Exact solutions to the fermion propagator Schwinger-Dyson equation in Minkowski space with on-shell renormalization for quenched QED

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

Jia, Shaoyang; Pennington, M. R.

With the introduction of a spectral representation, the Schwinger-Dyson equation (SDE) for the fermion propagator is formulated in Minkowski space in QED. After imposing the on-shell renormalization conditions, analytic solutions for the fermion propagator spectral functions are obtained in four dimensions with a renormalizable version of the Gauge Technique anzatz for the fermion-photon vertex in the quenched approximation in the Landau gauge. Despite the limitations of this model, having an explicit solution provides a guiding example of the fermion propagator with the correct analytic structure. The Padé approximation for the spectral functions is also investigated.

Analytical Debye-Huckel model for electrostatic potentials around dissolved DNA.

PubMed

Wagner, K; Keyes, E; Kephart, T W; Edwards, G

1997-07-01

We present an analytical, Green-function-based model for the electric potential of DNA in solution, treating the surrounding solvent with the Debye-Huckel approximation. The partial charge of each atom is accounted for by modeling DNA as linear distributions of atoms on concentric cylindrical surfaces. The condensed ions of the solvent are treated with the Debye-Huckel approximation. The resultant leading term of the potential is that of a continuous shielded line charge, and the higher order terms account for the helical structure. Within several angstroms of the surface there is sufficient information in the electric potential to distinguish features and symmetries of DNA. Plots of the potential and equipotential surfaces, dominated by the phosphate charges, reflect the structural differences between the A, B, and Z conformations and, to a smaller extent, the difference between base sequences. As the distances from the helices increase, the magnitudes of the potentials decrease. However, the bases and sugars account for a larger fraction of the double helix potential with increasing distance. We have found that when the solvent is treated with the Debye-Huckel approximation, the potential decays more rapidly in every direction from the surface than it did in the concentric dielectric cylinder approximation.

On the first crossing distributions in fractional Brownian motion and the mass function of dark matter haloes

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

Hiotelis, Nicos; Popolo, Antonino Del, E-mail: adelpopolo@oact.inaf.it, E-mail: hiotelis@ipta.demokritos.gr

We construct an integral equation for the first crossing distributions for fractional Brownian motion in the case of a constant barrier and we present an exact analytical solution. Additionally we present first crossing distributions derived by simulating paths from fractional Brownian motion. We compare the results of the analytical solutions with both those of simulations and those of some approximated solutions which have been used in the literature. Finally, we present multiplicity functions for dark matter structures resulting from our analytical approach and we compare with those resulting from N-body simulations. We show that the results of analytical solutions aremore » in good agreement with those of path simulations but differ significantly from those derived from approximated solutions. Additionally, multiplicity functions derived from fractional Brownian motion are poor fits of the those which result from N-body simulations. We also present comparisons with other models which are exist in the literature and we discuss different ways of improving the agreement between analytical results and N-body simulations.« less

Some Factor Analytic Approximations to Latent Class Structure.

ERIC Educational Resources Information Center

Dziuban, Charles D.; Denton, William T.

Three procedures, alpha, image, and uniqueness rescaling, were applied to a joint occurrence probability matrix. That matrix was the basis of a well-known latent class structure. The values of the recurring subscript elements were varied as follows: Case 1 - The known elements were input; Case 2 - The upper bounds to the recurring subscript…

Computational aspects of sensitivity calculations in linear transient structural analysis. Ph.D. Thesis - Virginia Polytechnic Inst. and State Univ.

NASA Technical Reports Server (NTRS)

Greene, William H.

1990-01-01

A study was performed focusing on the calculation of sensitivities of displacements, velocities, accelerations, and stresses in linear, structural, transient response problems. One significant goal of the study was to develop and evaluate sensitivity calculation techniques suitable for large-order finite element analyses. Accordingly, approximation vectors such as vibration mode shapes are used to reduce the dimensionality of the finite element model. Much of the research focused on the accuracy of both response quantities and sensitivities as a function of number of vectors used. Two types of sensitivity calculation techniques were developed and evaluated. The first type of technique is an overall finite difference method where the analysis is repeated for perturbed designs. The second type of technique is termed semi-analytical because it involves direct, analytical differentiation of the equations of motion with finite difference approximation of the coefficient matrices. To be computationally practical in large-order problems, the overall finite difference methods must use the approximation vectors from the original design in the analyses of the perturbed models. In several cases this fixed mode approach resulted in very poor approximations of the stress sensitivities. Almost all of the original modes were required for an accurate sensitivity and for small numbers of modes, the accuracy was extremely poor. To overcome this poor accuracy, two semi-analytical techniques were developed. The first technique accounts for the change in eigenvectors through approximate eigenvector derivatives. The second technique applies the mode acceleration method of transient analysis to the sensitivity calculations. Both result in accurate values of the stress sensitivities with a small number of modes and much lower computational costs than if the vibration modes were recalculated and then used in an overall finite difference method.

Analytical theory of the shear Alfvén continuum in the presence of a magnetic island

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

Cook, C. R., E-mail: cook@physics.wisc.edu; Hegna, C. C.

2015-04-15

The effect of a magnetic island chain on the shear Alfvén continuum is calculated analytically. Using a WKB approximation of the linearized ideal MHD equations, the island is shown to cause an upshift in the continuum accumulation point frequency. This minimum of the frequency spectrum is shifted from the rational surface to the island separatrix. The structure of the eigenmodes is also presented.

Nonperturbative confinement in quantum chromodynamics. I. Study of an approximate equation of Mandelstam

NASA Astrophysics Data System (ADS)

Atkinson, D.; Drohm, J. K.; Johnson, P. W.; Stam, K.

1981-11-01

An approximated form of the Dyson-Schwinger equation for the gluon propagator in quarkless QCD is subjected to nonlinear functional and numerical analysis. It is found that solutions exist, and that these have a double pole at the origin of the square of the propagator momentum, together with an accumulation of soft branch points. This analytic structure is strongly suggestive of confinement by infrared slavery.

Analytical Debye-Huckel model for electrostatic potentials around dissolved DNA.

PubMed Central

Wagner, K; Keyes, E; Kephart, T W; Edwards, G

1997-01-01

We present an analytical, Green-function-based model for the electric potential of DNA in solution, treating the surrounding solvent with the Debye-Huckel approximation. The partial charge of each atom is accounted for by modeling DNA as linear distributions of atoms on concentric cylindrical surfaces. The condensed ions of the solvent are treated with the Debye-Huckel approximation. The resultant leading term of the potential is that of a continuous shielded line charge, and the higher order terms account for the helical structure. Within several angstroms of the surface there is sufficient information in the electric potential to distinguish features and symmetries of DNA. Plots of the potential and equipotential surfaces, dominated by the phosphate charges, reflect the structural differences between the A, B, and Z conformations and, to a smaller extent, the difference between base sequences. As the distances from the helices increase, the magnitudes of the potentials decrease. However, the bases and sugars account for a larger fraction of the double helix potential with increasing distance. We have found that when the solvent is treated with the Debye-Huckel approximation, the potential decays more rapidly in every direction from the surface than it did in the concentric dielectric cylinder approximation. Images FIGURE 1 FIGURE 2 FIGURE 3 FIGURE 4 FIGURE 5 FIGURE 7 PMID:9199767

Finite element modeling of mitral leaflet tissue using a layered shell approximation

PubMed Central

Ratcliffe, Mark B.; Guccione, Julius M.

2012-01-01

The current study presents a finite element model of mitral leaflet tissue, which incorporates the anisotropic material response and approximates the layered structure. First, continuum mechanics and the theory of layered composites are used to develop an analytical representation of membrane stress in the leaflet material. This is done with an existing anisotropic constitutive law from literature. Then, the concept is implemented in a finite element (FE) model by overlapping and merging two layers of transversely isotropic membrane elements in LS-DYNA, which homogenizes the response. The FE model is then used to simulate various biaxial extension tests and out-of-plane pressure loading. Both the analytical and FE model show good agreement with experimental biaxial extension data, and show good mutual agreement. This confirms that the layered composite approximation presented in the current study is able to capture the exponential stiffening seen in both the circumferential and radial directions of mitral leaflets. PMID:22971896

Communication: Analytic continuation of the virial series through the critical point using parametric approximants.

PubMed

Barlow, Nathaniel S; Schultz, Andrew J; Weinstein, Steven J; Kofke, David A

2015-08-21

The mathematical structure imposed by the thermodynamic critical point motivates an approximant that synthesizes two theoretically sound equations of state: the parametric and the virial. The former is constructed to describe the critical region, incorporating all scaling laws; the latter is an expansion about zero density, developed from molecular considerations. The approximant is shown to yield an equation of state capable of accurately describing properties over a large portion of the thermodynamic parameter space, far greater than that covered by each treatment alone.

Asymptotically inspired moment-closure approximation for adaptive networks

NASA Astrophysics Data System (ADS)

Shkarayev, Maxim; Shaw, Leah

2012-02-01

Adaptive social networks, in which nodes and network structure co-evolve, are often described using a mean-field system of equations for the density of node and link types. These equations constitute an open system due to dependence on higher order topological structures. We propose a moment-closure approximation based on the analytical description of the system in an asymptotic regime. We apply the proposed approach to two examples of adaptive networks: recruitment to a cause model and epidemic spread model. We show a good agreement between the improved mean-field prediction and simulations of the full network system.

Asymptotically inspired moment-closure approximation for adaptive networks

NASA Astrophysics Data System (ADS)

Shkarayev, Maxim

2013-03-01

Dynamics of adaptive social networks, in which nodes and network structure co-evolve, are often described using a mean-field system of equations for the density of node and link types. These equations constitute an open system due to dependence on higher order topological structures. We propose a systematic approach to moment closure approximation based on the analytical description of the system in an asymptotic regime. We apply the proposed approach to two examples of adaptive networks: recruitment to a cause model and adaptive epidemic model. We show a good agreement between the mean-field prediction and simulations of the full network system.

Chemical Sensor Array Response Modeling Using Quantitative Structure-Activity Relationships Technique

NASA Astrophysics Data System (ADS)

Shevade, Abhijit V.; Ryan, Margaret A.; Homer, Margie L.; Zhou, Hanying; Manfreda, Allison M.; Lara, Liana M.; Yen, Shiao-Pin S.; Jewell, April D.; Manatt, Kenneth S.; Kisor, Adam K.

We have developed a Quantitative Structure-Activity Relationships (QSAR) based approach to correlate the response of chemical sensors in an array with molecular descriptors. A novel molecular descriptor set has been developed; this set combines descriptors of sensing film-analyte interactions, representing sensor response, with a basic analyte descriptor set commonly used in QSAR studies. The descriptors are obtained using a combination of molecular modeling tools and empirical and semi-empirical Quantitative Structure-Property Relationships (QSPR) methods. The sensors under investigation are polymer-carbon sensing films which have been exposed to analyte vapors at parts-per-million (ppm) concentrations; response is measured as change in film resistance. Statistically validated QSAR models have been developed using Genetic Function Approximations (GFA) for a sensor array for a given training data set. The applicability of the sensor response models has been tested by using it to predict the sensor activities for test analytes not considered in the training set for the model development. The validated QSAR sensor response models show good predictive ability. The QSAR approach is a promising computational tool for sensing materials evaluation and selection. It can also be used to predict response of an existing sensing film to new target analytes.

The Globular State of the Single-Stranded RNA: Effect of the Secondary Structure Rearrangements

PubMed Central

Grigoryan, Zareh A.; Karapetian, Armen T.

2015-01-01

The mutual influence of the slow rearrangements of secondary structure and fast collapse of the long single-stranded RNA (ssRNA) in approximation of coarse-grained model is studied with analytic calculations. It is assumed that the characteristic time of the secondary structure rearrangement is much longer than that for the formation of the tertiary structure. A nonequilibrium phase transition of the 2nd order has been observed. PMID:26345143

Efficiency of unconstrained minimization techniques in nonlinear analysis

NASA Technical Reports Server (NTRS)

Kamat, M. P.; Knight, N. F., Jr.

1978-01-01

Unconstrained minimization algorithms have been critically evaluated for their effectiveness in solving structural problems involving geometric and material nonlinearities. The algorithms have been categorized as being zeroth, first, or second order depending upon the highest derivative of the function required by the algorithm. The sensitivity of these algorithms to the accuracy of derivatives clearly suggests using analytically derived gradients instead of finite difference approximations. The use of analytic gradients results in better control of the number of minimizations required for convergence to the exact solution.

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

NASA Technical Reports Server (NTRS)

Dubois, George B; Ocvirk, Fred W

1953-01-01

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

Analytic second derivatives of the energy in the fragment molecular orbital method

NASA Astrophysics Data System (ADS)

Nakata, Hiroya; Nagata, Takeshi; Fedorov, Dmitri G.; Yokojima, Satoshi; Kitaura, Kazuo; Nakamura, Shinichiro

2013-04-01

We developed the analytic second derivatives of the energy for the fragment molecular orbital (FMO) method. First we derived the analytic expressions and then introduced some approximations related to the first and second order coupled perturbed Hartree-Fock equations. We developed a parallel program for the FMO Hessian with approximations in GAMESS and used it to calculate infrared (IR) spectra and Gibbs free energies and to locate the transition states in SN2 reactions. The accuracy of the Hessian is demonstrated in comparison to ab initio results for polypeptides and a water cluster. By using the two residues per fragment division, we achieved the accuracy of 3 cm-1 in the reduced mean square deviation of vibrational frequencies from ab initio for all three polyalanine isomers, while the zero point energy had the error not exceeding 0.3 kcal/mol. The role of the secondary structure on IR spectra, zero point energies, and Gibbs free energies is discussed.

Dependence of structure factor and correlation energy on the width of electron wires

NASA Astrophysics Data System (ADS)

Ashokan, Vinod; Bala, Renu; Morawetz, Klaus; Pathak, Kare Narain

2018-02-01

The structure factor and correlation energy of a quantum wire of thickness b ≪ a B are studied in random phase approximation (RPA) and for the less investigated region r s < 1. Using the single-loop approximation, analytical expressions of the structure factor are obtained. The exact expressions for the exchange energy are also derived for a cylindrical and harmonic wire. The correlation energy in RPA is found to be represented by ɛ c ( b, r s ) = α( r s )/ b + β( r s ) ln( b) + η( r s ), for small b and high densities. For a pragmatic width of the wire, the correlation energy is in agreement with the quantum Monte Carlo simulation data.

Pattern Storage, Bifurcations, and Groupwise Correlation Structure of an Exactly Solvable Asymmetric Neural Network Model.

PubMed

Fasoli, Diego; Cattani, Anna; Panzeri, Stefano

2018-05-01

Despite their biological plausibility, neural network models with asymmetric weights are rarely solved analytically, and closed-form solutions are available only in some limiting cases or in some mean-field approximations. We found exact analytical solutions of an asymmetric spin model of neural networks with arbitrary size without resorting to any approximation, and we comprehensively studied its dynamical and statistical properties. The network had discrete time evolution equations and binary firing rates, and it could be driven by noise with any distribution. We found analytical expressions of the conditional and stationary joint probability distributions of the membrane potentials and the firing rates. By manipulating the conditional probability distribution of the firing rates, we extend to stochastic networks the associating learning rule previously introduced by Personnaz and coworkers. The new learning rule allowed the safe storage, under the presence of noise, of point and cyclic attractors, with useful implications for content-addressable memories. Furthermore, we studied the bifurcation structure of the network dynamics in the zero-noise limit. We analytically derived examples of the codimension 1 and codimension 2 bifurcation diagrams of the network, which describe how the neuronal dynamics changes with the external stimuli. This showed that the network may undergo transitions among multistable regimes, oscillatory behavior elicited by asymmetric synaptic connections, and various forms of spontaneous symmetry breaking. We also calculated analytically groupwise correlations of neural activity in the network in the stationary regime. This revealed neuronal regimes where, statistically, the membrane potentials and the firing rates are either synchronous or asynchronous. Our results are valid for networks with any number of neurons, although our equations can be realistically solved only for small networks. For completeness, we also derived the network equations in the thermodynamic limit of infinite network size and we analytically studied their local bifurcations. All the analytical results were extensively validated by numerical simulations.

Finite element simulation of light transfer in turbid media under structured illumination

USDA-ARS?s Scientific Manuscript database

Spatial-frequency domain (SFD) imaging technique allows to estimate the optical properties of biological tissues in a wide field of view. The technique is, however, prone to error in measurement because the two crucial assumptions used for deriving the analytical solution to diffusion approximation ...

Numerical and analytic models of spontaneous frequency sweeping for energetic particle-driven Alfven eigenmodes

NASA Astrophysics Data System (ADS)

Wang, Ge; Berk, H. L.

2011-10-01

The frequency chirping signal arising from spontaneous a toroidial Alfven eigenmode (TAE) excited by energetic particles is studied for both numerical and analytic models. The time-dependent numerical model is based on the 1D Vlasov equation. We use a sophisticated tracking method to lock onto the resonant structure to enable the chirping frequency to be nearly constant in the calculation frame. The accuracy of the adiabatic approximation is tested during the simulation which justifies the appropriateness of our analytic model. The analytic model uses the adiabatic approximation which allows us to solve the wave evolution equation in frequency space. Then, the resonant interactions between energetic particles and TAE yield predictions for the chirping rate, wave frequency and amplitudes vs. time. Here, an adiabatic invariant J is defined on the separatrix of a chirping mode to determine the region of confinement of the wave trapped distribution function. We examine the asymptotic behavior of the chirping signal for its long time evolution and find agreement in essential features with the results of the simulation. Work supported by Department of Energy contract DE-FC02-08ER54988.

Analysis of the connection of the timber-fiber concrete composite structure

NASA Astrophysics Data System (ADS)

Holý, Milan; Vráblík, Lukáš; Petřík, Vojtěch

2017-09-01

This paper deals with an implementation of the material parameters of the connection to complex models for analysis of the timber-fiber concrete composite structures. The aim of this article is to present a possible way of idealization of the continuous contact model that approximates the actual behavior of timber-fiber reinforced concrete structures. The presented model of the connection was derived from push-out shear tests. It was approved by use of the nonlinear numerical analysis, that it can be achieved a very good compliance between results of numerical simulations and results of the experiments by a suitable choice of the material parameters of the continuous contact. Finally, an application for an analytical calculation of timber-fiber concrete composite structures is developed for the practical use in engineering praxis. The input material parameters for the analytical model was received using data from experiments.

Solving the Helmholtz equation in conformal mapped ARROW structures using homotopy perturbation method.

PubMed

Reck, Kasper; Thomsen, Erik V; Hansen, Ole

2011-01-31

The scalar wave equation, or Helmholtz equation, describes within a certain approximation the electromagnetic field distribution in a given system. In this paper we show how to solve the Helmholtz equation in complex geometries using conformal mapping and the homotopy perturbation method. The solution of the mapped Helmholtz equation is found by solving an infinite series of Poisson equations using two dimensional Fourier series. The solution is entirely based on analytical expressions and is not mesh dependent. The analytical results are compared to a numerical (finite element method) solution.

Radial distribution function for hard spheres in fractal dimensions: A heuristic approximation.

PubMed

Santos, Andrés; de Haro, Mariano López

2016-06-01

Analytic approximations for the radial distribution function, the structure factor, and the equation of state of hard-core fluids in fractal dimension d (1≤d≤3) are developed as heuristic interpolations from the knowledge of the exact and Percus-Yevick results for the hard-rod and hard-sphere fluids, respectively. In order to assess their value, such approximate results are compared with those of recent Monte Carlo simulations and numerical solutions of the Percus-Yevick equation for a fractal dimension [M. Heinen et al., Phys. Rev. Lett. 115, 097801 (2015)PRLTAO0031-900710.1103/PhysRevLett.115.097801], a good agreement being observed.

Analytical description of changes in the magnetic states of chromium-nickel steel under uniaxial elastic deformation

NASA Astrophysics Data System (ADS)

Gorkunov, E. S.; Yakushenko, E. I.; Zadvorkin, S. M.; Mushnikov, A. N.

2017-12-01

Dependences of magnetization and magnetic permeability of the 15KhN4D structural steel on the value of uniaxial stresses and magnetic field strength are obtained. A polynomial approximation fairly accurately describing the observed changes is proposed on the basis of experimental data.

Transient analysis of an adaptive system for optimization of design parameters

NASA Technical Reports Server (NTRS)

Bayard, D. S.

1992-01-01

Averaging methods are applied to analyzing and optimizing the transient response associated with the direct adaptive control of an oscillatory second-order minimum-phase system. The analytical design methods developed for a second-order plant can be applied with some approximation to a MIMO flexible structure having a single dominant mode.

Self-Consistent Field Theory of Gaussian Ring Polymers

NASA Astrophysics Data System (ADS)

Kim, Jaeup; Yang, Yong-Biao; Lee, Won Bo

2012-02-01

Ring polymers, being free from chain ends, have fundamental importance in understanding the polymer statics and dynamics which are strongly influenced by the chain end effects. At a glance, their theoretical treatment may not seem particularly difficult, but the absence of chain ends and the topological constraints make the problem non-trivial, which results in limited success in the analytical or semi-analytical formulation of ring polymer theory. Here, I present a self-consistent field theory (SCFT) formalism of Gaussian (topologically unconstrained) ring polymers for the first time. The resulting static property of homogeneous and inhomogeneous ring polymers are compared with the random phase approximation (RPA) results. The critical point for ring homopolymer system is exactly the same as the linear polymer case, χN = 2, since a critical point does not depend on local structures of polymers. The critical point for ring diblock copolymer melts is χN 17.795, which is approximately 1.7 times of that of linear diblock copolymer melts, χN 10.495. The difference is due to the ring structure constraint.

Stability analysis of magnetized neutron stars - a semi-analytic approach

NASA Astrophysics Data System (ADS)

Herbrik, Marlene; Kokkotas, Kostas D.

2017-04-01

We implement a semi-analytic approach for stability analysis, addressing the ongoing uncertainty about stability and structure of neutron star magnetic fields. Applying the energy variational principle, a model system is displaced from its equilibrium state. The related energy density variation is set up analytically, whereas its volume integration is carried out numerically. This facilitates the consideration of more realistic neutron star characteristics within the model compared to analytical treatments. At the same time, our method retains the possibility to yield general information about neutron star magnetic field and composition structures that are likely to be stable. In contrast to numerical studies, classes of parametrized systems can be studied at once, finally constraining realistic configurations for interior neutron star magnetic fields. We apply the stability analysis scheme on polytropic and non-barotropic neutron stars with toroidal, poloidal and mixed fields testing their stability in a Newtonian framework. Furthermore, we provide the analytical scheme for dropping the Cowling approximation in an axisymmetric system and investigate its impact. Our results confirm the instability of simple magnetized neutron star models as well as a stabilization tendency in the case of mixed fields and stratification. These findings agree with analytical studies whose spectrum of model systems we extend by lifting former simplifications.

Analytic Interatomic Forces in the Random Phase Approximation

NASA Astrophysics Data System (ADS)

Ramberger, Benjamin; Schäfer, Tobias; Kresse, Georg

2017-03-01

We discuss that in the random phase approximation (RPA) the first derivative of the energy with respect to the Green's function is the self-energy in the G W approximation. This relationship allows us to derive compact equations for the RPA interatomic forces. We also show that position dependent overlap operators are elegantly incorporated in the present framework. The RPA force equations have been implemented in the projector augmented wave formalism, and we present illustrative applications, including ab initio molecular dynamics simulations, the calculation of phonon dispersion relations for diamond and graphite, as well as structural relaxations for water on boron nitride. The present derivation establishes a concise framework for forces within perturbative approaches and is also applicable to more involved approximations for the correlation energy.

Analytic model for the long-term evolution of circular Earth satellite orbits including lunar node regression

NASA Astrophysics Data System (ADS)

Zhu, Ting-Lei; Zhao, Chang-Yin; Zhang, Ming-Jiang

2017-04-01

This paper aims to obtain an analytic approximation to the evolution of circular orbits governed by the Earth's J2 and the luni-solar gravitational perturbations. Assuming that the lunar orbital plane coincides with the ecliptic plane, Allan and Cook (Proc. R. Soc. A, Math. Phys. Eng. Sci. 280(1380):97, 1964) derived an analytic solution to the orbital plane evolution of circular orbits. Using their result as an intermediate solution, we establish an approximate analytic model with lunar orbital inclination and its node regression be taken into account. Finally, an approximate analytic expression is derived, which is accurate compared to the numerical results except for the resonant cases when the period of the reference orbit approximately equals the integer multiples (especially 1 or 2 times) of lunar node regression period.

An improved approximate network blocking probability model for all-optical WDM Networks with heterogeneous link capacities

NASA Astrophysics Data System (ADS)

Khan, Akhtar Nawaz

2017-11-01

Currently, analytical models are used to compute approximate blocking probabilities in opaque and all-optical WDM networks with the homogeneous link capacities. Existing analytical models can also be extended to opaque WDM networking with heterogeneous link capacities due to the wavelength conversion at each switch node. However, existing analytical models cannot be utilized for all-optical WDM networking with heterogeneous structure of link capacities due to the wavelength continuity constraint and unequal numbers of wavelength channels on different links. In this work, a mathematical model is extended for computing approximate network blocking probabilities in heterogeneous all-optical WDM networks in which the path blocking is dominated by the link along the path with fewer number of wavelength channels. A wavelength assignment scheme is also proposed for dynamic traffic, termed as last-fit-first wavelength assignment, in which a wavelength channel with maximum index is assigned first to a lightpath request. Due to heterogeneous structure of link capacities and the wavelength continuity constraint, the wavelength channels with maximum indexes are utilized for minimum hop routes. Similarly, the wavelength channels with minimum indexes are utilized for multi-hop routes between source and destination pairs. The proposed scheme has lower blocking probability values compared to the existing heuristic for wavelength assignments. Finally, numerical results are computed in different network scenarios which are approximately equal to values obtained from simulations. Since January 2016, he is serving as Head of Department and an Assistant Professor in the Department of Electrical Engineering at UET, Peshawar-Jalozai Campus, Pakistan. From May 2013 to June 2015, he served Department of Telecommunication Engineering as an Assistant Professor at UET, Peshawar-Mardan Campus, Pakistan. He also worked as an International Internship scholar in the Fukuda Laboratory, National Institute of Informatics, Tokyo, Japan on the topic large-scale simulation for internet topology analysis. His research interests include design and analysis of optical WDM networks, network algorithms, network routing, and network resource optimization problems.

A semi-analytical description of protein folding that incorporates detailed geometrical information

PubMed Central

Suzuki, Yoko; Noel, Jeffrey K.; Onuchic, José N.

2011-01-01

Much has been done to study the interplay between geometric and energetic effects on the protein folding energy landscape. Numerical techniques such as molecular dynamics simulations are able to maintain a precise geometrical representation of the protein. Analytical approaches, however, often focus on the energetic aspects of folding, including geometrical information only in an average way. Here, we investigate a semi-analytical expression of folding that explicitly includes geometrical effects. We consider a Hamiltonian corresponding to a Gaussian filament with structure-based interactions. The model captures local features of protein folding often averaged over by mean-field theories, for example, loop contact formation and excluded volume. We explore the thermodynamics and folding mechanisms of beta-hairpin and alpha-helical structures as functions of temperature and Q, the fraction of native contacts formed. Excluded volume is shown to be an important component of a protein Hamiltonian, since it both dominates the cooperativity of the folding transition and alters folding mechanisms. Understanding geometrical effects in analytical formulae will help illuminate the consequences of the approximations required for the study of larger proteins. PMID:21721664

Consistent Yokoya-Chen Approximation to Beamstrahlung(LCC-0010)

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

Peskin, M

2004-04-22

I reconsider the Yokoya-Chen approximate evolution equation for beamstrahlung and modify it slightly to generate simple, consistent analytical approximations for the electron and photon energy spectra. I compare these approximations to previous ones, and to simulation data.I reconsider the Yokoya-Chen approximate evolution equation for beamstrahlung and modify it slightly to generate simple, consistent analytical approximations for the electron and photon energy spectra. I compare these approximations to previous ones, and to simulation data.

Thrust and torque vector characteristics of axially-symmetric E-sail

NASA Astrophysics Data System (ADS)

Bassetto, Marco; Mengali, Giovanni; Quarta, Alessandro A.

2018-05-01

The Electric Solar Wind Sail is an innovative propulsion system concept that gains propulsive acceleration from the interaction with charged particles released by the Sun. The aim of this paper is to obtain analytical expressions for the thrust and torque vectors of a spinning sail of given shape. Under the only assumption that each tether belongs to a plane containing the spacecraft spin axis, a general analytical relation is found for the thrust and torque vectors as a function of the spacecraft attitude relative to an orbital reference frame. The results are then applied to the noteworthy situation of a Sun-facing sail, that is, when the spacecraft spin axis is aligned with the Sun-spacecraft line, which approximatively coincides with the solar wind direction. In that case, the paper discusses the equilibrium shape of the generic conducting tether as a function of the sail geometry and the spin rate, using both a numerical and an analytical (approximate) approach. As a result, the structural characteristics of the conducting tether are related to the spacecraft geometric parameters.

Multidisciplinary design optimization using multiobjective formulation techniques

NASA Technical Reports Server (NTRS)

Chattopadhyay, Aditi; Pagaldipti, Narayanan S.

1995-01-01

This report addresses the development of a multidisciplinary optimization procedure using an efficient semi-analytical sensitivity analysis technique and multilevel decomposition for the design of aerospace vehicles. A semi-analytical sensitivity analysis procedure is developed for calculating computational grid sensitivities and aerodynamic design sensitivities. Accuracy and efficiency of the sensitivity analysis procedure is established through comparison of the results with those obtained using a finite difference technique. The developed sensitivity analysis technique are then used within a multidisciplinary optimization procedure for designing aerospace vehicles. The optimization problem, with the integration of aerodynamics and structures, is decomposed into two levels. Optimization is performed for improved aerodynamic performance at the first level and improved structural performance at the second level. Aerodynamic analysis is performed by solving the three-dimensional parabolized Navier Stokes equations. A nonlinear programming technique and an approximate analysis procedure are used for optimization. The proceduredeveloped is applied to design the wing of a high speed aircraft. Results obtained show significant improvements in the aircraft aerodynamic and structural performance when compared to a reference or baseline configuration. The use of the semi-analytical sensitivity technique provides significant computational savings.

Super-sample covariance approximations and partial sky coverage

NASA Astrophysics Data System (ADS)

Lacasa, Fabien; Lima, Marcos; Aguena, Michel

2018-04-01

Super-sample covariance (SSC) is the dominant source of statistical error on large scale structure (LSS) observables for both current and future galaxy surveys. In this work, we concentrate on the SSC of cluster counts, also known as sample variance, which is particularly useful for the self-calibration of the cluster observable-mass relation; our approach can similarly be applied to other observables, such as galaxy clustering and lensing shear. We first examined the accuracy of two analytical approximations proposed in the literature for the flat sky limit, finding that they are accurate at the 15% and 30-35% level, respectively, for covariances of counts in the same redshift bin. We then developed a harmonic expansion formalism that allows for the prediction of SSC in an arbitrary survey mask geometry, such as large sky areas of current and future surveys. We show analytically and numerically that this formalism recovers the full sky and flat sky limits present in the literature. We then present an efficient numerical implementation of the formalism, which allows fast and easy runs of covariance predictions when the survey mask is modified. We applied our method to a mask that is broadly similar to the Dark Energy Survey footprint, finding a non-negligible negative cross-z covariance, i.e. redshift bins are anti-correlated. We also examined the case of data removal from holes due to, for example bright stars, quality cuts, or systematic removals, and find that this does not have noticeable effects on the structure of the SSC matrix, only rescaling its amplitude by the effective survey area. These advances enable analytical covariances of LSS observables to be computed for current and future galaxy surveys, which cover large areas of the sky where the flat sky approximation fails.

Approximated analytical solution to an Ebola optimal control problem

NASA Astrophysics Data System (ADS)

Hincapié-Palacio, Doracelly; Ospina, Juan; Torres, Delfim F. M.

2016-11-01

An analytical expression for the optimal control of an Ebola problem is obtained. The analytical solution is found as a first-order approximation to the Pontryagin Maximum Principle via the Euler-Lagrange equation. An implementation of the method is given using the computer algebra system Maple. Our analytical solutions confirm the results recently reported in the literature using numerical methods.

Analysis and Sizing for Transient Thermal Heating of Insulated Aerospace Vehicle Structures

NASA Technical Reports Server (NTRS)

Blosser, Max L.

2012-01-01

An analytical solution was derived for the transient response of an insulated structure subjected to a simplified heat pulse. The solution is solely a function of two nondimensional parameters. Simpler functions of these two parameters were developed to approximate the maximum structural temperature over a wide range of parameter values. Techniques were developed to choose constant, effective thermal properties to represent the relevant temperature and pressure-dependent properties for the insulator and structure. A technique was also developed to map a time-varying surface temperature history to an equivalent square heat pulse. Equations were also developed for the minimum mass required to maintain the inner, unheated surface below a specified temperature. In the course of the derivation, two figures of merit were identified. Required insulation masses calculated using the approximate equation were shown to typically agree with finite element results within 10%-20% over the relevant range of parameters studied.

Preliminary design methods for fiber reinforced composite structures employing a personal computer

NASA Technical Reports Server (NTRS)

Eastlake, C. N.

1986-01-01

The objective of this project was to develop a user-friendly interactive computer program to be used as an analytical tool by structural designers. Its intent was to do preliminary, approximate stress analysis to help select or verify sizing choices for composite structural members. The approach to the project was to provide a subroutine which uses classical lamination theory to predict an effective elastic modulus for a laminate of arbitrary material and ply orientation. This effective elastic modulus can then be used in a family of other subroutines which employ the familiar basic structural analysis methods for isotropic materials. This method is simple and convenient to use but only approximate, as is appropriate for a preliminary design tool which will be subsequently verified by more sophisticated analysis. Additional subroutines have been provided to calculate laminate coefficient of thermal expansion and to calculate ply-by-ply strains within a laminate.

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).

Analysis of fluid-structure interaction in a frame pipe undergoing plastic deformations

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

Khamlichi, A.; Jezequel, L.; Jacques, Y.

1995-11-01

Water hammer pressure waves of sufficiently large magnitude can cause plastic flexural deformations in a frame pipe. In this study, the authors propose a modelization of this problem based on plane wave approximation for the fluid equations and approximation of the structure motion by a single-degree-of-freedom elastic-plastic oscillator. Direct analytical integration of elastic-plastic equations through pipe sections, then over the pipe length is performed in order to identify the oscillator parameters. Comparison of the global load-displacement relationship obtained with the finite element solution was considered and has shown good agreement. Fluid-structure coupling is achieved by assuming elbows to act likemore » plane monopole sources, where localized jumps of fluid velocity occur and where net pressure forces are exerted on the structure. The authors have applied this method to analyze the fluid-structure interaction in this range of deformations. Energy exchange between the fluid and the structure and energy dissipation are quantified.« less

Bounded Linear Stability Analysis - A Time Delay Margin Estimation Approach for Adaptive Control

NASA Technical Reports Server (NTRS)

Nguyen, Nhan T.; Ishihara, Abraham K.; Krishnakumar, Kalmanje Srinlvas; Bakhtiari-Nejad, Maryam

2009-01-01

This paper presents a method for estimating time delay margin for model-reference adaptive control of systems with almost linear structured uncertainty. The bounded linear stability analysis method seeks to represent the conventional model-reference adaptive law by a locally bounded linear approximation within a small time window using the comparison lemma. The locally bounded linear approximation of the combined adaptive system is cast in a form of an input-time-delay differential equation over a small time window. The time delay margin of this system represents a local stability measure and is computed analytically by a matrix measure method, which provides a simple analytical technique for estimating an upper bound of time delay margin. Based on simulation results for a scalar model-reference adaptive control system, both the bounded linear stability method and the matrix measure method are seen to provide a reasonably accurate and yet not too conservative time delay margin estimation.

Computer simulation of formation and decomposition of Au13 nanoparticles

NASA Astrophysics Data System (ADS)

Stishenko, P.; Svalova, A.

2017-08-01

To study the Ostwald ripening process of Au13 nanoparticles a two-scale model is constructed: analytical approximation of average nanoparticle energy as function of nanoparticle size and structural motive, and the Monte Carlo model of 1000 particles ensemble. Simulation results show different behavior of particles of different structural motives. The change of the distributions of atom coordination numbers during the Ostwald ripening process was observed. The nanoparticles of the equal size and shape with the face-centered cubic structure of the largest sizes appeared to be the most stable.

Modeling direct interband tunneling. II. Lower-dimensional structures

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

Pan, Andrew, E-mail: pandrew@ucla.edu; Chui, Chi On; California NanoSystems Institute, University of California, Los Angeles, Los Angeles, California 90095

We investigate the applicability of the two-band Hamiltonian and the widely used Kane analytical formula to interband tunneling along unconfined directions in nanostructures. Through comparisons with k·p and tight-binding calculations and quantum transport simulations, we find that the primary correction is the change in effective band gap. For both constant fields and realistic tunnel field-effect transistors, dimensionally consistent band gap scaling of the Kane formula allows analytical and numerical device simulations to approximate non-equilibrium Green's function current characteristics without arbitrary fitting. This allows efficient first-order calibration of semiclassical models for interband tunneling in nanodevices.

