforakis, N.; Michael, L.

2017-12-01

The objective of this work is to improve the robustness and accuracy of numerical simulations of both ideal and non-ideal explosives by introducing temperature dependence in mechanical equations of state for reactants and products. To this end, we modify existing mechanical equations of state to appropriately approximate the temperature in the reaction zone. Mechanical equations of state of the Mie-Grüneisen form are developed with extensions, which allow the temperature to be evaluated appropriately and the temperature equilibrium condition to be applied robustly. Furthermore, the snow plow model is used to capture the effect of porosity on the reactant equation of state. We apply the methodology to predict the velocity of compliantly confined detonation waves. Once reaction rates are calibrated for unconfined detonation velocities, simulations of confined rate sticks and slabs are performed, and the experimental detonation velocities are matched without further parameter alteration, demonstrating the predictive capability of our simulations. We apply the same methodology to both ideal (PBX9502, a high explosive with principal ingredient TATB) and non-ideal (EM120D, an ANE or ammonium nitrate based emulsion) explosives.

Differential Item Functioning Detection with the Mantel-Haenszel Procedure: The Effects of Matching Types and Other Factors

ERIC Educational Resources Information Center

Socha, Alan; DeMars, Christine E.; Zilberberg, Anna; Phan, Ha

2015-01-01

The Mantel-Haenszel (MH) procedure is commonly used to detect items that function differentially for groups of examinees from various demographic and linguistic backgrounds--for example, in international assessments. As in some other DIF methods, the total score is used to match examinees on ability. In thin matching, each of the total score…

Quantification of Ethanol's Anti-Punishment Effect in Humans Using the Generalized Matching Equation

ERIC Educational Resources Information Center

Rasmussen, Erin B.; Newland, M. Christopher

2009-01-01

Increases in rates of punished behavior by the administration of drugs with anxiolytic effects (called antipunishment effects) are well established in animals but not humans. The present study examined antipunishment effects of ethanol in humans using a choice procedure. The behavior of 5 participants was placed under six concurrent…

Learning in Context: Linguistic and Attentional Constraints on Children's Color Term Learning

ERIC Educational Resources Information Center

O'Hanlon, Catherine G.; Roberson, Debi

2006-01-01

Three experiments investigated whether linguistic and/or attentional constraints might account for preschoolers' difficulties when learning color terms. Task structure and demands were equated across experiments, and both speed and degree of learning were compared. In Experiment 1, 3-year-olds who were matched on vocabulary score were taught new…

Face and Object Discrimination in Autism, and Relationship to IQ and Age

ERIC Educational Resources Information Center

Pallett, Pamela M.; Cohen, Shereen J.; Dobkins, Karen R.

2014-01-01

The current study tested fine discrimination of upright and inverted faces and objects in adolescents with Autism Spectrum Disorder (ASD) as compared to age- and IQ-matched controls. Discrimination sensitivity was tested using morphed faces and morphed objects, and all stimuli were equated in low-level visual characteristics (luminance, contrast,…

The Representational Status of Pretence: Evidence from Typical Development and Autism

ERIC Educational Resources Information Center

Jarrold, Christopher; Mansergh, Ruth; Whiting, Claire

2010-01-01

The question of whether understanding pretend play requires meta-representational skill was examined among typically developing children and individuals with autism. Participants were presented with closely equated true and false pretence trials in which they had to judge a protagonist's pretend reading of a situation, which either matched or…

Investigations on entropy layer along hypersonic hyperboloids using a defect boundary layer

NASA Technical Reports Server (NTRS)

Brazier, J. P.; Aupoix, B.; Cousteix, J.

1992-01-01

A defect approach coupled with matched asymptotic expansions is used to derive a new set of boundary layer equations. This method ensures a smooth matching of the boundary layer with the inviscid solution. These equations are solved to calculate boundary layers over hypersonic blunt bodies involving the entropy gradient effect. Systematic comparisons are made for both axisymmetric and plane flows in several cases with different Mach and Reynolds numbers. After a brief survey of the entropy layer characteristics, the defect boundary layer results are compared with standard boundary layer and full Navier-Stokes solutions. The entropy gradient effects are found to be more important in the axisymmetric case than in the plane one. The wall temperature has a great influence on the results through the displacement effect. Good predictions can be obtained with the defect approach over a cold wall in the nose region, with a first order solution. However, the defect approach gives less accurate results far from the nose on axisymmetric bodies because of the thinning of the entropy layer.

Nonspherically symmetric black string perturbations in the large dimension limit

NASA Astrophysics Data System (ADS)

Sadhu, Amruta; Suneeta, Vardarajan

2016-06-01

We consider nonspherically symmetric perturbations of the uncharged black string/flat black brane in the large dimension (D) limit of general relativity. We express the perturbations in a simplified form using variables introduced by Ishibashi and Kodama. We apply the large D limit to the equations and show that this leads to decoupling of the equations in the near-horizon and asymptotic regions. It also enables use of matched asymptotic expansions to obtain approximate analytical solutions and to analyze stability of the black string/brane. For a large class of nonspherically symmetric perturbations, we prove that there are no instabilities in the large D limit. For the rest, we provide additional matching arguments that indicate that the black string/brane is stable. In the static limit, we show that for all nonspherically symmetric perturbations, there is no instability. This is proof that the Gross-Perry-Yaffe mode for semiclassical black hole perturbations is the unique unstable mode even in the large D limit. This work is also a direct analytical indication that the only instability of the black string is the Gregory-Laflamme instability.

Detection of Abnormal Operation Noise Using CHLAC of Sound Spectrograph and Continuous DP Matching

NASA Astrophysics Data System (ADS)

Hattori, Koosuke; Ohmi, Taishi; Taguchi, Ryo; Umezaki, Taizo

It is a general way that the industrial product is tested by individual inspector. If the product involves sound factors, each inspector will evaluate the test product to sort out a strange engine noise from the natural sound. However, it is hard to cover the consistency in evaluation criteria due to the personal equation referred to the idea that every individual had an inherent bias, plus a physical and mental conditions can be a negative effect on his/her evaluation criteria. It would be ideal if the criteria would not be affected by anyone, anywhere, circumstances; accordingly the quality of products must be equated. In this paper, we propose a noise detection method based on Cubic Higher-order Local Auto-Correlation (CHLAC) scheme and DP Matching provided by Cepstrum Analysis to extract the correct solution. This technique is practically used for detecting any human abnormal movements out of a monitored video clip and identifying individual persons by voice. The study results are shown to be highly effective in our proposed method.

Mathematics for Physics

NASA Astrophysics Data System (ADS)

Stone, Michael; Goldbart, Paul

2009-07-01

Preface; 1. Calculus of variations; 2. Function spaces; 3. Linear ordinary differential equations; 4. Linear differential operators; 5. Green functions; 6. Partial differential equations; 7. The mathematics of real waves; 8. Special functions; 9. Integral equations; 10. Vectors and tensors; 11. Differential calculus on manifolds; 12. Integration on manifolds; 13. An introduction to differential topology; 14. Group and group representations; 15. Lie groups; 16. The geometry of fibre bundles; 17. Complex analysis I; 18. Applications of complex variables; 19. Special functions and complex variables; Appendixes; Reference; Index.

A Comparison of Grid-based and SPH Binary Mass-transfer and Merger Simulations

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

Motl, Patrick M.; Frank, Juhan; Clayton, Geoffrey C.

2017-04-01

There is currently a great amount of interest in the outcomes and astrophysical implications of mergers of double degenerate binaries. In a commonly adopted approximation, the components of such binaries are represented by polytropes with an index of n  = 3/2. We present detailed comparisons of stellar mass-transfer and merger simulations of polytropic binaries that have been carried out using two very different numerical algorithms—a finite-volume “grid” code and a smoothed-particle hydrodynamics (SPH) code. We find that there is agreement in both the ultimate outcomes of the evolutions and the intermediate stages if the initial conditions for each code are chosen to matchmore » as closely as possible. We find that even with closely matching initial setups, the time it takes to reach a concordant evolution differs between the two codes because the initial depth of contact cannot be matched exactly. There is a general tendency for SPH to yield higher mass transfer rates and faster evolution to the final outcome. We also present comparisons of simulations calculated from two different energy equations: in one series, we assume a polytropic equation of state and in the other series an ideal gas equation of state. In the latter series of simulations, an atmosphere forms around the accretor, which can exchange angular momentum and cause a more rapid loss of orbital angular momentum. In the simulations presented here, the effect of the ideal equation of state is to de-stabilize the binary in both SPH and grid simulations, but the effect is more pronounced in the grid code.« less

Is gravidity 4+ a risk factor for oral clefts? A case-control study in eight South american countries using structural equation modeling.

PubMed

Gili, Juan Antonio; Poletta, Fernando Adrián; Campaña, Hebe; Comas, Belén; Pawluk, Mariela; Rittler, Monica; López-Camelo, Jorge Santiago

2013-09-01

Background : There is disagreement about the association between cleft lip with or without cleft palate and multigravidity, which could be explained by differences of adjusting for maternal age, Amerindian ancestry, and socioeconomic status. Objective : The aim was to evaluate gravidity 4+ (four or more gestations) as a risk factor for cleft lip with or without cleft palate in South America. Design : We used a matched (1:1) case-control study with structural equation modeling for related causes. Data were obtained from 1,371,575 consecutive newborn infants weighing ≥500 g who were born in the hospitals of the Estudio Colaborativo Latinoamericano de Malformaciones Congénitas (ECLAMC) network between 1982 and 1999. There were a total of 1,271 cases with cleft lip with or without cleft palate (excluding midline and atypical cleft lip with or without cleft palate). A total of 1,227 case-control pairs were obtained, matched by maternal age, newborn gender, and year and place of birth. Potential confounders and intermediary variables were analyzed with structural equation modeling. Results : The crude risk of gravidity 4+ was 1.41 and the 95% confidence interval was 1.14 to 1.61. When applying structural equation modeling, the effect of multigravidity on the risk of cleft lip with or without cleft palate was 1.22 and the 95% confidence interval was 0.91 to 1.39. Conclusions : Multigravid mothers (more than four gestations) showed no greater risk of bearing children who had cleft lip with or without cleft palate than mothers with two or three births. Therefore, the often observed and reported association between multigravidity and oral clefts likely reflects the effect of other risk factors related to low socioeconomic status in South American populations.