A Model of High-Frequency Self-Mixing in Double-Barrier Rectifier

NASA Astrophysics Data System (ADS)

Palma, Fabrizio; Rao, R.

2018-03-01

In this paper, a new model of the frequency dependence of the double-barrier THz rectifier is presented. The new structure is of interest because it can be realized by CMOS image sensor technology. Its application in a complex field such as that of THz receivers requires the availability of an analytical model, which is reliable and able to highlight the dependence on the parameters of the physical structure. The model is based on the hydrodynamic semiconductor equations, solved in the small signal approximation. The model depicts the mechanisms of the THz modulation of the charge in the depleted regions of the double-barrier device and explains the self-mixing process, the frequency dependence, and the detection capability of the structure. The model thus substantially improves the analytical models of the THz rectification available in literature, mainly based on lamped equivalent circuits.

Precision of Sensitivity in the Design Optimization of Indeterminate Structures

NASA Technical Reports Server (NTRS)

Patnaik, Surya N.; Pai, Shantaram S.; Hopkins, Dale A.

2006-01-01

Design sensitivity is central to most optimization methods. The analytical sensitivity expression for an indeterminate structural design optimization problem can be factored into a simple determinate term and a complicated indeterminate component. Sensitivity can be approximated by retaining only the determinate term and setting the indeterminate factor to zero. The optimum solution is reached with the approximate sensitivity. The central processing unit (CPU) time to solution is substantially reduced. The benefit that accrues from using the approximate sensitivity is quantified by solving a set of problems in a controlled environment. Each problem is solved twice: first using the closed-form sensitivity expression, then using the approximation. The problem solutions use the CometBoards testbed as the optimization tool with the integrated force method as the analyzer. The modification that may be required, to use the stiffener method as the analysis tool in optimization, is discussed. The design optimization problem of an indeterminate structure contains many dependent constraints because of the implicit relationship between stresses, as well as the relationship between the stresses and displacements. The design optimization process can become problematic because the implicit relationship reduces the rank of the sensitivity matrix. The proposed approximation restores the full rank and enhances the robustness of the design optimization method.

Approximate analytical description of the elastic strain field due to an inclusion in a continuous medium with cubic anisotropy

NASA Astrophysics Data System (ADS)

Nenashev, A. V.; Koshkarev, A. A.; Dvurechenskii, A. V.

2018-03-01

We suggest an approach to the analytical calculation of the strain distribution due to an inclusion in elastically anisotropic media for the case of cubic anisotropy. The idea consists in the approximate reduction of the anisotropic problem to a (simpler) isotropic problem. This gives, for typical semiconductors, an improvement in accuracy by an order of magnitude, compared to the isotropic approximation. Our method allows using, in the case of elastically anisotropic media, analytical solutions obtained for isotropic media only, such as analytical formulas for the strain due to polyhedral inclusions. The present work substantially extends the applicability of analytical results, making them more suitable for describing real systems, such as epitaxial quantum dots.

Decoupling the NLO-coupled QED⊗QCD, DGLAP evolution equations, using Laplace transform method

NASA Astrophysics Data System (ADS)

Mottaghizadeh, Marzieh; Eslami, Parvin; Taghavi-Shahri, Fatemeh

2017-05-01

We analytically solved the QED⊗QCD-coupled DGLAP evolution equations at leading order (LO) quantum electrodynamics (QED) and next-to-leading order (NLO) quantum chromodynamics (QCD) approximations, using the Laplace transform method and then computed the proton structure function in terms of the unpolarized parton distribution functions. Our analytical solutions for parton densities are in good agreement with those from CT14QED (1.2952 < Q2 < 1010) (Ref. 6) global parametrizations and APFEL (A PDF Evolution Library) (2 < Q2 < 108) (Ref. 4). We also compared the proton structure function, F2p(x,Q2), with the experimental data released by the ZEUS and H1 collaborations at HERA. There is a nice agreement between them in the range of low and high x and Q2.

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

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

Optical properties of electrohydrodynamic convection patterns: rigorous and approximate methods.

PubMed

Bohley, Christian; Heuer, Jana; Stannarius, Ralf

2005-12-01

We analyze the optical behavior of two-dimensionally periodic structures that occur in electrohydrodynamic convection (EHC) patterns in nematic sandwich cells. These structures are anisotropic, locally uniaxial, and periodic on the scale of micrometers. For the first time, the optics of these structures is investigated with a rigorous method. The method used for the description of the electromagnetic waves interacting with EHC director patterns is a numerical approach that discretizes directly the Maxwell equations. It works as a space-grid-time-domain method and computes electric and magnetic fields in time steps. This so-called finite-difference-time-domain (FDTD) method is able to generate the fields with arbitrary accuracy. We compare this rigorous method with earlier attempts based on ray-tracing and analytical approximations. Results of optical studies of EHC structures made earlier based on ray-tracing methods are confirmed for thin cells, when the spatial periods of the pattern are sufficiently large. For the treatment of small-scale convection structures, the FDTD method is without alternatives.

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

NASA Astrophysics Data System (ADS)

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

2008-02-01

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

Nonlinear analysis for dual-frequency concurrent energy harvesting

NASA Astrophysics Data System (ADS)

Yan, Zhimiao; Lei, Hong; Tan, Ting; Sun, Weipeng; Huang, Wenhu

2018-05-01

The dual-frequency responses of the hybrid energy harvester undergoing the base excitation and galloping were analyzed numerically. In this work, an approximate dual-frequency analytical method is proposed for the nonlinear analysis of such a system. To obtain the approximate analytical solutions of the full coupled distributed-parameter model, the forcing interactions is first neglected. Then, the electromechanical decoupled governing equation is developed using the equivalent structure method. The hybrid mechanical response is finally separated to be the self-excited and forced responses for deriving the analytical solutions, which are confirmed by the numerical simulations of the full coupled model. The forced response has great impacts on the self-excited response. The boundary of Hopf bifurcation is analytically determined by the onset wind speed to galloping, which is linearly increased by the electrical damping. Quenching phenomenon appears when the increasing base excitation suppresses the galloping. The theoretical quenching boundary depends on the forced mode velocity. The quenching region increases with the base acceleration and electrical damping, but decreases with the wind speed. Superior to the base-excitation-alone case, the existence of the aerodynamic force protects the hybrid energy harvester at resonance from damages caused by the excessive large displacement. From the view of the harvested power, the hybrid system surpasses the base-excitation-alone system or the galloping-alone system. This study advances our knowledge on intrinsic nonlinear dynamics of the dual-frequency energy harvesting system by taking advantage of the analytical solutions.

Analytical approaches to the determination of spin-dependent parton distribution functions at NNLO approximation

NASA Astrophysics Data System (ADS)

Salajegheh, Maral; Nejad, S. Mohammad Moosavi; Khanpour, Hamzeh; Tehrani, S. Atashbar

2018-05-01

In this paper, we present SMKA18 analysis, which is a first attempt to extract the set of next-to-next-leading-order (NNLO) spin-dependent parton distribution functions (spin-dependent PDFs) and their uncertainties determined through the Laplace transform technique and Jacobi polynomial approach. Using the Laplace transformations, we present an analytical solution for the spin-dependent Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equations at NNLO approximation. The results are extracted using a wide range of proton g1p(x ,Q2) , neutron g1n(x ,Q2) , and deuteron g1d(x ,Q2) spin-dependent structure functions data set including the most recent high-precision measurements from COMPASS16 experiments at CERN, which are playing an increasingly important role in global spin-dependent fits. The careful estimations of uncertainties have been done using the standard Hessian error propagation. We will compare our results with the available spin-dependent inclusive deep inelastic scattering data set and other results for the spin-dependent PDFs in literature. The results obtained for the spin-dependent PDFs as well as spin-dependent structure functions are clearly explained both in the small and large values of x .

Analytical approximation for the Einstein-dilaton-Gauss-Bonnet black hole metric

NASA Astrophysics Data System (ADS)

Kokkotas, K. D.; Konoplya, R. A.; Zhidenko, A.

2017-09-01

We construct an analytical approximation for the numerical black hole metric of P. Kanti et al. [Phys. Rev. D 54, 5049 (1996), 10.1103/PhysRevD.54.5049] in the four-dimensional Einstein-dilaton-Gauss-Bonnet (EdGB) theory. The continued fraction expansion in terms of a compactified radial coordinate, used here, converges slowly when the dilaton coupling approaches its extremal values, but for a black hole far from the extremal state, the analytical formula has a maximal relative error of a fraction of one percent already within the third order of the continued fraction expansion. The suggested analytical representation of the numerical black hole metric is relatively compact and a good approximation in the whole space outside the black hole event horizon. Therefore, it can serve in the same way as an exact solution when analyzing particles' motion, perturbations, quasinormal modes, Hawking radiation, accreting disks, and many other problems in the vicinity of a black hole. In addition, we construct the approximate analytical expression for the dilaton field.

Landau-Zener extension of the Tavis-Cummings model: Structure of the solution

DOE PAGES

Sun, Chen; Sinitsyn, Nikolai A.

2016-09-07

We explore the recently discovered solution of the driven Tavis-Cummings model (DTCM). It describes interaction of an arbitrary number of two-level systems with a bosonic mode that has linearly time-dependent frequency. We derive compact and tractable expressions for transition probabilities in terms of the well-known special functions. In this form, our formulas are suitable for fast numerical calculations and analytical approximations. As an application, we obtain the semiclassical limit of the exact solution and compare it to prior approximations. Furthermore, we also reveal connection between DTCM and q-deformed binomial statistics.

GENERAL: The Analytic Solution of Schrödinger Equation with Potential Function Superposed by Six Terms with Positive-power and Inverse-power Potentials

NASA Astrophysics Data System (ADS)

Hu, Xian-Quan; Luo, Guang; Cui, Li-Peng; Li, Fang-Yu; Niu, Lian-Bin

2009-03-01

The analytic solution of the radial Schrödinger equation is studied by using the tight coupling condition of several positive-power and inverse-power potential functions in this article. Furthermore, the precisely analytic solutions and the conditions that decide the existence of analytic solution have been searched when the potential of the radial Schrödinger equation is V(r) = α1r8 + α2r3 + α3r2 + β3r-1 + β2r-3 + β1r-4. Generally speaking, there is only an approximate solution, but not analytic solution for Schrödinger equation with several potentials' superposition. However, the conditions that decide the existence of analytic solution have been found and the analytic solution and its energy level structure are obtained for the Schrödinger equation with the potential which is motioned above in this paper. According to the single-value, finite and continuous standard of wave function in a quantum system, the authors firstly solve the asymptotic solution through the radial coordinate r → and r → 0; secondly, they make the asymptotic solutions combining with the series solutions nearby the neighborhood of irregular singularities; and then they compare the power series coefficients, deduce a series of analytic solutions of the stationary state wave function and corresponding energy level structure by tight coupling among the coefficients of potential functions for the radial Schrödinger equation; and lastly, they discuss the solutions and make conclusions.

Indexing and retrieving point and region objects

NASA Astrophysics Data System (ADS)

Ibrahim, Azzam T.; Fotouhi, Farshad A.

1996-03-01

R-tree and its variants are examples of spatial data structures for paged-secondary memory. To process a query, these structures require multiple path traversals. In this paper, we present a new image access method, SB+-tree which requires a single path traversal to process a query. Also, SB+-tree will allow commercial databases an access method for spatial objects without a major change, since most commercial databases already support B+-tree as an access method for text data. The SB+-tree can be used for zero and non-zero size data objects. Non-zero size objects are approximated by their minimum bounding rectangles (MBRs). The number of SB+-trees generated is dependent upon the number of dimensions of the approximation of the object. The structure supports efficient spatial operations such as regions-overlap, distance and direction. In this paper, we experimentally and analytically demonstrate the superiority of SB+-tree over R-tree.

Structure and effective interactions in three-component hard sphere liquids.

PubMed

König, A; Ashcroft, N W

2001-04-01

Complete and simple analytical expressions for the partial structure factors of the ternary hard sphere mixture are obtained within the Percus-Yevick approximation and presented as functions of relative packing fractions and relative hard sphere diameters. These solutions follow from the Laplace transform method as applied to multicomponent systems by Lebowitz [Phys. Rev. 133, A895 (1964)]. As an important application, we examine effective interactions in hard sphere liquid mixtures using the microscopic information contained in their partial structure factors. Thus the ensuring pair potential for an effective one-component system is obtained from the correlation functions by using an approximate inversion, and examples of effective potentials for three-component hard sphere mixtures are given. These mixtures may be of particular interest for the study of the packing aspects of melts that form glasses or quasicrystals, since noncrystalline solids often emerge from melts with at least three atomic constituents.

An approximate analytical solution for interlaminar stresses in angle-ply laminates

NASA Technical Reports Server (NTRS)

Rose, Cheryl A.; Herakovich, Carl T.

1991-01-01

An improved approximate analytical solution for interlaminar stresses in finite width, symmetric, angle-ply laminated coupons subjected to axial loading is presented. The solution is based upon statically admissible stress fields which take into consideration local property mismatch effects and global equilibrium requirements. Unknown constants in the admissible stress states are determined through minimization of the complementary energy. Typical results are presented for through-the-thickness and interlaminar stress distributions for angle-ply laminates. It is shown that the results represent an improved approximate analytical solution for interlaminar stresses.

Decoupling of the Leading Order DGLAP Evolution Equation with Spin Dependent Structure Functions

NASA Astrophysics Data System (ADS)

Azadbakht, F. Teimoury; Boroun, G. R.

2018-02-01

We propose an analytical solution for DGLAP evolution equations with polarized splitting functions at the Leading Order (LO) approximation based on the Laplace transform method. It is shown that the DGLAP evolution equations can be decoupled completely into two second order differential equations which then are solved analytically by using the initial conditions δ FS(x,Q2)=F[partial δ FS0(x), δ FS0(x)] and {δ G}(x,Q2)=G[partial δ G0(x), δ G0(x)]. We used this method to obtain the polarized structure function of the proton as well as the polarized gluon distribution function inside the proton and compared the numerical results with experimental data of COMPASS, HERMES, and AAC'08 Collaborations. It was found that there is a good agreement between our predictions and the experiments.

Analytical theory of mesoscopic Bose-Einstein condensation in an ideal gas

NASA Astrophysics Data System (ADS)

Kocharovsky, Vitaly V.; Kocharovsky, Vladimir V.

2010-03-01

We find the universal structure and scaling of the Bose-Einstein condensation (BEC) statistics and thermodynamics (Gibbs free energy, average energy, heat capacity) for a mesoscopic canonical-ensemble ideal gas in a trap with an arbitrary number of atoms, any volume, and any temperature, including the whole critical region. We identify a universal constraint-cutoff mechanism that makes BEC fluctuations strongly non-Gaussian and is responsible for all unusual critical phenomena of the BEC phase transition in the ideal gas. The main result is an analytical solution to the problem of critical phenomena. It is derived by, first, calculating analytically the universal probability distribution of the noncondensate occupation, or a Landau function, and then using it for the analytical calculation of the universal functions for the particular physical quantities via the exact formulas which express the constraint-cutoff mechanism. We find asymptotics of that analytical solution as well as its simple analytical approximations which describe the universal structure of the critical region in terms of the parabolic cylinder or confluent hypergeometric functions. The obtained results for the order parameter, all higher-order moments of BEC fluctuations, and thermodynamic quantities perfectly match the known asymptotics outside the critical region for both low and high temperature limits. We suggest two- and three-level trap models of BEC and find their exact solutions in terms of the cutoff negative binomial distribution (which tends to the cutoff gamma distribution in the continuous limit) and the confluent hypergeometric distribution, respectively. Also, we present an exactly solvable cutoff Gaussian model of BEC in a degenerate interacting gas. All these exact solutions confirm the universality and constraint-cutoff origin of the strongly non-Gaussian BEC statistics. We introduce a regular refinement scheme for the condensate statistics approximations on the basis of the infrared universality of higher-order cumulants and the method of superposition and show how to model BEC statistics in the actual traps. In particular, we find that the three-level trap model with matching the first four or five cumulants is enough to yield remarkably accurate results for all interesting quantities in the whole critical region. We derive an exact multinomial expansion for the noncondensate occupation probability distribution and find its high-temperature asymptotics (Poisson distribution) and corrections to it. Finally, we demonstrate that the critical exponents and a few known terms of the Taylor expansion of the universal functions, which were calculated previously from fitting the finite-size simulations within the phenomenological renormalization-group theory, can be easily obtained from the presented full analytical solutions for the mesoscopic BEC as certain approximations in the close vicinity of the critical point.

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

PubMed

Căruntu, Bogdan; Bota, Constantin

2014-01-01

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

Characterization of maximally random jammed sphere packings. III. Transport and electromagnetic properties via correlation functions

NASA Astrophysics Data System (ADS)

Klatt, Michael A.; Torquato, Salvatore

2018-01-01

In the first two papers of this series, we characterized the structure of maximally random jammed (MRJ) sphere packings across length scales by computing a variety of different correlation functions, spectral functions, hole probabilities, and local density fluctuations. From the remarkable structural features of the MRJ packings, especially its disordered hyperuniformity, exceptional physical properties can be expected. Here we employ these structural descriptors to estimate effective transport and electromagnetic properties via rigorous bounds, exact expansions, and accurate analytical approximation formulas. These property formulas include interfacial bounds as well as universal scaling laws for the mean survival time and the fluid permeability. We also estimate the principal relaxation time associated with Brownian motion among perfectly absorbing traps. For the propagation of electromagnetic waves in the long-wavelength limit, we show that a dispersion of dielectric MRJ spheres within a matrix of another dielectric material forms, to a very good approximation, a dissipationless disordered and isotropic two-phase medium for any phase dielectric contrast ratio. We compare the effective properties of the MRJ sphere packings to those of overlapping spheres, equilibrium hard-sphere packings, and lattices of hard spheres. Moreover, we generalize results to micro- and macroscopically anisotropic packings of spheroids with tensorial effective properties. The analytic bounds predict the qualitative trend in the physical properties associated with these structures, which provides guidance to more time-consuming simulations and experiments. They especially provide impetus for experiments to design materials with unique bulk properties resulting from hyperuniformity, including structural-color and color-sensing applications.

A Galerkin method for linear PDE systems in circular geometries with structural acoustic applications

NASA Technical Reports Server (NTRS)

Smith, Ralph C.

1994-01-01

A Galerkin method for systems of PDE's in circular geometries is presented with motivating problems being drawn from structural, acoustic, and structural acoustic applications. Depending upon the application under consideration, piecewise splines or Legendre polynomials are used when approximating the system dynamics with modifications included to incorporate the analytic solution decay near the coordinate singularity. This provides an efficient method which retains its accuracy throughout the circular domain without degradation at singularity. Because the problems under consideration are linear or weakly nonlinear with constant or piecewise constant coefficients, transform methods for the problems are not investigated. While the specific method is developed for the two dimensional wave equations on a circular domain and the equation of transverse motion for a thin circular plate, examples demonstrating the extension of the techniques to a fully coupled structural acoustic system are used to illustrate the flexibility of the method when approximating the dynamics of more complex systems.

Analytical approximations to seawater optical phase functions of scattering

NASA Astrophysics Data System (ADS)

Haltrin, Vladimir I.

2004-11-01

This paper proposes a number of analytical approximations to the classic and recently measured seawater light scattering phase functions. The three types of analytical phase functions are derived: individual representations for 15 Petzold, 41 Mankovsky, and 91 Gulf of Mexico phase functions; collective fits to Petzold phase functions; and analytical representations that take into account dependencies between inherent optical properties of seawater. The proposed phase functions may be used for problems of radiative transfer, remote sensing, visibility and image propagation in natural waters of various turbidity.

Fast and Analytical EAP Approximation from a 4th-Order Tensor.

PubMed

Ghosh, Aurobrata; Deriche, Rachid

2012-01-01

Generalized diffusion tensor imaging (GDTI) was developed to model complex apparent diffusivity coefficient (ADC) using higher-order tensors (HOTs) and to overcome the inherent single-peak shortcoming of DTI. However, the geometry of a complex ADC profile does not correspond to the underlying structure of fibers. This tissue geometry can be inferred from the shape of the ensemble average propagator (EAP). Though interesting methods for estimating a positive ADC using 4th-order diffusion tensors were developed, GDTI in general was overtaken by other approaches, for example, the orientation distribution function (ODF), since it is considerably difficult to recuperate the EAP from a HOT model of the ADC in GDTI. In this paper, we present a novel closed-form approximation of the EAP using Hermite polynomials from a modified HOT model of the original GDTI-ADC. Since the solution is analytical, it is fast, differentiable, and the approximation converges well to the true EAP. This method also makes the effort of computing a positive ADC worthwhile, since now both the ADC and the EAP can be used and have closed forms. We demonstrate our approach with 4th-order tensors on synthetic data and in vivo human data.

Fast and Analytical EAP Approximation from a 4th-Order Tensor

PubMed Central

Ghosh, Aurobrata; Deriche, Rachid

2012-01-01

Generalized diffusion tensor imaging (GDTI) was developed to model complex apparent diffusivity coefficient (ADC) using higher-order tensors (HOTs) and to overcome the inherent single-peak shortcoming of DTI. However, the geometry of a complex ADC profile does not correspond to the underlying structure of fibers. This tissue geometry can be inferred from the shape of the ensemble average propagator (EAP). Though interesting methods for estimating a positive ADC using 4th-order diffusion tensors were developed, GDTI in general was overtaken by other approaches, for example, the orientation distribution function (ODF), since it is considerably difficult to recuperate the EAP from a HOT model of the ADC in GDTI. In this paper, we present a novel closed-form approximation of the EAP using Hermite polynomials from a modified HOT model of the original GDTI-ADC. Since the solution is analytical, it is fast, differentiable, and the approximation converges well to the true EAP. This method also makes the effort of computing a positive ADC worthwhile, since now both the ADC and the EAP can be used and have closed forms. We demonstrate our approach with 4th-order tensors on synthetic data and in vivo human data. PMID:23365552

Computational Aspects of Sensitivity Calculations in Linear Transient Structural Analysis. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Greene, William H.

1989-01-01

A study has been performed focusing on the calculation of sensitivities of displacements, velocities, accelerations, and stresses in linear, structural, transient response problems. One significant goal was to develop and evaluate sensitivity calculation techniques suitable for large-order finite element analyses. Accordingly, approximation vectors such as vibration mode shapes are used to reduce the dimensionality of the finite element model. Much of the research focused on the accuracy of both response quantities and sensitivities as a function of number of vectors used. Two types of sensitivity calculation techniques were developed and evaluated. The first type of technique is an overall finite difference method where the analysis is repeated for perturbed designs. The second type of technique is termed semianalytical because it involves direct, analytical differentiation of the equations of motion with finite difference approximation of the coefficient matrices. To be computationally practical in large-order problems, the overall finite difference methods must use the approximation vectors from the original design in the analyses of the perturbed models.

Approximate analytic solutions to 3D unconfined groundwater flow within regional 2D models

NASA Astrophysics Data System (ADS)

Luther, K.; Haitjema, H. M.

2000-04-01

We present methods for finding approximate analytic solutions to three-dimensional (3D) unconfined steady state groundwater flow near partially penetrating and horizontal wells, and for combining those solutions with regional two-dimensional (2D) models. The 3D solutions use distributed singularities (analytic elements) to enforce boundary conditions on the phreatic surface and seepage faces at vertical wells, and to maintain fixed-head boundary conditions, obtained from the 2D model, at the perimeter of the 3D model. The approximate 3D solutions are analytic (continuous and differentiable) everywhere, including on the phreatic surface itself. While continuity of flow is satisfied exactly in the infinite 3D flow domain, water balance errors can occur across the phreatic surface.

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

PubMed

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

2015-04-01

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

An analytical model for calculating microdosimetric distributions from heavy ions in nanometer site targets.

PubMed

Czopyk, L; Olko, P

2006-01-01

The analytical model of Xapsos used for calculating microdosimetric spectra is based on the observation that straggling of energy loss can be approximated by a log-normal distribution of energy deposition. The model was applied to calculate microdosimetric spectra in spherical targets of nanometer dimensions from heavy ions at energies between 0.3 and 500 MeV amu(-1). We recalculated the originally assumed 1/E(2) initial delta electrons spectrum by applying the Continuous Slowing Down Approximation for secondary electrons. We also modified the energy deposition from electrons of energy below 100 keV, taking into account the effective path length of the scattered electrons. Results of our model calculations agree favourably with results of Monte Carlo track structure simulations using MOCA-14 for light ions (Z = 1-8) of energy ranging from E = 0.3 to 10.0 MeV amu(-1) as well as with results of Nikjoo for a wall-less proportional counter (Z = 18).

Extended adiabatic blast waves and a model of the soft X-ray background. [interstellar matter

NASA Technical Reports Server (NTRS)

Cox, D. P.; Anderson, P. R.

1981-01-01

An analytical approximation is generated which follows the development of an adiabatic spherical blast wave in a homogeneous ambient medium of finite pressure. An analytical approximation is also presented for the electron temperature distribution resulting from coulomb collisional heating. The dynamical, thermal, ionization, and spectral structures are calculated for blast waves of energy E sub 0 = 5 x 10 to the 50th power ergs in a hot low-density interstellar environment. A formula is presented for estimating the luminosity evolution of such explosions. The B and C bands of the soft X-ray background, it is shown, are reproduced by such a model explosion if the ambient density is about .000004 cm, the blast radius is roughly 100 pc, and the solar system is located inside the shocked region. Evolution in a pre-existing cavity with a strong density gradient may, it is suggested, remove both the M band and OVI discrepancies.

Nonperturbative Quantum Physics from Low-Order Perturbation Theory.

PubMed

Mera, Héctor; Pedersen, Thomas G; Nikolić, Branislav K

2015-10-02

The Stark effect in hydrogen and the cubic anharmonic oscillator furnish examples of quantum systems where the perturbation results in a certain ionization probability by tunneling processes. Accordingly, the perturbed ground-state energy is shifted and broadened, thus acquiring an imaginary part which is considered to be a paradigm of nonperturbative behavior. Here we demonstrate how the low order coefficients of a divergent perturbation series can be used to obtain excellent approximations to both real and imaginary parts of the perturbed ground state eigenenergy. The key is to use analytic continuation functions with a built-in singularity structure within the complex plane of the coupling constant, which is tailored by means of Bender-Wu dispersion relations. In the examples discussed the analytic continuation functions are Gauss hypergeometric functions, which take as input fourth order perturbation theory and return excellent approximations to the complex perturbed eigenvalue. These functions are Borel consistent and dramatically outperform widely used Padé and Borel-Padé approaches, even for rather large values of the coupling constant.

Steady-state analytical model of suspended p-type 3C-SiC bridges under consideration of Joule heating

NASA Astrophysics Data System (ADS)

Balakrishnan, Vivekananthan; Dinh, Toan; Phan, Hoang-Phuong; Kozeki, Takahiro; Namazu, Takahiro; Viet Dao, Dzung; Nguyen, Nam-Trung

2017-07-01

This paper reports an analytical model and its validation for a released microscale heater made of 3C-SiC thin films. A model for the equivalent electrical and thermal parameters was developed for the two-layer multi-segment heat and electric conduction. The model is based on a 1D energy equation, which considers the temperature-dependent resistivity and allows for the prediction of voltage-current and power-current characteristics of the microheater. The steady-state analytical model was validated by experimental characterization. The results, in particular the nonlinearity caused by temperature dependency, are in good agreement. The low power consumption of the order of 0.18 mW at approximately 310 K indicates the potential use of the structure as thermal sensors in portable applications.

Unsteady Aerodynamic Force Sensing from Strain Data

NASA Technical Reports Server (NTRS)

Pak, Chan-Gi

2017-01-01

A simple approach for computing unsteady aerodynamic forces from simulated measured strain data is proposed in this study. First, the deflection and slope of the structure are computed from the unsteady strain using the two-step approach. Velocities and accelerations of the structure are computed using the autoregressive moving average model, on-line parameter estimator, low-pass filter, and a least-squares curve fitting method together with analytical derivatives with respect to time. Finally, aerodynamic forces over the wing are computed using modal aerodynamic influence coefficient matrices, a rational function approximation, and a time-marching algorithm.

Computing the universe: how large-scale simulations illuminate galaxies and dark energy

NASA Astrophysics Data System (ADS)

O'Shea, Brian

2015-04-01

High-performance and large-scale computing is absolutely to understanding astronomical objects such as stars, galaxies, and the cosmic web. This is because these are structures that operate on physical, temporal, and energy scales that cannot be reasonably approximated in the laboratory, and whose complexity and nonlinearity often defies analytic modeling. In this talk, I show how the growth of computing platforms over time has facilitated our understanding of astrophysical and cosmological phenomena, focusing primarily on galaxies and large-scale structure in the Universe.

Semi-Analytic Reconstruction of Flux in Finite Volume Formulations

NASA Technical Reports Server (NTRS)

Gnoffo, Peter A.

2006-01-01

Semi-analytic reconstruction uses the analytic solution to a second-order, steady, ordinary differential equation (ODE) to simultaneously evaluate the convective and diffusive flux at all interfaces of a finite volume formulation. The second-order ODE is itself a linearized approximation to the governing first- and second- order partial differential equation conservation laws. Thus, semi-analytic reconstruction defines a family of formulations for finite volume interface fluxes using analytic solutions to approximating equations. Limiters are not applied in a conventional sense; rather, diffusivity is adjusted in the vicinity of changes in sign of eigenvalues in order to achieve a sufficiently small cell Reynolds number in the analytic formulation across critical points. Several approaches for application of semi-analytic reconstruction for the solution of one-dimensional scalar equations are introduced. Results are compared with exact analytic solutions to Burger s Equation as well as a conventional, upwind discretization using Roe s method. One approach, the end-point wave speed (EPWS) approximation, is further developed for more complex applications. One-dimensional vector equations are tested on a quasi one-dimensional nozzle application. The EPWS algorithm has a more compact difference stencil than Roe s algorithm but reconstruction time is approximately a factor of four larger than for Roe. Though both are second-order accurate schemes, Roe s method approaches a grid converged solution with fewer grid points. Reconstruction of flux in the context of multi-dimensional, vector conservation laws including effects of thermochemical nonequilibrium in the Navier-Stokes equations is developed.

Validity of the Born approximation for beyond Gaussian weak lensing observables

DOE PAGES

Petri, Andrea; Haiman, Zoltan; May, Morgan

2017-06-06

Accurate forward modeling of weak lensing (WL) observables from cosmological parameters is necessary for upcoming galaxy surveys. Because WL probes structures in the nonlinear regime, analytical forward modeling is very challenging, if not impossible. Numerical simulations of WL features rely on ray tracing through the outputs of N-body simulations, which requires knowledge of the gravitational potential and accurate solvers for light ray trajectories. A less accurate procedure, based on the Born approximation, only requires knowledge of the density field, and can be implemented more efficiently and at a lower computational cost. In this work, we use simulations to show thatmore » deviations of the Born-approximated convergence power spectrum, skewness and kurtosis from their fully ray-traced counterparts are consistent with the smallest nontrivial O(Φ 3) post-Born corrections (so-called geodesic and lens-lens terms). Our results imply a cancellation among the larger O(Φ 4) (and higher order) terms, consistent with previous analytic work. We also find that cosmological parameter bias induced by the Born-approximated power spectrum is negligible even for a LSST-like survey, once galaxy shape noise is considered. When considering higher order statistics such as the κ skewness and kurtosis, however, we find significant bias of up to 2.5σ. Using the LensTools software suite, we show that the Born approximation saves a factor of 4 in computing time with respect to the full ray tracing in reconstructing the convergence.« less

Validity of the Born approximation for beyond Gaussian weak lensing observables

NASA Astrophysics Data System (ADS)

Petri, Andrea; Haiman, Zoltán; May, Morgan

2017-06-01

Accurate forward modeling of weak lensing (WL) observables from cosmological parameters is necessary for upcoming galaxy surveys. Because WL probes structures in the nonlinear regime, analytical forward modeling is very challenging, if not impossible. Numerical simulations of WL features rely on ray tracing through the outputs of N -body simulations, which requires knowledge of the gravitational potential and accurate solvers for light ray trajectories. A less accurate procedure, based on the Born approximation, only requires knowledge of the density field, and can be implemented more efficiently and at a lower computational cost. In this work, we use simulations to show that deviations of the Born-approximated convergence power spectrum, skewness and kurtosis from their fully ray-traced counterparts are consistent with the smallest nontrivial O (Φ3) post-Born corrections (so-called geodesic and lens-lens terms). Our results imply a cancellation among the larger O (Φ4) (and higher order) terms, consistent with previous analytic work. We also find that cosmological parameter bias induced by the Born-approximated power spectrum is negligible even for a LSST-like survey, once galaxy shape noise is considered. When considering higher order statistics such as the κ skewness and kurtosis, however, we find significant bias of up to 2.5 σ . Using the LensTools software suite, we show that the Born approximation saves a factor of 4 in computing time with respect to the full ray tracing in reconstructing the convergence.

Theory and Experiment of Binary Diffusion Coefficient of n-Alkanes in Dilute Gases.

PubMed

Liu, Changran; McGivern, W Sean; Manion, Jeffrey A; Wang, Hai

2016-10-10

Binary diffusion coefficients were measured for n-pentane, n-hexane, and n-octane in helium and of n-pentane in nitrogen over the temperature range of 300 to 600 K, using reversed-flow gas chromatography. A generalized, analytical theory is proposed for the binary diffusion coefficients of long-chain molecules in simple diluent gases, taking advantage of a recently developed gas-kinetic theory of the transport properties of nanoslender bodies in dilute free-molecular flows. The theory addresses the long-standing question about the applicability of the Chapman-Enskog theory in describing the transport properties of nonspherical molecular structures, or equivalently, the use of isotropic potentials of interaction for a roughly cylindrical molecular structure such as large normal alkanes. An approximate potential energy function is proposed for the intermolecular interaction of long-chain n-alkane with typical bath gases. Using this potential and the analytical theory for nanoslender bodies, we show that the diffusion coefficients of n-alkanes in typical bath gases can be treated by the resulting analytical model accurately, especially for compounds larger than n-butane.

General properties and analytical approximations of photorefractive solitons

NASA Astrophysics Data System (ADS)

Geisler, A.; Homann, F.; Schmidt, H.-J.

2004-08-01

We investigate general properties of spatial 1-dimensional bright photorefractive solitons and discuss various analytical approximations for the soliton profile and the half width, both depending on an intensity parameter r. The case of dark solitons is also briefly addressed.

Covariance of dynamic strain responses for structural damage detection

NASA Astrophysics Data System (ADS)

Li, X. Y.; Wang, L. X.; Law, S. S.; Nie, Z. H.

2017-10-01

A new approach to address the practical problems with condition evaluation/damage detection of structures is proposed based on the distinct features of a new damage index. The covariance of strain response function (CoS) is a function of modal parameters of the structure. A local stiffness reduction in structure would cause monotonous increase in the CoS. Its sensitivity matrix with respect to local damages of structure is negative and narrow-banded. The damage extent can be estimated with an approximation to the sensitivity matrix to decouple the identification equations. The CoS sensitivity can be calibrated in practice from two previous states of measurements to estimate approximately the damage extent of a structure. A seven-storey plane frame structure is numerically studied to illustrate the features of the CoS index and the proposed method. A steel circular arch in the laboratory is tested. Natural frequencies changed due to damage in the arch and the damage occurrence can be judged. However, the proposed CoS method can identify not only damage happening but also location, even damage extent without need of an analytical model. It is promising for structural condition evaluation of selected components.

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

NASA Technical Reports Server (NTRS)

Gayley, K. G.

1993-01-01

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

An Approximate Solution to the Equation of Motion for Large-Angle Oscillations of the Simple Pendulum with Initial Velocity

ERIC Educational Resources Information Center

Johannessen, Kim

2010-01-01

An analytic approximation of the solution to the differential equation describing the oscillations of a simple pendulum at large angles and with initial velocity is discussed. In the derivation, a sinusoidal approximation has been applied, and an analytic formula for the large-angle period of the simple pendulum is obtained, which also includes…

Effect of crash pulse shape on seat stroke requirements for limiting loads on occupants of aircraft

NASA Technical Reports Server (NTRS)

Carden, Huey D.

1992-01-01

An analytical study was made to provide comparative information on various crash pulse shapes that potentially could be used to test seats under conditions included in Federal Regulations Part 23 Paragraph 23.562(b)(1) for dynamic testing of general aviation seats, show the effects that crash pulse shape can have on the seat stroke requirements necessary to maintain a specified limit loading on the seat/occupant during crash pulse loadings, compare results from certain analytical model pulses with approximations of actual crash pulses, and compare analytical seat results with experimental airplace crash data. Structural and seat/occupant displacement equations in terms of the maximum deceleration, velocity change, limit seat pan load, and pulse time for five potentially useful pulse shapes were derived; from these, analytical seat stroke data were obtained for conditions as specified in Federal Regulations Part 23 Paragraph 23.562(b)(1) for dynamic testing of general aviation seats.

Light scattering by a nematic liquid crystal droplet: Wentzel–Kramers–Brillouin approximation

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

Loiko, V. A., E-mail: loiko@dragon.bas-net.by; Konkolovich, A. V.; Miskevich, A. A.