Development of low-frequency kernel-function aerodynamics for comparison with time-dependent finite-difference methods

NASA Technical Reports Server (NTRS)

Bland, S. R.

1982-01-01

Finite difference methods for unsteady transonic flow frequency use simplified equations in which certain of the time dependent terms are omitted from the governing equations. Kernel functions are derived for two dimensional subsonic flow, and provide accurate solutions of the linearized potential equation with the same time dependent terms omitted. These solutions make possible a direct evaluation of the finite difference codes for the linear problem. Calculations with two of these low frequency kernel functions verify the accuracy of the LTRAN2 and HYTRAN2 finite difference codes. Comparisons of the low frequency kernel function results with the Possio kernel function solution of the complete linear equations indicate the adequacy of the HYTRAN approximation for frequencies in the range of interest for flutter calculations.

Van der Waals equation of state revisited: importance of the dispersion correction.

PubMed

de Visser, Sam P

2011-04-28

One of the most basic equations of state describing nonideal gases and liquids is the van der Waals equation of state, and as a consequence, it is generally taught in most first year undergraduate chemistry courses. In this work, we show that the constants a and b in the van der Waals equation of state are linearly proportional to the polarizability volume of the molecules in a gas or liquid. Using this information, a new thermodynamic one-parameter equation of state is derived that contains experimentally measurable variables and physics constants only. This is the first equation of state apart from the Ideal Gas Law that contains experimentally measurable variables and physics constants only, and as such, it may be a very useful and practical equation for the description of dilute gases and liquids. The modified van der Waals equation of state describes pV as the sum of repulsive and attractive intermolecular interaction energies that are represented by an exponential repulsion function between the electron clouds of the molecules and a London dispersion component, respectively. The newly derived equation of state is tested against experimental data for several gas and liquid examples, and the agreement is satisfactory. The description of the equation of state as a one-parameter function also has implications on other thermodynamic functions, such as critical parameters, virial coefficients, and isothermal compressibilities. Using our modified van der Waals equation of state, we show that all of these properties are a function of the molecular polarizability volume. Correlations of experimental data confirm the derived proportionalities.

Existence and stability of dispersive solutions to the Kadomtsev-Petviashvili equation in the presence of dispersion effect

NASA Astrophysics Data System (ADS)

Das, Amiya; Ganguly, Asish

2017-07-01

The paper deals with Kadomtsev-Petviashvili (KP) equation in presence of a small dispersion effect. The nature of solutions are examined under the dispersion effect by using Lyapunov function and dynamical system theory. We prove that when dispersion is added to the KP equation, in certain regions, yet there exist bounded traveling wave solutions in the form of solitary waves, periodic and elliptic functions. The general solution of the equation with or without the dispersion effect are obtained in terms of Weirstrass ℘ functions and Jacobi elliptic functions. New form of kink-type solutions are established by exploring a new technique based on factorization method, use of functional transformation and the Abel's first order nonlinear equation. Furthermore, the stability analysis of the dispersive solutions are examined which shows that the traveling wave velocity is a bifurcation parameter which governs between different classes of waves. We use the phase plane analysis and show that at a critical velocity, the solution has a transcritical bifurcation.

Application of the Green's function method for 2- and 3-dimensional steady transonic flows

NASA Technical Reports Server (NTRS)

Tseng, K.

1984-01-01

A Time-Domain Green's function method for the nonlinear time-dependent three-dimensional aerodynamic potential equation is presented. The Green's theorem is being used to transform the partial differential equation into an integro-differential-delay equation. Finite-element and finite-difference methods are employed for the spatial and time discretizations to approximate the integral equation by a system of differential-delay equations. Solution may be obtained by solving for this nonlinear simultaneous system of equations in time. This paper discusses the application of the method to the Transonic Small Disturbance Equation and numerical results for lifting and nonlifting airfoils and wings in steady flows are presented.

Consistent description of kinetic equation with triangle anomaly

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

Pu Shi; Gao Jianhua; Wang Qun

2011-05-01

We provide a consistent description of the kinetic equation with a triangle anomaly which is compatible with the entropy principle of the second law of thermodynamics and the charge/energy-momentum conservation equations. In general an anomalous source term is necessary to ensure that the equations for the charge and energy-momentum conservation are satisfied and that the correction terms of distribution functions are compatible to these equations. The constraining equations from the entropy principle are derived for the anomaly-induced leading order corrections to the particle distribution functions. The correction terms can be determined for the minimum number of unknown coefficients in onemore » charge and two charge cases by solving the constraining equations.« less

Pair correlation function and nonlinear kinetic equation for a spatially uniform polarizable nonideal plasma

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

Belyi, V.V.; Kukharenko, Y.A.; Wallenborn, J.

Taking into account the first non-Markovian correction to the Balescu-Lenard equation, we have derived an expression for the pair correlation function and a nonlinear kinetic equation valid for a nonideal polarized classical plasma. This last equation allows for the description of the correlational energy evolution and shows the global conservation of energy with dynamical polarization. {copyright} {ital 1996 The American Physical Society.}

Gauge-invariant flow equation

NASA Astrophysics Data System (ADS)

Wetterich, C.

2018-06-01

We propose a closed gauge-invariant functional flow equation for Yang-Mills theories and quantum gravity that only involves one macroscopic gauge field or metric. It is based on a projection on physical and gauge fluctuations. Deriving this equation from a functional integral we employ the freedom in the precise choice of the macroscopic field and the effective average action in order to realize a closed and simple form of the flow equation.

The stability of quadratic-reciprocal functional equation

NASA Astrophysics Data System (ADS)

Song, Aimin; Song, Minwei

2018-04-01

A new quadratic-reciprocal functional equation f ((k +1 )x +k y )+f ((k +1 )x -k y )=2/f (x )f (y )[(k+1 ) 2f (y )+k2f (x )] [(k+1)2f (y )-k2f (x )] 2 is introduced. The Hyers-Ulam stability for the quadratic-reciprocal functional equations is proved in Banach spaces using the direct method and the fixed point method, respectively.

Quantum dot properties in the multiband envelope-function approximation using boundary conditions based upon first-principles quantum calculations

NASA Astrophysics Data System (ADS)

Flory, Curt A.; Musgrave, Charles B.; Zhang, Zhiyong

2008-05-01

A number of physical processes involving quantum dots depend critically upon the “evanescent” electron eigenstate wave function that extends outside of the material surface into the surrounding region. These processes include electron tunneling through quantum dots, as well as interactions between multiple quantum dot structures. In order to unambiguously determine these evanescent fields, appropriate boundary conditions have been developed to connect the electronic solutions interior to the semiconductor quantum dot to exterior vacuum solutions. In standard envelope function theory, the interior wave function consists of products of band edge and envelope functions, and both must be considered when matching to the external solution. While the envelope functions satisfy tractable equations, the band edge functions are generally not known. In this work, symmetry arguments in the spherically symmetric approximation are used in conjunction with the known qualitative behavior of bonding and antibonding orbitals to catalog the behavior of the band edge functions at the unit cell boundary. This physical approximation allows consolidation of the influence of the band edge functions to two simple surface parameters that are incorporated into the boundary conditions and are straightforwardly computed by using numerical first-principles quantum techniques. These new boundary conditions are employed to analyze an isolated spherically symmetric semiconductor quantum dot in vacuum within the analytical model of Sercel and Vahala [Phys. Rev. Lett. 65, 239 (1990); Phys. Rev. B 42, 3690 (1990)]. Results are obtained for quantum dots made of GaAs and InP, which are compared with ab initio calculations that have appeared in the literature.

Parametric Equations: Push 'Em Back, Push 'Em Back, Way Back!

ERIC Educational Resources Information Center

Cieply, Joseph F.

1993-01-01

Stresses using the features of graphing calculators to teach parametric equations much earlier in the curriculum than is presently done. Examples using parametric equations to teach slopes and lines in beginning algebra, inverse functions in advanced algebra, the wrapping function, and simulations of physical phenomena are presented. (MAZ)

Effect of Differential Item Functioning on Test Equating

ERIC Educational Resources Information Center

Kabasakal, Kübra Atalay; Kelecioglu, Hülya

2015-01-01

This study examines the effect of differential item functioning (DIF) items on test equating through multilevel item response models (MIRMs) and traditional IRMs. The performances of three different equating models were investigated under 24 different simulation conditions, and the variables whose effects were examined included sample size, test…

Tidal Love Numbers of Neutron Stars

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

Hinderer, Tanja

For a variety of fully relativistic polytropic neutron star models we calculate the star's tidal Love number k{sub 2}. Most realistic equations of state for neutron stars can be approximated as a polytrope with an effective index n {approx} 0.5-1.0. The equilibrium stellar model is obtained by numerical integration of the Tolman-Oppenheimer-Volkhov equations. We calculate the linear l = 2 static perturbations to the Schwarzschild spacetime following the method of Thorne and Campolattaro. Combining the perturbed Einstein equations into a single second-order differential equation for the perturbation to the metric coefficient g{sub tt} and matching the exterior solution to themore » asymptotic expansion of the metric in the star's local asymptotic rest frame gives the Love number. Our results agree well with the Newtonian results in the weak field limit. The fully relativistic values differ from the Newtonian values by up to {approx}24%. The Love number is potentially measurable in gravitational wave signals from inspiralling binary neutron stars.« less

Electroosmotic flow and Joule heating in preparative continuous annular electrochromatography.

PubMed

Laskowski, René; Bart, Hans-Jörg

2015-09-01

An openFOAM "computational fluid dynamic" simulation model was developed for the description of local interaction of hydrodynamics and Joule heating in annular electrochromatography. A local decline of electrical conductivity of the background eluent is caused by an electrokinetic migration of ions resulting in higher Joule heat generation. The model equations consider the Navier-Stokes equation for incompressible fluids, the energy equation for stationary temperature fields, and the mass transfer equation for the electrokinetic flow. The simulations were embedded in commercial ANSYS Fluent software and in open-source environment openFOAM. The annular gap (1 mm width) contained an inorganic C8 reverse-phase monolith as stationary phase prepared by an in situ sol-gel process. The process temperature generated by Joule heating was determined by thermal camera system. The local hydrodynamics in the prototype was detected by a gravimetric contact-free measurement method and experimental and simulated values matched quite well. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Calculation of Thermally-Induced Displacements in Spherically Domed Ion Engine Grids

NASA Technical Reports Server (NTRS)

Soulas, George C.