2016-01-15

Light scattering by an optically anisotropic liquid crystal (LC) droplet of a nematic in an isotropic polymer matrix is considered in the Wentzel–Kramers–Brillouin (WKB) approximation. General relations are obtained for elements of the amplitude matrix of light scattering by a droplet of arbitrary shape and for the structure of the director field. Analytic expressions for the amplitude matrices are derived for spherical LC droplets with a uniformly oriented structure of local optical axes for strictly forward and strictly backward scattering. The efficiency factors of extinction and backward scattering for a spherical nonabsorbing LC droplet depending on the LC optical anisotropy,more » refractive index of the polymer, illumination conditions, and orientation of the optical axis of the droplet are analyzed. Verification of the obtained solutions has been performed.« less

Black-Scholes finite difference modeling in forecasting of call warrant prices in Bursa Malaysia

NASA Astrophysics Data System (ADS)

Mansor, Nur Jariah; Jaffar, Maheran Mohd

2014-07-01

Call warrant is a type of structured warrant in Bursa Malaysia. It gives the holder the right to buy the underlying share at a specified price within a limited period of time. The issuer of the structured warrants usually uses European style to exercise the call warrant on the maturity date. Warrant is very similar to an option. Usually, practitioners of the financial field use Black-Scholes model to value the option. The Black-Scholes equation is hard to solve analytically. Therefore the finite difference approach is applied to approximate the value of the call warrant prices. The central in time and central in space scheme is produced to approximate the value of the call warrant prices. It allows the warrant holder to forecast the value of the call warrant prices before the expiry date.

N-point statistics of large-scale structure in the Zel'dovich approximation

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

Tassev, Svetlin, E-mail: tassev@astro.princeton.edu

2014-06-01

Motivated by the results presented in a companion paper, here we give a simple analytical expression for the matter n-point functions in the Zel'dovich approximation (ZA) both in real and in redshift space (including the angular case). We present numerical results for the 2-dimensional redshift-space correlation function, as well as for the equilateral configuration for the real-space 3-point function. We compare those to the tree-level results. Our analysis is easily extendable to include Lagrangian bias, as well as higher-order perturbative corrections to the ZA. The results should be especially useful for modelling probes of large-scale structure in the linear regime,more » such as the Baryon Acoustic Oscillations. We make the numerical code used in this paper freely available.« less

Nonequilibrium mechanisms of weak electrolyte electrification under the action of constant voltage

NASA Astrophysics Data System (ADS)

Stishkov, Yu. K.; Chirkov, V. A.

2016-07-01

The formation of space charge in weak electrolytes, specifically in liquid dielectrics, has been considered. An analytical solution is given to a simplified set of Nernst-Planck equations that describe the formation of nonequilibrium recombination layers in weak electrolytes. This approximate analytical solution is compared with computer simulation data for a complete set of Poisson-Nernst-Planck equations. It has been shown that the current passage in weak electrolytes can be described by a single dimensionless parameter that equals the length of a near-electrode recombination layer divided by the width of the interelectrode gap. The formation mechanism and the structure of charged nonequilibrium near-electrode layers in the nonstationary regime have been analyzed for different injection-to-conduction current ratios. It has been found that almost all charge structures encountered in weak dielectrics can be accounted for by the nonequilibrium dissociation-recombination mechanism of space charge formation.

Conservative Analytical Collision Probabilities for Orbital Formation Flying

NASA Technical Reports Server (NTRS)

Carpenter, J. Russell

2004-01-01

The literature offers a number of approximations for analytically and/or efficiently computing the probability of collision between two space objects. However, only one of these techniques is a completely analytical approximation that is suitable for use in the preliminary design phase, when it is more important to quickly analyze a large segment of the trade space than it is to precisely compute collision probabilities. Unfortunately, among the types of formations that one might consider, some combine a range of conditions for which this analytical method is less suitable. This work proposes a simple, conservative approximation that produces reasonable upper bounds on the collision probability in such conditions. Although its estimates are much too conservative under other conditions, such conditions are typically well suited for use of the existing method.

Conservative Analytical Collision Probability for Design of Orbital Formations

NASA Technical Reports Server (NTRS)

Carpenter, J. Russell

2004-01-01

The literature offers a number of approximations for analytically and/or efficiently computing the probability of collision between two space objects. However, only one of these techniques is a completely analytical approximation that is suitable for use in the preliminary design phase, when it is more important to quickly analyze a large segment of the trade space than it is to precisely compute collision probabilities. Unfortunately, among the types of formations that one might consider, some combine a range of conditions for which this analytical method is less suitable. This work proposes a simple, conservative approximation that produces reasonable upper bounds on the collision probability in such conditions. Although its estimates are much too conservative under other conditions, such conditions are typically well suited for use of the existing method.

Exploratory analysis regarding the domain definitions for computer based analytical models

NASA Astrophysics Data System (ADS)

Raicu, A.; Oanta, E.; Barhalescu, M.

2017-08-01

Our previous computer based studies dedicated to structural problems using analytical methods defined the composite cross section of a beam as a result of Boolean operations with so-called ‘simple’ shapes. Using generalisations, in the class of the ‘simple’ shapes were included areas bounded by curves approximated using spline functions and areas approximated as polygons. However, particular definitions lead to particular solutions. In order to ascend above the actual limitations, we conceived a general definition of the cross sections that are considered now calculus domains consisting of several subdomains. The according set of input data use complex parameterizations. This new vision allows us to naturally assign a general number of attributes to the subdomains. In this way there may be modelled new phenomena that use map-wise information, such as the metal alloys equilibrium diagrams. The hierarchy of the input data text files that use the comma-separated-value format and their structure are also presented and discussed in the paper. This new approach allows us to reuse the concepts and part of the data processing software instruments already developed. The according software to be subsequently developed will be modularised and generalised in order to be used in the upcoming projects that require rapid development of computer based models.

Coupled NASTRAN/boundary element formulation for acoustic scattering

NASA Technical Reports Server (NTRS)

Everstine, Gordon C.; Henderson, Francis M.; Schuetz, Luise S.

1987-01-01

A coupled finite element/boundary element capability is described for calculating the sound pressure field scattered by an arbitrary submerged 3-D elastic structure. Structural and fluid impedances are calculated with no approximation other than discretization. The surface fluid pressures and normal velocities are first calculated by coupling a NASTRAN finite element model of the structure with a discretized form of the Helmholtz surface integral equation for the exterior field. Far field pressures are then evaluated from the surface solution using the Helmholtz exterior integral equation. The overall approach is illustrated and validated using a known analytic solution for scattering from submerged spherical shells.

Highly Accurate Analytical Approximate Solution to a Nonlinear Pseudo-Oscillator

NASA Astrophysics Data System (ADS)

Wu, Baisheng; Liu, Weijia; Lim, C. W.

2017-07-01

A second-order Newton method is presented to construct analytical approximate solutions to a nonlinear pseudo-oscillator in which the restoring force is inversely proportional to the dependent variable. The nonlinear equation is first expressed in a specific form, and it is then solved in two steps, a predictor and a corrector step. In each step, the harmonic balance method is used in an appropriate manner to obtain a set of linear algebraic equations. With only one simple second-order Newton iteration step, a short, explicit, and highly accurate analytical approximate solution can be derived. The approximate solutions are valid for all amplitudes of the pseudo-oscillator. Furthermore, the method incorporates second-order Taylor expansion in a natural way, and it is of significant faster convergence rate.

Derivation of phase functions from multiply scattered sunlight transmitted through a hazy atmosphere

NASA Technical Reports Server (NTRS)

Weinman, J. A.; Twitty, J. T.; Browning, S. R.; Herman, B. M.

1975-01-01

The intensity of sunlight multiply scattered in model atmospheres is derived from the equation of radiative transfer by an analytical small-angle approximation. The approximate analytical solutions are compared to rigorous numerical solutions of the same problem. Results obtained from an aerosol-laden model atmosphere are presented. Agreement between the rigorous and the approximate solutions is found to be within a few per cent. The analytical solution to the problem which considers an aerosol-laden atmosphere is then inverted to yield a phase function which describes a single scattering event at small angles. The effect of noisy data on the derived phase function is discussed.

Substrate mass transfer: analytical approach for immobilized enzyme reactions

NASA Astrophysics Data System (ADS)

Senthamarai, R.; Saibavani, T. N.

2018-04-01

In this paper, the boundary value problem in immobilized enzyme reactions is formulated and approximate expression for substrate concentration without external mass transfer resistance is presented. He’s variational iteration method is used to give approximate and analytical solutions of non-linear differential equation containing a non linear term related to enzymatic reaction. The relevant analytical solution for the dimensionless substrate concentration profile is discussed in terms of dimensionless reaction parameters α and β.

Desorption electrospray ionization-mass spectrometry for the detection of analytes extracted by thin-film molecularly imprinted polymers.

PubMed

Van Biesen, Geert; Wiseman, Justin M; Li, Jessica; Bottaro, Christina S

2010-09-01

Desorption electrospray ionization-mass spectrometry (DESI-MS) is a powerful technique for the analysis of solid and liquid surfaces that has found numerous applications in the few years since its invention. For the first time, it is applied to the detection of analytes extracted by molecularly imprinted polymers (MIPs) in a thin-film format. MIPs formed with 2,4-dichlorophenoxyacetic acid (2,4-D) as the template were used for the extraction of this analyte from aqueous solutions spiked at concentrations of 0.0050-2.0 mg L(-1) (approximately 2 x 10(-8) to approximately 1 x 10(-5) M). The response was linear up to 0.50 mg L(-1), and then levelled off due to saturation of the active sites of the MIP. In MS/MS mode, the signal at 0.0050 mg L(-1) was still an order of magnitude higher than the signal of a blank. The MIP DESI-MS approach was also used for the analysis of tap water and river water spiked with 2,4-D and four analogues, which indicated that these analogues were also extracted to various extents. For practical applications of the MIP, a detection technique is required that can distinguish between these structurally similar compounds, and DESI-MS fulfills this purpose.

Trace level detection of compounds related to the chemical weapons convention by 1H-detected 13C NMR spectroscopy executed with a sensitivity-enhanced, cryogenic probehead.

PubMed

Cullinan, David B; Hondrogiannis, George; Henderson, Terry J

2008-04-15

Two-dimensional 1H-13C HSQC (heteronuclear single quantum correlation) and fast-HMQC (heteronuclear multiple quantum correlation) pulse sequences were implemented using a sensitivity-enhanced, cryogenic probehead for detecting compounds relevant to the Chemical Weapons Convention present in complex mixtures. The resulting methods demonstrated exceptional sensitivity for detecting the analytes at trace level concentrations. 1H-13C correlations of target analytes at < or = 25 microg/mL were easily detected in a sample where the 1H solvent signal was approximately 58,000-fold more intense than the analyte 1H signals. The problem of overlapping signals typically observed in conventional 1H spectroscopy was essentially eliminated, while 1H and 13C chemical shift information could be derived quickly and simultaneously from the resulting spectra. The fast-HMQC pulse sequences generated magnitude mode spectra suitable for detailed analysis in approximately 4.5 h and can be used in experiments to efficiently screen a large number of samples. The HSQC pulse sequences, on the other hand, required roughly twice the data acquisition time to produce suitable spectra. These spectra, however, were phase-sensitive, contained considerably more resolution in both dimensions, and proved to be superior for detecting analyte 1H-13C correlations. Furthermore, a HSQC spectrum collected with a multiplicity-edited pulse sequence provided additional structural information valuable for identifying target analytes. The HSQC pulse sequences are ideal for collecting high-quality data sets with overnight acquisitions and logically follow the use of fast-HMQC pulse sequences to rapidly screen samples for potential target analytes. Use of the pulse sequences considerably improves the performance of NMR spectroscopy as a complimentary technique for the screening, identification, and validation of chemical warfare agents and other small-molecule analytes present in complex mixtures and environmental samples.

The influence of anisotropy on the core structure of Shockley partial dislocations within FCC materials

NASA Astrophysics Data System (ADS)

Szajewski, B. A.; Hunter, A.; Luscher, D. J.; Beyerlein, I. J.

2018-01-01

Both theoretical and numerical models of dislocations often necessitate the assumption of elastic isotropy to retain analytical tractability in addition to reducing computational load. As dislocation based models evolve towards physically realistic material descriptions, the assumption of elastic isotropy becomes increasingly worthy of examination. We present an analytical dislocation model for calculating the full dissociated core structure of dislocations within anisotropic face centered cubic (FCC) crystals as a function of the degree of material elastic anisotropy, two misfit energy densities on the γ-surface ({γ }{{isf}}, {γ }{{usf}}) and the remaining elastic constants. Our solution is independent of any additional features of the γ-surface. Towards this pursuit, we first demonstrate that the dependence of the anisotropic elasticity tensor on the orientation of the dislocation line within the FCC crystalline lattice is small and may be reasonably neglected for typical materials. With this approximation, explicit analytic solutions for the anisotropic elasticity tensor {B} for both nominally edge and screw dislocations within an FCC crystalline lattice are devised, and employed towards defining a set of effective isotropic elastic constants which reproduce fully anisotropic results, however do not retain the bulk modulus. Conversely, Hill averaged elastic constants which both retain the bulk modulus and reasonably approximate the dislocation core structure are employed within subsequent numerical calculations. We examine a wide range of materials within this study, and the features of each partial dislocation core are sufficiently localized that application of discrete linear elasticity accurately describes the separation of each partial dislocation core. In addition, the local features (the partial dislocation core distribution) are well described by a Peierls-Nabarro dislocation model. We develop a model for the displacement profile which depends upon two disparate dislocation length scales which describe the core structure; (i) the equilibrium stacking fault width between two Shockley partial dislocations, R eq and (ii) the maximum slip gradient, χ, of each Shockley partial dislocation. We demonstrate excellent agreement between our own analytic predictions, numerical calculations, and R eq computed directly by both ab-initio and molecular statics methods found elsewhere within the literature. The results suggest that understanding of various plastic mechanisms, e.g., cross-slip and nucleation may be augmented with the inclusion of elastic anisotropy.

APPROXIMATE AND ANALYTICAL SOLUTIONS FOR SOLUTE TRANSPORT FROM AN INJECTION WELL INTO A SINGLE FRACTURE

EPA Science Inventory

In dealing with problems related to land-based nuclear waste management, a number of analytical and approximate solutions were developed to quantify radionuclide transport through fractures contained in the porous formation. t has been reported that by treating the radioactive de...

Analytical treatment of self-phase-modulation beyond the slowly varying envelope approximation

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

Syrchin, M.S.; Zheltikov, A.M.; International Laser Center, M.V. Lomonosov Moscow State University, 119899 Moscow

Analytical treatment of the self-phase-modulation of an ultrashort light pulse is extended beyond the slowly varying envelope approximation. The resulting wave equation is modified to include corrections to self-phase-modulation due to higher-order spatial and temporal derivatives. Analytical solutions are found in the limiting regimes of high nonlinearities and very short pulses. Our results reveal features that can significantly impact both pulse shape and the evolution of the phase.

Natural Frequency Testing and Model Correlation of Rocket Engine Structures in Liquid Hydrogen - Phase I, Cantilever Beam

NASA Technical Reports Server (NTRS)

Brown, Andrew M.; DeLessio, Jennifer L.; Jacobs, Preston W.

2018-01-01

Many structures in the launch vehicle industry operate in liquid hydrogen (LH2), from the hydrogen fuel tanks through the ducts and valves and into the pump sides of the turbopumps. Calculating the structural dynamic response of these structures is critical for successful qualification of this hardware, but accurate knowledge of the natural frequencies is based entirely on numerical or analytical predictions of frequency reduction due to the added-fluid-mass effect because testing in LH2 has always been considered too difficult and dangerous. This fluid effect is predicted to be approximately 4-5% using analytical formulations for simple cantilever beams. As part of a comprehensive test/analysis program to more accurately assess pump inducers operating in LH2, a series of frequency tests in LH2 were performed at NASA/Marshall Space Flight Center's unique cryogenic test facility. These frequency tests are coupled with modal tests in air and water to provide critical information not only on the mass effect of LH2, but also the cryogenic temperature effect on Young's Modulus for which the data is not extensive. The authors are unaware of any other reported natural frequency testing in this media. In addition to the inducer, a simple cantilever beam was also tested in the tank to provide a more easily modeled geometry as well as one that has an analytical solution for the mass effect. This data will prove critical for accurate structural dynamic analysis of these structures, which operate in a highly-dynamic environment.

Ultra-high-stability, pH-resistant sol-gel titania poly(tetrahydrofuran) coating for capillary microextraction on-line coupled to high-performance liquid chromatography.

PubMed

Segro, Scott S; Cabezas, Yaniel; Malik, Abdul

2009-05-15

A sol-gel titania poly(tetrahydrofuran) (poly-THF) coating was developed for capillary microextraction hyphenated on-line with high-performance liquid chromatography (HPLC). Poly-THF was covalently bonded to the sol-gel titania network which, in turn, became chemically anchored to the inner surface of a 0.25mm I.D. fused silica capillary. For sample preconcentration, a 38-cm segment of the sol-gel titania poly-THF coated capillary was installed on an HPLC injection port as a sampling loop. Aqueous samples containing a variety of analytes were passed through the capillary and, during this process, the analytes were extracted by the sol-gel titania poly-THF coating on the inner surface of the capillary. Using isocratic and gradient elution with acetonitrile/water mobile phases, the extracted analytes were desorbed into the on-line coupled HPLC column for separation and UV detection. The sol-gel titania poly-THF coating was especially efficient in extracting polar analytes, such as underivatized phenols, alcohols, amines, and aromatic carboxylic acids. In addition, this coating was capable of extracting moderately polar and nonpolar analytes, such as ketones and polycyclic aromatic hydrocarbons. The sol-gel titania poly-THF coated capillary was also able to extract polypeptides at pH values near their respective isoelectric points. Extraction of these compounds can be important for environmental and biomedical applications. The observed extraction behavior can be attributed to the polar and nonpolar moieties in the poly-THF structure. This coating was found to be stable under extremely low and high pH conditions-even after 18h of exposure to 1M HCl (pH approximately 0.0) and 1M NaOH (pH approximately 14.0).

Asymptotically inspired moment-closure approximation for adaptive networks

NASA Astrophysics Data System (ADS)

Shkarayev, Maxim S.; Shaw, Leah B.

2013-11-01

Adaptive social networks, in which nodes and network structure coevolve, are often described using a mean-field system of equations for the density of node and link types. These equations constitute an open system due to dependence on higher-order topological structures. We propose a new approach to moment closure based on the analytical description of the system in an asymptotic regime. We apply the proposed approach to two examples of adaptive networks: recruitment to a cause model and adaptive epidemic model. We show a good agreement between the improved mean-field prediction and simulations of the full network system.

Solution of the mean spherical approximation for polydisperse multi-Yukawa hard-sphere fluid mixture using orthogonal polynomial expansions

NASA Astrophysics Data System (ADS)

Kalyuzhnyi, Yurij V.; Cummings, Peter T.

2006-03-01

The Blum-Høye [J. Stat. Phys. 19 317 (1978)] solution of the mean spherical approximation for a multicomponent multi-Yukawa hard-sphere fluid is extended to a polydisperse multi-Yukawa hard-sphere fluid. Our extension is based on the application of the orthogonal polynomial expansion method of Lado [Phys. Rev. E 54, 4411 (1996)]. Closed form analytical expressions for the structural and thermodynamic properties of the model are presented. They are given in terms of the parameters that follow directly from the solution. By way of illustration the method of solution is applied to describe the thermodynamic properties of the one- and two-Yukawa versions of the model.

Electron scattering intensities and Patterson functions of Skyrmions

NASA Astrophysics Data System (ADS)

Karliner, M.; King, C.; Manton, N. S.

2016-06-01

The scattering of electrons off nuclei is one of the best methods of probing nuclear structure. In this paper we focus on electron scattering off nuclei with spin and isospin zero within the Skyrme model. We consider two distinct methods and simplify our calculations by use of the Born approximation. The first method is to calculate the form factor of the spherically averaged Skyrmion charge density; the second uses the Patterson function to calculate the scattering intensity off randomly oriented Skyrmions, and spherically averages at the end. We compare our findings with experimental scattering data. We also find approximate analytical formulae for the first zero and first stationary point of a form factor.

Approximate analytic expression for the Skyrmions crystal

NASA Astrophysics Data System (ADS)

Grandi, Nicolás; Sturla, Mauricio

2018-01-01

We find approximate solutions for the two-dimensional nonlinear Σ-model with Dzyalioshinkii-Moriya term, representing magnetic Skyrmions. They are built in an analytic form, by pasting different approximate solutions found in different regions of space. We verify that our construction reproduces the phenomenology known from numerical solutions and Monte Carlo simulations, giving rise to a Skyrmion lattice at an intermediate range of magnetic field, flanked by spiral and spin-polarized phases for low and high magnetic fields, respectively.

Comparison of three methods for wind turbine capacity factor estimation.

PubMed

Ditkovich, Y; Kuperman, A

2014-01-01

Three approaches to calculating capacity factor of fixed speed wind turbines are reviewed and compared using a case study. The first "quasiexact" approach utilizes discrete wind raw data (in the histogram form) and manufacturer-provided turbine power curve (also in discrete form) to numerically calculate the capacity factor. On the other hand, the second "analytic" approach employs a continuous probability distribution function, fitted to the wind data as well as continuous turbine power curve, resulting from double polynomial fitting of manufacturer-provided power curve data. The latter approach, while being an approximation, can be solved analytically thus providing a valuable insight into aspects, affecting the capacity factor. Moreover, several other merits of wind turbine performance may be derived based on the analytical approach. The third "approximate" approach, valid in case of Rayleigh winds only, employs a nonlinear approximation of the capacity factor versus average wind speed curve, only requiring rated power and rotor diameter of the turbine. It is shown that the results obtained by employing the three approaches are very close, enforcing the validity of the analytically derived approximations, which may be used for wind turbine performance evaluation.

Optimal estimation of large structure model errors. [in Space Shuttle controller design

NASA Technical Reports Server (NTRS)

Rodriguez, G.

1979-01-01

In-flight estimation of large structure model errors is usually required as a means of detecting inevitable deficiencies in large structure controller/estimator models. The present paper deals with a least-squares formulation which seeks to minimize a quadratic functional of the model errors. The properties of these error estimates are analyzed. It is shown that an arbitrary model error can be decomposed as the sum of two components that are orthogonal in a suitably defined function space. Relations between true and estimated errors are defined. The estimates are found to be approximations that retain many of the significant dynamics of the true model errors. Current efforts are directed toward application of the analytical results to a reference large structure model.

Electromagnetic field analysis and modeling of a relative position detection sensor for high speed maglev trains.

PubMed

Xue, Song; He, Ning; Long, Zhiqiang

2012-01-01

The long stator track for high speed maglev trains has a tooth-slot structure. The sensor obtains precise relative position information for the traction system by detecting the long stator tooth-slot structure based on nondestructive detection technology. The magnetic field modeling of the sensor is a typical three-dimensional (3-D) electromagnetic problem with complex boundary conditions, and is studied semi-analytically in this paper. A second-order vector potential (SOVP) is introduced to simplify the vector field problem to a scalar field one, the solution of which can be expressed in terms of series expansions according to Multipole Theory (MT) and the New Equivalent Source (NES) method. The coefficients of the expansions are determined by the least squares method based on the boundary conditions. Then, the solution is compared to the simulation result through Finite Element Analysis (FEA). The comparison results show that the semi-analytical solution agrees approximately with the numerical solution. Finally, based on electromagnetic modeling, a difference coil structure is designed to improve the sensitivity and accuracy of the sensor.

Electromagnetic Field Analysis and Modeling of a Relative Position Detection Sensor for High Speed Maglev Trains

PubMed Central

Xue, Song; He, Ning; Long, Zhiqiang

2012-01-01

The long stator track for high speed maglev trains has a tooth-slot structure. The sensor obtains precise relative position information for the traction system by detecting the long stator tooth-slot structure based on nondestructive detection technology. The magnetic field modeling of the sensor is a typical three-dimensional (3-D) electromagnetic problem with complex boundary conditions, and is studied semi-analytically in this paper. A second-order vector potential (SOVP) is introduced to simplify the vector field problem to a scalar field one, the solution of which can be expressed in terms of series expansions according to Multipole Theory (MT) and the New Equivalent Source (NES) method. The coefficients of the expansions are determined by the least squares method based on the boundary conditions. Then, the solution is compared to the simulation result through Finite Element Analysis (FEA). The comparison results show that the semi-analytical solution agrees approximately with the numerical solution. Finally, based on electromagnetic modeling, a difference coil structure is designed to improve the sensitivity and accuracy of the sensor. PMID:22778652

Frequency Response Function Based Damage Identification for Aerospace Structures

NASA Astrophysics Data System (ADS)

Oliver, Joseph Acton

Structural health monitoring technologies continue to be pursued for aerospace structures in the interests of increased safety and, when combined with health prognosis, efficiency in life-cycle management. The current dissertation develops and validates damage identification technology as a critical component for structural health monitoring of aerospace structures and, in particular, composite unmanned aerial vehicles. The primary innovation is a statistical least-squares damage identification algorithm based in concepts of parameter estimation and model update. The algorithm uses frequency response function based residual force vectors derived from distributed vibration measurements to update a structural finite element model through statistically weighted least-squares minimization producing location and quantification of the damage, estimation uncertainty, and an updated model. Advantages compared to other approaches include robust applicability to systems which are heavily damped, large, and noisy, with a relatively low number of distributed measurement points compared to the number of analytical degrees-of-freedom of an associated analytical structural model (e.g., modal finite element model). Motivation, research objectives, and a dissertation summary are discussed in Chapter 1 followed by a literature review in Chapter 2. Chapter 3 gives background theory and the damage identification algorithm derivation followed by a study of fundamental algorithm behavior on a two degree-of-freedom mass-spring system with generalized damping. Chapter 4 investigates the impact of noise then successfully proves the algorithm against competing methods using an analytical eight degree-of-freedom mass-spring system with non-proportional structural damping. Chapter 5 extends use of the algorithm to finite element models, including solutions for numerical issues, approaches for modeling damping approximately in reduced coordinates, and analytical validation using a composite sandwich plate model. Chapter 6 presents the final extension to experimental systems-including methods for initial baseline correlation and data reduction-and validates the algorithm on an experimental composite plate with impact damage. The final chapter deviates from development and validation of the primary algorithm to discuss development of an experimental scaled-wing test bed as part of a collaborative effort for developing structural health monitoring and prognosis technology. The dissertation concludes with an overview of technical conclusions and recommendations for future work.

Thin silica shell coated Ag assembled nanostructures for expanding generality of SERS analytes

PubMed Central

Kang, Yoo-Lee; Lee, Minwoo; Kang, Homan; Kim, Jaehi; Pham, Xuan-Hung; Kim, Tae Han; Hahm, Eunil; Lee, Yoon-Sik; Jeong, Dae Hong

2017-01-01

Surface-enhanced Raman scattering (SERS) provides a unique non-destructive spectroscopic fingerprint for chemical detection. However, intrinsic differences in affinity of analyte molecules to metal surface hinder SERS as a universal quantitative detection tool for various analyte molecules simultaneously. This must be overcome while keeping close proximity of analyte molecules to the metal surface. Moreover, assembled metal nanoparticles (NPs) structures might be beneficial for sensitive and reliable detection of chemicals than single NP structures. For this purpose, here we introduce thin silica-coated and assembled Ag NPs (SiO2@Ag@SiO2 NPs) for simultaneous and quantitative detection of chemicals that have different intrinsic affinities to silver metal. These SiO2@Ag@SiO2 NPs could detect each SERS peak of aniline or 4-aminothiophenol (4-ATP) from the mixture with limits of detection (LOD) of 93 ppm and 54 ppb, respectively. E-field distribution based on interparticle distance was simulated using discrete dipole approximation (DDA) calculation to gain insight into enhanced scattering of these thin silica coated Ag NP assemblies. These NPs were successfully applied to detect aniline in river water and tap water. Results suggest that SiO2@Ag@SiO2 NP-based SERS detection systems can be used as a simple and universal detection tool for environment pollutants and food safety. PMID:28570633

Hybrid-Wing-Body Vehicle Composite Fuselage Analysis and Case Study

NASA Technical Reports Server (NTRS)

Mukhopadhyay, Vivek

2014-01-01

Recent progress in the structural analysis of a Hybrid Wing-Body (HWB) fuselage concept is presented with the objective of structural weight reduction under a set of critical design loads. This pressurized efficient HWB fuselage design is presently being investigated by the NASA Environmentally Responsible Aviation (ERA) project in collaboration with the Boeing Company, Huntington Beach. The Pultruded Rod-Stiffened Efficient Unitized Structure (PRSEUS) composite concept, developed at the Boeing Company, is approximately modeled for an analytical study and finite element analysis. Stiffened plate linear theories are employed for a parametric case study. Maximum deflection and stress levels are obtained with appropriate assumptions for a set of feasible stiffened panel configurations. An analytical parametric case study is presented to examine the effects of discrete stiffener spacing and skin thickness on structural weight, deflection and stress. A finite-element model (FEM) of an integrated fuselage section with bulkhead is developed for an independent assessment. Stress analysis and scenario based case studies are conducted for design improvement. The FEM model specific weight of the improved fuselage concept is computed and compared to previous studies, in order to assess the relative weight/strength advantages of this advanced composite airframe technology

On the calculation of resonances by analytic continuation of eigenvalues from the stabilization graph

NASA Astrophysics Data System (ADS)

Haritan, Idan; Moiseyev, Nimrod

2017-07-01

Resonances play a major role in a large variety of fields in physics and chemistry. Accordingly, there is a growing interest in methods designed to calculate them. Recently, Landau et al. proposed a new approach to analytically dilate a single eigenvalue from the stabilization graph into the complex plane. This approach, termed Resonances Via Padé (RVP), utilizes the Padé approximant and is based on a unique analysis of the stabilization graph. Yet, analytic continuation of eigenvalues from the stabilization graph into the complex plane is not a new idea. In 1975, Jordan suggested an analytic continuation method based on the branch point structure of the stabilization graph. The method was later modified by McCurdy and McNutt, and it is still being used today. We refer to this method as the Truncated Characteristic Polynomial (TCP) method. In this manuscript, we perform an in-depth comparison between the RVP and the TCP methods. We demonstrate that while both methods are important and complementary, the advantage of one method over the other is problem-dependent. Illustrative examples are provided in the manuscript.

Approximate analytical relationships for linear optimal aeroelastic flight control laws

NASA Astrophysics Data System (ADS)

Kassem, Ayman Hamdy

1998-09-01

This dissertation introduces new methods to uncover functional relationships between design parameters of a contemporary control design technique and the resulting closed-loop properties. Three new methods are developed for generating such relationships through analytical expressions: the Direct Eigen-Based Technique, the Order of Magnitude Technique, and the Cost Function Imbedding Technique. Efforts concentrated on the linear-quadratic state-feedback control-design technique applied to an aeroelastic flight control task. For this specific application, simple and accurate analytical expressions for the closed-loop eigenvalues and zeros in terms of basic parameters such as stability and control derivatives, structural vibration damping and natural frequency, and cost function weights are generated. These expressions explicitly indicate how the weights augment the short period and aeroelastic modes, as well as the closed-loop zeros, and by what physical mechanism. The analytical expressions are used to address topics such as damping, nonminimum phase behavior, stability, and performance with robustness considerations, and design modifications. This type of knowledge is invaluable to the flight control designer and would be more difficult to formulate when obtained from numerical-based sensitivity analysis.

Analytical approximations for effective relative permeability in the capillary limit

NASA Astrophysics Data System (ADS)

Rabinovich, Avinoam; Li, Boxiao; Durlofsky, Louis J.

2016-10-01

We present an analytical method for calculating two-phase effective relative permeability, krjeff, where j designates phase (here CO2 and water), under steady state and capillary-limit assumptions. These effective relative permeabilities may be applied in experimental settings and for upscaling in the context of numerical flow simulations, e.g., for CO2 storage. An exact solution for effective absolute permeability, keff, in two-dimensional log-normally distributed isotropic permeability (k) fields is the geometric mean. We show that this does not hold for krjeff since log normality is not maintained in the capillary-limit phase permeability field (Kj=k·krj) when capillary pressure, and thus the saturation field, is varied. Nevertheless, the geometric mean is still shown to be suitable for approximating krjeff when the variance of ln⁡k is low. For high-variance cases, we apply a correction to the geometric average gas effective relative permeability using a Winsorized mean, which neglects large and small Kj values symmetrically. The analytical method is extended to anisotropically correlated log-normal permeability fields using power law averaging. In these cases, the Winsorized mean treatment is applied to the gas curves for cases described by negative power law exponents (flow across incomplete layers). The accuracy of our analytical expressions for krjeff is demonstrated through extensive numerical tests, using low-variance and high-variance permeability realizations with a range of correlation structures. We also present integral expressions for geometric-mean and power law average krjeff for the systems considered, which enable derivation of closed-form series solutions for krjeff without generating permeability realizations.

Precise analytic approximations for the Bessel function J1 (x)

NASA Astrophysics Data System (ADS)

Maass, Fernando; Martin, Pablo

2018-03-01

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

Phonons in random alloys: The itinerant coherent-potential approximation

NASA Astrophysics Data System (ADS)

Ghosh, Subhradip; Leath, P. L.; Cohen, Morrel H.

2002-12-01

We present the itinerant coherent-potential approximation (ICPA), an analytic, translationally invariant, and tractable form of augmented-space-based multiple-scattering theory18 in a single-site approximation for harmonic phonons in realistic random binary alloys with mass and force-constant disorder. We provide expressions for quantities needed for comparison with experimental structure factors such as partial and average spectral functions and derive the sum rules associated with them. Numerical results are presented for Ni55Pd45 and Ni50Pt50 alloys which serve as test cases, the former for weak force-constant disorder and the latter for strong. We present results on dispersion curves and disorder-induced widths. Direct comparisons with the single-site coherent potential approximation (CPA) and experiment are made which provide insight into the physics of force-constant changes in random alloys. The CPA accounts well for the weak force-constant disorder case but fails for strong force-constant disorder where the ICPA succeeds.

A hybrid analytical model for open-circuit field calculation of multilayer interior permanent magnet machines

NASA Astrophysics Data System (ADS)

Zhang, Zhen; Xia, Changliang; Yan, Yan; Geng, Qiang; Shi, Tingna

2017-08-01

Due to the complicated rotor structure and nonlinear saturation of rotor bridges, it is difficult to build a fast and accurate analytical field calculation model for multilayer interior permanent magnet (IPM) machines. In this paper, a hybrid analytical model suitable for the open-circuit field calculation of multilayer IPM machines is proposed by coupling the magnetic equivalent circuit (MEC) method and the subdomain technique. In the proposed analytical model, the rotor magnetic field is calculated by the MEC method based on the Kirchhoff's law, while the field in the stator slot, slot opening and air-gap is calculated by subdomain technique based on the Maxwell's equation. To solve the whole field distribution of the multilayer IPM machines, the coupled boundary conditions on the rotor surface are deduced for the coupling of the rotor MEC and the analytical field distribution of the stator slot, slot opening and air-gap. The hybrid analytical model can be used to calculate the open-circuit air-gap field distribution, back electromotive force (EMF) and cogging torque of multilayer IPM machines. Compared with finite element analysis (FEA), it has the advantages of faster modeling, less computation source occupying and shorter time consuming, and meanwhile achieves the approximate accuracy. The analytical model is helpful and applicable for the open-circuit field calculation of multilayer IPM machines with any size and pole/slot number combination.

Characterization of Perovskite Oxide/Semiconductor Heterostructures

NASA Astrophysics Data System (ADS)

Walker, Phillip

The tools developed for the use of investigating dynamical systems have provided critical understanding to a wide range of physical phenomena. Here these tools are used to gain further insight into scalar transport, and how it is affected by mixing. The aim of this research is to investigate the efficiency of several different partitioning methods which demarcate flow fields into dynamically distinct regions, and the correlation of finite-time statistics from the advection-diffusion equation to these regions. For autonomous systems, invariant manifold theory can be used to separate the system into dynamically distinct regions. Despite there being no equivalent method for nonautonomous systems, a similar analysis can be done. Systems with general time dependencies must resort to using finite-time transport barriers for partitioning; these barriers are the edges of Lagrangian coherent structures (LCS), the analog to the stable and unstable manifolds of invariant manifold theory. Using the coherent structures of a flow to analyze the statistics of trapping, flight, and residence times, the signature of anomalous diffusion are obtained. This research also investigates the use of linear models for approximating the elements of the covariance matrix of nonlinear flows, and then applying the covariance matrix approximation over coherent regions. The first and second-order moments can be used to fully describe an ensemble evolution in linear systems, however there is no direct method for nonlinear systems. The problem is only compounded by the fact that the moments for nonlinear flows typically don't have analytic representations, therefore direct numerical simulations would be needed to obtain the moments throughout the domain. To circumvent these many computations, the nonlinear system is approximated as many linear systems for which analytic expressions for the moments exist. The parameters introduced in the linear models are obtained locally from the nonlinear deformation tensor.

Probabilistic structural mechanics research for parallel processing computers

NASA Technical Reports Server (NTRS)

Sues, Robert H.; Chen, Heh-Chyun; Twisdale, Lawrence A.; Martin, William R.