2006-01-01

An analytical method for predicting the thermally-induced normal and tangential displacements of spherically domed ion optics grids under an axisymmetric thermal loading is presented. A fixed edge support that could be thermally expanded is used for this analysis. Equations for the displacements both normal and tangential to the surface of the spherical shell are derived. A simplified equation for the displacement at the center of the spherical dome is also derived. The effects of plate perforation on displacements and stresses are determined by modeling the perforated plate as an equivalent solid plate with modified, or effective, material properties. Analytical model results are compared to the results from a finite element model. For the solid shell, comparisons showed that the analytical model produces results that closely match the finite element model results. The simplified equation for the normal displacement of the spherical dome center is also found to accurately predict this displacement. For the perforated shells, the analytical solution and simplified equation produce accurate results for materials with low thermal expansion coefficients.

Optimization of GM(1,1) power model

NASA Astrophysics Data System (ADS)

Luo, Dang; Sun, Yu-ling; Song, Bo

2013-10-01

GM (1,1) power model is the expansion of traditional GM (1,1) model and Grey Verhulst model. Compared with the traditional models, GM (1,1) power model has the following advantage: The power exponent in the model which best matches the actual data values can be found by certain technology. So, GM (1,1) power model can reflect nonlinear features of the data, simulate and forecast with high accuracy. It's very important to determine the best power exponent during the modeling process. In this paper, according to the GM(1,1) power model of albino equation is Bernoulli equation, through variable substitution, turning it into the GM(1,1) model of the linear albino equation form, and then through the grey differential equation properly built, established GM(1,1) power model, and parameters with pattern search method solution. Finally, we illustrate the effectiveness of the new methods with the example of simulating and forecasting the promotion rates from senior secondary schools to higher education in China.

Global boundary flattening transforms for acoustic propagation under rough sea surfaces.

PubMed

Oba, Roger M

2010-07-01

This paper introduces a conformal transform of an acoustic domain under a one-dimensional, rough sea surface onto a domain with a flat top. This non-perturbative transform can include many hundreds of wavelengths of the surface variation. The resulting two-dimensional, flat-topped domain allows direct application of any existing, acoustic propagation model of the Helmholtz or wave equation using transformed sound speeds. Such a transform-model combination applies where the surface particle velocity is much slower than sound speed, such that the boundary motion can be neglected. Once the acoustic field is computed, the bijective (one-to-one and onto) mapping permits the field interpolation in terms of the original coordinates. The Bergstrom method for inverse Riemann maps determines the transform by iterated solution of an integral equation for a surface matching term. Rough sea surface forward scatter test cases provide verification of the method using a particular parabolic equation model of the Helmholtz equation.

On the Maxwellian distribution, symmetric form, and entropy conservation for the Euler equations

NASA Technical Reports Server (NTRS)

Deshpande, S. M.

1986-01-01

The Euler equations of gas dynamics have some very interesting properties in that the flux vector is a homogeneous function of the unknowns and the equations can be cast in symmetric hyperbolic form and satisfy the entropy conservation. The Euler equations are the moments of the Boltzmann equation of the kinetic theory of gases when the velocity distribution function is a Maxwellian. The present paper shows the relationship between the symmetrizability and the Maxwellian velocity distribution. The entropy conservation is in terms of the H-function, which is a slight modification of the H-function first introduced by Boltzmann in his famous H-theorem. In view of the H-theorem, it is suggested that the development of total H-diminishing (THD) numerical methods may be more profitable than the usual total variation diminishing (TVD) methods for obtaining wiggle-free solutions.

A new stream function formulation for the Euler equations

NASA Technical Reports Server (NTRS)

Atkins, H. L.; Hassan, H. A.

1983-01-01

A new stream function formulation is developed for the solution of Euler's equations in the transonic flow region. The stream function and the density are the dependent variables in this method, while the governing equations for adiabatic flow are the momentum equations which are solved in the strong conservation law form. The application of this method does not require a knowledge of the vorticity. The algorithm is combined with the automatic grid solver (GRAPE) of Steger and Sorenson (1979) in order to study arbitrary geometries. Results of the application of this method are presented for the NACA 0012 airfoil at various Mach numbers and angles of attack, and cylinders. In addition, detailed comparisons are made with other solutions of the Euler equations.

Proton pump inhibitors and functional decline in older adults discharged from acute care hospitals.

PubMed

Corsonello, Andrea; Maggio, Marcello; Fusco, Sergio; Adamo, Bakhita; Amantea, Diana; Pedone, Claudio; Garasto, Sabrina; Ceda, Gian Paolo; Corica, Francesco; Lattanzio, Fabrizia; Antonelli Incalzi, Raffaele

2014-06-01

To investigate the relationship between use of proton pump inhibitors (PPIs) and incident dependency in older adults discharged from acute care hospitals. Prospective observational study. Eleven geriatric and internal medicine acute care wards located throughout Italy. Individuals (mean age 79.2 ± 5.5) who were not completely dependent at the time of discharge from participating wards (N = 401). The outcome of interest was the loss of at least one basic activity of daily living (ADL) from discharge to the end of follow-up (12 months). The relationship between PPI use and functional decline was investigated using logistic regression analysis before and after propensity score matching. Use of PPIs was significantly associated with functional decline before (odds ratio (OR) = 1.75, 95% confidence interval (CI) = 1.17-2.60) and after propensity score matching (OR = 2.44; 95% CI = 1.36-4.41). Other predictors of functional decline were hypoalbuminemia (OR = 3.10, 95% CI = 1.36-7.10 before matching, OR = 2.81, 95% CI = 1.09-7.77 after matching) and cognitive impairment (OR = 4.08, 95% CI = 1.63-10.2 before matching, OR = 6.35, 95% CI = 1.70-24.0 after matching). Use of PPIs is associated with functional decline during 12 months of follow-up in older adults discharged from acute care hospitals. © 2014, Copyright the Authors Journal compilation © 2014, The American Geriatrics Society.

General equations for optimal selection of diagnostic image acquisition parameters in clinical X-ray imaging.

PubMed

Zheng, Xiaoming

2017-12-01

The purpose of this work was to examine the effects of relationship functions between diagnostic image quality and radiation dose on the governing equations for image acquisition parameter variations in X-ray imaging. Various equations were derived for the optimal selection of peak kilovoltage (kVp) and exposure parameter (milliAmpere second, mAs) in computed tomography (CT), computed radiography (CR), and direct digital radiography. Logistic, logarithmic, and linear functions were employed to establish the relationship between radiation dose and diagnostic image quality. The radiation dose to the patient, as a function of image acquisition parameters (kVp, mAs) and patient size (d), was used in radiation dose and image quality optimization. Both logistic and logarithmic functions resulted in the same governing equation for optimal selection of image acquisition parameters using a dose efficiency index. For image quality as a linear function of radiation dose, the same governing equation was derived from the linear relationship. The general equations should be used in guiding clinical X-ray imaging through optimal selection of image acquisition parameters. The radiation dose to the patient could be reduced from current levels in medical X-ray imaging.

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.

Numerical Solution of 3D Poisson-Nernst-Planck Equations Coupled with Classical Density Functional Theory for Modeling Ion and Electron Transport in a Confined Environment

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

Meng, Da; Zheng, Bin; Lin, Guang

2014-08-29

We have developed efficient numerical algorithms for the solution of 3D steady-state Poisson-Nernst-Planck equations (PNP) with excess chemical potentials described by the classical density functional theory (cDFT). The coupled PNP equations are discretized by finite difference scheme and solved iteratively by Gummel method with relaxation. The Nernst-Planck equations are transformed into Laplace equations through the Slotboom transformation. Algebraic multigrid method is then applied to efficiently solve the Poisson equation and the transformed Nernst-Planck equations. A novel strategy for calculating excess chemical potentials through fast Fourier transforms is proposed which reduces computational complexity from O(N2) to O(NlogN) where N is themore » number of grid points. Integrals involving Dirac delta function are evaluated directly by coordinate transformation which yields more accurate result compared to applying numerical quadrature to an approximated delta function. Numerical results for ion and electron transport in solid electrolyte for Li ion batteries are shown to be in good agreement with the experimental data and the results from previous studies.« less

Prolongation structures of nonlinear evolution equations

NASA Technical Reports Server (NTRS)

Wahlquist, H. D.; Estabrook, F. B.

1975-01-01

A technique is developed for systematically deriving a 'prolongation structure' - a set of interrelated potentials and pseudopotentials - for nonlinear partial differential equations in two independent variables. When this is applied to the Korteweg-de Vries equation, a new infinite set of conserved quantities is obtained. Known solution techniques are shown to result from the discovery of such a structure: related partial differential equations for the potential functions, linear 'inverse scattering' equations for auxiliary functions, Backlund transformations. Generalizations of these techniques will result from the use of irreducible matrix representations of the prolongation structure.

Equation for wave processes in inhomogeneous moving media and functional solution of the acoustic tomography problem based on it

NASA Astrophysics Data System (ADS)

Rumyantseva, O. D.; Shurup, A. S.

2017-01-01

The paper considers the derivation of the wave equation and Helmholtz equation for solving the tomographic problem of reconstruction combined scalar-vector inhomogeneities describing perturbations of the sound velocity and absorption, the vector field of flows, and perturbations of the density of the medium. Restrictive conditions under which the obtained equations are meaningful are analyzed. Results of numerical simulation of the two-dimensional functional-analytical Novikov-Agaltsov algorithm for reconstructing the flow velocity using the the obtained Helmholtz equation are presented.

Bidirectional plant canopy reflection models derived from the radiation transfer equation

NASA Technical Reports Server (NTRS)

Beeth, D. R.

1975-01-01

A collection of bidirectional canopy reflection models was obtained from the solution of the radiation transfer equation for a horizontally homogeneous canopy. A phase function is derived for a collection of bidirectionally reflecting and transmitting planar elements characterized geometrically by slope and azimuth density functions. Two approaches to solving the radiation transfer equation for the canopy are presented. One approach factors the radiation transfer equation into a solvable set of three first-order linear differential equations by assuming that the radiation field within the canopy can be initially approximated by three components: uniformly diffuse downwelling, uniformly diffuse upwelling, and attenuated specular. The solution to these equations, which can be iterated to any degree of accuracy, was used to obtain overall canopy reflection from the formal solution to the radiation transfer equation. A programable solution to canopy overall bidirectional reflection is given for this approach. The special example of Lambertian leaves with constant leaf bidirectional reflection and scattering functions is considered, and a programmable solution for this example is given. The other approach to solving the radiation transfer equation, a generalized Chandrasekhar technique, is presented in the appendix.