1991-01-01

Aerospace structures and spacecraft are a complex assemblage of structural components that are subjected to a variety of complex, cyclic, and transient loading conditions. Significant modeling uncertainties are present in these structures, in addition to the inherent randomness of material properties and loads. To properly account for these uncertainties in evaluating and assessing the reliability of these components and structures, probabilistic structural mechanics (PSM) procedures must be used. Much research has focused on basic theory development and the development of approximate analytic solution methods in random vibrations and structural reliability. Practical application of PSM methods was hampered by their computationally intense nature. Solution of PSM problems requires repeated analyses of structures that are often large, and exhibit nonlinear and/or dynamic response behavior. These methods are all inherently parallel and ideally suited to implementation on parallel processing computers. New hardware architectures and innovative control software and solution methodologies are needed to make solution of large scale PSM problems practical.

Response to ``Comment on `Scalings for radiation from plasma bubbles' '' [Phys. Plasmas 18, 034701 (2011)

NASA Astrophysics Data System (ADS)

Thomas, A. G. R.

2011-03-01

In the preceding Comment, Corde, Stordeur, and Malka claim that the trapping threshold derived in my recent paper is incorrect. Their principal argument is that the elliptical orbits I used are not exact solutions of the equation of motion in the fields of the bubble. The original paper never claimed this—rather I claimed that the use of elliptical orbits was a reasonable approximation, which I based on observations from particle-in-cell simulations. Integration of the equation of motion for analytical expressions for idealized bubble fields (either analytically [I. Kostyukov, E. Nerush, A. Pukhov, and V. Seredov, Phys. Rev. Lett. 103, 175003 (2009)] or numerically [S. Corde, A. Stordeur, and V. Malka, "Comment on `Scalings for radiation from plasma bubbles,' " Phys. Plasmas 18, 034701 (2011)]) produces a trapping threshold wholly inconsistent with experiments and full particle-in-cell (PIC) simulations (e.g., requiring an estimated laser intensity of a0˜30 for ne˜1019 cm-3). The inconsistency in the particle trajectories between PIC and the numeric model used by the comment authors arises due to the fact that the analytical fields are only approximately true for "real" plasma bubbles, and lack certain key features of the field structure. Two possible methods of resolution to this inconsistency are either to find ever more complicated but accurate models for the bubble fields or to find approximate solutions to the equations of motion that capture the essential features of the self-consistent electron trajectories. The latter, heuristic approach used in my recent paper produced a threshold that is better matched to experimental observations. In this reply, I will also revisit the problem and examine the relationship between bubble radius and electron momentum at the point of trapping without reference to a particular trajectory.

General rotating quantum vortex filaments in the low-temperature Svistunov model of the local induction approximation

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

Van Gorder, Robert A., E-mail: rav@knights.ucf.edu

2014-06-15

In his study of superfluid turbulence in the low-temperature limit, Svistunov [“Superfluid turbulence in the low-temperature limit,” Phys. Rev. B 52, 3647 (1995)] derived a Hamiltonian equation for the self-induced motion of a vortex filament. Under the local induction approximation (LIA), the Svistunov formulation is equivalent to a nonlinear dispersive partial differential equation. In this paper, we consider a family of rotating vortex filament solutions for the LIA reduction of the Svistunov formulation, which we refer to as the 2D LIA (since it permits a potential formulation in terms of two of the three Cartesian coordinates). This class of solutionsmore » holds the well-known Hasimoto-type planar vortex filament [H. Hasimoto, “Motion of a vortex filament and its relation to elastica,” J. Phys. Soc. Jpn. 31, 293 (1971)] as one reduction and helical solutions as another. More generally, we obtain solutions which are periodic in the space variable. A systematic analytical study of the behavior of such solutions is carried out. In the case where vortex filaments have small deviations from the axis of rotation, closed analytical forms of the filament solutions are given. A variety of numerical simulations are provided to demonstrate the wide range of rotating filament behaviors possible. Doing so, we are able to determine a number of vortex filament structures not previously studied. We find that the solution structure progresses from planar to helical, and then to more intricate and complex filament structures, possibly indicating the onset of superfluid turbulence.« less

On the Application of Euler Deconvolution to the Analytic Signal

NASA Astrophysics Data System (ADS)

Fedi, M.; Florio, G.; Pasteka, R.

2005-05-01

In the last years papers on Euler deconvolution (ED) used formulations that accounted for the unknown background field, allowing to consider the structural index (N) an unknown to be solved for, together with the source coordinates. Among them, Hsu (2002) and Fedi and Florio (2002) independently pointed out that the use of an adequate m-order derivative of the field, instead than the field itself, allowed solving for both N and source position. For the same reason, Keating and Pilkington (2004) proposed the ED of the analytic signal. A function being analyzed by ED must be homogeneous but also harmonic, because it must be possible to compute its vertical derivative, as well known from potential field theory. Huang et al. (1995), demonstrated that analytic signal is a homogeneous function, but, for instance, it is rather obvious that the magnetic field modulus (corresponding to the analytic signal of a gravity field) is not a harmonic function (e.g.: Grant & West, 1965). Thus, it appears that a straightforward application of ED to the analytic signal is not possible because a vertical derivation of this function is not correct by using standard potential fields analysis tools. In this note we want to theoretically and empirically check what kind of error are caused in the ED by such wrong assumption about analytic signal harmonicity. We will discuss results on profile and map synthetic data, and use a simple method to compute the vertical derivative of non-harmonic functions measured on a horizontal plane. Our main conclusions are: 1. To approximate a correct evaluation of the vertical derivative of a non-harmonic function it is useful to compute it with finite-difference, by using upward continuation. 2. We found that the errors on the vertical derivative computed as if the analytic signal was harmonic reflects mainly on the structural index estimate; these errors can mislead an interpretation even though the depth estimates are almost correct. 3. Consistent estimates of depth and S.I. are instead obtained by using a finite-difference vertical derivative of the analytic signal. 4. Analysis of a case history confirms the strong error in the estimation of structural index if the analytic signal is treated as an harmonic function.

The singular values of the imbedding operators of some classes of analytic functions of several variables

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

Parfenov, O.G.

1994-12-25

We discuss three results. The first exhibits the order of decrease of the s-values as a function of the CR-dimension of a compact set on which we approximate the class of analytic functions being studied. The second is an asymptotic formula for the case when the domain of analyticity and the compact set are Reinhart domains. The third is the computation of the s-values of a special operator that is of interest for approximation theory on one-dimensional manifolds.

Numerical modeling and analytical evaluation of light absorption by gold nanostars

NASA Astrophysics Data System (ADS)

Zarkov, Sergey; Akchurin, Georgy; Yakunin, Alexander; Avetisyan, Yuri; Akchurin, Garif; Tuchin, Valery

2018-04-01

In this paper, the regularity of local light absorption by gold nanostars (AuNSts) model is studied by method of numerical simulation. The mutual diffraction influence of individual geometric fragments of AuNSts is analyzed. A comparison is made with an approximate analytical approach for estimating the average bulk density of absorbed power and total absorbed power by individual geometric fragments of AuNSts. It is shown that the results of the approximate analytical estimate are in qualitative agreement with the numerical calculations of the light absorption by AuNSts.

A semi-analytical bearing model considering outer race flexibility for model based bearing load monitoring

NASA Astrophysics Data System (ADS)

Kerst, Stijn; Shyrokau, Barys; Holweg, Edward

2018-05-01

This paper proposes a novel semi-analytical bearing model addressing flexibility of the bearing outer race structure. It furthermore presents the application of this model in a bearing load condition monitoring approach. The bearing model is developed as current computational low cost bearing models fail to provide an accurate description of the more and more common flexible size and weight optimized bearing designs due to their assumptions of rigidity. In the proposed bearing model raceway flexibility is described by the use of static deformation shapes. The excitation of the deformation shapes is calculated based on the modelled rolling element loads and a Fourier series based compliance approximation. The resulting model is computational low cost and provides an accurate description of the rolling element loads for flexible outer raceway structures. The latter is validated by a simulation-based comparison study with a well-established bearing simulation software tool. An experimental study finally shows the potential of the proposed model in a bearing load monitoring approach.

Multi-disciplinary optimization of aeroservoelastic systems

NASA Technical Reports Server (NTRS)

Karpel, Mordechay

1990-01-01

Efficient analytical and computational tools for simultaneous optimal design of the structural and control components of aeroservoelastic systems are presented. The optimization objective is to achieve aircraft performance requirements and sufficient flutter and control stability margins with a minimal weight penalty and without violating the design constraints. Analytical sensitivity derivatives facilitate an efficient optimization process which allows a relatively large number of design variables. Standard finite element and unsteady aerodynamic routines are used to construct a modal data base. Minimum State aerodynamic approximations and dynamic residualization methods are used to construct a high accuracy, low order aeroservoelastic model. Sensitivity derivatives of flutter dynamic pressure, control stability margins and control effectiveness with respect to structural and control design variables are presented. The performance requirements are utilized by equality constraints which affect the sensitivity derivatives. A gradient-based optimization algorithm is used to minimize an overall cost function. A realistic numerical example of a composite wing with four controls is used to demonstrate the modeling technique, the optimization process, and their accuracy and efficiency.

Multidisciplinary optimization of aeroservoelastic systems using reduced-size models

NASA Technical Reports Server (NTRS)

Karpel, Mordechay

1992-01-01

Efficient analytical and computational tools for simultaneous optimal design of the structural and control components of aeroservoelastic systems are presented. The optimization objective is to achieve aircraft performance requirements and sufficient flutter and control stability margins with a minimal weight penalty and without violating the design constraints. Analytical sensitivity derivatives facilitate an efficient optimization process which allows a relatively large number of design variables. Standard finite element and unsteady aerodynamic routines are used to construct a modal data base. Minimum State aerodynamic approximations and dynamic residualization methods are used to construct a high accuracy, low order aeroservoelastic model. Sensitivity derivatives of flutter dynamic pressure, control stability margins and control effectiveness with respect to structural and control design variables are presented. The performance requirements are utilized by equality constraints which affect the sensitivity derivatives. A gradient-based optimization algorithm is used to minimize an overall cost function. A realistic numerical example of a composite wing with four controls is used to demonstrate the modeling technique, the optimization process, and their accuracy and efficiency.

The Excursion set approach: Stratonovich approximation and Cholesky decomposition

NASA Astrophysics Data System (ADS)

Nikakhtar, Farnik; Ayromlou, Mohammadreza; Baghram, Shant; Rahvar, Sohrab; Tabar, M. Reza Rahimi; Sheth, Ravi K.

2018-05-01

The excursion set approach is a framework for estimating how the number density of nonlinear structures in the cosmic web depends on the expansion history of the universe and the nature of gravity. A key part of the approach is the estimation of the first crossing distribution of a suitably chosen barrier by random walks having correlated steps: The shape of the barrier is determined by the physics of nonlinear collapse, and the correlations between steps by the nature of the initial density fluctuation field. We describe analytic and numerical methods for calculating such first up-crossing distributions. While the exact solution can be written formally as an infinite series, we show how to approximate it efficiently using the Stratonovich approximation. We demonstrate its accuracy using Monte-Carlo realizations of the walks, which we generate using a novel Cholesky-decomposition based algorithm, which is significantly faster than the algorithm that is currently in the literature.

Exchange potential from the common energy denominator approximation for the Kohn-Sham Green's function: Application to (hyper)polarizabilities of molecular chains

NASA Astrophysics Data System (ADS)

Grüning, M.; Gritsenko, O. V.; Baerends, E. J.

2002-04-01

An approximate Kohn-Sham (KS) exchange potential vxσCEDA is developed, based on the common energy denominator approximation (CEDA) for the static orbital Green's function, which preserves the essential structure of the density response function. vxσCEDA is an explicit functional of the occupied KS orbitals, which has the Slater vSσ and response vrespσCEDA potentials as its components. The latter exhibits the characteristic step structure with "diagonal" contributions from the orbital densities |ψiσ|2, as well as "off-diagonal" ones from the occupied-occupied orbital products ψiσψj(≠1)σ*. Comparison of the results of atomic and molecular ground-state CEDA calculations with those of the Krieger-Li-Iafrate (KLI), exact exchange (EXX), and Hartree-Fock (HF) methods show, that both KLI and CEDA potentials can be considered as very good analytical "closure approximations" to the exact KS exchange potential. The total CEDA and KLI energies nearly coincide with the EXX ones and the corresponding orbital energies ɛiσ are rather close to each other for the light atoms and small molecules considered. The CEDA, KLI, EXX-ɛiσ values provide the qualitatively correct order of ionizations and they give an estimate of VIPs comparable to that of the HF Koopmans' theorem. However, the additional off-diagonal orbital structure of vxσCEDA appears to be essential for the calculated response properties of molecular chains. KLI already considerably improves the calculated (hyper)polarizabilities of the prototype hydrogen chains Hn over local density approximation (LDA) and standard generalized gradient approximations (GGAs), while the CEDA results are definitely an improvement over the KLI ones. The reasons of this success are the specific orbital structures of the CEDA and KLI response potentials, which produce in an external field an ultranonlocal field-counteracting exchange potential.

Analytic approximations to the modon dispersion relation. [in oceanography

NASA Technical Reports Server (NTRS)

Boyd, J. P.

1981-01-01

Three explicit analytic approximations are given to the modon dispersion relation developed by Flierl et al. (1980) to describe Gulf Stream rings and related phenomena in the oceans and atmosphere. The solutions are in the form of k(q), and are developed in the form of a power series in q for small q, an inverse power series in 1/q for large q, and a two-point Pade approximant. The low order Pade approximant is shown to yield a solution for the dispersion relation with a maximum relative error for the lowest branch of the function equal to one in 700 in the q interval zero to infinity.

Analytical solutions of the Klein-Gordon equation for Manning-Rosen potential with centrifugal term through Nikiforov-Uvarov method

NASA Astrophysics Data System (ADS)

Hatami, N.; Setare, M. R.

2017-10-01

We present approximate analytical solutions of the Klein-Gordon equation with arbitrary l state for the Manning-Rosen potential using the Nikiforov-Uvarov method and adopting the approximation scheme for the centrifugal term. We provide the bound state energy spectrum and the wave function in terms of the hypergeometric functions.

Analytical computation of three-dimensional synthetic seismograms by Modal Summation: method, validation and applications

NASA Astrophysics Data System (ADS)

La Mura, Cristina; Gholami, Vahid; Panza, Giuliano F.

2013-04-01

In order to enable realistic and reliable earthquake hazard assessment and reliable estimation of the ground motion response to an earthquake, three-dimensional velocity models have to be considered. The propagation of seismic waves in complex laterally varying 3D layered structures is a complicated process. Analytical solutions of the elastodynamic equations for such types of media are not known. The most common approaches to the formal description of seismic wavefields in such complex structures are methods based on direct numerical solutions of the elastodynamic equations, e.g. finite-difference, finite-element method, and approximate asymptotic methods. In this work, we present an innovative methodology for computing synthetic seismograms, complete of the main direct, refracted, converted phases and surface waves in three-dimensional anelastic models based on the combination of the Modal Summation technique with the Asymptotic Ray Theory in the framework of the WKBJ - approximation. The three - dimensional models are constructed using a set of vertically heterogeneous sections (1D structures) that are juxtaposed on a regular grid. The distribution of these sections in the grid is done in such a way to fulfill the requirement of weak lateral inhomogeneity in order to satisfy the condition of applicability of the WKBJ - approximation, i.e. the lateral gradient of the parameters characterizing the 1D structure has to be small with respect to the prevailing wavelength. The new method has been validated comparing synthetic seismograms with the records available of three different earthquakes in three different regions: Kanto basin (Japan) triggered by the 1990 Odawara earthquake Mw= 5.1, Romanian territory triggered by the 30 May 1990 Vrancea intermediate-depth earthquake Mw= 6.9 and Iranian territory affected by the 26 December 2003 Bam earthquake Mw= 6.6. Besides the advantage of being a useful tool for assessment of seismic hazard and seismic risk reduction, it is characterized by high efficiency, in fact, once the study region is identified and the 3D model is constructed, the computation, at each station, of the three components of the synthetic signal (displacement, velocity, and acceleration) takes less than 3 hours on a 2 GHz CPU.

Structure of ternary additive hard-sphere fluid mixtures.

PubMed

Malijevský, Alexander; Malijevský, Anatol; Yuste, Santos B; Santos, Andrés; López de Haro, Mariano

2002-12-01

Monte Carlo simulations on the structural properties of ternary fluid mixtures of additive hard spheres are reported. The results are compared with those obtained from a recent analytical approximation [S. B. Yuste, A. Santos, and M. López de Haro, J. Chem. Phys. 108, 3683 (1998)] to the radial distribution functions of hard-sphere mixtures and with the results derived from the solution of the Ornstein-Zernike integral equation with both the Martynov-Sarkisov and the Percus-Yevick closures. Very good agreement between the results of the first two approaches and simulation is observed, with a noticeable improvement over the Percus-Yevick predictions especially near contact.

Quantum currents and pair correlation of electrons in a chain of localized dots

NASA Astrophysics Data System (ADS)

Morawetz, Klaus

2017-03-01

The quantum transport of electrons in a wire of localized dots by hopping, interaction and dissipation is calculated and a representation by an equivalent RCL circuit is found. The exact solution for the electric-field induced currents allows to discuss the role of virtual currents to decay initial correlations and Bloch oscillations. The dynamical response function in random phase approximation (RPA) is calculated analytically with the help of which the static structure function and pair correlation function are determined. The pair correlation function contains a form factor from the Brillouin zone and a structure factor caused by the localized dots in the wire.

Asymptotic approximations to posterior distributions via conditional moment equations

USGS Publications Warehouse

Yee, J.L.; Johnson, W.O.; Samaniego, F.J.

2002-01-01

We consider asymptotic approximations to joint posterior distributions in situations where the full conditional distributions referred to in Gibbs sampling are asymptotically normal. Our development focuses on problems where data augmentation facilitates simpler calculations, but results hold more generally. Asymptotic mean vectors are obtained as simultaneous solutions to fixed point equations that arise naturally in the development. Asymptotic covariance matrices flow naturally from the work of Arnold & Press (1989) and involve the conditional asymptotic covariance matrices and first derivative matrices for conditional mean functions. When the fixed point equations admit an analytical solution, explicit formulae are subsequently obtained for the covariance structure of the joint limiting distribution, which may shed light on the use of the given statistical model. Two illustrations are given. ?? 2002 Biometrika Trust.

Probability density function learning by unsupervised neurons.

PubMed

Fiori, S

2001-10-01

In a recent work, we introduced the concept of pseudo-polynomial adaptive activation function neuron (FAN) and presented an unsupervised information-theoretic learning theory for such structure. The learning model is based on entropy optimization and provides a way of learning probability distributions from incomplete data. The aim of the present paper is to illustrate some theoretical features of the FAN neuron, to extend its learning theory to asymmetrical density function approximation, and to provide an analytical and numerical comparison with other known density function estimation methods, with special emphasis to the universal approximation ability. The paper also provides a survey of PDF learning from incomplete data, as well as results of several experiments performed on real-world problems and signals.

Nonlinear core deflection in injection molding

NASA Astrophysics Data System (ADS)

Poungthong, P.; Giacomin, A. J.; Saengow, C.; Kolitawong, C.; Liao, H.-C.; Tseng, S.-C.

2018-05-01

Injection molding of thin slender parts is often complicated by core deflection. This deflection is caused by molten plastics race tracking through the slit between the core and the rigid cavity wall. The pressure of this liquid exerts a lateral force of the slender core causing the core to bend, and this bending is governed by a nonlinear fifth order ordinary differential equation for the deflection that is not directly in the position along the core. Here we subject this differential equation to 6 sets of boundary conditions, corresponding to 6 commercial core constraints. For each such set of boundary conditions, we develop an explicit approximate analytical solution, including both a linear term and a nonlinear term. By comparison with finite difference solutions, we find our new analytical solutions to be accurate. We then use these solutions to derive explicit analytical approximations for maximum deflections and for the core position of these maximum deflections. Our experiments on the base-gated free-tip boundary condition agree closely with our new explicit approximate analytical solution.

Analytical approximations for the oscillators with anti-symmetric quadratic nonlinearity

NASA Astrophysics Data System (ADS)

Alal Hosen, Md.; Chowdhury, M. S. H.; Yeakub Ali, Mohammad; Faris Ismail, Ahmad

2017-12-01

A second-order ordinary differential equation involving anti-symmetric quadratic nonlinearity changes sign. The behaviour of the oscillators with an anti-symmetric quadratic nonlinearity is assumed to oscillate different in the positive and negative directions. In this reason, Harmonic Balance Method (HBM) cannot be directly applied. The main purpose of the present paper is to propose an analytical approximation technique based on the HBM for obtaining approximate angular frequencies and the corresponding periodic solutions of the oscillators with anti-symmetric quadratic nonlinearity. After applying HBM, a set of complicated nonlinear algebraic equations is found. Analytical approach is not always fruitful for solving such kinds of nonlinear algebraic equations. In this article, two small parameters are found, for which the power series solution produces desired results. Moreover, the amplitude-frequency relationship has also been determined in a novel analytical way. The presented technique gives excellent results as compared with the corresponding numerical results and is better than the existing ones.

Modeling of phonon scattering in n-type nanowire transistors using one-shot analytic continuation technique

NASA Astrophysics Data System (ADS)

Bescond, Marc; Li, Changsheng; Mera, Hector; Cavassilas, Nicolas; Lannoo, Michel

2013-10-01

We present a one-shot current-conserving approach to model the influence of electron-phonon scattering in nano-transistors using the non-equilibrium Green's function formalism. The approach is based on the lowest order approximation (LOA) to the current and its simplest analytic continuation (LOA+AC). By means of a scaling argument, we show how both LOA and LOA+AC can be easily obtained from the first iteration of the usual self-consistent Born approximation (SCBA) algorithm. Both LOA and LOA+AC are then applied to model n-type silicon nanowire field-effect-transistors and are compared to SCBA current characteristics. In this system, the LOA fails to describe electron-phonon scattering, mainly because of the interactions with acoustic phonons at the band edges. In contrast, the LOA+AC still well approximates the SCBA current characteristics, thus demonstrating the power of analytic continuation techniques. The limits of validity of LOA+AC are also discussed, and more sophisticated and general analytic continuation techniques are suggested for more demanding cases.

Dynamics of a spin-boson model with structured spectral density

NASA Astrophysics Data System (ADS)

Kurt, Arzu; Eryigit, Resul

2018-05-01

We report the results of a study of the dynamics of a two-state system coupled to an environment with peaked spectral density. An exact analytical expression for the bath correlation function is obtained. Validity range of various approximations to the correlation function for calculating the population difference of the system is discussed as function of tunneling splitting, oscillator frequency, coupling constant, damping rate and the temperature of the bath. An exact expression for the population difference, for a limited range of parameters, is derived.

Comparison of permutationally invariant polynomials, neural networks, and Gaussian approximation potentials in representing water interactions through many-body expansions

NASA Astrophysics Data System (ADS)

Nguyen, Thuong T.; Székely, Eszter; Imbalzano, Giulio; Behler, Jörg; Csányi, Gábor; Ceriotti, Michele; Götz, Andreas W.; Paesani, Francesco

2018-06-01

The accurate representation of multidimensional potential energy surfaces is a necessary requirement for realistic computer simulations of molecular systems. The continued increase in computer power accompanied by advances in correlated electronic structure methods nowadays enables routine calculations of accurate interaction energies for small systems, which can then be used as references for the development of analytical potential energy functions (PEFs) rigorously derived from many-body (MB) expansions. Building on the accuracy of the MB-pol many-body PEF, we investigate here the performance of permutationally invariant polynomials (PIPs), neural networks, and Gaussian approximation potentials (GAPs) in representing water two-body and three-body interaction energies, denoting the resulting potentials PIP-MB-pol, Behler-Parrinello neural network-MB-pol, and GAP-MB-pol, respectively. Our analysis shows that all three analytical representations exhibit similar levels of accuracy in reproducing both two-body and three-body reference data as well as interaction energies of small water clusters obtained from calculations carried out at the coupled cluster level of theory, the current gold standard for chemical accuracy. These results demonstrate the synergy between interatomic potentials formulated in terms of a many-body expansion, such as MB-pol, that are physically sound and transferable, and machine-learning techniques that provide a flexible framework to approximate the short-range interaction energy terms.

Expected distributions of root-mean-square positional deviations in proteins.

PubMed

Pitera, Jed W

2014-06-19

The atom positional root-mean-square deviation (RMSD) is a standard tool for comparing the similarity of two molecular structures. It is used to characterize the quality of biomolecular simulations, to cluster conformations, and as a reaction coordinate for conformational changes. This work presents an approximate analytic form for the expected distribution of RMSD values for a protein or polymer fluctuating about a stable native structure. The mean and maximum of the expected distribution are independent of chain length for long chains and linearly proportional to the average atom positional root-mean-square fluctuations (RMSF). To approximate the RMSD distribution for random-coil or unfolded ensembles, numerical distributions of RMSD were generated for ensembles of self-avoiding and non-self-avoiding random walks. In both cases, for all reference structures tested for chains more than three monomers long, the distributions have a maximum distant from the origin with a power-law dependence on chain length. The purely entropic nature of this result implies that care must be taken when interpreting stable high-RMSD regions of the free-energy landscape as "intermediates" or well-defined stable states.

Methods in the study of discrete upper hybrid waves

NASA Astrophysics Data System (ADS)

Yoon, P. H.; Ye, S.; Labelle, J.; Weatherwax, A. T.; Menietti, J. D.

2007-11-01

Naturally occurring plasma waves characterized by fine frequency structure or discrete spectrum, detected by satellite, rocket-borne instruments, or ground-based receivers, can be interpreted as eigenmodes excited and trapped in field-aligned density structures. This paper overviews various theoretical methods to study such phenomena for a one-dimensional (1-D) density structure. Among the various methods are parabolic approximation, eikonal matching, eigenfunction matching, and full numerical solution based upon shooting method. Various approaches are compared against the full numerical solution. Among the analytic methods it is found that the eigenfunction matching technique best approximates the actual numerical solution. The analysis is further extended to 2-D geometry. A detailed comparative analysis between the eigenfunction matching and fully numerical methods is carried out for the 2-D case. Although in general the two methods compare favorably, significant differences are also found such that for application to actual observations it is prudent to employ the fully numerical method. Application of the methods developed in the present paper to actual geophysical problems will be given in a companion paper.

Methods for analysis of cracks in three-dimensional solids

NASA Technical Reports Server (NTRS)

Raju, I. S.; Newman, J. C., Jr.

1984-01-01

Analytical and numerical methods evaluating the stress-intensity factors for three-dimensional cracks in solids are presented, with reference to fatigue failure in aerospace structures. The exact solutions for embedded elliptical and circular cracks in infinite solids, and the approximate methods, including the finite-element, the boundary-integral equation, the line-spring models, and the mixed methods are discussed. Among the mixed methods, the superposition of analytical and finite element methods, the stress-difference, the discretization-error, the alternating, and the finite element-alternating methods are reviewed. Comparison of the stress-intensity factor solutions for some three-dimensional crack configurations showed good agreement. Thus, the choice of a particular method in evaluating the stress-intensity factor is limited only to the availability of resources and computer programs.

Analytical model for the threshold voltage of III-V nanowire transistors including quantum effects

NASA Astrophysics Data System (ADS)

Marin, E. G.; Ruiz, F. G.; Tienda-Luna, I. M.; Godoy, A.; Gámiz, F.

2014-02-01

In this work we propose an analytical model for the threshold voltage (VT) of III-V cylindrical nanowires, that takes into consideration the two dimensional quantum confinement of the carriers, the Fermi-Dirac statistics, the wave-function penetration into the gate insulator and the non-parabolicity of the conduction band structure. A simple expression for VT is obtained assuming some suitable approximations. The model results are compared to those of a 2D self consistent Schrödinger-Poisson solver, demonstrating a good fit for different III-V materials, insulator thicknesses and nanowire sizes with diameter down to 5 nm. The VT dependence on the confinement effective mass is discussed. The different contributions to VT are analyzed showing significant variations among different III-V materials.

Tunable Snell's law for spin waves in heterochiral magnetic films

NASA Astrophysics Data System (ADS)

Mulkers, Jeroen; Van Waeyenberge, Bartel; Milošević, Milorad V.

2018-03-01

Thin ferromagnetic films with an interfacially induced DMI exhibit nontrivial asymmetric dispersion relations that lead to unique and useful magnonic properties. Here we derive an analytical expression for the magnon propagation angle within the micromagnetic framework and show how the dispersion relation can be approximated with a comprehensible geometrical interpretation in the k space of the propagation of spin waves. We further explore the refraction of spin waves at DMI interfaces in heterochiral magnetic films, after deriving a generalized Snell's law tunable by an in-plane magnetic field, that yields analytical expressions for critical incident angles. The found asymmetric Brewster angles at interfaces of regions with different DMI strengths, adjustable by magnetic field, support the conclusion that heterochiral ferromagnetic structures are an ideal platform for versatile spin-wave guides.

Evaluation Applied to Reliability Analysis of Reconfigurable, Highly Reliable, Fault-Tolerant, Computing Systems for Avionics

NASA Technical Reports Server (NTRS)

Migneault, G. E.

1979-01-01

Emulation techniques are proposed as a solution to a difficulty arising in the analysis of the reliability of highly reliable computer systems for future commercial aircraft. The difficulty, viz., the lack of credible precision in reliability estimates obtained by analytical modeling techniques are established. The difficulty is shown to be an unavoidable consequence of: (1) a high reliability requirement so demanding as to make system evaluation by use testing infeasible, (2) a complex system design technique, fault tolerance, (3) system reliability dominated by errors due to flaws in the system definition, and (4) elaborate analytical modeling techniques whose precision outputs are quite sensitive to errors of approximation in their input data. The technique of emulation is described, indicating how its input is a simple description of the logical structure of a system and its output is the consequent behavior. The use of emulation techniques is discussed for pseudo-testing systems to evaluate bounds on the parameter values needed for the analytical techniques.

Revisiting the West Clearwater Lake Impact Structure, Canada

NASA Technical Reports Server (NTRS)

Osinski, G. R.; Brunner, A.; Collins, G.; Cohen, B. A.; Coulter, A.; Elphic, R.; Grieve, R. A. F.; Hodges, K.; Horne, A.; Kerrigan, M.

2015-01-01

The West and East Clearwater Lake impact structures are two of the most distinctive and recognizable impact structures on Earth. Known regionally as the "Clearwater Lake Complex", these structures are located in northern Quebec, Canada (56 deg 10 N, 74 deg 20 W) approximately 125 km east of Hudson Bay. The currently accepted diameters are 36 km and 26 km for the West and East structures, respectively. Long thought to represent a rare example of a double impact, recent age dating has called this into question with ages of approximately 286 Ma and approximately 460-470 Ma being proposed for the West and East structures, respectively. Relatively little is known about the East Clearwater Lake structure. There is no surface exposure and what information there is comes from geophysics and two drill cores obtained in the 1960s. In contrast, the West Clearwater Lake structure is relatively well preserved with large ring of islands in the approximately 30 km diameter lake. Much of the work done on West Clearwater stems from field investigations carried out in 1977 driven by the Apollo program, with a focus on the impact melt rocks and other impactites, which are well exposed on the ring of islands. To our knowledge, the Clearwater Lake impact structures have not been the focus of detailed impact geology field investigations since the 1977 expedition and the only geological map that exists is from the 1960s and is at the reconnaissance level. Our knowledge of impact cratering processes have increased substantially since this time, as have the analytical techniques available for samples. This provided the motivation for a joint Canadian-US-UK expedition to the West Clearwater Lake impact structure in August and September 2015, under the auspices of the FINESSE (Field Investigations to Enable Solar System Science and Exploration) project, part of NASA's Solar System Exploration Research Virtual Institute (SSERVI). We focus here on the impactites of the West Clearwater Lake impact structure. Other ongoing studies, also presented at this conference, focus on central uplift formation, the impact-generated hydrothermal system, xxxx and using WCIS as an analog test site for crew studies of sampling protocols].

Scattering of an electronic wave packet by a one-dimensional electron-phonon-coupled structure

NASA Astrophysics Data System (ADS)

Brockt, C.; Jeckelmann, E.

2017-02-01

We investigate the scattering of an electron by phonons in a small structure between two one-dimensional tight-binding leads. This model mimics the quantum electron transport through atomic wires or molecular junctions coupled to metallic leads. The electron-phonon-coupled structure is represented by the Holstein model. We observe permanent energy transfer from the electron to the phonon system (dissipation), transient self-trapping of the electron in the electron-phonon-coupled structure (due to polaron formation and multiple reflections at the structure edges), and transmission resonances that depend strongly on the strength of the electron-phonon coupling and the adiabaticity ratio. A recently developed TEBD algorithm, optimized for bosonic degrees of freedom, is used to simulate the quantum dynamics of a wave packet launched against the electron-phonon-coupled structure. Exact results are calculated for a single electron-phonon site using scattering theory and analytical approximations are obtained for limiting cases.

An analytical technique for approximating unsteady aerodynamics in the time domain

NASA Technical Reports Server (NTRS)

Dunn, H. J.

1980-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2001-06-01

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

Mathematical modeling and statistical analysis of SPE-OCDMA systems utilizing second harmonic generation effect in thick crystal receivers

NASA Astrophysics Data System (ADS)

Matinfar, Mehdi D.; Salehi, Jawad A.

2009-11-01

In this paper we analytically study and evaluate the performance of a Spectral-Phase-Encoded Optical CDMA system for different parameters such as the user's code length and the number of users in the network. In this system an advanced receiver structure in which the Second Harmonic Generation effect imposed in a thick crystal is employed as the nonlinear pre-processor prior to the conventional low speed photodetector. We consider ASE noise of the optical amplifiers, effective in low power conditions, besides the multiple access interference (MAI) noise which is the dominant source of noise in any OCDMA communications system. We use the results of the previous work which we analyzed the statistical behavior of the thick crystals in an optically amplified digital lightwave communication system to evaluate the performance of the SPE-OCDMA system with thick crystals receiver structure. The error probability is evaluated using Saddle-Point approximation and the approximation is verified by Monte-Carlo simulation.

A ridge tracking algorithm and error estimate for efficient computation of Lagrangian coherent structures.

PubMed

Lipinski, Doug; Mohseni, Kamran

2010-03-01

A ridge tracking algorithm for the computation and extraction of Lagrangian coherent structures (LCS) is developed. This algorithm takes advantage of the spatial coherence of LCS by tracking the ridges which form LCS to avoid unnecessary computations away from the ridges. We also make use of the temporal coherence of LCS by approximating the time dependent motion of the LCS with passive tracer particles. To justify this approximation, we provide an estimate of the difference between the motion of the LCS and that of tracer particles which begin on the LCS. In addition to the speedup in computational time, the ridge tracking algorithm uses less memory and results in smaller output files than the standard LCS algorithm. Finally, we apply our ridge tracking algorithm to two test cases, an analytically defined double gyre as well as the more complicated example of the numerical simulation of a swimming jellyfish. In our test cases, we find up to a 35 times speedup when compared with the standard LCS algorithm.

A kinetic Monte Carlo approach to diffusion-controlled thermal desorption spectroscopy

NASA Astrophysics Data System (ADS)

Schablitzki, T.; Rogal, J.; Drautz, R.

2017-06-01

Atomistic simulations of thermal desorption spectra for effusion from bulk materials to characterize binding or trapping sites are a challenging task as large system sizes as well as extended time scales are required. Here, we introduce an approach where we combine kinetic Monte Carlo with an analytic approximation of the superbasins within the framework of absorbing Markov chains. We apply our approach to the effusion of hydrogen from BCC iron, where the diffusion within bulk grains is coarse grained using absorbing Markov chains, which provide an exact solution of the dynamics within a superbasin. Our analytic approximation to the superbasin is transferable with respect to grain size and elliptical shapes and can be applied in simulations with constant temperature as well as constant heating rate. The resulting thermal desorption spectra are in close agreement with direct kinetic Monte Carlo simulations, but the calculations are computationally much more efficient. Our approach is thus applicable to much larger system sizes and provides a first step towards an atomistic understanding of the influence of structural features on the position and shape of peaks in thermal desorption spectra. This article is part of the themed issue 'The challenges of hydrogen and metals'.

An analytic performance model of disk arrays and its application

NASA Technical Reports Server (NTRS)

Lee, Edward K.; Katz, Randy H.

1991-01-01

As disk arrays become widely used, tools for understanding and analyzing their performance become increasingly important. In particular, performance models can be invaluable in both configuring and designing disk arrays. Accurate analytic performance models are desirable over other types of models because they can be quickly evaluated, are applicable under a wide range of system and workload parameters, and can be manipulated by a range of mathematical techniques. Unfortunately, analytical performance models of disk arrays are difficult to formulate due to the presence of queuing and fork-join synchronization; a disk array request is broken up into independent disk requests which must all complete to satisfy the original request. We develop, validate, and apply an analytic performance model for disk arrays. We derive simple equations for approximating their utilization, response time, and throughput. We then validate the analytic model via simulation and investigate the accuracy of each approximation used in deriving the analytical model. Finally, we apply the analytical model to derive an equation for the optimal unit of data striping in disk arrays.

On the Gibbs phenomenon 5: Recovering exponential accuracy from collocation point values of a piecewise analytic function

NASA Technical Reports Server (NTRS)

Gottlieb, David; Shu, Chi-Wang

1994-01-01

The paper presents a method to recover exponential accuracy at all points (including at the discontinuities themselves), from the knowledge of an approximation to the interpolation polynomial (or trigonometrical polynomial). We show that if we are given the collocation point values (or a highly accurate approximation) at the Gauss or Gauss-Lobatto points, we can reconstruct a uniform exponentially convergent approximation to the function f(x) in any sub-interval of analyticity. The proof covers the cases of Fourier, Chebyshev, Legendre, and more general Gegenbauer collocation methods.

Efficient time-dependent density functional theory approximations for hybrid density functionals: analytical gradients and parallelization.

PubMed

Petrenko, Taras; Kossmann, Simone; Neese, Frank

2011-02-07

In this paper, we present the implementation of efficient approximations to time-dependent density functional theory (TDDFT) within the Tamm-Dancoff approximation (TDA) for hybrid density functionals. For the calculation of the TDDFT/TDA excitation energies and analytical gradients, we combine the resolution of identity (RI-J) algorithm for the computation of the Coulomb terms and the recently introduced "chain of spheres exchange" (COSX) algorithm for the calculation of the exchange terms. It is shown that for extended basis sets, the RIJCOSX approximation leads to speedups of up to 2 orders of magnitude compared to traditional methods, as demonstrated for hydrocarbon chains. The accuracy of the adiabatic transition energies, excited state structures, and vibrational frequencies is assessed on a set of 27 excited states for 25 molecules with the configuration interaction singles and hybrid TDDFT/TDA methods using various basis sets. Compared to the canonical values, the typical error in transition energies is of the order of 0.01 eV. Similar to the ground-state results, excited state equilibrium geometries differ by less than 0.3 pm in the bond distances and 0.5° in the bond angles from the canonical values. The typical error in the calculated excited state normal coordinate displacements is of the order of 0.01, and relative error in the calculated excited state vibrational frequencies is less than 1%. The errors introduced by the RIJCOSX approximation are, thus, insignificant compared to the errors related to the approximate nature of the TDDFT methods and basis set truncation. For TDDFT/TDA energy and gradient calculations on Ag-TB2-helicate (156 atoms, 2732 basis functions), it is demonstrated that the COSX algorithm parallelizes almost perfectly (speedup ~26-29 for 30 processors). The exchange-correlation terms also parallelize well (speedup ~27-29 for 30 processors). The solution of the Z-vector equations shows a speedup of ~24 on 30 processors. The parallelization efficiency for the Coulomb terms can be somewhat smaller (speedup ~15-25 for 30 processors), but their contribution to the total calculation time is small. Thus, the parallel program completes a Becke3-Lee-Yang-Parr energy and gradient calculation on the Ag-TB2-helicate in less than 4 h on 30 processors. We also present the necessary extension of the Lagrangian formalism, which enables the calculation of the TDDFT excited state properties in the frozen-core approximation. The algorithms described in this work are implemented into the ORCA electronic structure system.

Analytical Studies of Boundary Layer Generated Aircraft Interior Noise

NASA Technical Reports Server (NTRS)

Howe, M. S.; Shah, P. L.

1997-01-01

An analysis is made of the "interior noise" produced by high, subsonic turbulent flow over a thin elastic plate partitioned into "panels" by straight edges transverse to the mean flow direction. This configuration models a section of an aircraft fuselage that may be regarded as locally flat. The analytical problem can be solved in closed form to represent the acoustic radiation in terms of prescribed turbulent boundary layer pressure fluctuations. Two cases are considered: (i) the production of sound at an isolated panel edge (i.e., in the approximation in which the correlation between sound and vibrations generated at neighboring edges is neglected), and (ii) the sound generated by a periodic arrangement of identical panels. The latter problem is amenable to exact analytical treatment provided the panel edge conditions are the same for all panels. Detailed predictions of the interior noise depend on a knowledge of the turbulent boundary layer wall pressure spectrum, and are given here in terms of an empirical spectrum proposed by Laganelli and Wolfe. It is expected that these analytical representations of the sound generated by simplified models of fluid-structure interactions can used to validate more general numerical schemes.

The effect of massive neutrinos on the BAO peak

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

Peloso, Marco; Pietroni, Massimo; Viel, Matteo

2015-07-01

We study the impact of neutrino masses on the shape and height of the BAO peak of the matter correlation function, both in real and redshift space. In order to describe the nonlinear evolution of the BAO peak we run N-body simulations and compare them with simple analytic formulae. We show that the evolution with redshift of the correlation function and its dependence on the neutrino masses is well reproduced in a simplified version of the Zel'dovich approximation, in which the mode-coupling contribution to the power spectrum is neglected. While in linear theory the BAO peak decreases for increasing neutrinomore » masses, the effect of nonlinear structure formation goes in the opposite direction, since the peak broadening by large scale flows is less effective. As a result of this combined effect, the peak decreases by ∼ 0.6 % for  ∑ m{sub ν} = 0.15 eV and increases by ∼1.2% for  ∑ m{sub ν} = 0.3 eV, with respect to a massless neutrino cosmology with equal value of the other cosmological parameters. We extend our analysis to redshift space and to halos, and confirm the agreement between simulations and the analytic formulae. We argue that all analytical approaches having the Zel'dovich propagator in their lowest order approximation should give comparable performances, irrespectively to their formulation in Lagrangian or in Eulerian space.« less

Analogue solution for electrical capacity of membrane covered square cylinders in square array at high concentration.

PubMed

Cole, K S

1975-12-01

Analytical solutions of Laplace equations have given the electrical characteristics of membranes and interiors of spherical, ellipsoidal, and cylindrical cells in suspensions and tissues from impedance measurements, but the underlying assumptions may be invalid above 50% volume concentrations. However, resistance measurements on several nonconducting, close-packing forms in two and three dimensions closely predicted volume concentrations up to 100% by equations derived from Maxwell and Rayleigh. Calculations of membrane capacities of cells in suspensions and tissues from extensions of theory, as developed by Fricke and by Cole, have been useful but of unknown validity at high concentrations. A resistor analogue has been used to solve the finite difference approximation to the Laplace equation for the resistance and capacity of a square array of square cylindrical cells with surface capacity. An 11 x 11 array of resistors, simulating a quarter of the unit structure, was separated into intra- and extra-cellular regions by rows of capacitors corresponding to surface membrane areas from 3 x 3 to 11 x 11 or 7.5% to 100%. The extended Rayleigh equation predicted the cell concentrations and membrane capacities to within a few percent from boundary resistance and capacity measurements at low frequencies. This single example suggests that analytical solutions for other, similar two- and three-dimensional problems may be approximated up to near 100% concentrations and that there may be analytical justifications for such analogue solutions of Laplace equations.

Definition of ground test for verification of large space structure control

NASA Technical Reports Server (NTRS)

Seltzer, S. M.; Doane, G. B., III

1985-01-01

Directions regarding the analytical models were received. A counter balance arm with weights was added at the top of the ASTROMAST to offset the arm with the gimbals. In addition to this model, three more models were requested from MSFC: structure as in the revised model with the addition of lumped masses at bays 46 and 91 of the ASTROMAST; cantilevered cruciform structure with lumped masses at bays 46 and 91, and an all up cruciform structure with lumped masses at bays 46 and 91. Figures for each model and their corresponding natural frequencies and general mode shapes associated with these frequencies are included. The drawbar in use in the cruciform models must be incorporated into the antenna and ASTROMAST models. The total tensile load carrying capability of the ASTROMAST is approximately 840 pounds.

Excitation, response, and fatigue life estimation methods for the structural design of externally blown flaps

NASA Technical Reports Server (NTRS)

Ungar, E. E.; Chandiramani, K. L.; Barger, J. E.

1972-01-01

Means for predicting the fluctuating pressures acting on externally blown flap surfaces are developed on the basis of generalizations derived from non-dimensionalized empirical data. Approaches for estimation of the fatigue lives of skin-stringer and honeycomb-core sandwich flap structures are derived from vibration response analyses and panel fatigue data. Approximate expressions for fluctuating pressures, structural response, and fatigue life are combined to reveal the important parametric dependences. The two-dimensional equations of motion of multi-element flap systems are derived in general form, so that they can be specialized readily for any particular system. An introduction is presented of an approach to characterizing the excitation pressures and structural responses which makes use of space-time spectral concepts and promises to provide useful insights, as well as experimental and analytical savings.

On the evolution of perturbations to solutions of the Kadomtsev-Petviashvilli equation using the Benney-Luke equation

NASA Astrophysics Data System (ADS)

Ablowitz, Mark J.; Curtis, Christopher W.

2011-05-01

The Benney-Luke equation, which arises as a long wave asymptotic approximation of water waves, contains the Kadomtsev-Petviashvilli (KP) equation as a leading-order maximal balanced approximation. The question analyzed is how the Benney-Luke equation modifies the so-called web solutions of the KP equation. It is found that the Benney-Luke equation introduces dispersive radiation which breaks each of the symmetric soliton-like humps well away from the interaction region of the KP web solution into a tail of multi-peaked oscillating profiles behind the main solitary hump. Computation indicates that the wave structure is modified near the center of the interaction region. Both analytical and numerical techniques are employed for working with non-periodic, non-decaying solutions on unbounded domains.

Method and apparatus for ion sequestration and a nanostructured metal phosphate

DOEpatents

Mattigod, Shas V [Richland, WA; Fryxell, Glen E [Kennewic, WA; Li, Xiaohong [Richland, WA; Parker, Kent E [Kennewick, WA; Wellman, Dawn M [West Richland, WA

2010-04-06

A nanostructured substance, a process for sequestration of ionic waste, and an ion-sequestration apparatus are disclosed in the specification. The nanostructured substance can comprise a Lewis acid transition metal bound to a phosphate, wherein the phosphate comprises a primary structural component of the substance and the Lewis acid transition metal is a reducing agent. The nanostructured substance has a Brunner-Emmet-Teller (BET) surface area greater than or equal to approximately 100 m.sup.2/g, and a distribution coefficient for an analyte, K.sub.d, greater than or equal to approximately 5000 ml/g. The process can comprise contacting a fluid and a nanostructured metal phosphate. The apparatus can comprise a vessel and a nanostructured metal phosphate. The vessel defines a volume wherein a fluid contacts the nanostructured metal phosphate.

The analysis of solutions behaviour of Van der Pol Duffing equation describing local brain hemodynamics

NASA Astrophysics Data System (ADS)

Cherevko, A. A.; Bord, E. E.; Khe, A. K.; Panarin, V. A.; Orlov, K. J.

2017-10-01

This article proposes the generalized model of Van der Pol — Duffing equation for describing the relaxation oscillations in local brain hemodynamics. This equation connects the velocity and pressure of blood flow in cerebral vessels. The equation is individual for each patient, since the coefficients are unique. Each set of coefficients is built based on clinical data obtained during neurosurgical operation in Siberian Federal Biomedical Research Center named after Academician E. N. Meshalkin. The equation has solutions of different structure defined by the coefficients and right side. We investigate the equations for different patients considering peculiarities of their vessel systems. The properties of approximate analytical solutions are studied. Amplitude-frequency and phase-frequency characteristics are built for the small-dimensional solution approximations.

Superexchange and spin-glass formation in semimagnetic semiconductors

NASA Astrophysics Data System (ADS)

Rusin, Tomasz M.

1996-05-01

The Mn-Mn superexchange interaction in semimagnetic semiconductors A1-xMnxB (where A=Zn, Cd and B=S, Se, Te) is studied within the three-level model of the band structure. We focus on the dependence of the interaction on the interion distance Jdd(r)=J0f(r). In the present work, the function f(r) is obtained analytically. This, only weakly material-dependent function is found to decrease with Mn-Mn distance much slower than its Gaussian approximation derived previously. The exact form of the decay of the superexchange can be approximated by a power law J0r-8.5. This is close to an experimental result, J0r-6.8, determined on the basis of the spin-glass transition temperature on the composition.

Flow and Transport in Highly Heterogeneous Porous Formations: Numerical Experiments Performed Using the Analytic Element Method

NASA Astrophysics Data System (ADS)

Jankovic, I.

2002-05-01

Flow and transport in porous formations are analyzed using numerical simulations. Hydraulic conductivity is treated as a spatial random function characterized by a probability density function and a two-point covariance function. Simulations are performed for a multi-indicator conductivity structure developed by Gedeon Dagan (personal communication). This conductivity structure contains inhomogeneities (inclusions) of elliptical and ellipsoidal geometry that are embedded in a homogeneous background. By varying the distribution of sizes and conductivities of inclusions, any probability density function and two-point covariance may be reproduced. The multi-indicator structure is selected since it yields simple approximate transport solutions (Aldo Fiori, personal communication) and accurate numerical solutions (based on the Analytic Element Method). The dispersion is examined for two conceptual models. Both models are based on the multi-indicator conductivity structure. The first model is designed to examine dispersion in aquifers with continuously varying conductivity. The inclusions in this model cover as much area/volume of the porous formation as possible. The second model is designed for aquifers that contain clay/sand/gravel lenses embedded in otherwise homogeneous background. The dispersion in both aquifer types is simulated numerically. Simulation results are compared to those obtained using simple approximate solutions. In order to infer transport statistics that are representative of an infinite domain using the numerical experiments, the inclusions are placed in a domain that was shaped as a large ellipse (2D) and a large spheroid (3D) that were submerged in an unbounded homogeneous medium. On a large scale, the large body of inclusions behaves like a single large inhomogeneity. The analytic solution for a uniform flow past the single inhomogeneity of such geometry yields uniform velocity inside the domain. The velocity differs from that at infinity and can be used to infer the effective conductivity of the medium. As many as 100,000 inhomogeneities are placed inside the domain for 2D simulations. Simulations in 3D were limited to 50,000 inclusions. A large number of simulations was conducted on a massively parallel supercomputer cluster at the Center for Computational Research, University at Buffalo. Simulations range from mildly heterogeneous formations to highly heterogeneous formations (variance of the logarithm of conductivity equal to 10) and from sparsely populated systems to systems where inhomogeneities cover 95% of the volume. Particles are released and tracked inside the core of constant mean velocity. Following the particle tracking, various medium, flow, and transport statistics are computed. These include: spatial moments of particle positions, probability density function of hydraulic conductivity and each component of velocity, their two-point covariance function in the direction of flow and normal to it, covariance of Lagrangean velocities, and probability density function of travel times to various break-through locations. Following the analytic nature of the flow solution, all the results are presented in dimensionless forms. For example, the dispersion coefficients are made dimensionless with respect to the mean velocity and size of inhomogeneities. Detailed results will be presented and compared to well known first-order results and the results that are based on simple approximate transport solutions of Aldo Fiori.

A semi-analytical study of positive corona discharge in wire-plane electrode configuration

NASA Astrophysics Data System (ADS)

Yanallah, K.; Pontiga, F.; Chen, J. H.

2013-08-01

Wire-to-plane positive corona discharge in air has been studied using an analytical model of two species (electrons and positive ions). The spatial distributions of electric field and charged species are obtained by integrating Gauss's law and the continuity equations of species along the Laplacian field lines. The experimental values of corona current intensity and applied voltage, together with Warburg's law, have been used to formulate the boundary condition for the electron density on the corona wire. To test the accuracy of the model, the approximate electric field distribution has been compared with the exact numerical solution obtained from a finite element analysis. A parametrical study of wire-to-plane corona discharge has then been undertaken using the approximate semi-analytical solutions. Thus, the spatial distributions of electric field and charged particles have been computed for different values of the gas pressure, wire radius and electrode separation. Also, the two dimensional distribution of ozone density has been obtained using a simplified plasma chemistry model. The approximate semi-analytical solutions can be evaluated in a negligible computational time, yet provide precise estimates of corona discharge variables.

The relationship between multilevel models and non-parametric multilevel mixture models: Discrete approximation of intraclass correlation, random coefficient distributions, and residual heteroscedasticity.

PubMed

Rights, Jason D; Sterba, Sonya K

2016-11-01

Multilevel data structures are common in the social sciences. Often, such nested data are analysed with multilevel models (MLMs) in which heterogeneity between clusters is modelled by continuously distributed random intercepts and/or slopes. Alternatively, the non-parametric multilevel regression mixture model (NPMM) can accommodate the same nested data structures through discrete latent class variation. The purpose of this article is to delineate analytic relationships between NPMM and MLM parameters that are useful for understanding the indirect interpretation of the NPMM as a non-parametric approximation of the MLM, with relaxed distributional assumptions. We define how seven standard and non-standard MLM specifications can be indirectly approximated by particular NPMM specifications. We provide formulas showing how the NPMM can serve as an approximation of the MLM in terms of intraclass correlation, random coefficient means and (co)variances, heteroscedasticity of residuals at level 1, and heteroscedasticity of residuals at level 2. Further, we discuss how these relationships can be useful in practice. The specific relationships are illustrated with simulated graphical demonstrations, and direct and indirect interpretations of NPMM classes are contrasted. We provide an R function to aid in implementing and visualizing an indirect interpretation of NPMM classes. An empirical example is presented and future directions are discussed. © 2016 The British Psychological Society.

Observations and analysis of self-similar branching topology in glacier networks

USGS Publications Warehouse

Bahr, D.B.; Peckham, S.D.

1996-01-01

Glaciers, like rivers, have a branching structure which can be characterized by topological trees or networks. Probability distributions of various topological quantities in the networks are shown to satisfy the criterion for self-similarity, a symmetry structure which might be used to simplify future models of glacier dynamics. Two analytical methods of describing river networks, Shreve's random topology model and deterministic self-similar trees, are applied to the six glaciers of south central Alaska studied in this analysis. Self-similar trees capture the topological behavior observed for all of the glaciers, and most of the networks are also reasonably approximated by Shreve's theory. Copyright 1996 by the American Geophysical Union.

Shape determination and control for large space structures

NASA Technical Reports Server (NTRS)

Weeks, C. J.

1981-01-01

An integral operator approach is used to derive solutions to static shape determination and control problems associated with large space structures. Problem assumptions include a linear self-adjoint system model, observations and control forces at discrete points, and performance criteria for the comparison of estimates or control forms. Results are illustrated by simulations in the one dimensional case with a flexible beam model, and in the multidimensional case with a finite model of a large space antenna. Modal expansions for terms in the solution algorithms are presented, using modes from the static or associated dynamic mode. These expansions provide approximated solutions in the event that a used form analytical solution to the system boundary value problem is not available.

Vibration studies of a lightweight three-sided membrane suitable for space application

NASA Technical Reports Server (NTRS)

Sewell, J. L.; Miserentino, R.; Pappa, R. S.

1983-01-01

Vibration studies carried out in a vacuum chamber are reported for a three-sided membrane with inwardly curved edges. Uniform tension was transmitted by thin steel cables encased in the edges. Variation of ambient air pressure from atmospheric to near vacuum resulted in increased response frequencies and amplitudes. The first few vibration modes measured in a near vacuum are shown to be predictable by a finite element structural analysis over a range of applied tension loads. The complicated vibration mode behavior observed during tests at various air pressures is studied analytically with a nonstructural effective air-mass approximation. The membrane structure is a candidate for reflective surfaces in space antennas.

A finite element study of the EIDI system. [Electro-Impulse De-Icing System

NASA Technical Reports Server (NTRS)

Khatkhate, A. A.; Scavuzzo, R. J.; Chu, M. L.

1988-01-01

This paper presents a method for modeling the structural dynamics of an Electro-Impulse De-Icing System, using finite element analyses procedures. A guideline for building a representative finite element model is discussed. Modeling was done initially using four noded cubic elements, four noded isoparametric plate elements and eight noded isoparametric shell elements. Due to the size of the problem and due to the underestimation of shear stress results when compared to previous analytical work an approximate model was created to predict possible areas of shedding of ice. There appears to be good agreement with the test data provided by The Boeing Commercial Airplane Company. Thus these initial results of this method were found to be encouraging. Additional analytical work and comparison with experiment is needed in order to completely evaluate this approach.

Variational Gaussian approximation for Poisson data

NASA Astrophysics Data System (ADS)

Arridge, Simon R.; Ito, Kazufumi; Jin, Bangti; Zhang, Chen

2018-02-01

The Poisson model is frequently employed to describe count data, but in a Bayesian context it leads to an analytically intractable posterior probability distribution. In this work, we analyze a variational Gaussian approximation to the posterior distribution arising from the Poisson model with a Gaussian prior. This is achieved by seeking an optimal Gaussian distribution minimizing the Kullback-Leibler divergence from the posterior distribution to the approximation, or equivalently maximizing the lower bound for the model evidence. We derive an explicit expression for the lower bound, and show the existence and uniqueness of the optimal Gaussian approximation. The lower bound functional can be viewed as a variant of classical Tikhonov regularization that penalizes also the covariance. Then we develop an efficient alternating direction maximization algorithm for solving the optimization problem, and analyze its convergence. We discuss strategies for reducing the computational complexity via low rank structure of the forward operator and the sparsity of the covariance. Further, as an application of the lower bound, we discuss hierarchical Bayesian modeling for selecting the hyperparameter in the prior distribution, and propose a monotonically convergent algorithm for determining the hyperparameter. We present extensive numerical experiments to illustrate the Gaussian approximation and the algorithms.

The exact solutions and approximate analytic solutions of the (2 + 1)-dimensional KP equation based on symmetry method.

PubMed

Gai, Litao; Bilige, Sudao; Jie, Yingmo

2016-01-01

In this paper, we successfully obtained the exact solutions and the approximate analytic solutions of the (2 + 1)-dimensional KP equation based on the Lie symmetry, the extended tanh method and the homotopy perturbation method. In first part, we obtained the symmetries of the (2 + 1)-dimensional KP equation based on the Wu-differential characteristic set algorithm and reduced it. In the second part, we constructed the abundant exact travelling wave solutions by using the extended tanh method. These solutions are expressed by the hyperbolic functions, the trigonometric functions and the rational functions respectively. It should be noted that when the parameters are taken as special values, some solitary wave solutions are derived from the hyperbolic function solutions. Finally, we apply the homotopy perturbation method to obtain the approximate analytic solutions based on four kinds of initial conditions.

Analytical mass formula and nuclear surface properties in the ETF approximation. Part II: asymmetric nuclei

NASA Astrophysics Data System (ADS)

Aymard, François; Gulminelli, Francesca; Margueron, Jérôme

2016-08-01

We have recently addressed the problem of the determination of the nuclear surface energy for symmetric nuclei in the framework of the extended Thomas-Fermi (ETF) approximation using Skyrme functionals. We presently extend this formalism to the case of asymmetric nuclei and the question of the surface symmetry energy. We propose an approximate expression for the diffuseness and the surface energy. These quantities are analytically related to the parameters of the energy functional. In particular, the influence of the different equation of state parameters can be explicitly quantified. Detailed analyses of the different energy components (local/non-local, isoscalar/isovector, surface/curvature and higher order) are also performed. Our analytical solution of the ETF integral improves previous models and leads to a precision of better than 200 keV per nucleon in the determination of the nuclear binding energy for dripline nuclei.

Analytical approximations to the dynamics of an array of coupled DC SQUIDs

NASA Astrophysics Data System (ADS)

Berggren, Susan; Palacios, Antonio

2014-04-01

Coupled dynamical systems that operate near the onset of a bifurcation can lead, under certain conditions, to strong signal amplification effects. Over the past years we have studied this generic feature on a wide range of systems, including: magnetic and electric fields sensors, gyroscopic devices, and arrays of loops of superconducting quantum interference devices, also known as SQUIDs. In this work, we consider an array of SQUID loops connected in series as a case study to derive asymptotic analytical approximations to the exact solutions through perturbation analysis. Two approaches are considered. First, a straightforward expansion in which the non-linear parameter related to the inductance of the DC SQUID is treated as the small perturbation parameter. Second, a more accurate procedure that considers the SQUID phase dynamics as non-uniform motion on a circle. This second procedure is readily extended to the series array and it could serve as a mathematical framework to find approximate solutions to related complex systems with high-dimensionality. To the best of our knowledge, an approximate analytical solutions to an array of SQUIDs has not been reported yet in the literature.

Nuclear magnetic resonance signal dynamics of liquids in the presence of distant dipolar fields, revisited

PubMed Central

Barros, Wilson; Gochberg, Daniel F.; Gore, John C.

2009-01-01

The description of the nuclear magnetic resonance magnetization dynamics in the presence of long-range dipolar interactions, which is based upon approximate solutions of Bloch–Torrey equations including the effect of a distant dipolar field, has been revisited. New experiments show that approximate analytic solutions have a broader regime of validity as well as dependencies on pulse-sequence parameters that seem to have been overlooked. In order to explain these experimental results, we developed a new method consisting of calculating the magnetization via an iterative formalism where both diffusion and distant dipolar field contributions are treated as integral operators incorporated into the Bloch–Torrey equations. The solution can be organized as a perturbative series, whereby access to higher order terms allows one to set better boundaries on validity regimes for analytic first-order approximations. Finally, the method legitimizes the use of simple analytic first-order approximations under less demanding experimental conditions, it predicts new pulse-sequence parameter dependencies for the range of validity, and clarifies weak points in previous calculations. PMID:19425789

Recent activities within the Aeroservoelasticity Branch at the NASA Langley Research Center

NASA Technical Reports Server (NTRS)

Noll, Thomas E.; Perry, Boyd, III; Gilbert, Michael G.

1989-01-01

The objective of research in aeroservoelasticity at the NASA Langley Research Center is to enhance the modeling, analysis, and multidisciplinary design methodologies for obtaining multifunction digital control systems for application to flexible flight vehicles. Recent accomplishments are discussed, and a status report on current activities within the Aeroservoelasticity Branch is presented. In the area of modeling, improvements to the Minimum-State Method of approximating unsteady aerodynamics are shown to provide precise, low-order aeroservoelastic models for design and simulation activities. Analytical methods based on Matched Filter Theory and Random Process Theory to provide efficient and direct predictions of the critical gust profile and the time-correlated gust loads for linear structural design considerations are also discussed. Two research projects leading towards improved design methodology are summarized. The first program is developing an integrated structure/control design capability based on hierarchical problem decomposition, multilevel optimization and analytical sensitivities. The second program provides procedures for obtaining low-order, robust digital control laws for aeroelastic applications. In terms of methodology validation and application the current activities associated with the Active Flexible Wing project are reviewed.

Heat and mass transfer in combustion - Fundamental concepts and analytical techniques

NASA Technical Reports Server (NTRS)

Law, C. K.

1984-01-01

Fundamental combustion phenomena and the associated flame structures in laminar gaseous flows are discussed on physical bases within the framework of the three nondimensional parameters of interest to heat and mass transfer in chemically-reacting flows, namely the Damkoehler number, the Lewis number, and the Arrhenius number which is the ratio of the reaction activation energy to the characteristic thermal energy. The model problems selected for illustration are droplet combustion, boundary layer combustion, and the propagation, flammability, and stability of premixed flames. Fundamental concepts discussed include the flame structures for large activation energy reactions, S-curve interpretation of the ignition and extinctin states, reaction-induced local-similarity and non-similarity in boundary layer flows, the origin and removal of the cold boundary difficulty in modeling flame propagation, and effects of flame stretch and preferential diffusion on flame extinction and stability. Analytical techniques introduced include the Shvab-Zeldovich formulation, the local Shvab-Zeldovich formulation, flame-sheet approximation and the associated jump formulation, and large activation energy matched asymptotic analysis. Potentially promising research areas are suggested.

Transition From Ideal To Viscous Mach Cones In A Partonic Transport Model

NASA Astrophysics Data System (ADS)

Bouras, I.; El, A.; Fochler, O.; Niemi, H.; Xu, Z.; Greiner, C.

2013-09-01

Using a partonic transport model we investigate the evolution of conical structures in ultrarelativistic matter. Using two different source terms and varying the transport properties of the matter we study the formation of Mach Cones. Furthermore, in an additional study we extract the two-particle correlations from the numerical calculations and compare them to an analytical approximation. The influence of the viscosity to the shape of Mach Cones and the corresponding two-particle correlations is studied by adjusting the cross section of the medium.

Elastic model for crimped collagen fibrils

NASA Technical Reports Server (NTRS)

Freed, Alan D.; Doehring, Todd C.

2005-01-01

A physiologic constitutive expression is presented in algorithmic format for the nonlinear elastic response of wavy collagen fibrils found in soft connective tissues. The model is based on the observation that crimped fibrils in a fascicle have a three-dimensional structure at the micron scale that we approximate as a helical spring. The symmetry of this wave form allows the force/displacement relationship derived from Castigliano's theorem to be solved in closed form: all integrals become analytic. Model predictions are in good agreement with experimental observations for mitral-valve chordae tendinece.

Another self-similar blast wave: Early time asymptote with shock heated electrons and high thermal conductivity

NASA Technical Reports Server (NTRS)

Cox, D. P.; Edgar, R. J.

1982-01-01

Accurate approximations are presented for the self-similar structures of nonradiating blast waves with adiabatic ions, isothermal electrons, and equation ion and electron temperatures at the shock. The cases considered evolve in cavities with power law ambient densities (including the uniform density case) and have negligible external pressure. The results provide the early time asymptote for systems with shock heating of electrons and strong thermal conduction. In addition, they provide analytical results against which two fluid numerical hydrodynamic codes can be checked.

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

NASA Astrophysics Data System (ADS)

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

2017-02-01

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

Characterizing traveling-wave collisions in granular chains starting from integrable limits: the case of the Korteweg-de Vries equation and the Toda lattice.

PubMed

Shen, Y; Kevrekidis, P G; Sen, S; Hoffman, A

2014-08-01

Our aim in the present work is to develop approximations for the collisional dynamics of traveling waves in the context of granular chains in the presence of precompression. To that effect, we aim to quantify approximations of the relevant Hertzian FPU-type lattice through both the Korteweg-de Vries (KdV) equation and the Toda lattice. Using the availability in such settings of both one-soliton and two-soliton solutions in explicit analytical form, we initialize such coherent structures in the granular chain and observe the proximity of the resulting evolution to the underlying integrable (KdV or Toda) model. While the KdV offers the possibility to accurately capture collisions of solitary waves propagating in the same direction, the Toda lattice enables capturing both copropagating and counterpropagating soliton collisions. The error in the approximation is quantified numerically and connections to bounds established in the mathematical literature are also given.

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

NASA Astrophysics Data System (ADS)

Cummings, Patrick

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

Optimization of Turbine Engine Cycle Analysis with Analytic Derivatives

NASA Technical Reports Server (NTRS)

Hearn, Tristan; Hendricks, Eric; Chin, Jeffrey; Gray, Justin; Moore, Kenneth T.

2016-01-01

A new engine cycle analysis tool, called Pycycle, was built using the OpenMDAO framework. Pycycle provides analytic derivatives allowing for an efficient use of gradient-based optimization methods on engine cycle models, without requiring the use of finite difference derivative approximation methods. To demonstrate this, a gradient-based design optimization was performed on a turbofan engine model. Results demonstrate very favorable performance compared to an optimization of an identical model using finite-difference approximated derivatives.

Spacing of bending-induced fractures at saturation: Numerical models and approximate analytical solution

NASA Astrophysics Data System (ADS)

Schöpfer, Martin; Lehner, Florian; Grasemann, Bernhard; Kaserer, Klemens; Hinsch, Ralph

2017-04-01

John G. Ramsay's sketch of structures developed in a layer progressively folded and deformed by tangential longitudinal strain (Figure 7-65 in Folding and Fracturing of Rocks) and the associated strain pattern analysis have been reproduced in many monographs on Structural Geology and are referred to in numerous publications. Although the origin of outer-arc extension fractures is well-understood and documented in many natural examples, geomechanical factors controlling their (finite or saturation) spacing are hitherto unexplored. This study investigates the formation of bending-induced fractures during constant-curvature forced folding using Distinct Element Method (DEM) numerical modelling. The DEM model comprises a central brittle layer embedded within weaker (low modulus) elastic layers; the layer interfaces are frictionless (free slip). Folding of this three-layer system is enforced by a velocity boundary condition at the model base, while a constant overburden pressure is maintained at the model top. The models illustrate several key stages of fracture array development: (i) Prior to the onset of fracture, the neutral surface is located midway between the layer boundaries; (ii) A first set of regularly spaced fractures develops once the tensile stress in the outer-arc equals the tensile strength of the layer. Since the layer boundaries are frictionless, these bending-induced fractures propagate through the entire layer; (iii) After the appearance of the first fracture set, the rate of fracture formation decreases rapidly and so-called infill fractures develop approximately midway between two existing fractures (sequential infilling); (iv) Eventually no new fractures form, irrespective of any further increase in fold curvature (fracture saturation). Analysis of the interfacial normal stress distributions suggests that at saturation the fracture-bound blocks are subjected to a loading condition similar to three-point bending. Using classical beam theory an analytical solution is derived for the critical fracture spacing, i.e. the spacing below which the maximum tensile stress cannot reach the layer strength. The model results are consistent with an approximate analytical solution, and illustrate that the spacing of bending-induced fractures is proportional to layer thickness and a square root function of the ratio of layer tensile strength to confining pressure. Although highly idealised, models and analysis presented in this study offer an explanation for fracture saturation during folding and point towards certain key factors that may control fracture spacing in natural systems.

Three-dimensional structures of equatorial waves and the resulting super-rotation in the atmosphere of a tidally locked hot Jupiter

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

Tsai, Shang-Min; Gu, Pin-Gao; Dobbs-Dixon, Ian

Three-dimensional (3D) equatorial trapped waves excited by stellar isolation and the resulting equatorial super-rotating jet in a vertical stratified atmosphere of a tidally locked hot Jupiter are investigated. Taking the hot Jupiter HD 189733b as a fiducial example, we analytically solve linear equations subject to stationary stellar heating with a uniform zonal-mean flow included. We also extract wave information in the final equilibrium state of the atmosphere from our radiative hydrodynamical simulation for HD 189733b. Our analytic wave solutions are able to qualitatively explain the 3D simulation results. Apart from previous wave studies, investigating the vertical structure of waves allowsmore » us to explore new wave features such as the wavefronts tilts related to the Rossby-wave resonance as well as dispersive equatorial waves. We also attempt to apply our linear wave analysis to explain some numerical features associated with the equatorial jet development seen in the general circulation model by Showman and Polvani. During the spin-up phase of the equatorial jet, the acceleration of the jet can be in principle boosted by the Rossby-wave resonance. However, we also find that as the jet speed increases, the Rossby-wave structure shifts eastward, while the Kelvin-wave structure remains approximately stationary, leading to the decline of the acceleration rate. Our analytic model of jet evolution implies that there exists only one stable equilibrium state of the atmosphere, possibly implying that the final state of the atmosphere is independent of initial conditions in the linear regime. Limitations of our linear model and future improvements are also discussed.« less

Stabilizing potentials in bound state analytic continuation methods for electronic resonances in polyatomic molecules

DOE PAGES

White, Alec F.; Head-Gordon, Martin; McCurdy, C. William

2017-01-30

The computation of Siegert energies by analytic continuation of bound state energies has recently been applied to shape resonances in polyatomic molecules by several authors. Here, we critically evaluate a recently proposed analytic continuation method based on low order (type III) Padé approximants as well as an analytic continuation method based on high order (type II) Padé approximants. We compare three classes of stabilizing potentials: Coulomb potentials, Gaussian potentials, and attenuated Coulomb potentials. These methods are applied to a model potential where the correct answer is known exactly and to the 2Π g shape resonance of N 2 - whichmore » has been studied extensively by other methods. Both the choice of stabilizing potential and method of analytic continuation prove to be important to the accuracy of the results. We then conclude that an attenuated Coulomb potential is the most effective of the three for bound state analytic continuation methods. With the proper potential, such methods show promise for algorithmic determination of the positions and widths of molecular shape resonances.« less

Stabilizing potentials in bound state analytic continuation methods for electronic resonances in polyatomic molecules

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

White, Alec F.; Head-Gordon, Martin; McCurdy, C. William

The computation of Siegert energies by analytic continuation of bound state energies has recently been applied to shape resonances in polyatomic molecules by several authors. Here, we critically evaluate a recently proposed analytic continuation method based on low order (type III) Padé approximants as well as an analytic continuation method based on high order (type II) Padé approximants. We compare three classes of stabilizing potentials: Coulomb potentials, Gaussian potentials, and attenuated Coulomb potentials. These methods are applied to a model potential where the correct answer is known exactly and to the 2Π g shape resonance of N 2 - whichmore » has been studied extensively by other methods. Both the choice of stabilizing potential and method of analytic continuation prove to be important to the accuracy of the results. We then conclude that an attenuated Coulomb potential is the most effective of the three for bound state analytic continuation methods. With the proper potential, such methods show promise for algorithmic determination of the positions and widths of molecular shape resonances.« less

Using block pulse functions for seismic vibration semi-active control of structures with MR dampers

NASA Astrophysics Data System (ADS)

Rahimi Gendeshmin, Saeed; Davarnia, Daniel

2018-03-01

This article applied the idea of block pulse functions in the semi-active control of structures. The BP functions give effective tools to approximate complex problems. The applied control algorithm has a major effect on the performance of the controlled system and the requirements of the control devices. In control problems, it is important to devise an accurate analytical technique with less computational cost. It is proved that the BP functions are fundamental tools in approximation problems which have been applied in disparate areas in last decades. This study focuses on the employment of BP functions in control algorithm concerning reduction the computational cost. Magneto-rheological (MR) dampers are one of the well-known semi-active tools that can be used to control the response of civil Structures during earthquake. For validation purposes, numerical simulations of a 5-story shear building frame with MR dampers are presented. The results of suggested method were compared with results obtained by controlling the frame by the optimal control method based on linear quadratic regulator theory. It can be seen from simulation results that the suggested method can be helpful in reducing seismic structural responses. Besides, this method has acceptable accuracy and is in agreement with optimal control method with less computational costs.