GLASS VISCOSITY AS A FUNCTION OF TEMPERATURE AND COMPOSITION: A MODEL BASED ON ADAM-GIBBS EQUATION

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

Hrma, Pavel R.

2008-07-01

Within the temperature range and composition region of processing and product forming, the viscosity of commercial and waste glasses spans over 12 orders of magnitude. This paper shows that a generalized Adam-Gibbs relationship reasonably approximates the real behavior of glasses with four temperature-independent parameters of which two are linear functions of the composition vector. The equation is subjected to two constraints, one requiring that the viscosity-temperature relationship approaches the Arrhenius function at high temperatures with a composition-independent pre-exponential factor and the other that the viscosity value is independent of composition at the glass-transition temperature. Several sets of constant coefficients weremore » obtained by fitting the generalized Adam-Gibbs equation to data of two glass families: float glass and Hanford waste glass. Other equations (the Vogel-Fulcher-Tammann equation, original and modified, the Avramov equation, and the Douglass-Doremus equation) were fitted to float glass data series and compared with the Adam-Gibbs equation, showing that Adam-Gibbs glass appears an excellent approximation of real glasses even as compared with other candidate constitutive relations.« less

New analytical exact solutions of time fractional KdV-KZK equation by Kudryashov methods

NASA Astrophysics Data System (ADS)

S Saha, Ray

2016-04-01

In this paper, new exact solutions of the time fractional KdV-Khokhlov-Zabolotskaya-Kuznetsov (KdV-KZK) equation are obtained by the classical Kudryashov method and modified Kudryashov method respectively. For this purpose, the modified Riemann-Liouville derivative is used to convert the nonlinear time fractional KdV-KZK equation into the nonlinear ordinary differential equation. In the present analysis, the classical Kudryashov method and modified Kudryashov method are both used successively to compute the analytical solutions of the time fractional KdV-KZK equation. As a result, new exact solutions involving the symmetrical Fibonacci function, hyperbolic function and exponential function are obtained for the first time. The methods under consideration are reliable and efficient, and can be used as an alternative to establish new exact solutions of different types of fractional differential equations arising from mathematical physics. The obtained results are exhibited graphically in order to demonstrate the efficiencies and applicabilities of these proposed methods of solving the nonlinear time fractional KdV-KZK equation.

Holonomicity analysis of electromechanical systems

NASA Astrophysics Data System (ADS)

Wcislik, Miroslaw; Suchenia, Karol

2017-12-01

Electromechanical systems are described using state variables that contain electrical and mechanical components. The equations of motion, both electrical and mechanical, describe the relationships between these components. These equations are obtained using Lagrange functions. On the basis of the function and Lagrange - d'Alembert equation the methodology of obtaining equations for electromechanical systems was presented, together with a discussion of the nonholonomicity of these systems. The electromechanical system in the form of a single-phase reluctance motor was used to verify the presented method. Mechanical system was built as a system, which can oscillate as the element of physical pendulum. On the base of the pendulum oscillation, parameters of the electromechanical system were defined. The identification of the motor electric parameters as a function of the rotation angle was carried out. In this paper the characteristics and motion equations parameters of the motor are presented. The parameters of the motion equations obtained from the experiment and from the second order Lagrange equations are compared.

Expansion shock waves in regularized shallow-water theory

NASA Astrophysics Data System (ADS)

El, Gennady A.; Hoefer, Mark A.; Shearer, Michael

2016-05-01

We identify a new type of shock wave by constructing a stationary expansion shock solution of a class of regularized shallow-water equations that include the Benjamin-Bona-Mahony and Boussinesq equations. An expansion shock exhibits divergent characteristics, thereby contravening the classical Lax entropy condition. The persistence of the expansion shock in initial value problems is analysed and justified using matched asymptotic expansions and numerical simulations. The expansion shock's existence is traced to the presence of a non-local dispersive term in the governing equation. We establish the algebraic decay of the shock as it is gradually eroded by a simple wave on either side. More generally, we observe a robustness of the expansion shock in the presence of weak dissipation and in simulations of asymmetric initial conditions where a train of solitary waves is shed from one side of the shock.

An examination of the rheology of flocculated clay suspensions

NASA Astrophysics Data System (ADS)

Spearman, Jeremy

2017-04-01

A dense cohesive sediment suspension, sometimes referred to as fluid mud, is a thixotropic fluid with a true yield stress. Current rheological formulations struggle to reconcile the structural dynamics of cohesive sediment suspensions with the equilibrium behaviour of these suspensions across the range of concentrations and shear. This paper is concerned with establishing a rheological framework for the range of sediment concentrations from the yield point to Newtonian flow. The shear stress equation is based on floc fractal theory, put forward by Mills and Snabre (1988). This results in a Casson-like rheology equation. Additional structural dynamics is then added, using a theory on the self-similarity of clay suspensions proposed by Coussot (1995), giving an equation which has the ability to match the equilibrium and time-dependent viscous rheology of a wide range of suspensions of different concentration and mineralogy.

Solution of Grad-Shafranov equation by the method of fundamental solutions

NASA Astrophysics Data System (ADS)

Nath, D.; Kalra, M. S.; Kalra

2014-06-01

In this paper we have used the Method of Fundamental Solutions (MFS) to solve the Grad-Shafranov (GS) equation for the axisymmetric equilibria of tokamak plasmas with monomial sources. These monomials are the individual terms appearing on the right-hand side of the GS equation if one expands the nonlinear terms into polynomials. Unlike the Boundary Element Method (BEM), the MFS does not involve any singular integrals and is a meshless boundary-alone method. Its basic idea is to create a fictitious boundary around the actual physical boundary of the computational domain. This automatically removes the involvement of singular integrals. The results obtained by the MFS match well with the earlier results obtained using the BEM. The method is also applied to Solov'ev profiles and it is found that the results are in good agreement with analytical results.

Matrix form of Legendre polynomials for solving linear integro-differential equations of high order

NASA Astrophysics Data System (ADS)

Kammuji, M.; Eshkuvatov, Z. K.; Yunus, Arif A. M.

2017-04-01

This paper presents an effective approximate solution of high order of Fredholm-Volterra integro-differential equations (FVIDEs) with boundary condition. Legendre truncated series is used as a basis functions to estimate the unknown function. Matrix operation of Legendre polynomials is used to transform FVIDEs with boundary conditions into matrix equation of Fredholm-Volterra type. Gauss Legendre quadrature formula and collocation method are applied to transfer the matrix equation into system of linear algebraic equations. The latter equation is solved by Gauss elimination method. The accuracy and validity of this method are discussed by solving two numerical examples and comparisons with wavelet and methods.

Green's function solution to heat transfer of a transparent gas through a tube

NASA Technical Reports Server (NTRS)

Frankel, J. I.

1989-01-01

A heat transfer analysis of a transparent gas flowing through a circular tube of finite thickness is presented. This study includes the effects of wall conduction, internal radiative exchange, and convective heat transfer. The natural mathematical formulation produces a nonlinear, integrodifferential equation governing the wall temperature and an ordinary differential equation describing the gas temperature. This investigation proposes to convert the original system of equations into an equivalent system of integral equations. The Green's function method permits the conversion of an integrodifferential equation into a pure integral equation. The proposed integral formulation and subsequent computational procedure are shown to be stable and accurate.

New exact solutions of the Tzitzéica-type equations in non-linear optics using the expa function method

NASA Astrophysics Data System (ADS)

Hosseini, K.; Ayati, Z.; Ansari, R.

2018-04-01

One specific class of non-linear evolution equations, known as the Tzitzéica-type equations, has received great attention from a group of researchers involved in non-linear science. In this article, new exact solutions of the Tzitzéica-type equations arising in non-linear optics, including the Tzitzéica, Dodd-Bullough-Mikhailov and Tzitzéica-Dodd-Bullough equations, are obtained using the expa function method. The integration technique actually suggests a useful and reliable method to extract new exact solutions of a wide range of non-linear evolution equations.

Generalized Boltzmann-Type Equations for Aggregation in Gases

NASA Astrophysics Data System (ADS)

Adzhiev, S. Z.; Vedenyapin, V. V.; Volkov, Yu. A.; Melikhov, I. V.

2017-12-01

The coalescence and fragmentation of particles in a dispersion system are investigated by applying kinetic theory methods, namely, by generalizing the Boltzmann kinetic equation to coalescence and fragmentation processes. Dynamic equations for the particle concentrations in the system are derived using the kinetic equations of motion. For particle coalescence and fragmentation, equations for the particle momentum, coordinate, and mass distribution functions are obtained and the coalescence and fragmentation coefficients are calculated. The equilibrium mass and velocity distribution functions of the particles in the dispersion system are found in the approximation of an active terminal group (Becker-Döring-type equation). The transition to a continuum description is performed.

Molecular Dynamics Information Improves cis-Peptide-Based Function Annotation of Proteins.

PubMed

Das, Sreetama; Bhadra, Pratiti; Ramakumar, Suryanarayanarao; Pal, Debnath

2017-08-04

cis-Peptide bonds, whose occurrence in proteins is rare but evolutionarily conserved, are implicated to play an important role in protein function. This has led to their previous use in a homology-independent, fragment-match-based protein function annotation method. However, proteins are not static molecules; dynamics is integral to their activity. This is nicely epitomized by the geometric isomerization of cis-peptide to trans form for molecular activity. Hence we have incorporated both static (cis-peptide) and dynamics information to improve the prediction of protein molecular function. Our results show that cis-peptide information alone cannot detect functional matches in cases where cis-trans isomerization exists but 3D coordinates have been obtained for only the trans isomer or when the cis-peptide bond is incorrectly assigned as trans. On the contrary, use of dynamics information alone includes false-positive matches for cases where fragments with similar secondary structure show similar dynamics, but the proteins do not share a common function. Combining the two methods reduces errors while detecting the true matches, thereby enhancing the utility of our method in function annotation. A combined approach, therefore, opens up new avenues of improving existing automated function annotation methodologies.

Validation of cystatin C-based equations for evaluating residual renal function in patients on continuous ambulatory peritoneal dialysis.

PubMed

Zhong, Hui; Zhang, Wei; Qin, Min; Gou, ZhongPing; Feng, Ping

2017-06-01

Residual renal function needs to be assessed frequently in patients on continuous ambulatory peritoneal dialysis (CAPD). A commonly used method is to measure creatinine (Cr) and urea clearance in urine collected over 24 h, but collection can be cumbersome and difficult to manage. A faster, simpler alternative is to measure levels of cystatin C (CysC) in serum, but the accuracy and reliability of this method is controversial. Our study aims to validate published CysC-based equations for estimating residual renal function in patients on CAPD. Residual renal function was measured by calculating average clearance of urea and Cr in 24-h urine as well as by applying CysC- or Cr-based equations published by Hoek and Yang. We then compared the performance of the equations against the 24-h urine results. In our sample of 255 patients ages 47.9 ± 15.6 years, the serum CysC level was 6.43 ± 1.13 mg/L. Serum CysC level was not significantly associated with age, gender, height, weight, body mass index, hemoglobin, intact parathyroid hormone, normalized protein catabolic rate or the presence of diabetes. In contrast, serum CysC levels did correlate with peritoneal clearance of CysC and with levels of prealbumin and high-sensitivity C-reactive protein. Residual renal function was 2.56 ± 2.07 mL/min/1.73 m 2 based on 24-h urine sampling, compared with estimates (mL/min/1.73 m 2 ) of 2.98 ± 0.66 for Hoek's equation, 2.03 ± 0.97 for Yang's CysC-based equation and 2.70 ± 1.30 for Yang's Cr-based equation. Accuracies within 30%/50% of measured residual renal function for the three equations were 29.02/48.24, 34.90/56.86 and 31.37/54.90. The three equations for estimating residual renal function showed similar limits of agreement and differed significantly from the measured value. Published CysC-based equations do not appear to be particularly reliable for patients on CAPD. Further development and validation of CysC-based equations should take into account peritoneal clearance of CysC and other relevant factors. © The Author 2016. Published by Oxford University Press on behalf of ERA-EDTA. All rights reserved.

Wave Functions for Time-Dependent Dirac Equation under GUP

NASA Astrophysics Data System (ADS)

Zhang, Meng-Yao; Long, Chao-Yun; Long, Zheng-Wen

2018-04-01

In this work, the time-dependent Dirac equation is investigated under generalized uncertainty principle (GUP) framework. It is possible to construct the exact solutions of Dirac equation when the time-dependent potentials satisfied the proper conditions. In (1+1) dimensions, the analytical wave functions of the Dirac equation under GUP have been obtained for the two kinds time-dependent potentials. Supported by the National Natural Science Foundation of China under Grant No. 11565009

The Existence of the Solution to One Kind of Algebraic Riccati Equation

NASA Astrophysics Data System (ADS)

Liu, Jianming

2018-03-01

The matrix equation ATX + XA + XRX + Q = O is called algebraic Riccati equation, which is very important in the fields of automatic control and other engineering applications. Many researchers have studied the solutions to various algebraic Riccati equations and most of them mainly applied the matrix methods, while few used the functional analysis theories. This paper mainly studies the existence of the solution to the following kind of algebraic Riccati equation from the functional view point: ATX + XA + XRX ‑λX + Q = O Here, X, A, R, Q ∈ n×n , Q is a symmetric matrix, and R is a positive or negative semi-definite matrix, λ is arbitrary constants. This paper uses functional approach such as fixed point theorem and contraction mapping thinking so as to provide two sufficient conditions for the solvability about this kind of Riccati equation and to arrive at some relevant conclusions.

Density Weighted FDF Equations for Simulations of Turbulent Reacting Flows

NASA Technical Reports Server (NTRS)

Shih, Tsan-Hsing; Liu, Nan-Suey

2011-01-01

In this report, we briefly revisit the formulation of density weighted filtered density function (DW-FDF) for large eddy simulation (LES) of turbulent reacting flows, which was proposed by Jaberi et al. (Jaberi, F.A., Colucci, P.J., James, S., Givi, P. and Pope, S.B., Filtered mass density function for Large-eddy simulation of turbulent reacting flows, J. Fluid Mech., vol. 401, pp. 85-121, 1999). At first, we proceed the traditional derivation of the DW-FDF equations by using the fine grained probability density function (FG-PDF), then we explore another way of constructing the DW-FDF equations by starting directly from the compressible Navier-Stokes equations. We observe that the terms which are unclosed in the traditional DW-FDF equations are now closed in the newly constructed DW-FDF equations. This significant difference and its practical impact on the computational simulations may deserve further studies.

A hierarchy of generalized Jaulent-Miodek equations and their explicit solutions

NASA Astrophysics Data System (ADS)

Geng, Xianguo; Guan, Liang; Xue, Bo

A hierarchy of generalized Jaulent-Miodek (JM) equations related to a new spectral problem with energy-dependent potentials is proposed. Depending on the Lax matrix and elliptic variables, the generalized JM hierarchy is decomposed into two systems of solvable ordinary differential equations. Explicit theta function representations of the meromorphic function and the Baker-Akhiezer function are constructed, the solutions of the hierarchy are obtained based on the theory of algebraic curves.

Green functions and Langevin equations for nonlinear diffusion equations: A comment on ‘Markov processes, Hurst exponents, and nonlinear diffusion equations’ by Bassler et al.

NASA Astrophysics Data System (ADS)

Frank, T. D.

2008-02-01

We discuss two central claims made in the study by Bassler et al. [K.E. Bassler, G.H. Gunaratne, J.L. McCauley, Physica A 369 (2006) 343]. Bassler et al. claimed that Green functions and Langevin equations cannot be defined for nonlinear diffusion equations. In addition, they claimed that nonlinear diffusion equations are linear partial differential equations disguised as nonlinear ones. We review bottom-up and top-down approaches that have been used in the literature to derive Green functions for nonlinear diffusion equations and, in doing so, show that the first claim needs to be revised. We show that the second claim as well needs to be revised. To this end, we point out similarities and differences between non-autonomous linear Fokker-Planck equations and autonomous nonlinear Fokker-Planck equations. In this context, we raise the question whether Bassler et al.’s approach to financial markets is physically plausible because it necessitates the introduction of external traders and causes. Such external entities can easily be eliminated when taking self-organization principles and concepts of nonextensive thermostatistics into account and modeling financial processes by means of nonlinear Fokker-Planck equations.

Learning the dynamics of objects by optimal functional interpolation.

PubMed

Ahn, Jong-Hoon; Kim, In Young

2012-09-01

Many areas of science and engineering rely on functional data and their numerical analysis. The need to analyze time-varying functional data raises the general problem of interpolation, that is, how to learn a smooth time evolution from a finite number of observations. Here, we introduce optimal functional interpolation (OFI), a numerical algorithm that interpolates functional data over time. Unlike the usual interpolation or learning algorithms, the OFI algorithm obeys the continuity equation, which describes the transport of some types of conserved quantities, and its implementation shows smooth, continuous flows of quantities. Without the need to take into account equations of motion such as the Navier-Stokes equation or the diffusion equation, OFI is capable of learning the dynamics of objects such as those represented by mass, image intensity, particle concentration, heat, spectral density, and probability density.

Mathematical Methods for Physics and Engineering Third Edition Paperback Set

NASA Astrophysics Data System (ADS)

Riley, Ken F.; Hobson, Mike P.; Bence, Stephen J.

2006-06-01

Prefaces; 1. Preliminary algebra; 2. Preliminary calculus; 3. Complex numbers and hyperbolic functions; 4. Series and limits; 5. Partial differentiation; 6. Multiple integrals; 7. Vector algebra; 8. Matrices and vector spaces; 9. Normal modes; 10. Vector calculus; 11. Line, surface and volume integrals; 12. Fourier series; 13. Integral transforms; 14. First-order ordinary differential equations; 15. Higher-order ordinary differential equations; 16. Series solutions of ordinary differential equations; 17. Eigenfunction methods for differential equations; 18. Special functions; 19. Quantum operators; 20. Partial differential equations: general and particular; 21. Partial differential equations: separation of variables; 22. Calculus of variations; 23. Integral equations; 24. Complex variables; 25. Application of complex variables; 26. Tensors; 27. Numerical methods; 28. Group theory; 29. Representation theory; 30. Probability; 31. Statistics; Index.

A family of solutions to the Einstein-Maxwell system of equations describing relativistic charged fluid spheres

NASA Astrophysics Data System (ADS)

Komathiraj, K.; Sharma, Ranjan

2018-05-01

In this paper, we present a formalism to generate a family of interior solutions to the Einstein-Maxwell system of equations for a spherically symmetric relativistic charged fluid sphere matched to the exterior Reissner-Nordström space-time. By reducing the Einstein-Maxwell system to a recurrence relation with variable rational coefficients, we show that it is possible to obtain closed-form solutions for a specific range of model parameters. A large class of solutions obtained previously are shown to be contained in our general class of solutions. We also analyse the physical viability of our new class of solutions.

Dissipative nonlinear waves in a gravitating quantum fluid

NASA Astrophysics Data System (ADS)

Sahu, Biswajit; Sinha, Anjana; Roychoudhury, Rajkumar

2018-02-01

Nonlinear wave propagation is studied in a dissipative, self-gravitating Bose-Einstein condensate, starting from the Gross-Pitaevskii equation. In the absence of an exact analytical result, approximate methods like the linear analysis and perturbative approach are applied. The linear dispersion relation puts a restriction on the permissible range of the dissipation parameter. The waves get damped due to dissipation. The small amplitude analysis using reductive perturbation technique is found to yield a modified form of KdV equation, which is solved both analytically as well as numerically. Interestingly, the analytical and numerical plots match excellently with each other, in the realm of weak dissipation.

Solution of fractional kinetic equation by a class of integral transform of pathway type

NASA Astrophysics Data System (ADS)

Kumar, Dilip

2013-04-01

Solutions of fractional kinetic equations are obtained through an integral transform named Pα-transform introduced in this paper. The Pα-transform is a binomial type transform containing many class of transforms including the well known Laplace transform. The paper is motivated by the idea of pathway model introduced by Mathai [Linear Algebra Appl. 396, 317-328 (2005), 10.1016/j.laa.2004.09.022]. The composition of the transform with differential and integral operators are proved along with convolution theorem. As an illustration of applications to the general theory of differential equations, a simple differential equation is solved by the new transform. Being a new transform, the Pα-transform of some elementary functions as well as some generalized special functions such as H-function, G-function, Wright generalized hypergeometric function, generalized hypergeometric function, and Mittag-Leffler function are also obtained. The results for the classical Laplace transform is retrieved by letting α → 1.