Convergence and approximate calculation of average degree under different network sizes for decreasing random birth-and-death networks

NASA Astrophysics Data System (ADS)

Long, Yin; Zhang, Xiao-Jun; Wang, Kui

2018-05-01

In this paper, convergence and approximate calculation of average degree under different network sizes for decreasing random birth-and-death networks (RBDNs) are studied. First, we find and demonstrate that the average degree is convergent in the form of power law. Meanwhile, we discover that the ratios of the back items to front items of convergent reminder are independent of network link number for large network size, and we theoretically prove that the limit of the ratio is a constant. Moreover, since it is difficult to calculate the analytical solution of the average degree for large network sizes, we adopt numerical method to obtain approximate expression of the average degree to approximate its analytical solution. Finally, simulations are presented to verify our theoretical results.

Emulation applied to reliability analysis of reconfigurable, highly reliable, fault-tolerant computing systems

NASA Technical Reports Server (NTRS)

Migneault, G. E.

1979-01-01

Emulation techniques applied to the analysis of the reliability of highly reliable computer systems for future commercial aircraft are described. The lack of credible precision in reliability estimates obtained by analytical modeling techniques is first established. The difficulty is shown to be an unavoidable consequence of: (1) a high reliability requirement so demanding as to make system evaluation by use testing infeasible; (2) a complex system design technique, fault tolerance; (3) system reliability dominated by errors due to flaws in the system definition; and (4) elaborate analytical modeling techniques whose precision outputs are quite sensitive to errors of approximation in their input data. Next, the technique of emulation is described, indicating how its input is a simple description of the logical structure of a system and its output is the consequent behavior. Use of emulation techniques is discussed for pseudo-testing systems to evaluate bounds on the parameter values needed for the analytical techniques. Finally an illustrative example is presented to demonstrate from actual use the promise of the proposed application of emulation.

Analytical model of diffuse reflectance spectrum of skin tissue

NASA Astrophysics Data System (ADS)

Lisenko, S. A.; Kugeiko, M. M.; Firago, V. A.; Sobchuk, A. N.

2014-01-01

We have derived simple analytical expressions that enable highly accurate calculation of diffusely reflected light signals of skin in the spectral range from 450 to 800 nm at a distance from the region of delivery of exciting radiation. The expressions, taking into account the dependence of the detected signals on the refractive index, transport scattering coefficient, absorption coefficient and anisotropy factor of the medium, have been obtained in the approximation of a two-layer medium model (epidermis and dermis) for the same parameters of light scattering but different absorption coefficients of layers. Numerical experiments on the retrieval of the skin biophysical parameters from the diffuse reflectance spectra simulated by the Monte Carlo method show that commercially available fibre-optic spectrophotometers with a fixed distance between the radiation source and detector can reliably determine the concentration of bilirubin, oxy- and deoxyhaemoglobin in the dermis tissues and the tissue structure parameter characterising the size of its effective scatterers. We present the examples of quantitative analysis of the experimental data, confirming the correctness of estimates of biophysical parameters of skin using the obtained analytical expressions.

Modified symplectic schemes with nearly-analytic discrete operators for acoustic wave simulations

NASA Astrophysics Data System (ADS)

Liu, Shaolin; Yang, Dinghui; Lang, Chao; Wang, Wenshuai; Pan, Zhide

2017-04-01

Using a structure-preserving algorithm significantly increases the computational efficiency of solving wave equations. However, only a few explicit symplectic schemes are available in the literature, and the capabilities of these symplectic schemes have not been sufficiently exploited. Here, we propose a modified strategy to construct explicit symplectic schemes for time advance. The acoustic wave equation is transformed into a Hamiltonian system. The classical symplectic partitioned Runge-Kutta (PRK) method is used for the temporal discretization. Additional spatial differential terms are added to the PRK schemes to form the modified symplectic methods and then two modified time-advancing symplectic methods with all of positive symplectic coefficients are then constructed. The spatial differential operators are approximated by nearly-analytic discrete (NAD) operators, and we call the fully discretized scheme modified symplectic nearly analytic discrete (MSNAD) method. Theoretical analyses show that the MSNAD methods exhibit less numerical dispersion and higher stability limits than conventional methods. Three numerical experiments are conducted to verify the advantages of the MSNAD methods, such as their numerical accuracy, computational cost, stability, and long-term calculation capability.

Padé Approximant and Minimax Rational Approximation in Standard Cosmology

NASA Astrophysics Data System (ADS)

Zaninetti, Lorenzo

2016-02-01

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

Analytical mass formula and nuclear surface properties in the ETF approximation. Part I: symmetric nuclei

NASA Astrophysics Data System (ADS)

Aymard, François; Gulminelli, Francesca; Margueron, Jérôme

2016-08-01

The problem of determination of nuclear surface energy is addressed within the framework of the extended Thomas Fermi (ETF) approximation using Skyrme functionals. We propose an analytical model for the density profiles with variationally determined diffuseness parameters. In this first paper, we consider the case of symmetric nuclei. In this situation, the ETF functional can be exactly integrated, leading to an analytical formula expressing the surface energy as a function of the couplings of the energy functional. The importance of non-local terms is stressed and it is shown that they cannot be deduced simply from the local part of the functional, as it was suggested in previous works.

Documentation for a Structural Optimization Procedure Developed Using the Engineering Analysis Language (EAL)

NASA Technical Reports Server (NTRS)

Martin, Carl J., Jr.

1996-01-01

This report describes a structural optimization procedure developed for use with the Engineering Analysis Language (EAL) finite element analysis system. The procedure is written primarily in the EAL command language. Three external processors which are written in FORTRAN generate equivalent stiffnesses and evaluate stress and local buckling constraints for the sections. Several built-up structural sections were coded into the design procedures. These structural sections were selected for use in aircraft design, but are suitable for other applications. Sensitivity calculations use the semi-analytic method, and an extensive effort has been made to increase the execution speed and reduce the storage requirements. There is also an approximate sensitivity update method included which can significantly reduce computational time. The optimization is performed by an implementation of the MINOS V5.4 linear programming routine in a sequential liner programming procedure.

AN ANALYTIC RADIATIVE-CONVECTIVE MODEL FOR PLANETARY ATMOSPHERES

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

Robinson, Tyler D.; Catling, David C., E-mail: robinson@astro.washington.edu

2012-09-20

We present an analytic one-dimensional radiative-convective model of the thermal structure of planetary atmospheres. Our model assumes that thermal radiative transfer is gray and can be represented by the two-stream approximation. Model atmospheres are assumed to be in hydrostatic equilibrium, with a power-law scaling between the atmospheric pressure and the gray thermal optical depth. The convective portions of our models are taken to follow adiabats that account for condensation of volatiles through a scaling parameter to the dry adiabat. By combining these assumptions, we produce simple, analytic expressions that allow calculations of the atmospheric-pressure-temperature profile, as well as expressions formore » the profiles of thermal radiative flux and convective flux. We explore the general behaviors of our model. These investigations encompass (1) worlds where atmospheric attenuation of sunlight is weak, which we show tend to have relatively high radiative-convective boundaries; (2) worlds with some attenuation of sunlight throughout the atmosphere, which we show can produce either shallow or deep radiative-convective boundaries, depending on the strength of sunlight attenuation; and (3) strongly irradiated giant planets (including hot Jupiters), where we explore the conditions under which these worlds acquire detached convective regions in their mid-tropospheres. Finally, we validate our model and demonstrate its utility through comparisons to the average observed thermal structure of Venus, Jupiter, and Titan, and by comparing computed flux profiles to more complex models.« less

Determination of boiling point of petrochemicals by gas chromatography-mass spectrometry and multivariate regression analysis of structural activity relationship.

PubMed

Fakayode, Sayo O; Mitchell, Breanna S; Pollard, David A

2014-08-01

Accurate understanding of analyte boiling points (BP) is of critical importance in gas chromatographic (GC) separation and crude oil refinery operation in petrochemical industries. This study reported the first combined use of GC separation and partial-least-square (PLS1) multivariate regression analysis of petrochemical structural activity relationship (SAR) for accurate BP determination of two commercially available (D3710 and MA VHP) calibration gas mix samples. The results of the BP determination using PLS1 multivariate regression were further compared with the results of traditional simulated distillation method of BP determination. The developed PLS1 regression was able to correctly predict analytes BP in D3710 and MA VHP calibration gas mix samples, with a root-mean-square-%-relative-error (RMS%RE) of 6.4%, and 10.8% respectively. In contrast, the overall RMS%RE of 32.9% and 40.4%, respectively obtained for BP determination in D3710 and MA VHP using a traditional simulated distillation method were approximately four times larger than the corresponding RMS%RE of BP prediction using MRA, demonstrating the better predictive ability of MRA. The reported method is rapid, robust, and promising, and can be potentially used routinely for fast analysis, pattern recognition, and analyte BP determination in petrochemical industries. Copyright © 2014 Elsevier B.V. All rights reserved.

Anharmonic effects in the quantum cluster equilibrium method

NASA Astrophysics Data System (ADS)

von Domaros, Michael; Perlt, Eva

2017-03-01

The well-established quantum cluster equilibrium (QCE) model provides a statistical thermodynamic framework to apply high-level ab initio calculations of finite cluster structures to macroscopic liquid phases using the partition function. So far, the harmonic approximation has been applied throughout the calculations. In this article, we apply an important correction in the evaluation of the one-particle partition function and account for anharmonicity. Therefore, we implemented an analytical approximation to the Morse partition function and the derivatives of its logarithm with respect to temperature, which are required for the evaluation of thermodynamic quantities. This anharmonic QCE approach has been applied to liquid hydrogen chloride and cluster distributions, and the molar volume, the volumetric thermal expansion coefficient, and the isobaric heat capacity have been calculated. An improved description for all properties is observed if anharmonic effects are considered.

Landau-Zener extension of the Tavis-Cummings model: structure of the solution

NASA Astrophysics Data System (ADS)

Sun, Chen; Sinitsyn, Nikolai

We explore the recently discovered solution of the driven Tavis-Cummings model (DTCM). It describes interaction of arbitrary number of two-level systems with a bosonic mode that has linearly time-dependent frequency. We derive compact and tractable expressions for transition probabilities in terms of the well known special functions. In the new form, our formulas are suitable for fast numerical calculations and analytical approximations. As an application, we obtain the semiclassical limit of the exact solution and compare it to prior approximations. We also reveal connection between DTCM and q-deformed binomial statistics. Under the auspices of the National Nuclear Security Administration of the U.S. Department of Energy at Los Alamos National Laboratory under Contract No. DE-AC52-06NA25396. Authors also thank the support from the LDRD program at LANL.

Design for active and passive flutter suppression and gust alleviation. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Karpel, M.

1981-01-01

Analytical design techniques for active and passive control of aeroelastic systems are based on a rational approximation of the unsteady aerodynamic loads in the entire Laplace domain, which yields matrix equations of motion with constant coefficients. Some existing schemes are reviewed, the matrix Pade approximant is modified, and a technique which yields a minimal number of augmented states for a desired accuracy is presented. The state-space aeroelastic model is used to design an active control system for simultaneous flutter suppression and gust alleviation. The design target is for a continuous controller which transfers some measurements taken on the vehicle to a control command applied to a control surface. Structural modifications are formulated in a way which enables the treatment of passive flutter suppression system with the same procedures by which active control systems are designed.

Improving the analytical performance and versatility of paper spray mass spectrometry via paper microfluidics.

PubMed

Murray, Ian; Walker, Glenn; Bereman, Michael S

2016-06-20

Two paper-based microfluidic techniques, photolithography and wax patterning, were investigated for their potential to improve upon the sensitivity, reproducibility, and versatility of paper spray mass spectrometry. The main limitation of photolithography was the significant signal (approximately three orders of magnitude) above background which was attributed to the chemicals used in the photoresist process. Hydrophobic barriers created via wax patterning were discovered to have approximately 2 orders of magnitude less background signal compared to analogous barriers created using photolithography. A minimum printed wax barrier thickness of approximately 0.3 mm was necessary to consistently retain commonly used paper spray solvents (1 : 1 water : acetonitrile/methanol) and avoid leakage. Constricting capillary flow via wax-printed channels yielded both a significant increase in signal and detection time for detection of model analytes. This signal increase, which was attributed to restricting the radial flow of analyte/solvent on paper (i.e., a concentrating effect), afforded a significant increase in sensitivity (p ≪ 0.05) for the detection of pesticides spiked into residential tap water using a five-point calibration curve. Finally, unique mixing designs using wax patterning can be envisioned to perform on-paper analyte derivatization.

Approximate Analytical Solutions for Hypersonic Flow Over Slender Power Law Bodies

NASA Technical Reports Server (NTRS)

Mirels, Harold

1959-01-01

Approximate analytical solutions are presented for two-dimensional and axisymmetric hypersonic flow over slender power law bodies. Both zero order (M approaches infinity) and first order (small but nonvanishing values of 1/(M(Delta)(sup 2) solutions are presented, where M is free-stream Mach number and Delta is a characteristic slope. These solutions are compared with exact numerical integration of the equations of motion and appear to be accurate particularly when the shock is relatively close to the body.

On accelerated flow of MHD powell-eyring fluid via homotopy analysis method

NASA Astrophysics Data System (ADS)

Salah, Faisal; Viswanathan, K. K.; Aziz, Zainal Abdul

2017-09-01

The aim of this article is to obtain the approximate analytical solution for incompressible magnetohydrodynamic (MHD) flow for Powell-Eyring fluid induced by an accelerated plate. Both constant and variable accelerated cases are investigated. Approximate analytical solution in each case is obtained by using the Homotopy Analysis Method (HAM). The resulting nonlinear analysis is carried out to generate the series solution. Finally, Graphical outcomes of different values of the material constants parameters on the velocity flow field are discussed and analyzed.

Analytic Approximate Solutions to the Boundary Layer Flow Equation over a Stretching Wall with Partial Slip at the Boundary.

PubMed

Ene, Remus-Daniel; Marinca, Vasile; Marinca, Bogdan

2016-01-01

Analytic approximate solutions using Optimal Homotopy Perturbation Method (OHPM) are given for steady boundary layer flow over a nonlinearly stretching wall in presence of partial slip at the boundary. The governing equations are reduced to nonlinear ordinary differential equation by means of similarity transformations. Some examples are considered and the effects of different parameters are shown. OHPM is a very efficient procedure, ensuring a very rapid convergence of the solutions after only two iterations.

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.

Solutions of the Dirac Equation with the Shifted DENG-FAN Potential Including Yukawa-Like Tensor Interaction

NASA Astrophysics Data System (ADS)

Yahya, W. A.; Falaye, B. J.; Oluwadare, O. J.; Oyewumi, K. J.

2013-08-01

By using the Nikiforov-Uvarov method, we give the approximate analytical solutions of the Dirac equation with the shifted Deng-Fan potential including the Yukawa-like tensor interaction under the spin and pseudospin symmetry conditions. After using an improved approximation scheme, we solved the resulting schr\\"{o}dinger-like equation analytically. Numerical results of the energy eigenvalues are also obtained, as expected, the tensor interaction removes degeneracies between spin and pseudospin doublets.

Analytic Approximate Solutions to the Boundary Layer Flow Equation over a Stretching Wall with Partial Slip at the Boundary

PubMed Central

Ene, Remus-Daniel; Marinca, Vasile; Marinca, Bogdan

2016-01-01

Analytic approximate solutions using Optimal Homotopy Perturbation Method (OHPM) are given for steady boundary layer flow over a nonlinearly stretching wall in presence of partial slip at the boundary. The governing equations are reduced to nonlinear ordinary differential equation by means of similarity transformations. Some examples are considered and the effects of different parameters are shown. OHPM is a very efficient procedure, ensuring a very rapid convergence of the solutions after only two iterations. PMID:27031232

Development of Finite Elements for Two-Dimensional Structural Analysis Using the Integrated Force Method

NASA Technical Reports Server (NTRS)

Kaljevic, Igor; Patnaik, Surya N.; Hopkins, Dale A.

1996-01-01

The Integrated Force Method has been developed in recent years for the analysis of structural mechanics problems. This method treats all independent internal forces as unknown variables that can be calculated by simultaneously imposing equations of equilibrium and compatibility conditions. In this paper a finite element library for analyzing two-dimensional problems by the Integrated Force Method is presented. Triangular- and quadrilateral-shaped elements capable of modeling arbitrary domain configurations are presented. The element equilibrium and flexibility matrices are derived by discretizing the expressions for potential and complementary energies, respectively. The displacement and stress fields within the finite elements are independently approximated. The displacement field is interpolated as it is in the standard displacement method, and the stress field is approximated by using complete polynomials of the correct order. A procedure that uses the definitions of stress components in terms of an Airy stress function is developed to derive the stress interpolation polynomials. Such derived stress fields identically satisfy the equations of equilibrium. Moreover, the resulting element matrices are insensitive to the orientation of local coordinate systems. A method is devised to calculate the number of rigid body modes, and the present elements are shown to be free of spurious zero-energy modes. A number of example problems are solved by using the present library, and the results are compared with corresponding analytical solutions and with results from the standard displacement finite element method. The Integrated Force Method not only gives results that agree well with analytical and displacement method results but also outperforms the displacement method in stress calculations.

A radio-frequency sheath model for complex waveforms

NASA Astrophysics Data System (ADS)

Turner, M. M.; Chabert, P.

2014-04-01

Plasma sheaths driven by radio-frequency voltages occur in contexts ranging from plasma processing to magnetically confined fusion experiments. An analytical understanding of such sheaths is therefore important, both intrinsically and as an element in more elaborate theoretical structures. Radio-frequency sheaths are commonly excited by highly anharmonic waveforms, but no analytical model exists for this general case. We present a mathematically simple sheath model that is in good agreement with earlier models for single frequency excitation, yet can be solved for arbitrary excitation waveforms. As examples, we discuss dual-frequency and pulse-like waveforms. The model employs the ansatz that the time-averaged electron density is a constant fraction of the ion density. In the cases we discuss, the error introduced by this approximation is small, and in general it can be quantified through an internal consistency condition of the model. This simple and accurate model is likely to have wide application.

Non-Markovian decay and dynamics of decoherence in private and public environments

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

Dente, A. D.; Zangara, P. R.; Pastawski, H. M.

2011-10-15

We study the decay process in an open system, emphasizing the relevance of the environment's spectral structure. Non-Markovian effects are included to quantitatively analyze the degradation rate of the coherent evolution. The way in which a two-level system is coupled to different environments is specifically addressed: multiple connections to a single bath (public environment) or single connections to multiple baths (private environments). We numerically evaluate the decay rate of a local excitation by using the survival probability and the Loschmidt echo. These rates are compared to analytical results obtained from the standard Fermi golden rule (FGR) in wide band approximation,more » and a self-consistent evaluation that accounts for the bath's memory in cases where an exact analytical solution is possible. We observe that the correlations appearing in a public bath introduce further deviations from the FGR as compared with a private bath.« less

Non-Markovian decay and dynamics of decoherence in private and public environments

NASA Astrophysics Data System (ADS)

Dente, A. D.; Zangara, P. R.; Pastawski, H. M.

2011-10-01

We study the decay process in an open system, emphasizing the relevance of the environment’s spectral structure. Non-Markovian effects are included to quantitatively analyze the degradation rate of the coherent evolution. The way in which a two-level system is coupled to different environments is specifically addressed: multiple connections to a single bath (public environment) or single connections to multiple baths (private environments). We numerically evaluate the decay rate of a local excitation by using the survival probability and the Loschmidt echo. These rates are compared to analytical results obtained from the standard Fermi golden rule (FGR) in wide band approximation, and a self-consistent evaluation that accounts for the bath’s memory in cases where an exact analytical solution is possible. We observe that the correlations appearing in a public bath introduce further deviations from the FGR as compared with a private bath.

Sideways wall force produced during tokamak disruptions

NASA Astrophysics Data System (ADS)

Strauss, H.; Paccagnella, R.; Breslau, J.; Sugiyama, L.; Jardin, S.

2013-07-01

A critical issue for ITER is to evaluate the forces produced on the surrounding conducting structures during plasma disruptions. We calculate the non-axisymmetric ‘sideways’ wall force Fx, produced in disruptions. Simulations were carried out of disruptions produced by destabilization of n = 1 modes by a vertical displacement event (VDE). The force depends strongly on γτwall, where γ is the mode growth rate and τwall is the wall penetration time, and is largest for γτwall = constant, which depends on initial conditions. Simulations of disruptions caused by a model of massive gas injection were also performed. It was found that the wall force increases approximately offset linearly with the displacement from the magnetic axis produced by a VDE. These results are also obtained with an analytical model. Disruptions are accompanied by toroidal variation of the plasma current Iφ. This is caused by toroidal variation of the halo current, as verified computationally and analytically.

A simplified method of evaluating the stress wave environment of internal equipment

NASA Technical Reports Server (NTRS)

Colton, J. D.; Desmond, T. P.

1979-01-01

A simplified method called the transfer function technique (TFT) was devised for evaluating the stress wave environment in a structure containing internal equipment. The TFT consists of following the initial in-plane stress wave that propagates through a structure subjected to a dynamic load and characterizing how the wave is altered as it is transmitted through intersections of structural members. As a basis for evaluating the TFT, impact experiments and detailed stress wave analyses were performed for structures with two or three, or more members. Transfer functions that relate the wave transmitted through an intersection to the incident wave were deduced from the predicted wave response. By sequentially applying these transfer functions to a structure with several intersections, it was found that the environment produced by the initial stress wave propagating through the structure can be approximated well. The TFT can be used as a design tool or as an analytical tool to determine whether a more detailed wave analysis is warranted.

Analytical approximations for spiral waves

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

Löber, Jakob, E-mail: jakob@physik.tu-berlin.de; Engel, Harald

2013-12-15

We propose a non-perturbative attempt to solve the kinematic equations for spiral waves in excitable media. From the eikonal equation for the wave front we derive an implicit analytical relation between rotation frequency Ω and core radius R{sub 0}. For free, rigidly rotating spiral waves our analytical prediction is in good agreement with numerical solutions of the linear eikonal equation not only for very large but also for intermediate and small values of the core radius. An equivalent Ω(R{sub +}) dependence improves the result by Keener and Tyson for spiral waves pinned to a circular defect of radius R{sub +}more » with Neumann boundaries at the periphery. Simultaneously, analytical approximations for the shape of free and pinned spirals are given. We discuss the reasons why the ansatz fails to correctly describe the dependence of the rotation frequency on the excitability of the medium.« less

Block matrix based LU decomposition to analyze kinetic damping in active plasma resonance spectroscopy

NASA Astrophysics Data System (ADS)

Roehl, Jan Hendrik; Oberrath, Jens

2016-09-01

``Active plasma resonance spectroscopy'' (APRS) is a widely used diagnostic method to measure plasma parameter like electron density. Measurements with APRS probes in plasmas of a few Pa typically show a broadening of the spectrum due to kinetic effects. To analyze the broadening a general kinetic model in electrostatic approximation based on functional analytic methods has been presented [ 1 ] . One of the main results is, that the system response function Y(ω) is given in terms of the matrix elements of the resolvent of the dynamic operator evaluated for values on the imaginary axis. To determine the response function of a specific probe the resolvent has to be approximated by a huge matrix which is given by a banded block structure. Due to this structure a block based LU decomposition can be implemented. It leads to a solution of Y(ω) which is given only by products of matrices of the inner block size. This LU decomposition allows to analyze the influence of kinetic effects on the broadening and saves memory and calculation time. Gratitude is expressed to the internal funding of Leuphana University.

Average configuration of the distant (less than 220-earth-radii) magnetotail - Initial ISEE-3 magnetic field results

NASA Technical Reports Server (NTRS)

Slavin, J. A.; Tsurutani, B. T.; Smith, E. J.; Jones, D. E.; Sibeck, D. G.

1983-01-01

Magnetic field measurements from the first two passes of the ISEE-3 GEOTAIL Mission have been used to study the structure of the trans-lunar tail. Good agreement was found between the ISEE-3 magnetopause crossings and the Explorer 33, 35 model of Howe and Binsack (1972). Neutral sheet location was well ordered by the hinged current sheet models based upon near earth measurements. Between X = -20 and -120 earth radii the radius of the tail increases by about 30 percent while the lobe field strength decreases by approximately 60 percent. Beyond X = -100 to -1200 earth radii the tail diameter and lobe field magnitude become nearly constant at terminal values of approximately 60 earth radii and 9 nT, respectively. The distance at which the tail was observed to cease flaring, 100-120 earth radii, is in close agreement with the predictions of the analytic tail model of Coroniti and Kennel (1972). Overall, the findings of this study suggest that the magnetotail retains much of its near earth structure out to X = -220 earth radii.

Analysis of solar ultraviolet lines

NASA Technical Reports Server (NTRS)

Chipman, E.

1971-01-01

The formation of the strongest ultra-violet emission lines of Mg II, O I, C II, and C III in the solar atmosphere is studied in detail. The equations of statistical equilibrium and radiative transfer for each ion are solved using a general computer program that is capable of solving non-LTE line-formation problems for arbitrary atmospheric and atomic models. Interpreting the results in terms of the structure of the solar atmosphere, it is concluded that the HSRA atmosphere has a temperature too low by about 500 K near h = 1100 km and that a temperature plateau with T sub e approximately = 18,000 K and width close to 60 km exists in the upper chromosphere. The structure of the solar atmosphere in the range 20,000 to 100,000 K and the effects of microturbulence on the formation of lines are also investigated. Approximate analytic line-formation problems are solved, and more exact solutions are derived later. An attempt is made to make the best possible fit to the Ca II K line center-to-limb profiles with a one-component atmosphere, with an assumed source function and microturbulent velocity.

Evaluation of Analytical Modeling Functions for the Phonation Onset Process.

PubMed

Petermann, Simon; Kniesburges, Stefan; Ziethe, Anke; Schützenberger, Anne; Döllinger, Michael

2016-01-01

The human voice originates from oscillations of the vocal folds in the larynx. The duration of the voice onset (VO), called the voice onset time (VOT), is currently under investigation as a clinical indicator for correct laryngeal functionality. Different analytical approaches for computing the VOT based on endoscopic imaging were compared to determine the most reliable method to quantify automatically the transient vocal fold oscillations during VO. Transnasal endoscopic imaging in combination with a high-speed camera (8000 fps) was applied to visualize the phonation onset process. Two different definitions of VO interval were investigated. Six analytical functions were tested that approximate the envelope of the filtered or unfiltered glottal area waveform (GAW) during phonation onset. A total of 126 recordings from nine healthy males and 210 recordings from 15 healthy females were evaluated. Three criteria were analyzed to determine the most appropriate computation approach: (1) reliability of the fit function for a correct approximation of VO; (2) consistency represented by the standard deviation of VOT; and (3) accuracy of the approximation of VO. The results suggest the computation of VOT by a fourth-order polynomial approximation in the interval between 32.2 and 67.8% of the saturation amplitude of the filtered GAW.

Development and application of accurate analytical models for single active electron potentials

NASA Astrophysics Data System (ADS)

Miller, Michelle; Jaron-Becker, Agnieszka; Becker, Andreas

2015-05-01

The single active electron (SAE) approximation is a theoretical model frequently employed to study scenarios in which inner-shell electrons may productively be treated as frozen spectators to a physical process of interest, and accurate analytical approximations for these potentials are sought as a useful simulation tool. Density function theory is often used to construct a SAE potential, requiring that a further approximation for the exchange correlation functional be enacted. In this study, we employ the Krieger, Li, and Iafrate (KLI) modification to the optimized-effective-potential (OEP) method to reduce the complexity of the problem to the straightforward solution of a system of linear equations through simple arguments regarding the behavior of the exchange-correlation potential in regions where a single orbital dominates. We employ this method for the solution of atomic and molecular potentials, and use the resultant curve to devise a systematic construction for highly accurate and useful analytical approximations for several systems. Supported by the U.S. Department of Energy (Grant No. DE-FG02-09ER16103), and the U.S. National Science Foundation (Graduate Research Fellowship, Grants No. PHY-1125844 and No. PHY-1068706).

Proxy-SU(3) symmetry in heavy deformed nuclei

NASA Astrophysics Data System (ADS)

Bonatsos, Dennis; Assimakis, I. E.; Minkov, N.; Martinou, Andriana; Cakirli, R. B.; Casten, R. F.; Blaum, K.

2017-06-01

Background: Microscopic calculations of heavy nuclei face considerable difficulties due to the sizes of the matrices that need to be solved. Various approximation schemes have been invoked, for example by truncating the spaces, imposing seniority limits, or appealing to various symmetry schemes such as pseudo-SU(3). This paper proposes a new symmetry scheme also based on SU(3). This proxy-SU(3) can be applied to well-deformed nuclei, is simple to use, and can yield analytic predictions. Purpose: To present the new scheme and its microscopic motivation, and to test it using a Nilsson model calculation with the original shell model orbits and with the new proxy set. Method: We invoke an approximate, analytic, treatment of the Nilsson model, that allows the above vetting and yet is also transparent in understanding the approximations involved in the new proxy-SU(3). Results: It is found that the new scheme yields a Nilsson diagram for well-deformed nuclei that is very close to the original Nilsson diagram. The specific levels of approximation in the new scheme are also shown, for each major shell. Conclusions: The new proxy-SU(3) scheme is a good approximation to the full set of orbits in a major shell. Being able to replace a complex shell model calculation with a symmetry-based description now opens up the possibility to predict many properties of nuclei analytically and often in a parameter-free way. The new scheme works best for heavier nuclei, precisely where full microscopic calculations are most challenged. Some cases in which the new scheme can be used, often analytically, to make specific predictions, are shown in a subsequent paper.

Analytical ground state for the Jaynes-Cummings model with ultrastrong coupling

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

Zhang Yuanwei; Institute of Theoretical Physics, Shanxi University, Taiyuan 030006; Chen Gang

2011-06-15

We present a generalized variational method to analytically obtain the ground-state properties of the Jaynes-Cummings model with the ultrastrong coupling. An explicit expression for the ground-state energy, which agrees well with the numerical simulation in a wide range of the experimental parameters, is given. In particular, the introduced method can successfully solve this Jaynes-Cummings model with the positive detuning (the atomic resonant level is larger than the photon frequency), which cannot be treated in the adiabatical approximation and the generalized rotating-wave approximation. Finally, we also demonstrate analytically how to control the mean photon number by means of the current experimentalmore » parameters including the photon frequency, the coupling strength, and especially the atomic resonant level.« less

Similarity solution of the Boussinesq equation

NASA Astrophysics Data System (ADS)

Lockington, D. A.; Parlange, J.-Y.; Parlange, M. B.; Selker, J.

Similarity transforms of the Boussinesq equation in a semi-infinite medium are available when the boundary conditions are a power of time. The Boussinesq equation is reduced from a partial differential equation to a boundary-value problem. Chen et al. [Trans Porous Media 1995;18:15-36] use a hodograph method to derive an integral equation formulation of the new differential equation which they solve by numerical iteration. In the present paper, the convergence of their scheme is improved such that numerical iteration can be avoided for all practical purposes. However, a simpler analytical approach is also presented which is based on Shampine's transformation of the boundary value problem to an initial value problem. This analytical approximation is remarkably simple and yet more accurate than the analytical hodograph approximations.

Quantitative Characterization of the Microstructure and Transport Properties of Biopolymer Networks

PubMed Central

Jiao, Yang; Torquato, Salvatore

2012-01-01

Biopolymer networks are of fundamental importance to many biological processes in normal and tumorous tissues. In this paper, we employ the panoply of theoretical and simulation techniques developed for characterizing heterogeneous materials to quantify the microstructure and effective diffusive transport properties (diffusion coefficient De and mean survival time τ) of collagen type I networks at various collagen concentrations. In particular, we compute the pore-size probability density function P(δ) for the networks and present a variety of analytical estimates of the effective diffusion coefficient De for finite-sized diffusing particles, including the low-density approximation, the Ogston approximation, and the Torquato approximation. The Hashin-Strikman upper bound on the effective diffusion coefficient De and the pore-size lower bound on the mean survival time τ are used as benchmarks to test our analytical approximations and numerical results. Moreover, we generalize the efficient first-passage-time techniques for Brownian-motion simulations in suspensions of spheres to the case of fiber networks and compute the associated effective diffusion coefficient De as well as the mean survival time τ, which is related to nuclear magnetic resonance (NMR) relaxation times. Our numerical results for De are in excellent agreement with analytical results for simple network microstructures, such as periodic arrays of parallel cylinders. Specifically, the Torquato approximation provides the most accurate estimates of De for all collagen concentrations among all of the analytical approximations we consider. We formulate a universal curve for τ for the networks at different collagen concentrations, extending the work of Yeong and Torquato [J. Chem. Phys. 106, 8814 (1997)]. We apply rigorous cross-property relations to estimate the effective bulk modulus of collagen networks from a knowledge of the effective diffusion coefficient computed here. The use of cross-property relations to link other physical properties to the transport properties of collagen networks is also discussed. PMID:22683739

Recent Developments in the Speciation and Determination of Mercury Using Various Analytical Techniques

PubMed Central

Suvarapu, Lakshmi Narayana; Baek, Sung-Ok

2015-01-01

This paper reviews the speciation and determination of mercury by various analytical techniques such as atomic absorption spectrometry, voltammetry, inductively coupled plasma techniques, spectrophotometry, spectrofluorometry, high performance liquid chromatography, and gas chromatography. Approximately 126 research papers on the speciation and determination of mercury by various analytical techniques published in international journals since 2013 are reviewed. PMID:26236539

Evolutionary snowdrift game incorporating costly punishment in structured populations

NASA Astrophysics Data System (ADS)

Chan, Nat W. H.; Xu, C.; Tey, Siew Kian; Yap, Yee Jiun; Hui, P. M.

2013-01-01

The role of punishment and the effects of a structured population in promoting cooperation are important issues. Within a recent model of snowdrift game (SG) incorporating a costly punishing strategy (P), we study the effects of a population connected through a square lattice. The punishers, who carry basically a cooperative (C) character, are willing to pay a cost α so as to punish a non-cooperative (D) opponent by β. Depending on α, β, the cost-to-benefit ratio r in SG, and the initial conditions, the system evolves into different phases that could be homogeneous or inhomogeneous. The spatial structure imposes geometrical constraint on how one agent is affected by neighboring agents. Results of extensive numerical simulations, both for the steady state and the dynamics, are presented. Possible phases are identified and discussed, and isolated phases in the r-β space are identified as special local structures of strategies that are stable due to the lattice structure. In contrast to a well-mixed population where punishers are suppressed due to the cost of punishment, the altruistic punishing strategy can flourish and prevail for appropriate values of the parameters, implying an enhancement in cooperation by imposing punishments in a structured population. The system could evolve to a phase corresponding to the coexistence of C, D, and P strategies at some particular payoff parameters, and such a phase is absent in a well-mixed population. The pair approximation, a commonly used analytic approach, is extended from a two-strategy system to a three-strategy system. We show that the pair approximation can, at best, capture the numerical results only qualitatively. Due to the improper way of including spatial correlation imposed by the lattice structure, the approximation does not give the frequencies of C, D, and P accurately and fails to give the homogeneous AllD and AllP phases.

Modeling of large amplitude plasma blobs in three-dimensions

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

Angus, Justin R.; Umansky, Maxim V.

2014-01-15

Fluctuations in fusion boundary and similar plasmas often have the form of filamentary structures, or blobs, that convectively propagate radially. This may lead to the degradation of plasma facing components as well as plasma confinement. Theoretical analysis of plasma blobs usually takes advantage of the so-called Boussinesq approximation of the potential vorticity equation, which greatly simplifies the treatment analytically and numerically. This approximation is only strictly justified when the blob density amplitude is small with respect to that of the background plasma. However, this is not the case for typical plasma blobs in the far scrape-off layer region, where themore » background density is small compared to that of the blob, and results obtained based on the Boussinesq approximation are questionable. In this report, the solution of the full vorticity equation, without the usual Boussinesq approximation, is proposed via a novel numerical approach. The method is used to solve for the evolution of 2D and 3D plasma blobs in a regime where the Boussinesq approximation is not valid. The Boussinesq solution under predicts the cross field transport in 2D. However, in 3D, for parameters typical of current tokamaks, the disparity between the radial cross field transport from the Boussinesq approximation and full solution is virtually non-existent due to the effects of the drift wave instability.« less

Fundamental (f) oscillations in a magnetically coupled solar interior-atmosphere system - An analytical approach

NASA Astrophysics Data System (ADS)

Pintér, Balázs; Erdélyi, R.