Langevin dynamics for vector variables driven by multiplicative white noise: A functional formalism

NASA Astrophysics Data System (ADS)

Moreno, Miguel Vera; Arenas, Zochil González; Barci, Daniel G.

2015-04-01

We discuss general multidimensional stochastic processes driven by a system of Langevin equations with multiplicative white noise. In particular, we address the problem of how time reversal diffusion processes are affected by the variety of conventions available to deal with stochastic integrals. We present a functional formalism to build up the generating functional of correlation functions without any type of discretization of the Langevin equations at any intermediate step. The generating functional is characterized by a functional integration over two sets of commuting variables, as well as Grassmann variables. In this representation, time reversal transformation became a linear transformation in the extended variables, simplifying in this way the complexity introduced by the mixture of prescriptions and the associated calculus rules. The stochastic calculus is codified in our formalism in the structure of the Grassmann algebra. We study some examples such as higher order derivative Langevin equations and the functional representation of the micromagnetic stochastic Landau-Lifshitz-Gilbert equation.

Coarse-grained forms for equations describing the microscopic motion of particles in a fluid.

PubMed

Das, Shankar P; Yoshimori, Akira

2013-10-01

Exact equations of motion for the microscopically defined collective density ρ(x,t) and the momentum density ĝ(x,t) of a fluid have been obtained in the past starting from the corresponding Langevin equations representing the dynamics of the fluid particles. In the present work we average these exact equations of microscopic dynamics over the local equilibrium distribution to obtain stochastic partial differential equations for the coarse-grained densities with smooth spatial and temporal dependence. In particular, we consider Dean's exact balance equation for the microscopic density of a system of interacting Brownian particles to obtain the basic equation of the dynamic density functional theory with noise. Our analysis demonstrates that on thermal averaging the dependence of the exact equations on the bare interaction potential is converted to dependence on the corresponding thermodynamic direct correlation functions in the coarse-grained equations.

New soliton solution to the longitudinal wave equation in a magneto-electro-elastic circular rod

NASA Astrophysics Data System (ADS)

Seadawy, Aly R.; Manafian, Jalil

2018-03-01

This paper examines the effectiveness of an integration scheme which called the extended trial equation method (ETEM) in exactly solving a well-known nonlinear equation of partial differential equations (PDEs). In this respect, the longitudinal wave equation (LWE) that arises in mathematical physics with dispersion caused by the transverse Poisson's effect in a magneto-electro-elastic (MEE) circular rod, which a series of exact traveling wave solutions for the aforementioned equation is formally extracted. Explicit new exact solutions are derived in different form such as dark solitons, bright solitons, solitary wave, periodic solitary wave, rational function, and elliptic function solutions of the longitudinal wave equation. The movements of obtained solutions are shown graphically, which helps to understand the physical phenomena of this longitudinal wave equation. Many other such types of nonlinear equations arising in non-destructive evaluation of structures made of the advanced MEE material can also be solved by this method.

The Value of the Studied Item in the Matching Criterion in Differential Item Functioning (DIF) Analysis. Research Report. ETS RR-10-13

ERIC Educational Resources Information Center

Tan, Xuan; Xiang, Bihua; Dorans, Neil J.; Qu, Yanxuan

2010-01-01

The nature of the matching criterion (usually the total score) in the study of differential item functioning (DIF) has been shown to impact the accuracy of different DIF detection procedures. One of the topics related to the nature of the matching criterion is whether the studied item should be included. Although many studies exist that suggest…

Quantum dynamics in continuum for proton transport—Generalized correlation

NASA Astrophysics Data System (ADS)

Chen, Duan; Wei, Guo-Wei

2012-04-01

As a key process of many biological reactions such as biological energy transduction or human sensory systems, proton transport has attracted much research attention in biological, biophysical, and mathematical fields. A quantum dynamics in continuum framework has been proposed to study proton permeation through membrane proteins in our earlier work and the present work focuses on the generalized correlation of protons with their environment. Being complementary to electrostatic potentials, generalized correlations consist of proton-proton, proton-ion, proton-protein, and proton-water interactions. In our approach, protons are treated as quantum particles while other components of generalized correlations are described classically and in different levels of approximations upon simulation feasibility and difficulty. Specifically, the membrane protein is modeled as a group of discrete atoms, while ion densities are approximated by Boltzmann distributions, and water molecules are represented as a dielectric continuum. These proton-environment interactions are formulated as convolutions between number densities of species and their corresponding interaction kernels, in which parameters are obtained from experimental data. In the present formulation, generalized correlations are important components in the total Hamiltonian of protons, and thus is seamlessly embedded in the multiscale/multiphysics total variational model of the system. It takes care of non-electrostatic interactions, including the finite size effect, the geometry confinement induced channel barriers, dehydration and hydrogen bond effects, etc. The variational principle or the Euler-Lagrange equation is utilized to minimize the total energy functional, which includes the total Hamiltonian of protons, and obtain a new version of generalized Laplace-Beltrami equation, generalized Poisson-Boltzmann equation and generalized Kohn-Sham equation. A set of numerical algorithms, such as the matched interface and boundary method, the Dirichlet to Neumann mapping, Gummel iteration, and Krylov space techniques, is employed to improve the accuracy, efficiency, and robustness of model simulations. Finally, comparisons between the present model predictions and experimental data of current-voltage curves, as well as current-concentration curves of the Gramicidin A channel, verify our new model.

Resonant coherent excitation of hydrogen-like ions planar channeled in a crystal; Transition into the first excited state

NASA Astrophysics Data System (ADS)

Babaev, A.; Pivovarov, Yu. L.

2012-03-01

The presented program is designed to simulate the characteristics of resonant coherent excitation of hydrogen-like ions planar-channeled in a crystal. The program realizes the numerical algorithm to solve the Schrödinger equation for the ion-bound electron at a special resonance excitation condition. The calculated wave function of the bound electron defines probabilities for the ion to be in the either ground or first excited state, or to be ionized. Finally, in the outgoing beam the fractions of ions in the ground state, in the first excited state, and ionized by collisions with target electrons, are defined. The program code is written on C++ and is designed for multiprocessing systems (clusters). The output data are presented in the table. Program summaryProgram title: RCE_H-like_1 Catalogue identifier: AEKX_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEKX_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 2813 No. of bytes in distributed program, including test data, etc.: 34 667 Distribution format: tar.gz Programming language: C++ (g++, icc compilers) Computer: Multiprocessor systems (clusters) Operating system: Any OS based on LINUX; program was tested under Novell SLES 10 Has the code been vectorized or parallelized?: Yes. Contains MPI directives RAM: <1 MB per processor Classification: 2.1, 2.6, 7.10 External routines: MPI library for GNU C++, Intel C++ compilers Nature of problem: When relativistic hydrogen-like ion moves in the crystal in the planar channeling regime, in the ion rest frame the time-periodic electric field acts on the bound electron. If the frequency of this field matches the transition frequency between electronic energy levels, the resonant coherent excitation can take place. Therefore, ions in the different states may be observed in the outgoing beam behind the crystal. To get the probabilities for the ion to be in the ground state or in the first excited state, or to be ionized, the Schrödinger equation is solved for the electron of ion. The numerical solving of the Schrödinger equation is carried out taking into account the fine structure of electronic energy levels, the Stark effect due to the influence of the crystal electric field on electronic energy levels and the ionization of ion due to the collisions with crystal electrons. Solution method: The wave function of the electron of ion is the superposition of the wave functions of stationary states with time-dependent coefficients. These stationary wave functions and corresponding energies are defined from the stationary Schrödinger equation. The equation is reduced to the problem of the eigen values and vectors of Hermitian matrix. The corresponding matrix equation is considered as the linear equation system. Then the time-dependent coefficients of the electron wave function are defined from the Schrödinger equation, with a time-periodic crystal field. The time-periodic field is responsible for the transitions between the stationary states. The final time-dependent Schrödinger equation represents the matrix equation which has been solved by means of the QR-algorithm. Restrictions: As expected the program gives the correct results for relativistic hydrogen-like ions with the kinetic energies up to 1 GeV/u and at the crystal thicknesses of 1-100 μm. The restrictions are: first, the program might give inadequate results, when the ion kinetic energy is too large (>10 GeV/u); second, the unaccounted physical factors may be significant at specific conditions. For example, the spontaneous emission by exited highly charged ions, as well as both energy and angular spread of the incident beam, could lead to additional broadening of the resonance. The medium polarization by the electric field of ion can influence the electronic energy levels of the ion in the non-relativistic case. The role of these factors was discussed in the references. Also, the large crystal thickness may require large computational time. Running time: In general, the running time depends on the number of processors. In our tests we used the crystal thickness up to 100 μm and the number of 2.66 GHz processors was up to 100. The running time was about 1 hour in these conditions.

Coupling finite element and spectral methods: First results

NASA Technical Reports Server (NTRS)

Bernardi, Christine; Debit, Naima; Maday, Yvon

1987-01-01

A Poisson equation on a rectangular domain is solved by coupling two methods: the domain is divided in two squares, a finite element approximation is used on the first square and a spectral discretization is used on the second one. Two kinds of matching conditions on the interface are presented and compared. In both cases, error estimates are proved.

Relationship between Children's Sleep and Mental Health in Mothers of Children with and without Autism

ERIC Educational Resources Information Center

Hodge, Danelle; Hoffman, Charles D.; Sweeney, Dwight P.; Riggs, Matt L.

2013-01-01

The study employed 90 children with autism spectrum disorders (ASDs) who were matched to 90 typically developing children on age, gender, and ethnicity. Using structural equation modeling, maternal sleep and maternal stress mediated the relationship between children's sleep and mothers' mental health for mothers of children with and without ASDs.…

Nonlinear equations of dynamics for spinning paraboloidal antennas

NASA Technical Reports Server (NTRS)

Utku, S.; Shoemaker, W. L.; Salama, M.

1983-01-01

The nonlinear strain-displacement and velocity-displacement relations of spinning imperfect rotational paraboloidal thin shell antennas are derived for nonaxisymmetrical deformations. Using these relations with the admissible trial functions in the principle functional of dynamics, the nonlinear equations of stress inducing motion are expressed in the form of a set of quasi-linear ordinary differential equations of the undetermined functions by means of the Rayleigh-Ritz procedure. These equations include all nonlinear terms up to and including the third degree. Explicit expressions are given for the coefficient matrices appearing in these equations. Both translational and rotational off-sets of the axis of revolution (and also the apex point of the paraboloid) with respect to the spin axis are considered. Although the material of the antenna is assumed linearly elastic, it can be anisotropic.