2018-01-01

Solar fundamental (f) acoustic mode oscillations are investigated analytically in a magnetohydrodynamic (MHD) model. The model consists of three layers in planar geometry, representing the solar interior, the magnetic atmosphere, and a transitional layer sandwiched between them. Since we focus on the fundamental mode here, we assume the plasma is incompressible. A horizontal, canopy-like, magnetic field is introduced to the atmosphere, in which degenerated slow MHD waves can exist. The global (f-mode) oscillations can couple to local atmospheric Alfvén waves, resulting, e.g., in a frequency shift of the oscillations. The dispersion relation of the global oscillation mode is derived, and is solved analytically for the thin-transitional layer approximation and for the weak-field approximation. Analytical formulae are also provided for the frequency shifts due to the presence of a thin transitional layer and a weak atmospheric magnetic field. The analytical results generally indicate that, compared to the fundamental value (ω =√{ gk }), the mode frequency is reduced by the presence of an atmosphere by a few per cent. A thin transitional layer reduces the eigen-frequencies further by about an additional hundred microhertz. Finally, a weak atmospheric magnetic field can slightly, by a few percent, increase the frequency of the eigen-mode. Stronger magnetic fields, however, can increase the f-mode frequency by even up to ten per cent, which cannot be seen in observed data. The presence of a magnetic atmosphere in the three-layer model also introduces non-permitted propagation windows in the frequency spectrum; here, f-mode oscillations cannot exist with certain values of the harmonic degree. The eigen-frequencies can be sensitive to the background physical parameters, such as an atmospheric density scale-height or the rate of the plasma density drop at the photosphere. Such information, if ever observed with high-resolution instrumentation and inverted, could help to gain further insight into solar magnetic structures by means of solar magneto-seismology, and could provide further insight into the role of magnetism in solar oscillations.

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

NASA Technical Reports Server (NTRS)

Warming, Robert F.; Beam, Richard M.

1988-01-01

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

Optimization of Turbine Engine Cycle Analysis with Analytic Derivatives

NASA Technical Reports Server (NTRS)

Hearn, Tristan; Hendricks, Eric; Chin, Jeffrey; Gray, Justin; Moore, Kenneth T.

2016-01-01

A new engine cycle analysis tool, called Pycycle, was recently built using the OpenMDAO framework. This tool uses equilibrium chemistry based thermodynamics, and provides analytic derivatives. This allows for stable and efficient use of gradient-based optimization and sensitivity analysis methods on engine cycle models, without requiring the use of finite difference derivative approximation methods. To demonstrate this, a gradient-based design optimization was performed on a multi-point turbofan engine model. Results demonstrate very favorable performance compared to an optimization of an identical model using finite-difference approximated derivatives.

Fractional Fourier transform of truncated elliptical Gaussian beams.

PubMed

Du, Xinyue; Zhao, Daomu

2006-12-20

Based on the fact that a hard-edged elliptical aperture can be expanded approximately as a finite sum of complex Gaussian functions in tensor form, an analytical expression for an elliptical Gaussian beam (EGB) truncated by an elliptical aperture and passing through a fractional Fourier transform system is derived by use of vector integration. The approximate analytical results provide more convenience for studying the propagation and transformation of truncated EGBs than the usual way by using the integral formula directly, and the efficiency of numerical calculation is significantly improved.

Periodized Daubechies wavelets

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

Restrepo, J.M.; Leaf, G.K.; Schlossnagle, G.

1996-03-01

The properties of periodized Daubechies wavelets on [0,1] are detailed and counterparts which form a basis for L{sup 2}(R). Numerical examples illustrate the analytical estimates for convergence and demonstrated by comparison with Fourier spectral methods the superiority of wavelet projection methods for approximations. The analytical solution to inner products of periodized wavelets and their derivatives, which are known as connection coefficients, is presented, and their use ius illustrated in the approximation of two commonly used differential operators. The periodization of the connection coefficients in Galerkin schemes is presented in detail.

Analytical investigation of a three-dimensional FRP-retrofitted reinforced concrete structure's behaviour under earthquake load effect in ANSYS program

NASA Astrophysics Data System (ADS)

Altun, F.; Birdal, F.

2012-12-01

In this study, a 1:3 scaled, three-storey, FRP (Fiber Reinforced Polymer) retrofitted reinforced concrete model structure whose behaviour and crack development were identified experimentally in the laboratory was investigated analytically. Determination of structural behaviour under earthquake load is only possible in a laboratory environment with a specific scale, as carrying out structural experiments is difficult due to the evaluation of increased parameter numbers and because it requires an expensive laboratory setup. In an analytical study, structure was modelled using ANSYS Finite Element Package Program (2007), and its behaviour and crack development were revealed. When experimental difficulties are taken into consideration, analytical investigation of structure behaviour is more economic and much faster. At the end of the study, experimental results of structural behaviour and crack development were compared with analytical data. It was concluded that in a model structure retrofitted with FRP, the behaviour and cracking model can be determined without testing by determining the reasons for the points where analytical results are not converged with experimental data. Better understanding of structural behaviour is analytically enabled with the study.

Hybrid perturbation methods based on statistical time series models

NASA Astrophysics Data System (ADS)

San-Juan, Juan Félix; San-Martín, Montserrat; Pérez, Iván; López, Rosario

2016-04-01

In this work we present a new methodology for orbit propagation, the hybrid perturbation theory, based on the combination of an integration method and a prediction technique. The former, which can be a numerical, analytical or semianalytical theory, generates an initial approximation that contains some inaccuracies derived from the fact that, in order to simplify the expressions and subsequent computations, not all the involved forces are taken into account and only low-order terms are considered, not to mention the fact that mathematical models of perturbations not always reproduce physical phenomena with absolute precision. The prediction technique, which can be based on either statistical time series models or computational intelligence methods, is aimed at modelling and reproducing missing dynamics in the previously integrated approximation. This combination results in the precision improvement of conventional numerical, analytical and semianalytical theories for determining the position and velocity of any artificial satellite or space debris object. In order to validate this methodology, we present a family of three hybrid orbit propagators formed by the combination of three different orders of approximation of an analytical theory and a statistical time series model, and analyse their capability to process the effect produced by the flattening of the Earth. The three considered analytical components are the integration of the Kepler problem, a first-order and a second-order analytical theories, whereas the prediction technique is the same in the three cases, namely an additive Holt-Winters method.

Analysis of the impacts of horizontal translation and scaling on wavefront approximation coefficients with rectangular pupils for Chebyshev and Legendre polynomials.

PubMed

Sun, Wenqing; Chen, Lei; Tuya, Wulan; He, Yong; Zhu, Rihong

2013-12-01

Chebyshev and Legendre polynomials are frequently used in rectangular pupils for wavefront approximation. Ideally, the dataset completely fits with the polynomial basis, which provides the full-pupil approximation coefficients and the corresponding geometric aberrations. However, if there are horizontal translation and scaling, the terms in the original polynomials will become the linear combinations of the coefficients of the other terms. This paper introduces analytical expressions for two typical situations after translation and scaling. With a small translation, first-order Taylor expansion could be used to simplify the computation. Several representative terms could be selected as inputs to compute the coefficient changes before and after translation and scaling. Results show that the outcomes of the analytical solutions and the approximated values under discrete sampling are consistent. With the computation of a group of randomly generated coefficients, we contrasted the changes under different translation and scaling conditions. The larger ratios correlate the larger deviation from the approximated values to the original ones. Finally, we analyzed the peak-to-valley (PV) and root mean square (RMS) deviations from the uses of the first-order approximation and the direct expansion under different translation values. The results show that when the translation is less than 4%, the most deviated 5th term in the first-order 1D-Legendre expansion has a PV deviation less than 7% and an RMS deviation less than 2%. The analytical expressions and the computed results under discrete sampling given in this paper for the multiple typical function basis during translation and scaling in the rectangular areas could be applied in wavefront approximation and analysis.

High coronal structure of high velocity solar wind stream sources

NASA Technical Reports Server (NTRS)

Nolte, J. T.; Krieger, A. S.; Roelof, E. C.; Gold, R. E.

1977-01-01

It is shown analytically that the transition from a high-speed stream source to the ambient coronal conditions is quite rapid in longitude in the high corona. This sharp eastern coronal boundary for the solar wind stream sources is strongly suggested by the solar wind 'dwells' which appear in plots of solar wind velocity against constant-radial-velocity-approximation source longitudes. The possibility of a systematic velocity-dependent effect in the constant-radial-velocity approximation, which would cause this boundary to appear sharper than it is, is investigated. A velocity-dependent interplanetary propagation effect or a velocity-dependent 'source altitude' are two possible sources of such a systematic effect. It is shown that, for at least some dwells, significant interplanetary effects are not likely. The variation of the Alfvenic critical radius in solar wind dwells is calculated, showing that the high-velocity stream originates from a significantly lower altitude than the ambient solar wind.

Speed-up of the volumetric method of moments for the approximate RCS of large arbitrary-shaped dielectric targets

NASA Astrophysics Data System (ADS)

Moreno, Javier; Somolinos, Álvaro; Romero, Gustavo; González, Iván; Cátedra, Felipe

2017-08-01

A method for the rigorous computation of the electromagnetic scattering of large dielectric volumes is presented. One goal is to simplify the analysis of large dielectric targets with translational symmetries taken advantage of their Toeplitz symmetry. Then, the matrix-fill stage of the Method of Moments is efficiently obtained because the number of coupling terms to compute is reduced. The Multilevel Fast Multipole Method is applied to solve the problem. Structured meshes are obtained efficiently to approximate the dielectric volumes. The regular mesh grid is achieved by using parallelepipeds whose centres have been identified as internal to the target. The ray casting algorithm is used to classify the parallelepiped centres. It may become a bottleneck when too many points are evaluated in volumes defined by parametric surfaces, so a hierarchical algorithm is proposed to minimize the number of evaluations. Measurements and analytical results are included for validation purposes.

SSME structural dynamic model development

NASA Technical Reports Server (NTRS)

Foley, Michael J.

1989-01-01

The high pressure fuel turbopump (HPFTP) is a major component of the Space Shuttle Main Engine (SSME) powerhead. The device is a three stage centrifugal pump that is directly driven by a two stage hot gas turbine. The purpose of the pump is to deliver fuel (liquid hydrogen) from the low pressure fuel turbopump (LPFTP) through the main fuel valve (MFV) to the thrust chamber coolant circuits. In doing so, the pump pressurizes the fuel from an inlet pressure of approximately 178 psi to a discharge pressure of over 6000 psi. At full power level (FPL), the pump rotates at a speed of over 37,000 rpm while generating approximately 77,000 horsepower. Obviously, a pump failure at these speeds and power levels could jeopardize the mission. Results are summarized for work in which the solutions obtained from analytical models of the fuel turbopump impellers are compared with the results obtained from dynamic tests.

An analytically solvable three-body break-up model problem in hyperspherical coordinates

NASA Astrophysics Data System (ADS)

Ancarani, L. U.; Gasaneo, G.; Mitnik, D. M.

2012-10-01

An analytically solvable S-wave model for three particles break-up processes is presented. The scattering process is represented by a non-homogeneous Coulombic Schrödinger equation where the driven term is given by a Coulomb-like interaction multiplied by the product of a continuum wave function and a bound state in the particles coordinates. The closed form solution is derived in hyperspherical coordinates leading to an analytic expression for the associated scattering transition amplitude. The proposed scattering model contains most of the difficulties encountered in real three-body scattering problem, e.g., non-separability in the electrons' spherical coordinates and Coulombic asymptotic behavior. Since the coordinates' coupling is completely different, the model provides an alternative test to that given by the Temkin-Poet model. The knowledge of the analytic solution provides an interesting benchmark to test numerical methods dealing with the double continuum, in particular in the asymptotic regions. An hyperspherical Sturmian approach recently developed for three-body collisional problems is used to reproduce to high accuracy the analytical results. In addition to this, we generalized the model generating an approximate wave function possessing the correct radial asymptotic behavior corresponding to an S-wave three-body Coulomb problem. The model allows us to explore the typical structure of the solution of a three-body driven equation, to identify three regions (the driven, the Coulombic and the asymptotic), and to analyze how far one has to go to extract the transition amplitude.

Soliton polarization rotation in fiber lasers

NASA Astrophysics Data System (ADS)

Afanasjev, V. V.

1995-02-01

I have found the approximate analytical solution in explicit form for a vector soliton with an arbitrary component ratio. My solution describes the dependence of soliton intensity on polarization angle and also nonlinear polarization rotation. The analytical results agree well with the numerical simulations.

Goal-Oriented Probability Density Function Methods for Uncertainty Quantification

DTIC Science & Technology

2015-12-11

approximations or data-driven approaches. We investigated the accuracy of analytical tech- niques based Kubo -Van Kampen operator cumulant expansions for...analytical techniques based Kubo -Van Kampen operator cumulant expansions for Langevin equations driven by fractional Brownian motion and other noises

Demonstration/Validation of the Snap Sampler Passive Ground Water Sampling Device for Sampling Inorganic Analytes at the Former Pease Air Force Base

DTIC Science & Technology

2009-07-01

viii Unit Conversion Factors...sampler is also an economic alternative for sampling for inorganic analytes. ERDC/CRREL TR-09-12 xii Unit Conversion Factors Multiply By To Obtain...head- space and then covered with two layers of tightly fitting aluminum foil. To dissolve the analytes, the solutions were stirred for approximately

Dynamics of a bistable Miura-origami structure

NASA Astrophysics Data System (ADS)

Fang, Hongbin; Li, Suyi; Ji, Huimin; Wang, K. W.

2017-05-01

Origami-inspired structures and materials have shown extraordinary properties and performances originating from the intricate geometries of folding. However, current state of the art studies have mostly focused on static and quasistatic characteristics. This research performs a comprehensive experimental and analytical study on the dynamics of origami folding through investigating a stacked Miura-Ori (SMO) structure with intrinsic bistability. We fabricate and experimentally investigated a bistable SMO prototype with rigid facets and flexible crease lines. Under harmonic base excitation, the SMO exhibits both intrawell and interwell oscillations. Spectrum analyses reveal that the dominant nonlinearities of SMO are quadratic and cubic, which generate rich dynamics including subharmonic and chaotic oscillations. The identified nonlinearities indicate that a third-order polynomial can be employed to approximate the measured force-displacement relationship. Such an approximation is validated via numerical study by qualitatively reproducing the phenomena observed in the experiments. The dynamic characteristics of the bistable SMO resemble those of a Helmholtz-Duffing oscillator (HDO); this suggests the possibility of applying the established tools and insights of HDO to predict origami dynamics. We also show that the bistability of SMO can be programmed within a large design space via tailoring the crease stiffness and initial stress-free configurations. The results of this research offer a wealth of fundamental insights into the dynamics of origami folding, and provide a solid foundation for developing foldable and deployable structures and materials with embedded dynamic functionalities.

A two-dimensional computational study on the fluid-structure interaction cause of wing pitch changes in dipteran flapping flight.

PubMed

Ishihara, Daisuke; Horie, T; Denda, Mitsunori

2009-01-01

In this study, the passive pitching due to wing torsional flexibility and its lift generation in dipteran flight were investigated using (a) the non-linear finite element method for the fluid-structure interaction, which analyzes the precise motions of the passive pitching of the wing interacting with the surrounding fluid flow, (b) the fluid-structure interaction similarity law, which characterizes insect flight, (c) the lumped torsional flexibility model as a simplified dipteran wing, and (d) the analytical wing model, which explains the characteristics of the passive pitching motion in the simulation. Given sinusoidal flapping with a frequency below the natural frequency of the wing torsion, the resulting passive pitching in the steady state, under fluid damping, is approximately sinusoidal with the advanced phase shift. We demonstrate that the generated lift can support the weight of some Diptera.

Modular structure of the full-length DNA gyrase B subunit revealed by small-angle X-ray scattering.

PubMed

Costenaro, Lionel; Grossmann, J Günter; Ebel, Christine; Maxwell, Anthony

2007-03-01

DNA gyrase, the only topoisomerase able to introduce negative supercoils into DNA, is essential for bacterial transcription and replication; absent from humans, it is a successful target for antibacterials. From biophysical experiments in solution, we report a structural model at approximately 12-15 A resolution of the full-length B subunit (GyrB). Analytical ultracentrifugation shows that GyrB is mainly a nonglobular monomer. Ab initio modeling of small-angle X-ray scattering data for GyrB consistently yields a "tadpole"-like envelope. It allows us to propose an organization of GyrB into three domains-ATPase, Toprim, and Tail-based on their crystallographic and modeled structures. Our study reveals the modular organization of GyrB and points out its potential flexibility, needed during the gyrase catalytic cycle. It provides important insights into the supercoiling mechanism by gyrase and suggests new lines of research.

JPL Energy Consumption Program (ECP) documentation: A computer model simulating heating, cooling and energy loads in buildings. [low cost solar array efficiency

NASA Technical Reports Server (NTRS)

Lansing, F. L.; Chai, V. W.; Lascu, D.; Urbenajo, R.; Wong, P.

1978-01-01

The engineering manual provides a complete companion documentation about the structure of the main program and subroutines, the preparation of input data, the interpretation of output results, access and use of the program, and the detailed description of all the analytic, logical expressions and flow charts used in computations and program structure. A numerical example is provided and solved completely to show the sequence of computations followed. The program is carefully structured to reduce both user's time and costs without sacrificing accuracy. The user would expect a cost of CPU time of approximately $5.00 per building zone excluding printing costs. The accuracy, on the other hand, measured by deviation of simulated consumption from watt-hour meter readings, was found by many simulation tests not to exceed + or - 10 percent margin.

Structure of Weakly Charged Polyelectrolyte Brushes: Monomer Density Profiles

NASA Astrophysics Data System (ADS)

Borisov, O. V.; Zhulina, E. B.

1997-03-01

The internal structure (the monomer density profiles) of weakly charged polyelectrolyte brushes of different morphologies has been analyzed on the basis of the self-consistent-field approach. In contrast to previous studies based on the local electroneutrality approximation valid for sufficiently strongly charged or densely grafted (“osmotic") brushes we consider the opposite limit of sparse brushes which are unable to retain the counterions inside the brush. We have shown that an exact analytical solution of the SCF-equations is available in the case of a planar brush. In contrast to Gaussian monomer density profile known for “osmotic" polyelectrolyte brushes we have found that weakly charged brushes are characterized by constant monomer density. At the same time free ends of grafted polyions are distributed throughout the brush. Thus, the structural cross-over between polyelectrolyte “mushrooms" and dense brush regimes is established.

COI Structural Analysis Presentation

NASA Technical Reports Server (NTRS)

Cline, Todd; Stahl, H. Philip (Technical Monitor)

2001-01-01

This report discusses the structural analysis of the Next Generation Space Telescope Mirror System Demonstrator (NMSD) developed by Composite Optics Incorporated (COI) in support of the Next Generation Space Telescope (NGST) project. The mirror was submitted to Marshall Space Flight Center (MSFC) for cryogenic testing and evaluation. Once at MSFC, the mirror was lowered to approximately 40 K and the optical surface distortions were measured. Alongside this experiment, an analytical model was developed and used to compare to the test results. A NASTRAN finite element model was provided by COI and a thermal model was developed from it. Using the thermal model, steady state nodal temperatures were calculated based on the predicted environment of the large cryogenic test chamber at MSFC. This temperature distribution was applied in the structural analysis to solve for the deflections of the optical surface. Finally, these deflections were submitted for optical analysis and comparison to the interferometer test data.

Physics of cosmological cascades and observable properties

NASA Astrophysics Data System (ADS)

Fitoussi, T.; Belmont, R.; Malzac, J.; Marcowith, A.; Cohen-Tanugi, J.; Jean, P.

2017-04-01

TeV photons from extragalactic sources are absorbed in the intergalactic medium and initiate electromagnetic cascades. These cascades offer a unique tool to probe the properties of the universe at cosmological scales. We present a new Monte Carlo code dedicated to the physics of such cascades. This code has been tested against both published results and analytical approximations, and is made publicly available. Using this numerical tool, we investigate the main cascade properties (spectrum, halo extension and time delays), and study in detail their dependence on the physical parameters (extragalactic magnetic field, extragalactic background light, source redshift, source spectrum and beaming emission). The limitations of analytical solutions are emphasized. In particular, analytical approximations account only for the first generation of photons and higher branches of the cascade tree are neglected.

Transport of phase space densities through tetrahedral meshes using discrete flow mapping

NASA Astrophysics Data System (ADS)

Bajars, Janis; Chappell, David J.; Søndergaard, Niels; Tanner, Gregor

2017-01-01

Discrete flow mapping was recently introduced as an efficient ray based method determining wave energy distributions in complex built up structures. Wave energy densities are transported along ray trajectories through polygonal mesh elements using a finite dimensional approximation of a ray transfer operator. In this way the method can be viewed as a smoothed ray tracing method defined over meshed surfaces. Many applications require the resolution of wave energy distributions in three-dimensional domains, such as in room acoustics, underwater acoustics and for electromagnetic cavity problems. In this work we extend discrete flow mapping to three-dimensional domains by propagating wave energy densities through tetrahedral meshes. The geometric simplicity of the tetrahedral mesh elements is utilised to efficiently compute the ray transfer operator using a mixture of analytic and spectrally accurate numerical integration. The important issue of how to choose a suitable basis approximation in phase space whilst maintaining a reasonable computational cost is addressed via low order local approximations on tetrahedral faces in the position coordinate and high order orthogonal polynomial expansions in momentum space.

Use of the thin sheath approximation for obtaining ion temperatures from the ISEE 1 limited aperture RPA. [for magnetosphere

NASA Technical Reports Server (NTRS)

Comfort, R. H.; Baugher, C. R.; Chappell, C. R.

1982-01-01

A procedure for analyzing low-energy (less than approximately 100 eV) ion data from the plasma composition experiment on ISEE 1 is set forth. The method is based on a derived analytic expression for particle flux to a limited aperture retarding potential analyzer (RPA) in the thin sheath approximation, which makes allowance for some effects of a charged spacecraft on plasma particle trajectories. Calculations using simulated data are employed in testing the efficacy and accuracy of the technique. On the basis of an analysis of these calculation results and the mathematical model, the method is seen as being able to provide accurate ion temperatures from all good plasmaspheric RPA data. It is noted that corresponding densities and spacecraft potentials should be accurate when spacecraft potentials are negative but that they are subject to error for positive spacecraft potentials, particularly when ion Mach numbers are much less than 1. An analysis of data from a representative ISEE 1 pass produces a plasmasphere temperature profile that is consistent in overall structure with previous observations.

Bending of an Infinite beam on a base with two parameters in the absence of a part of the base

NASA Astrophysics Data System (ADS)

Aleksandrovskiy, Maxim; Zaharova, Lidiya

2018-03-01

Currently, in connection with the rapid development of high-rise construction and the improvement of joint operation of high-rise structures and bases models, the questions connected with the use of various calculation methods become topical. The rigor of analytical methods is capable of more detailed and accurate characterization of the structures behavior, which will affect the reliability of objects and can lead to a reduction in their cost. In the article, a model with two parameters is used as a computational model of the base that can effectively take into account the distributive properties of the base by varying the coefficient reflecting the shift parameter. The paper constructs the effective analytical solution of the problem of a beam of infinite length interacting with a two-parameter voided base. Using the Fourier integral equations, the original differential equation is reduced to the Fredholm integral equation of the second kind with a degenerate kernel, and all the integrals are solved analytically and explicitly, which leads to an increase in the accuracy of the computations in comparison with the approximate methods. The paper consider the solution of the problem of a beam loaded with a concentrated force applied at the point of origin with a fixed value of the length of the dip section. The paper gives the analysis of the obtained results values for various parameters of coefficient taking into account cohesion of the ground.

Large-amplitude nonlinear normal modes of the discrete sine lattices.

PubMed

Smirnov, Valeri V; Manevitch, Leonid I

2017-02-01

We present an analytical description of the large-amplitude stationary oscillations of the finite discrete system of harmonically coupled pendulums without any restrictions on their amplitudes (excluding a vicinity of π). Although this model has numerous applications in different fields of physics, it was studied earlier in the infinite limit only. The discrete chain with a finite length can be considered as a well analytical analog of the coarse-grain models of flexible polymers in the molecular dynamics simulations. The developed approach allows to find the dispersion relations for arbitrary amplitudes of the nonlinear normal modes. We emphasize that the long-wavelength approximation, which is described by well-known sine-Gordon equation, leads to an inadequate zone structure for the amplitudes of about π/2 even if the chain is long enough. An extremely complex zone structure at the large amplitudes corresponds to multiple resonances between nonlinear normal modes even with strongly different wave numbers. Due to the complexity of the dispersion relations the modes with shorter wavelengths may have smaller frequencies. The stability of the nonlinear normal modes under condition of the resonant interaction are discussed. It is shown that this interaction of the modes in the vicinity of the long wavelength edge of the spectrum leads to the localization of the oscillations. The thresholds of instability and localization are determined explicitly. The numerical simulation of the dynamics of a finite-length chain is in a good agreement with obtained analytical predictions.

Analytical and finite element performance evaluation of embedded piezoelectric sensors in polyethylene

NASA Astrophysics Data System (ADS)

Safaei, Mohsen; Anton, Steven R.

2017-04-01

A common application of piezoelectric transducers is to obtain operational data from working structures and dynamic components. Collected data can then be used to evaluate dynamic characterization of the system, perform structural health monitoring, or implement various other assessments. In some applications, piezoelectric transducers are bonded inside the host structure to satisfy system requirements; for example, piezoelectric transducers can be embedded inside the biopolymers of total joint replacements to evaluate the functionality of the artificial joint. The interactions between the piezoelectric device (inhomogeneity) and the surrounding polymer matrix determine the mechanical behavior of the matrix and the electromechanical behavior of the sensor. In this work, an analytical approach is employed to evaluate the electromechanical performance of 2-D plane strain piezoelectric elements of both circular and rectangular-shape inhomogeneities. These piezoelectric elements are embedded inside medical grade ultra-high molecular weight (UHMW) polyethylene, a material commonly used for bearing surfaces of joint replacements, such as total knee replacements (TKRs). Using the famous Eshelby inhomogeneity solution, the stress and electric field inside the circular (elliptical) inhomogeneity is obtained by decoupling the solution into purely elastic and dielectric systems of equations. For rectangular (non-elliptical) inhomogeneities, an approximation method based on the boundary integral function is utilized and the same decoupling method is employed. In order to validate the analytical result, a finite element analysis is performed for both the circular and rectangular inhomogeneities and the error for each case is calculated. For elliptical geometry, the error is less than 1% for stress and electric fields inside and outside the piezoelectric inhomogeneity, whereas, the error for non-elliptical geometry is obtained as 11% and 7% for stress and electric field inside the inhomogeneity, respectively.

Efficient finite element modeling of radiation forces on elastic particles of arbitrary size and geometry.

PubMed

Glynne-Jones, Peter; Mishra, Puja P; Boltryk, Rosemary J; Hill, Martyn

2013-04-01

A finite element based method is presented for calculating the acoustic radiation force on arbitrarily shaped elastic and fluid particles. Importantly for future applications, this development will permit the modeling of acoustic forces on complex structures such as biological cells, and the interactions between them and other bodies. The model is based on a non-viscous approximation, allowing the results from an efficient, numerical, linear scattering model to provide the basis for the second-order forces. Simulation times are of the order of a few seconds for an axi-symmetric structure. The model is verified against a range of existing analytical solutions (typical accuracy better than 0.1%), including those for cylinders, elastic spheres that are of significant size compared to the acoustic wavelength, and spheroidal particles.

THEORETICAL METHODS FOR COMPUTING ELECTRICAL CONDITIONS IN WIRE-PLATE ELECTROSTATIC PRECIPITATORS

EPA Science Inventory

The paper describes a new semi-empirical, approximate theory for predicting electrical conditions. In the approximate theory, analytical expressions are derived for calculating voltage-current characteristics and electric potential, electric field, and space charge density distri...

Investigating the two-moment characterisation of subcellular biochemical networks.

PubMed

Ullah, Mukhtar; Wolkenhauer, Olaf

2009-10-07

While ordinary differential equations (ODEs) form the conceptual framework for modelling many cellular processes, specific situations demand stochastic models to capture the influence of noise. The most common formulation of stochastic models for biochemical networks is the chemical master equation (CME). While stochastic simulations are a practical way to realise the CME, analytical approximations offer more insight into the influence of noise. Towards that end, the two-moment approximation (2MA) is a promising addition to the established analytical approaches including the chemical Langevin equation (CLE) and the related linear noise approximation (LNA). The 2MA approach directly tracks the mean and (co)variance which are coupled in general. This coupling is not obvious in CME and CLE and ignored by LNA and conventional ODE models. We extend previous derivations of 2MA by allowing (a) non-elementary reactions and (b) relative concentrations. Often, several elementary reactions are approximated by a single step. Furthermore, practical situations often require the use of relative concentrations. We investigate the applicability of the 2MA approach to the well-established fission yeast cell cycle model. Our analytical model reproduces the clustering of cycle times observed in experiments. This is explained through multiple resettings of M-phase promoting factor (MPF), caused by the coupling between mean and (co)variance, near the G2/M transition.

Calculation of Thermal Conductivity Coefficients of Electrons in Magnetized Dense Matter

NASA Astrophysics Data System (ADS)

Bisnovatyi-Kogan, G. S.; Glushikhina, M. V.

2018-04-01

The solution of Boltzmann equation for plasma in magnetic field with arbitrarily degenerate electrons and nondegenerate nuclei is obtained by Chapman-Enskog method. Functions generalizing Sonine polynomials are used for obtaining an approximate solution. Fully ionized plasma is considered. The tensor of the heat conductivity coefficients in nonquantized magnetic field is calculated. For nondegenerate and strongly degenerate plasma the asymptotic analytic formulas are obtained and compared with results of previous authors. The Lorentz approximation with neglecting of electron-electron encounters is asymptotically exact for strongly degenerate plasma. For the first time, analytical expressions for the heat conductivity tensor for nondegenerate electrons in the presence of a magnetic field are obtained in the three-polynomial approximation with account of electron-electron collisions. Account of the third polynomial improved substantially the precision of results. In the two-polynomial approximation, the obtained solution coincides with the published results. For strongly degenerate electrons, an asymptotically exact analytical solution for the heat conductivity tensor in the presence of a magnetic field is obtained for the first time. This solution has a considerably more complicated dependence on the magnetic field than those in previous publications and gives a several times smaller relative value of the thermal conductivity across the magnetic field at ωτ * 0.8.

Spatial dynamics of invasion: the geometry of introduced species.

PubMed

Korniss, Gyorgy; Caraco, Thomas

2005-03-07

Many exotic species combine low probability of establishment at each introduction with rapid population growth once introduction does succeed. To analyse this phenomenon, we note that invaders often cluster spatially when rare, and consequently an introduced exotic's population dynamics should depend on locally structured interactions. Ecological theory for spatially structured invasion relies on deterministic approximations, and determinism does not address the observed uncertainty of the exotic-introduction process. We take a new approach to the population dynamics of invasion and, by extension, to the general question of invasibility in any spatial ecology. We apply the physical theory for nucleation of spatial systems to a lattice-based model of competition between plant species, a resident and an invader, and the analysis reaches conclusions that differ qualitatively from the standard ecological theories. Nucleation theory distinguishes between dynamics of single- and multi-cluster invasion. Low introduction rates and small system size produce single-cluster dynamics, where success or failure of introduction is inherently stochastic. Single-cluster invasion occurs only if the cluster reaches a critical size, typically preceded by a number of failed attempts. For this case, we identify the functional form of the probability distribution of time elapsing until invasion succeeds. Although multi-cluster invasion for sufficiently large systems exhibits spatial averaging and almost-deterministic dynamics of the global densities, an analytical approximation from nucleation theory, known as Avrami's law, describes our simulation results far better than standard ecological approximations.

Integrated Analytic and Linearized Inverse Kinematics for Precise Full Body Interactions

NASA Astrophysics Data System (ADS)

Boulic, Ronan; Raunhardt, Daniel

Despite the large success of games grounded on movement-based interactions the current state of full body motion capture technologies still prevents the exploitation of precise interactions with complex environments. This paper focuses on ensuring a precise spatial correspondence between the user and the avatar. We build upon our past effort in human postural control with a Prioritized Inverse Kinematics framework. One of its key advantage is to ease the dynamic combination of postural and collision avoidance constraints. However its reliance on a linearized approximation of the problem makes it vulnerable to the well-known full extension singularity of the limbs. In such context the tracking performance is reduced and/or less believable intermediate postural solutions are produced. We address this issue by introducing a new type of analytic constraint that smoothly integrates within the prioritized Inverse Kinematics framework. The paper first recalls the background of full body 3D interactions and the advantages and drawbacks of the linearized IK solution. Then the Flexion-EXTension constraint (FLEXT in short) is introduced for the partial position control of limb-like articulated structures. Comparative results illustrate the interest of this new type of integrated analytical and linearized IK control.

Analytical assessment of some characteristic ratios for s-wave superconductors

NASA Astrophysics Data System (ADS)

Gonczarek, Ryszard; Krzyzosiak, Mateusz; Gonczarek, Adam; Jacak, Lucjan

2018-04-01

We evaluate some thermodynamic quantities and characteristic ratios that describe low- and high-temperature s-wave superconducting systems. Based on a set of fundamental equations derived within the conformal transformation method, a simple model is proposed and studied analytically. After including a one-parameter class of fluctuations in the density of states, the mathematical structure of the s-wave superconducting gap, the free energy difference, and the specific heat difference is found and discussed in an analytic manner. Both the zero-temperature limit T = 0 and the subcritical temperature range T ≲ T c are discussed using the method of successive approximations. The equation for the ratio R 1, relating the zero-temperature energy gap and the critical temperature, is formulated and solved numerically for various values of the model parameter. Other thermodynamic quantities are analyzed, including a characteristic ratio R 2, quantifying the dynamics of the specific heat jump at the critical temperature. It is shown that the obtained model results coincide with experimental data for low- T c superconductors. The prospect of application of the presented model in studies of high- T c superconductors and other superconducting systems of the new generation is also discussed.

The H I-to-H2 Transition in a Turbulent Medium

NASA Astrophysics Data System (ADS)

Bialy, Shmuel; Burkhart, Blakesley; Sternberg, Amiel

2017-07-01

We study the effect of density fluctuations induced by turbulence on the H I/H2 structure in photodissociation regions (PDRs) both analytically and numerically. We perform magnetohydrodynamic numerical simulations for both subsonic and supersonic turbulent gas and chemical H I/H2 balance calculations. We derive atomic-to-molecular density profiles and the H I column density probability density function (PDF) assuming chemical equilibrium. We find that, while the H I/H2 density profiles are strongly perturbed in turbulent gas, the mean H I column density is well approximated by the uniform-density analytic formula of Sternberg et al. The PDF width depends on (a) the radiation intensity-to-mean density ratio, (b) the sonic Mach number, and (c) the turbulence decorrelation scale, or driving scale. We derive an analytic model for the H I PDF and demonstrate how our model, combined with 21 cm observations, can be used to constrain the Mach number and driving scale of turbulent gas. As an example, we apply our model to observations of H I in the Perseus molecular cloud. We show that a narrow observed H I PDF may imply small-scale decorrelation, pointing to the potential importance of subcloud-scale turbulence driving.

Ultra-performance liquid chromatography/tandem mass spectrometric quantification of structurally diverse drug mixtures using an ESI-APCI multimode ionization source.

PubMed

Yu, Kate; Di, Li; Kerns, Edward; Li, Susan Q; Alden, Peter; Plumb, Robert S

2007-01-01

We report in this paper an ultra-performance liquid chromatography/tandem mass spectrometric (UPLC(R)/MS/MS) method utilizing an ESI-APCI multimode ionization source to quantify structurally diverse analytes. Eight commercial drugs were used as test compounds. Each LC injection was completed in 1 min using a UPLC system coupled with MS/MS multiple reaction monitoring (MRM) detection. Results from three separate sets of experiments are reported. In the first set of experiments, the eight test compounds were analyzed as a single mixture. The mass spectrometer was switching rapidly among four ionization modes (ESI+, ESI-, APCI-, and APCI+) during an LC run. Approximately 8-10 data points were collected across each LC peak. This was insufficient for a quantitative analysis. In the second set of experiments, four compounds were analyzed as a single mixture. The mass spectrometer was switching rapidly among four ionization modes during an LC run. Approximately 15 data points were obtained for each LC peak. Quantification results were obtained with a limit of detection (LOD) as low as 0.01 ng/mL. For the third set of experiments, the eight test compounds were analyzed as a batch. During each LC injection, a single compound was analyzed. The mass spectrometer was detecting at a particular ionization mode during each LC injection. More than 20 data points were obtained for each LC peak. Quantification results were also obtained. This single-compound analytical method was applied to a microsomal stability test. Compared with a typical HPLC method currently used for the microsomal stability test, the injection-to-injection cycle time was reduced to 1.5 min (UPLC method) from 3.5 min (HPLC method). The microsome stability results were comparable with those obtained by traditional HPLC/MS/MS.

Three-body correlations and conditional forces in suspensions of active hard disks

NASA Astrophysics Data System (ADS)

Härtel, Andreas; Richard, David; Speck, Thomas

2018-01-01

Self-propelled Brownian particles show rich out-of-equilibrium physics, for instance, the motility-induced phase separation (MIPS). While decades of studying the structure of liquids have established a deep understanding of passive systems, not much is known about correlations in active suspensions. In this work we derive an approximate analytic theory for three-body correlations and forces in systems of active Brownian disks starting from the many-body Smoluchowski equation. We use our theory to predict the conditional forces that act on a tagged particle and their dependence on the propulsion speed of self-propelled disks. We identify preferred directions of these forces in relation to the direction of propulsion and the positions of the surrounding particles. We further relate our theory to the effective swimming speed of the active disks, which is relevant for the physics of MIPS. To test and validate our theory, we additionally run particle-resolved computer simulations, for which we explicitly calculate the three-body forces. In this context, we discuss the modeling of active Brownian swimmers with nearly hard interaction potentials. We find very good agreement between our simulations and numerical solutions of our theory, especially for the nonequilibrium pair-distribution function. For our analytical results, we carefully discuss their range of validity in the context of the different levels of approximation we applied. This discussion allows us to study the individual contribution of particles to three-body forces and to the emerging structure. Thus, our work sheds light on the collective behavior, provides the basis for further studies of correlations in active suspensions, and makes a step towards an emerging liquid state theory.