Analytical study of fractional equations describing anomalous diffusion of energetic particles

NASA Astrophysics Data System (ADS)

Tawfik, A. M.; Fichtner, H.; Schlickeiser, R.; Elhanbaly, A.

2017-06-01

To present the main influence of anomalous diffusion on the energetic particle propagation, the fractional derivative model of transport is developed by deriving the fractional modified Telegraph and Rayleigh equations. Analytical solutions of the fractional modified Telegraph and the fractional Rayleigh equations, which are defined in terms of Caputo fractional derivatives, are obtained by using the Laplace transform and the Mittag-Leffler function method. The solutions of these fractional equations are given in terms of special functions like Fox’s H, Mittag-Leffler, Hermite and Hyper-geometric functions. The predicted travelling pulse solutions are discussed in each case for different values of fractional order.

Exact traveling wave solutions of the KP-BBM equation by using the new approach of generalized (G'/G)-expansion method.

PubMed

Alam, Md Nur; Akbar, M Ali

2013-01-01

The new approach of the generalized (G'/G)-expansion method is an effective and powerful mathematical tool in finding exact traveling wave solutions of nonlinear evolution equations (NLEEs) in science, engineering and mathematical physics. In this article, the new approach of the generalized (G'/G)-expansion method is applied to construct traveling wave solutions of the Kadomtsev-Petviashvili-Benjamin-Bona-Mahony (KP-BBM) equation. The solutions are expressed in terms of the hyperbolic functions, the trigonometric functions and the rational functions. By means of this scheme, we found some new traveling wave solutions of the above mentioned equation.

Schwarzschild and linear potentials in Mannheim's model of conformal gravity

NASA Astrophysics Data System (ADS)

Phillips, Peter R.

2018-05-01

We study the equations of conformal gravity, as given by Mannheim, in the weak field limit, so that a linear approximation is adequate. Specialising to static fields with spherical symmetry, we obtain a second-order equation for one of the metric functions. We obtain the Green function for this equation, and represent the metric function in the form of integrals over the source. Near a compact source such as the Sun the solution no longer has a form that is compatible with observations. We conclude that a solution of Mannheim type (a Schwarzschild term plus a linear potential of galactic scale) cannot exist for these field equations.

Some Exact Results for the Schroedinger Wave Equation with a Time Dependent Potential

NASA Technical Reports Server (NTRS)

Campbell, Joel

2009-01-01

The time dependent Schroedinger equation with a time dependent delta function potential is solved exactly for many special cases. In all other cases the problem can be reduced to an integral equation of the Volterra type. It is shown that by knowing the wave function at the origin, one may derive the wave function everywhere. Thus, the problem is reduced from a PDE in two variables to an integral equation in one. These results are used to compare adiabatic versus sudden changes in the potential. It is shown that adiabatic changes in the p otential lead to conservation of the normalization of the probability density.

Solution of D dimensional Dirac equation for coulombic potential using NU method and its thermodynamics properties

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

Cari, C., E-mail: cari@staff.uns.ac.id; Suparmi, A., E-mail: soeparmi@staff.uns.ac.id; Yunianto, M., E-mail: muhtaryunianto@staff.uns.ac.id

2016-02-08

The analytical solution of Ddimensional Dirac equation for Coulombic potential is investigated using Nikiforov-Uvarov method. The D dimensional relativistic energy spectra are obtained from relativistic energy eigenvalue equation by using Mat Lab software.The corresponding D dimensional radial wave functions are formulated in the form of generalized Jacobi and Laguerre Polynomials. In the non-relativistic limit, the relativistic energy equation reduces to the non-relativistic energy which will be applied to determine some thermodynamical properties of the system. The thermodynamical properties of the system are expressed in terms of error function and imaginary error function.

Modelling difficulties in abstract thinking in psychosis: the importance of socio-developmental background.

PubMed

Berg, A O; Melle, I; Zuber, V; Simonsen, C; Nerhus, M; Ueland, T; Andreassen, O A; Sundet, K; Vaskinn, A

2017-01-01

Abstract thinking is important in modern understanding of neurocognitive abilities, and a symptom of thought disorder in psychosis. In patients with psychosis, we assessed if socio-developmental background influences abstract thinking, and the association with executive functioning and clinical psychosis symptoms. Participants (n = 174) had a diagnosis of psychotic or bipolar disorder, were 17-65 years, intelligence quotient (IQ) > 70, fluent in a Scandinavian language, and their full primary education in Norway. Immigrants (N = 58) were matched (1:2) with participants without a history of migration (N = 116). All participants completed a neurocognitive and clinical assessment. Socio-developmental background was operationalised as human developmental index (HDI) of country of birth, at year of birth. Structural equation modelling was used to assess the model with best fit. The model with best fit, χ 2  = 96.591, df = 33, p < .001, confirmed a significant indirect effect of HDI scores on abstract thinking through executive functioning, but not through clinical psychosis symptoms. This study found that socio-developmental background influences abstract thinking in psychosis by indirect effect through executive functioning. We should take into account socio-developmental background in the interpretation of neurocognitive performance in patients with psychosis, and prioritise cognitive remediation in treatment of immigrant patients.

Unsteady Solution of Non-Linear Differential Equations Using Walsh Function Series

NASA Technical Reports Server (NTRS)

Gnoffo, Peter A.

2015-01-01

Walsh functions form an orthonormal basis set consisting of square waves. The discontinuous nature of square waves make the system well suited for representing functions with discontinuities. The product of any two Walsh functions is another Walsh function - a feature that can radically change an algorithm for solving non-linear partial differential equations (PDEs). The solution algorithm of non-linear differential equations using Walsh function series is unique in that integrals and derivatives may be computed using simple matrix multiplication of series representations of functions. Solutions to PDEs are derived as functions of wave component amplitude. Three sample problems are presented to illustrate the Walsh function series approach to solving unsteady PDEs. These include an advection equation, a Burgers equation, and a Riemann problem. The sample problems demonstrate the use of the Walsh function solution algorithms, exploiting Fast Walsh Transforms in multi-dimensions (O(Nlog(N))). Details of a Fast Walsh Reciprocal, defined here for the first time, enable inversion of aWalsh Symmetric Matrix in O(Nlog(N)) operations. Walsh functions have been derived using a fractal recursion algorithm and these fractal patterns are observed in the progression of pairs of wave number amplitudes in the solutions. These patterns are most easily observed in a remapping defined as a fractal fingerprint (FFP). A prolongation of existing solutions to the next highest order exploits these patterns. The algorithms presented here are considered a work in progress that provide new alternatives and new insights into the solution of non-linear PDEs.

Cylindrical optical resonators: fundamental properties and bio-sensing characteristics

NASA Astrophysics Data System (ADS)

Khozeymeh, Foroogh; Razaghi, Mohammad

2018-04-01

In this paper, detailed theoretical analysis of cylindrical resonators is demonstrated. As illustrated, these kinds of resonators can be used as optical bio-sensing devices. The proposed structure is analyzed using an analytical method based on Lam's approximation. This method is systematic and has simplified the tedious process of whispering-gallery mode (WGM) wavelength analysis in optical cylindrical biosensors. By this method, analysis of higher radial orders of high angular momentum WGMs has been possible. Using closed-form analytical equations, resonance wavelengths of higher radial and angular order WGMs of TE and TM polarization waves are calculated. It is shown that high angular momentum WGMs are more appropriate for bio-sensing applications. Some of the calculations are done using a numerical non-linear Newton method. A perfect match of 99.84% between the analytical and the numerical methods has been achieved. In order to verify the validity of the calculations, Meep simulations based on the finite difference time domain (FDTD) method are performed. In this case, a match of 96.70% between the analytical and FDTD results has been obtained. The analytical predictions are in good agreement with other experimental work (99.99% match). These results validate the proposed analytical modelling for the fast design of optical cylindrical biosensors. It is shown that by extending the proposed two-layer resonator structure analyzing scheme, it is possible to study a three-layer cylindrical resonator structure as well. Moreover, by this method, fast sensitivity optimization in cylindrical resonator-based biosensors has been possible. Sensitivity of the WGM resonances is analyzed as a function of the structural parameters of the cylindrical resonators. Based on the results, fourth radial order WGMs, with a resonator radius of 50 μm, display the most bulk refractive index sensitivity of 41.50 (nm/RIU).

Jugular venous valved conduit (Contegra) matches allograft performance in infant truncus arteriosus repair.

PubMed

Hickey, Edward J; McCrindle, Brian W; Blackstone, Eugene H; Yeh, Thomas; Pigula, Frank; Clarke, David; Tchervenkov, Christo I; Hawkins, John

2008-05-01

Limited availability and durability of allograft conduits require that alternatives be considered. We compared bovine jugular venous valved (JVV) and allograft conduit performance in 107 infants who survived truncus arteriosus repair. Children were prospectively recruited between 2003 and 2007 from 17 institutions. The median z-score for JVV (n=27, all 12 mm) was +2.1 (range +1.2 to +3.2) and allograft (n=80, 9-15mm) was +1.7 (range -0.4 to +3.6). Propensity-adjusted comparison of conduit survival was undertaken using parametric risk-hazard analysis and competing risks techniques. All available echocardiograms (n=745) were used to model deterioration of conduit function in regression equations adjusted for repeated measures. Overall conduit survival was 64+/-9% at 3 years. Conduit replacement was for conduit stenosis (n=16) and/or pulmonary artery stenosis (n=18) or regurgitation (n=1). The propensity-adjusted 3-year freedom from replacement for in-conduit stenosis was 96+/-4% for JVV and 69+/-8% for allograft (p=0.05). The risk of intervention or replacement for branch pulmonary artery stenosis was similar for JVV and allograft. Smaller conduit z-score predicted poor conduit performance (p<0.01) with best outcome between +1 and +3. Although JVV conduits were a uniform diameter, their z-score more consistently matched this ideal. JVV exhibited a non-significant trend towards slower progression of conduit regurgitation and peak right ventricular outflow tract (RVOT) gradient. In addition, catheter intervention was more successful at slowing subsequent gradient progression in children with JVV versus those with allograft (p<0.01). JVV does match allograft performance and may be advantageous. It is an appropriate first choice for repair of truncus arteriosus, and perhaps other small infants requiring RVOT reconstruction.

Mid-infrared frequency comb generation via cascaded quadratic nonlinearities in quasi-phase-matched waveguides

NASA Astrophysics Data System (ADS)

Kowligy, Abijith S.; Lind, Alex; Hickstein, Daniel D.; Carlson, David R.; Timmers, Henry; Nader, Nima; Cruz, Flavio C.; Ycas, Gabriel; Papp, Scott B.; Diddams, Scott A.

2018-04-01

We experimentally demonstrate a simple configuration for mid-infrared (MIR) frequency comb generation in quasi-phase-matched lithium niobate waveguides using the cascaded-$\\chi^{(2)}$ nonlinearity. With nanojoule-scale pulses from an Er:fiber laser, we observe octave-spanning supercontinuum in the near-infrared with dispersive-wave generation in the 2.5--3 $\\text{\\mu}$m region and intra-pulse difference-frequency generation in the 4--5 $\\text{\\mu}$m region. By engineering the quasi-phase-matched grating profiles, tunable, narrow-band MIR and broadband MIR spectra are both observed in this geometry. Finally, we perform numerical modeling using a nonlinear envelope equation, which shows good quantitative agreement with the experiment---and can be used to inform waveguide designs to tailor the MIR frequency combs. Our results identify a path to a simple single-branch approach to mid-infrared frequency comb generation in a compact platform using commercial Er:fiber technology.

Mid-infrared frequency comb generation via cascaded quadratic nonlinearities in quasi-phase-matched waveguides.

PubMed

Kowligy, Abijith S; Lind, Alex; Hickstein, Daniel D; Carlson, David R; Timmers, Henry; Nader, Nima; Cruz, Flavio C; Ycas, Gabriel; Papp, Scott B; Diddams, Scott A

2018-04-15

We experimentally demonstrate a simple configuration for mid-infrared (MIR) frequency comb generation in quasi-phase-matched lithium niobate waveguides using the cascaded-χ (2) nonlinearity. With nanojoule-scale pulses from an Er:fiber laser, we observe octave-spanning supercontinuum in the near-infrared with dispersive wave generation in the 2.5-3 μm region and intrapulse difference frequency generation in the 4-5 μm region. By engineering the quasi-phase-matched grating profiles, tunable, narrowband MIR and broadband MIR spectra are both observed in this geometry. Finally, we perform numerical modeling using a nonlinear envelope equation, which shows good quantitative agreement with the experiment-and can be used to inform waveguide designs to tailor the MIR frequency combs. Our results identify a path to a simple single-branch approach to mid-infrared frequency comb generation in a compact platform using commercial Er:fiber technology.

Equation for the Nakanishi Weight Function Using the Inverse Stieltjes Transform

NASA Astrophysics Data System (ADS)

Karmanov, V. A.; Carbonell, J.; Frederico, T.

2018-05-01

The bound state Bethe-Salpeter amplitude was expressed by Nakanishi in terms of a smooth weight function g. By using the generalized Stieltjes transform, we derive an integral equation for the Nakanishi function g for a bound state case. It has the standard form g= \\hat{V} g, where \\hat{V} is a two-dimensional integral operator. The prescription for obtaining the kernel V starting with the kernel K of the Bethe-Salpeter equation is given.

A new method for constructing analytic elements for groundwater flow.

NASA Astrophysics Data System (ADS)

Strack, O. D.

2007-12-01

The analytic element method is based upon the superposition of analytic functions that are defined throughout the infinite domain, and can be used to meet a variety of boundary conditions. Analytic elements have been use successfully for a number of problems, mainly dealing with the Poisson equation (see, e.g., Theory and Applications of the Analytic Element Method, Reviews of Geophysics, 41,2/1005 2003 by O.D.L. Strack). The majority of these analytic elements consists of functions that exhibit jumps along lines or curves. Such linear analytic elements have been developed also for other partial differential equations, e.g., the modified Helmholz equation and the heat equation, and were constructed by integrating elementary solutions, the point sink and the point doublet, along a line. This approach is limiting for two reasons. First, the existence is required of the elementary solutions, and, second, the integration tends to limit the range of solutions that can be obtained. We present a procedure for generating analytic elements that requires merely the existence of a harmonic function with the desired properties; such functions exist in abundance. The procedure to be presented is used to generalize this harmonic function in such a way that the resulting expression satisfies the applicable differential equation. The approach will be applied, along with numerical examples, for the modified Helmholz equation and for the heat equation, while it is noted that the method is in no way restricted to these equations. The procedure is carried out entirely in terms of complex variables, using Wirtinger calculus.

Semi-analytical Karhunen-Loeve representation of irregular waves based on the prolate spheroidal wave functions

NASA Astrophysics Data System (ADS)

Lee, Gibbeum; Cho, Yeunwoo

2018-01-01

A new semi-analytical approach is presented to solving the matrix eigenvalue problem or the integral equation in Karhunen-Loeve (K-L) representation of random data such as irregular ocean waves. Instead of direct numerical approach to this matrix eigenvalue problem, which may suffer from the computational inaccuracy for big data, a pair of integral and differential equations are considered, which are related to the so-called prolate spheroidal wave functions (PSWF). First, the PSWF is expressed as a summation of a small number of the analytical Legendre functions. After substituting them into the PSWF differential equation, a much smaller size matrix eigenvalue problem is obtained than the direct numerical K-L matrix eigenvalue problem. By solving this with a minimal numerical effort, the PSWF and the associated eigenvalue of the PSWF differential equation are obtained. Then, the eigenvalue of the PSWF integral equation is analytically expressed by the functional values of the PSWF and the eigenvalues obtained in the PSWF differential equation. Finally, the analytically expressed PSWFs and the eigenvalues in the PWSF integral equation are used to form the kernel matrix in the K-L integral equation for the representation of exemplary wave data such as ordinary irregular waves. It is found that, with the same accuracy, the required memory size of the present method is smaller than that of the direct numerical K-L representation and the computation time of the present method is shorter than that of the semi-analytical method based on the sinusoidal functions.

Are diagrams always helpful tools? developmental and individual differences in the effect of presentation format on student problem solving.

PubMed

Booth, Julie L; Koedinger, Kenneth R

2012-09-01

High school and college students demonstrate a verbal, or textual, advantage whereby beginning algebra problems in story format are easier to solve than matched equations (Koedinger & Nathan, 2004). Adding diagrams to the stories may further facilitate solution (Hembree, 1992; Koedinger & Terao, 2002). However, diagrams may not be universally beneficial (Ainsworth, 2006; Larkin & Simon, 1987). To identify developmental and individual differences in the use of diagrams, story, and equation representations in problem solving. When do diagrams begin to aid problem-solving performance? Does the verbal advantage replicate for younger students? Three hundred and seventy-three students (121 sixth, 117 seventh, 135 eighth grade) from an ethnically diverse middle school in the American Midwest participated in Experiment 1. In Experiment 2, 84 sixth graders who had participated in Experiment 1 were followed up in seventh and eighth grades. In both experiments, students solved algebra problems in three matched presentation formats (equation, story, story + diagram). The textual advantage was replicated for all groups. While diagrams enhance performance of older and higher ability students, younger and lower-ability students do not benefit, and may even be hindered by a diagram's presence. The textual advantage is in place by sixth grade. Diagrams are not inherently helpful aids to student understanding and should be used cautiously in the middle school years, as students are developing competency for diagram comprehension during this time. ©2011 The British Psychological Society.

Warfarin Initiation, Atrial Fibrillation, and Kidney Function: Comparative Effectiveness and Safety of Warfarin in Older Adults With Newly Diagnosed Atrial Fibrillation.

PubMed

Jun, Min; James, Matthew T; Ma, Zhihai; Zhang, Jianguo; Tonelli, Marcello; McAlister, Finlay A; Manns, Braden J; Ravani, Pietro; Quinn, Robert R; Wiebe, Natasha; Perkovic, Vlado; Wilton, Stephen B; Winkelmayer, Wolfgang C; Hemmelgarn, Brenda R

2017-06-01

The effectiveness and safety of warfarin use among patients with atrial fibrillation (AF) and reduced kidney function are uncertain. Community-based retrospective cohort study (May 1, 2003, to March 31, 2012) using province-wide laboratory and administrative data in Alberta, Canada. 14,892 adults 66 years or older with new AF and a measurement of kidney function. Long-term dialysis patients or kidney transplant recipients were excluded. Propensity scores were used to construct a matched-pairs cohort of patients with AF who did and did not have a warfarin prescription within a 60-day period surrounding their AF diagnosis. Within 1 year of initiating warfarin therapy (or the matched date for nonusers): (1) the composite of all-cause death, ischemic stroke, or transient ischemic attack (also assessed as separate end points) and (2) first hospitalization or emergency department visit for a major bleeding episode defined as an intracranial, upper or lower gastrointestinal, or other bleeding. Baseline glomerular filtration rate (GFR) was estimated using the CKD-EPI creatinine equation. Patients were matched within estimated GFR (eGFR) categories: ≥90, 60 to 89, 45 to 59, 30 to 44, and <30mL/min/1.73m 2 . Information for baseline characteristics (sociodemographics, comorbid conditions, and prescription drug use) was obtained. Across eGFR categories, warfarin therapy initiation was associated with lower risk for the composite outcome compared to nonuse (adjusted HRs [95% CI] for eGFR categories ≥ 90, 60-89, 45-59, 30-44, and <30mL/min/1.73m 2 : 0.59 [0.35-1.01], 0.61 [0.54-0.70], 0.55 [0.47-0.65], 0.54 [0.44-0.67], and 0.64 [0.47-0.87] mL/min/1.73m 2 , respectively). Compared to nonuse, warfarin therapy was not associated with higher risk for major bleeding except for those with eGFRs of 60 to 89mL/min/1.73m 2 (HR, 1.36; 95% CI, 1.13-1.64). Selection bias. Among older adults with AF, warfarin therapy initiation was associated with a significantly lower 1-year risk for the composite outcome across all strata of kidney function. The risk for major bleeding associated with warfarin use was increased only among those with eGFRs of 60 to 89mL/min/1.73m 2 . Copyright © 2016 National Kidney Foundation, Inc. Published by Elsevier Inc. All rights reserved.