Effect of coulomb spline on rotor dynamic response

NASA Technical Reports Server (NTRS)

Nataraj, C.; Nelson, H. D.; Arakere, N.

1985-01-01

A rigid rotor system coupled by a coulomb spline is modelled and analyzed by approximate analytical and numerical analytical methods. Expressions are derived for the variables of the resulting limit cycle and are shown to be quite accurate for a small departure from isotropy.

Analytical Solution for the Anisotropic Rabi Model: Effects of Counter-Rotating Terms

NASA Astrophysics Data System (ADS)

Zhang, Guofeng; Zhu, Hanjie

2015-03-01

The anisotropic Rabi model, which was proposed recently, differs from the original Rabi model: the rotating and counter-rotating terms are governed by two different coupling constants. This feature allows us to vary the counter-rotating interaction independently and explore the effects of it on some quantum properties. In this paper, we eliminate the counter-rotating terms approximately and obtain the analytical energy spectrums and wavefunctions. These analytical results agree well with the numerical calculations in a wide range of the parameters including the ultrastrong coupling regime. In the weak counter-rotating coupling limit we find out that the counter-rotating terms can be considered as the shifts to the parameters of the Jaynes-Cummings model. This modification shows the validness of the rotating-wave approximation on the assumption of near-resonance and relatively weak coupling. Moreover, the analytical expressions of several physics quantities are also derived, and the results show the break-down of the U(1)-symmetry and the deviation from the Jaynes-Cummings model.

Analytical solution for the anisotropic Rabi model: effects of counter-rotating terms.

PubMed

Zhang, Guofeng; Zhu, Hanjie

2015-03-04

The anisotropic Rabi model, which was proposed recently, differs from the original Rabi model: the rotating and counter-rotating terms are governed by two different coupling constants. This feature allows us to vary the counter-rotating interaction independently and explore the effects of it on some quantum properties. In this paper, we eliminate the counter-rotating terms approximately and obtain the analytical energy spectrums and wavefunctions. These analytical results agree well with the numerical calculations in a wide range of the parameters including the ultrastrong coupling regime. In the weak counter-rotating coupling limit we find out that the counter-rotating terms can be considered as the shifts to the parameters of the Jaynes-Cummings model. This modification shows the validness of the rotating-wave approximation on the assumption of near-resonance and relatively weak coupling. Moreover, the analytical expressions of several physics quantities are also derived, and the results show the break-down of the U(1)-symmetry and the deviation from the Jaynes-Cummings model.

Non-Schwarzschild black-hole metric in four dimensional higher derivative gravity: Analytical approximation

NASA Astrophysics Data System (ADS)

Kokkotas, K. D.; Konoplya, R. A.; Zhidenko, A.

2017-09-01

Higher derivative extensions of Einstein gravity are important within the string theory approach to gravity and as alternative and effective theories of gravity. H. Lü, A. Perkins, C. Pope, and K. Stelle [Phys. Rev. Lett. 114, 171601 (2015), 10.1103/PhysRevLett.114.171601] found a numerical solution describing a spherically symmetric non-Schwarzschild asymptotically flat black hole in Einstein gravity with added higher derivative terms. Using the general and quickly convergent parametrization in terms of the continued fractions, we represent this numerical solution in the analytical form, which is accurate not only near the event horizon or far from the black hole, but in the whole space. Thereby, the obtained analytical form of the metric allows one to study easily all the further properties of the black hole, such as thermodynamics, Hawking radiation, particle motion, accretion, perturbations, stability, quasinormal spectrum, etc. Thus, the found analytical approximate representation can serve in the same way as an exact solution.

Analytical Solution for the Anisotropic Rabi Model: Effects of Counter-Rotating Terms

PubMed Central

Zhang, Guofeng; Zhu, Hanjie

2015-01-01

The anisotropic Rabi model, which was proposed recently, differs from the original Rabi model: the rotating and counter-rotating terms are governed by two different coupling constants. This feature allows us to vary the counter-rotating interaction independently and explore the effects of it on some quantum properties. In this paper, we eliminate the counter-rotating terms approximately and obtain the analytical energy spectrums and wavefunctions. These analytical results agree well with the numerical calculations in a wide range of the parameters including the ultrastrong coupling regime. In the weak counter-rotating coupling limit we find out that the counter-rotating terms can be considered as the shifts to the parameters of the Jaynes-Cummings model. This modification shows the validness of the rotating-wave approximation on the assumption of near-resonance and relatively weak coupling. Moreover, the analytical expressions of several physics quantities are also derived, and the results show the break-down of the U(1)-symmetry and the deviation from the Jaynes-Cummings model. PMID:25736827

Unbiased Scanning Method and Data Banking Approach Using Ultra-High Performance Liquid Chromatography Coupled with High-Resolution Mass Spectrometry for Quantitative Comparison of Metabolite Exposure in Plasma across Species Analyzed at Different Dates.

PubMed

Gao, Hongying; Deng, Shibing; Obach, R Scott

2015-12-01

An unbiased scanning methodology using ultra high-performance liquid chromatography coupled with high-resolution mass spectrometry was used to bank data and plasma samples for comparing the data generated at different dates. This method was applied to bank the data generated earlier in animal samples and then to compare the exposure to metabolites in animal versus human for safety assessment. With neither authentic standards nor prior knowledge of the identities and structures of metabolites, full scans for precursor ions and all ion fragments (AIF) were employed with a generic gradient LC method to analyze plasma samples at positive and negative polarity, respectively. In a total of 22 tested drugs and metabolites, 21 analytes were detected using this unbiased scanning method except that naproxen was not detected due to low sensitivity at negative polarity and interference at positive polarity; and 4'- or 5-hydroxy diclofenac was not separated by a generic UPLC method. Statistical analysis of the peak area ratios of the analytes versus the internal standard in five repetitive analyses over approximately 1 year demonstrated that the analysis variation was significantly different from sample instability. The confidence limits for comparing the exposure using peak area ratio of metabolites in animal plasma versus human plasma measured over approximately 1 year apart were comparable to the analysis undertaken side by side on the same days. These statistical analysis results showed it was feasible to compare data generated at different dates with neither authentic standards nor prior knowledge of the analytes.

Analytical approximation of a distorted reflector surface defined by a discrete set of points

NASA Technical Reports Server (NTRS)

Acosta, Roberto J.; Zaman, Afroz A.

1988-01-01

Reflector antennas on Earth orbiting spacecrafts generally cannot be described analytically. The reflector surface is subjected to a large temperature fluctuation and gradients, and is thus warped from its true geometrical shape. Aside from distortion by thermal stresses, reflector surfaces are often purposely shaped to minimize phase aberrations and scanning losses. To analyze distorted reflector antennas defined by discrete surface points, a numerical technique must be applied to compute an interpolatory surface passing through a grid of discrete points. In this paper, the distorted reflector surface points are approximated by two analytical components: an undistorted surface component and a surface error component. The undistorted surface component is a best fit paraboloid polynomial for the given set of points and the surface error component is a Fourier series expansion of the deviation of the actual surface points, from the best fit paraboloid. By applying the numerical technique to approximate the surface normals of the distorted reflector surface, the induced surface current can be obtained using physical optics technique. These surface currents are integrated to find the far field radiation pattern.

Energy analysis in the elliptic restricted three-body problem

NASA Astrophysics Data System (ADS)

Qi, Yi; de Ruiter, Anton

2018-07-01

The gravity assist or flyby is investigated by analysing the inertial energy of a test particle in the elliptic restricted three-body problem (ERTBP), where two primary bodies are moving in elliptic orbits. First, the expression of the derivation of energy is obtained and discussed. Then, the approximate expressions of energy change in a circular neighbourhood of the smaller primary are derived. Numerical computation indicates that the obtained expressions can be applied to study the flyby problem of the nine planets and the Moon in the Solar system. Parameters related to the flyby are discussed analytically and numerically. The optimal conditions, including the position and time of the periapsis, for a flyby orbit are found to make a maximum energy gain or loss. Finally, the mechanical process of a flyby orbit is uncovered by an approximate expression in the ERTBP. Numerical computations testify that our analytical results well approximate the mechanical process of flyby orbits obtained by the numerical simulation in the ERTBP. Compared with the previous research established in the patched-conic method and numerical calculation, our analytical investigations based on a more elaborate derivation get more original results.

Analysis of THG modes for femtosecond laser pulse

NASA Astrophysics Data System (ADS)

Trofimov, Vyacheslav A.; Sidorov, Pavel S.

2017-05-01

THG is used nowadays in many practical applications such as a substance diagnostics, and biological objects imaging, and etc. With developing of new materials and technology (for example, photonic crystal) an attention to THG process analysis grow. Therefore, THG features understanding are a modern problem. Early we have developed new analytical approach based on using the problem invariant for analytical solution construction of the THG process. It should be stressed that we did not use a basic wave non-depletion approximation. Nevertheless, a long pulse duration approximation and plane wave approximation has applied. The analytical solution demonstrates, in particular, an optical bistability property (and may other regimes of frequency tripling) for the third harmonic generation process. But, obviously, this approach does not reflect an influence of a medium dispersion on the frequency tripling. Therefore, in this paper we analyze THG efficiency of a femtosecond laser pulse taking into account a second order dispersion affect as well as self- and crossmodulation of the interacting waves affect on the frequency conversion process. Analysis is made using a computer simulation on the base of Schrödinger equations describing the process under consideration.

Energy Analysis in the Elliptic Restricted Three-body Problem

NASA Astrophysics Data System (ADS)

Qi, Yi; de Ruiter, Anton

2018-05-01

The gravity assist or flyby is investigated by analyzing the inertial energy of a test particle in the elliptic restricted three-body problem (ERTBP), where two primary bodies are moving in elliptic orbits. Firstly, the expression of the derivation of energy is obtained and discussed. Then, the approximate expressions of energy change in a circular neighborhood of the smaller primary are derived. Numerical computation indicates that the obtained expressions can be applied to study the flyby problem of the nine planets and the Moon in the solar system. Parameters related to the flyby are discussed analytically and numerically. The optimal conditions, including the position and time of the periapsis, for a flyby orbit are found to make a maximum energy gain or loss. Finally, the mechanical process of a flyby orbit is uncovered by an approximate expression in the ERTBP. Numerical computations testify that our analytical results well approximate the mechanical process of flyby orbits obtained by the numerical simulation in the ERTBP. Compared with the previous research established in the patched-conic method and numerical calculation, our analytical investigations based on a more elaborate derivation get more original results.

Small-x asymptotics of the quark helicity distribution: Analytic results

DOE PAGES

Kovchegov, Yuri V.; Pitonyak, Daniel; Sievert, Matthew D.

2017-06-15

In this Letter, we analytically solve the evolution equations for the small-x asymptotic behavior of the (flavor singlet) quark helicity distribution in the large- N c limit. Here, these evolution equations form a set of coupled integro-differential equations, which previously could only be solved numerically. This approximate numerical solution, however, revealed simplifying properties of the small-x asymptotics, which we exploit here to obtain an analytic solution.

Analytic representation of FK/Fπ in two loop chiral perturbation theory

NASA Astrophysics Data System (ADS)

Ananthanarayan, B.; Bijnens, Johan; Friot, Samuel; Ghosh, Shayan

2018-05-01

We present an analytic representation of FK/Fπ as calculated in three-flavor two-loop chiral perturbation theory, which involves expressing three mass scale sunsets in terms of Kampé de Fériet series. We demonstrate how approximations may be made to obtain relatively compact analytic representations. An illustrative set of fits using lattice data is also presented, which shows good agreement with existing fits.

Spiral trajectory design: a flexible numerical algorithm and base analytical equations.

PubMed

Pipe, James G; Zwart, Nicholas R

2014-01-01

Spiral-based trajectories for magnetic resonance imaging can be advantageous, but are often cumbersome to design or create. This work presents a flexible numerical algorithm for designing trajectories based on explicit definition of radial undersampling, and also gives several analytical expressions for charactering the base (critically sampled) class of these trajectories. Expressions for the gradient waveform, based on slew and amplitude limits, are developed such that a desired pitch in the spiral k-space trajectory is followed. The source code for this algorithm, written in C, is publicly available. Analytical expressions approximating the spiral trajectory (ignoring the radial component) are given to characterize measurement time, gradient heating, maximum gradient amplitude, and off-resonance phase for slew-limited and gradient amplitude-limited cases. Several numerically calculated trajectories are illustrated, and base Archimedean spirals are compared with analytically obtained results. Several different waveforms illustrate that the desired slew and amplitude limits are reached, as are the desired undersampling patterns, using the numerical method. For base Archimedean spirals, the results of the numerical and analytical approaches are in good agreement. A versatile numerical algorithm was developed, and was written in publicly available code. Approximate analytical formulas are given that help characterize spiral trajectories. Copyright © 2013 Wiley Periodicals, Inc.

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

On the effect of the degeneracy among dark energy parameters

NASA Astrophysics Data System (ADS)

Gong, Yungui; Gao, Qing

2014-01-01

The dynamics of scalar fields as dark energy is well approximated by some general relations between the equation of state parameter and the fractional energy density . Based on the approximation, for slowly rolling scalar fields, we derived the analytical expressions of which reduce to the popular Chevallier-Polarski-Linder parametrization with an explicit degeneracy relation between and . The models approximate the dynamics of scalar fields well and help eliminate the degeneracies among , , and . With the explicit degeneracy relations, we test their effects on the constraints of the cosmological parameters. We find that: (1) The analytical relations between and for the two models are consistent with observational data. (2) The degeneracies have little effect on . (3) The error of was reduced about 30 % with the degeneracy relations.

Local CC2 response method based on the Laplace transform: analytic energy gradients for ground and excited states.

PubMed

Ledermüller, Katrin; Schütz, Martin

2014-04-28

A multistate local CC2 response method for the calculation of analytic energy gradients with respect to nuclear displacements is presented for ground and electronically excited states. The gradient enables the search for equilibrium geometries of extended molecular systems. Laplace transform is used to partition the eigenvalue problem in order to obtain an effective singles eigenvalue problem and adaptive, state-specific local approximations. This leads to an approximation in the energy Lagrangian, which however is shown (by comparison with the corresponding gradient method without Laplace transform) to be of no concern for geometry optimizations. The accuracy of the local approximation is tested and the efficiency of the new code is demonstrated by application calculations devoted to a photocatalytic decarboxylation process of present interest.

Analytical methods for determination of mycotoxins: a review.

PubMed

Turner, Nicholas W; Subrahmanyam, Sreenath; Piletsky, Sergey A

2009-01-26

Mycotoxins are small (MW approximately 700), toxic chemical products formed as secondary metabolites by a few fungal species that readily colonise crops and contaminate them with toxins in the field or after harvest. Ochratoxins and Aflatoxins are mycotoxins of major significance and hence there has been significant research on broad range of analytical and detection techniques that could be useful and practical. Due to the variety of structures of these toxins, it is impossible to use one standard technique for analysis and/or detection. Practical requirements for high-sensitivity analysis and the need for a specialist laboratory setting create challenges for routine analysis. Several existing analytical techniques, which offer flexible and broad-based methods of analysis and in some cases detection, have been discussed in this manuscript. There are a number of methods used, of which many are lab-based, but to our knowledge there seems to be no single technique that stands out above the rest, although analytical liquid chromatography, commonly linked with mass spectroscopy is likely to be popular. This review manuscript discusses (a) sample pre-treatment methods such as liquid-liquid extraction (LLE), supercritical fluid extraction (SFE), solid phase extraction (SPE), (b) separation methods such as (TLC), high performance liquid chromatography (HPLC), gas chromatography (GC), and capillary electrophoresis (CE) and (c) others such as ELISA. Further currents trends, advantages and disadvantages and future prospects of these methods have been discussed.

Dynamics of the surveying gyrocompass

NASA Astrophysics Data System (ADS)

Petrenko, V. E.; Zakharenko, S. A.; Ponomarenko, A. E.

The dynamics of the surveying gyrocompass is investigated analytically for the case of perturbations due to ball bearing imperfections. Approximate analytical expressions are obtained for calculating the natural frequencies of the compass in the presence of parametric perturbations of this kind. An example of natural frequency calculations is presented.

Fixation Times in Deme Structured, Finite Populations with Rare Migration

NASA Astrophysics Data System (ADS)

Hauert, Christoph; Chen, Yu-Ting; Imhof, Lorens A.

2014-08-01

Population structure affects both the outcome and the speed of evolutionary dynamics. Here we consider a finite population that is divided into subpopulations called demes. The dynamics within the demes are stochastic and frequency-dependent. Individuals can adopt one of two strategic types, or . The fitness of each individual is determined by interactions with other individuals in the same deme. With small probability, proportional to fitness, individuals migrate to other demes. The outcome of these dynamics has been studied earlier by analyzing the fixation probability of a single mutant in an otherwise homogeneous population. These results give only a partial picture of the dynamics, because the time when fixation occurs can be exceedingly large. In this paper, we study the impact of deme structures on the speed of evolution. We derive analytical approximations of fixation times in the limit of rare migration and rare mutation. In this limit, the conditional fixation time of a single mutant in a population is the same as that of a single in an population. For the prisoner's dilemma game, simulation results fit very well with our analytical predictions and demonstrate that fixation takes place in a moderate amount of time as compared to the expected waiting time until a mutant successfully invades and fixates. The simulations also confirm that the conditional fixation time of a single cooperator is indeed the same as that of a single defector.

CMB weak-lensing beyond the Born approximation: a numerical approach

NASA Astrophysics Data System (ADS)

Fabbian, Giulio; Calabrese, Matteo; Carbone, Carmelita

2018-02-01

We perform a complete study of the gravitational lensing effect beyond the Born approximation on the Cosmic Microwave Background (CMB) anisotropies using a multiple-lens raytracing technique through cosmological N-body simulations of the DEMNUni suite. The impact of second-order effects accounting for the non-linear evolution of large-scale structures is evaluated propagating for the first time the full CMB lensing jacobian together with the light rays trajectories. We carefully investigate the robustness of our approach against several numerical effects in the raytracing procedure and in the N-body simulation itself, and find no evidence of large contaminations. We discuss the impact of beyond-Born corrections on lensed CMB observables, and compare our results with recent analytical predictions that appeared in the literature, finding a good agreement, and extend these results to smaller angular scales. We measure the gravitationally-induced CMB polarization rotation that appears in the geodesic equation at second order, and compare this result with the latest analytical predictions. We then present the detection prospect of beyond-Born effects with the future CMB-S4 experiment. We show that corrections to the temperature power spectrum can be measured only if a good control of the extragalactic foregrounds is achieved. Conversely, the beyond-Born corrections on E and B-modes power spectra will be much more difficult to detect.

Gaussian closure technique applied to the hysteretic Bouc model with non-zero mean white noise excitation

NASA Astrophysics Data System (ADS)

Waubke, Holger; Kasess, Christian H.

2016-11-01

Devices that emit structure-borne sound are commonly decoupled by elastic components to shield the environment from acoustical noise and vibrations. The elastic elements often have a hysteretic behavior that is typically neglected. In order to take hysteretic behavior into account, Bouc developed a differential equation for such materials, especially joints made of rubber or equipped with dampers. In this work, the Bouc model is solved by means of the Gaussian closure technique based on the Kolmogorov equation. Kolmogorov developed a method to derive probability density functions for arbitrary explicit first-order vector differential equations under white noise excitation using a partial differential equation of a multivariate conditional probability distribution. Up to now no analytical solution of the Kolmogorov equation in conjunction with the Bouc model exists. Therefore a wide range of approximate solutions, especially the statistical linearization, were developed. Using the Gaussian closure technique that is an approximation to the Kolmogorov equation assuming a multivariate Gaussian distribution an analytic solution is derived in this paper for the Bouc model. For the stationary case the two methods yield equivalent results, however, in contrast to statistical linearization the presented solution allows to calculate the transient behavior explicitly. Further, stationary case leads to an implicit set of equations that can be solved iteratively with a small number of iterations and without instabilities for specific parameter sets.

Unimolecular diffusion-mediated reactions with a nonrandom time-modulated absorbing barrier

NASA Technical Reports Server (NTRS)

Bashford, D.; Weaver, D. L.

1986-01-01

A diffusion-reaction model with time-dependent reactivity is formulated and applied to unimolecular reactions. The model is solved exactly numerically and approximately analytically for the unreacted fraction as a function of time. It is shown that the approximate analytical solution is valid even when the system is far from equilibrium, and when the reactivity probability is more complicated than a square-wave function of time. A discussion is also given of an approach to problems of this type using a stochastically fluctuating reactivity, and the first-passage time for a particular example is derived.

Spline methods for approximating quantile functions and generating random samples

NASA Technical Reports Server (NTRS)

Schiess, J. R.; Matthews, C. G.

1985-01-01

Two cubic spline formulations are presented for representing the quantile function (inverse cumulative distribution function) of a random sample of data. Both B-spline and rational spline approximations are compared with analytic representations of the quantile function. It is also shown how these representations can be used to generate random samples for use in simulation studies. Comparisons are made on samples generated from known distributions and a sample of experimental data. The spline representations are more accurate for multimodal and skewed samples and to require much less time to generate samples than the analytic representation.

Analytical Method of Approximating the Motion of a Spinning Vehicle with Variable Mass and Inertia Properties Acted Upon by Several Disturbing Parameters

NASA Technical Reports Server (NTRS)

Buglia, James J.; Young, George R.; Timmons, Jesse D.; Brinkworth, Helen S.

1961-01-01

An analytical method has been developed which approximates the dispersion of a spinning symmetrical body in a vacuum, with time-varying mass and inertia characteristics, under the action of several external disturbances-initial pitching rate, thrust misalignment, and dynamic unbalance. The ratio of the roll inertia to the pitch or yaw inertia is assumed constant. Spin was found to be very effective in reducing the dispersion due to an initial pitch rate or thrust misalignment, but was completely Ineffective in reducing the dispersion of a dynamically unbalanced body.

Theoretical Assessment of Compressibility Factor of Gases by Using Second Virial Coefficient

NASA Astrophysics Data System (ADS)

Mamedov, Bahtiyar A.; Somuncu, Elif; Askerov, Iskender M.

2018-01-01

We present a new analytical approximation for determining the compressibility factor of real gases at various temperature values. This algorithm is suitable for the accurate evaluation of the compressibility factor using the second virial coefficient with a Lennard-Jones (12-6) potential. Numerical examples are presented for the gases H2, N2, He, CO2, CH4 and air, and the results are compared with other studies in the literature. Our results showed good agreement with the data in the literature. The consistency of the results demonstrates the effectiveness of our analytical approximation for real gases.

Approximate Solutions for Ideal Dam-Break Sediment-Laden Flows on Uniform Slopes

NASA Astrophysics Data System (ADS)

Ni, Yufang; Cao, Zhixian; Borthwick, Alistair; Liu, Qingquan

2018-04-01

Shallow water hydro-sediment-morphodynamic (SHSM) models have been applied increasingly widely in hydraulic engineering and geomorphological studies over the past few decades. Analytical and approximate solutions are usually sought to verify such models and therefore confirm their credibility. Dam-break flows are often evoked because such flows normally feature shock waves and contact discontinuities that warrant refined numerical schemes to solve. While analytical and approximate solutions to clear-water dam-break flows have been available for some time, such solutions are rare for sediment transport in dam-break flows. Here we aim to derive approximate solutions for ideal dam-break sediment-laden flows resulting from the sudden release of a finite volume of frictionless, incompressible water-sediment mixture on a uniform slope. The approximate solutions are presented for three typical sediment transport scenarios, i.e., pure advection, pure sedimentation, and concurrent entrainment and deposition. Although the cases considered in this paper are not real, the approximate solutions derived facilitate suitable benchmark tests for evaluating SHSM models, especially presently when shock waves can be numerically resolved accurately with a suite of finite volume methods, while the accuracy of the numerical solutions of contact discontinuities in sediment transport remains generally poorer.

Error analysis of analytic solutions for self-excited near-symmetric rigid bodies - A numerical study

NASA Technical Reports Server (NTRS)

Kia, T.; Longuski, J. M.

1984-01-01

Analytic error bounds are presented for the solutions of approximate models for self-excited near-symmetric rigid bodies. The error bounds are developed for analytic solutions to Euler's equations of motion. The results are applied to obtain a simplified analytic solution for Eulerian rates and angles. The results of a sample application of the range and error bound expressions for the case of the Galileo spacecraft experiencing transverse torques demonstrate the use of the bounds in analyses of rigid body spin change maneuvers.

Two-dimensional analytic weighting functions for limb scattering

NASA Astrophysics Data System (ADS)

Zawada, D. J.; Bourassa, A. E.; Degenstein, D. A.

2017-10-01

Through the inversion of limb scatter measurements it is possible to obtain vertical profiles of trace species in the atmosphere. Many of these inversion methods require what is often referred to as weighting functions, or derivatives of the radiance with respect to concentrations of trace species in the atmosphere. Several radiative transfer models have implemented analytic methods to calculate weighting functions, alleviating the computational burden of traditional numerical perturbation methods. Here we describe the implementation of analytic two-dimensional weighting functions, where derivatives are calculated relative to atmospheric constituents in a two-dimensional grid of altitude and angle along the line of sight direction, in the SASKTRAN-HR radiative transfer model. Two-dimensional weighting functions are required for two-dimensional inversions of limb scatter measurements. Examples are presented where the analytic two-dimensional weighting functions are calculated with an underlying one-dimensional atmosphere. It is shown that the analytic weighting functions are more accurate than ones calculated with a single scatter approximation, and are orders of magnitude faster than a typical perturbation method. Evidence is presented that weighting functions for stratospheric aerosols calculated under a single scatter approximation may not be suitable for use in retrieval algorithms under solar backscatter conditions.

An improved 3D MoF method based on analytical partial derivatives

NASA Astrophysics Data System (ADS)

Chen, Xiang; Zhang, Xiong

2016-12-01

MoF (Moment of Fluid) method is one of the most accurate approaches among various surface reconstruction algorithms. As other second order methods, MoF method needs to solve an implicit optimization problem to obtain the optimal approximate surface. Therefore, the partial derivatives of the objective function have to be involved during the iteration for efficiency and accuracy. However, to the best of our knowledge, the derivatives are currently estimated numerically by finite difference approximation because it is very difficult to obtain the analytical derivatives of the object function for an implicit optimization problem. Employing numerical derivatives in an iteration not only increase the computational cost, but also deteriorate the convergence rate and robustness of the iteration due to their numerical error. In this paper, the analytical first order partial derivatives of the objective function are deduced for 3D problems. The analytical derivatives can be calculated accurately, so they are incorporated into the MoF method to improve its accuracy, efficiency and robustness. Numerical studies show that by using the analytical derivatives the iterations are converged in all mixed cells with the efficiency improvement of 3 to 4 times.

Testing approximations for non-linear gravitational clustering

NASA Technical Reports Server (NTRS)

Coles, Peter; Melott, Adrian L.; Shandarin, Sergei F.

1993-01-01

The accuracy of various analytic approximations for following the evolution of cosmological density fluctuations into the nonlinear regime is investigated. The Zel'dovich approximation is found to be consistently the best approximation scheme. It is extremely accurate for power spectra characterized by n = -1 or less; when the approximation is 'enhanced' by truncating highly nonlinear Fourier modes the approximation is excellent even for n = +1. The performance of linear theory is less spectrum-dependent, but this approximation is less accurate than the Zel'dovich one for all cases because of the failure to treat dynamics. The lognormal approximation generally provides a very poor fit to the spatial pattern.

Approximation and inference methods for stochastic biochemical kinetics—a tutorial review

NASA Astrophysics Data System (ADS)

Schnoerr, David; Sanguinetti, Guido; Grima, Ramon

2017-03-01

Stochastic fluctuations of molecule numbers are ubiquitous in biological systems. Important examples include gene expression and enzymatic processes in living cells. Such systems are typically modelled as chemical reaction networks whose dynamics are governed by the chemical master equation. Despite its simple structure, no analytic solutions to the chemical master equation are known for most systems. Moreover, stochastic simulations are computationally expensive, making systematic analysis and statistical inference a challenging task. Consequently, significant effort has been spent in recent decades on the development of efficient approximation and inference methods. This article gives an introduction to basic modelling concepts as well as an overview of state of the art methods. First, we motivate and introduce deterministic and stochastic methods for modelling chemical networks, and give an overview of simulation and exact solution methods. Next, we discuss several approximation methods, including the chemical Langevin equation, the system size expansion, moment closure approximations, time-scale separation approximations and hybrid methods. We discuss their various properties and review recent advances and remaining challenges for these methods. We present a comparison of several of these methods by means of a numerical case study and highlight some of their respective advantages and disadvantages. Finally, we discuss the problem of inference from experimental data in the Bayesian framework and review recent methods developed the literature. In summary, this review gives a self-contained introduction to modelling, approximations and inference methods for stochastic chemical kinetics.

Testing higher-order Lagrangian perturbation theory against numerical simulation. 1: Pancake models

NASA Technical Reports Server (NTRS)

Buchert, T.; Melott, A. L.; Weiss, A. G.

1993-01-01

We present results showing an improvement of the accuracy of perturbation theory as applied to cosmological structure formation for a useful range of quasi-linear scales. The Lagrangian theory of gravitational instability of an Einstein-de Sitter dust cosmogony investigated and solved up to the third order is compared with numerical simulations. In this paper we study the dynamics of pancake models as a first step. In previous work the accuracy of several analytical approximations for the modeling of large-scale structure in the mildly non-linear regime was analyzed in the same way, allowing for direct comparison of the accuracy of various approximations. In particular, the Zel'dovich approximation (hereafter ZA) as a subclass of the first-order Lagrangian perturbation solutions was found to provide an excellent approximation to the density field in the mildly non-linear regime (i.e. up to a linear r.m.s. density contrast of sigma is approximately 2). The performance of ZA in hierarchical clustering models can be greatly improved by truncating the initial power spectrum (smoothing the initial data). We here explore whether this approximation can be further improved with higher-order corrections in the displacement mapping from homogeneity. We study a single pancake model (truncated power-spectrum with power-spectrum with power-index n = -1) using cross-correlation statistics employed in previous work. We found that for all statistical methods used the higher-order corrections improve the results obtained for the first-order solution up to the stage when sigma (linear theory) is approximately 1. While this improvement can be seen for all spatial scales, later stages retain this feature only above a certain scale which is increasing with time. However, third-order is not much improvement over second-order at any stage. The total breakdown of the perturbation approach is observed at the stage, where sigma (linear theory) is approximately 2, which corresponds to the onset of hierarchical clustering. This success is found at a considerable higher non-linearity than is usual for perturbation theory. Whether a truncation of the initial power-spectrum in hierarchical models retains this improvement will be analyzed in a forthcoming work.

Scaling and percolation in the small-world network model

NASA Astrophysics Data System (ADS)

Newman, M. E. J.; Watts, D. J.

1999-12-01

In this paper we study the small-world network model of Watts and Strogatz, which mimics some aspects of the structure of networks of social interactions. We argue that there is one nontrivial length-scale in the model, analogous to the correlation length in other systems, which is well-defined in the limit of infinite system size and which diverges continuously as the randomness in the network tends to zero, giving a normal critical point in this limit. This length-scale governs the crossover from large- to small-world behavior in the model, as well as the number of vertices in a neighborhood of given radius on the network. We derive the value of the single critical exponent controlling behavior in the critical region and the finite size scaling form for the average vertex-vertex distance on the network, and, using series expansion and Padé approximants, find an approximate analytic form for the scaling function. We calculate the effective dimension of small-world graphs and show that this dimension varies as a function of the length-scale on which it is measured, in a manner reminiscent of multifractals. We also study the problem of site percolation on small-world networks as a simple model of disease propagation, and derive an approximate expression for the percolation probability at which a giant component of connected vertices first forms (in epidemiological terms, the point at which an epidemic occurs). The typical cluster radius satisfies the expected finite size scaling form with a cluster size exponent close to that for a random graph. All our analytic results are confirmed by extensive numerical simulations of the model.

Cosmological Perturbation Theory and the Spherical Collapse model - I. Gaussian initial conditions

NASA Astrophysics Data System (ADS)

Fosalba, Pablo; Gaztanaga, Enrique

1998-12-01

We present a simple and intuitive approximation for solving the perturbation theory (PT) of small cosmic fluctuations. We consider only the spherically symmetric or monopole contribution to the PT integrals, which yields the exact result for tree-graphs (i.e. at leading order). We find that the non-linear evolution in Lagrangian space is then given by a simple local transformation over the initial conditions, although it is not local in Euler space. This transformation is found to be described by the spherical collapse (SC) dynamics, as it is the exact solution in the shearless (and therefore local) approximation in Lagrangian space. Taking advantage of this property, it is straightforward to derive the one-point cumulants, xi_J, for both the unsmoothed and smoothed density fields to arbitrary order in the perturbative regime. To leading-order this reproduces, and provides us with a simple explanation for, the exact results obtained by Bernardeau. We then show that the SC model leads to accurate estimates for the next corrective terms when compared with the results derived in the exact perturbation theory making use of the loop calculations. The agreement is within a few per cent for the hierarchical ratios S_J=xi_J/xi^J-1_2. We compare our analytic results with N-body simulations, which turn out to be in very good agreement up to scales where sigma~1. A similar treatment is presented to estimate higher order corrections in the Zel'dovich approximation. These results represent a powerful and readily usable tool to produce analytical predictions that describe the gravitational clustering of large-scale structure in the weakly non-linear regime.

Analytical Solutions for Radiative Transfer: Implications for Giant Planet Formation by Disk Instability

NASA Astrophysics Data System (ADS)

Boss, Alan P.

2009-03-01

The disk instability mechanism for giant planet formation is based on the formation of clumps in a marginally gravitationally unstable protoplanetary disk, which must lose thermal energy through a combination of convection and radiative cooling if they are to survive and contract to become giant protoplanets. While there is good observational support for forming at least some giant planets by disk instability, the mechanism has become theoretically contentious, with different three-dimensional radiative hydrodynamics codes often yielding different results. Rigorous code testing is required to make further progress. Here we present two new analytical solutions for radiative transfer in spherical coordinates, suitable for testing the code employed in all of the Boss disk instability calculations. The testing shows that the Boss code radiative transfer routines do an excellent job of relaxing to and maintaining the analytical results for the radial temperature and radiative flux profiles for a spherical cloud with high or moderate optical depths, including the transition from optically thick to optically thin regions. These radial test results are independent of whether the Eddington approximation, diffusion approximation, or flux-limited diffusion approximation routines are employed. The Boss code does an equally excellent job of relaxing to and maintaining the analytical results for the vertical (θ) temperature and radiative flux profiles for a disk with a height proportional to the radial distance. These tests strongly support the disk instability mechanism for forming giant planets.

The varieties of symmetric stellar rings and radial caustics in galaxy disks

NASA Technical Reports Server (NTRS)

Struck-Marcell, Curtis; Lotan, Pnina

1990-01-01

Numerical, restricted three-body and analytic calculations are used to study the formation and propagation of cylindrically symmetric stellar ring waves in galaxy disks. It is shown that such waves can evolve in a variety of ways, depending on the amplitude of the perturbation and the potential of the target galaxy. Rings can thicken as they propagate outward, remain at a nearly constant width, or be pinched off at large radii. Multiple, closely spaced rings can result from a low-amplitude collision, while an outer ring can appear well-separated from overlapping inner rings or an apparent lens structure in halo-dominated potentials. All the single-encounter rings consist of paired fold caustics. The simple, impulsive, kinematic oscillation equations appear to provide a remarkably accurate model of the numerical simulations. Simple analytic approximations to these equations permit very good estimates of oscillation periods and amplitudes, the evolution of ring widths, and ring birth and propagation characteristics.

Magnetoacoustic Waves and the Kelvin-Helmholtz Instability in a Steady Asymmetric Slab. I: The Effects of Varying Density Ratios

NASA Astrophysics Data System (ADS)

Barbulescu, M.; Erdélyi, R.

2018-06-01

Recent observations have shown that bulk flow motions in structured solar plasmas, most evidently in coronal mass ejections (CMEs), may lead to the formation of Kelvin-Helmholtz instabilities (KHIs). Analytical models are thus essential in understanding both how the flows affect the propagation of magnetohydrodynamic (MHD) waves, and what the critical flow speed is for the formation of the KHI. We investigate both these aspects in a novel way: in a steady magnetic slab embedded in an asymmetric environment. The exterior of the slab is defined as having different equilibrium values of the background density, pressure, and temperature on either side. A steady flow and constant magnetic field are present in the slab interior. Approximate solutions to the dispersion relation are obtained analytically and classified with respect to mode and speed. General solutions and the KHI thresholds are obtained numerically. It is shown that, generally, both the KHI critical value and the cut-off speeds for magnetoacoustic waves are lowered by the external asymmetry.

Solution of the spatial neutral model yields new bounds on the Amazonian species richness

NASA Astrophysics Data System (ADS)

Shem-Tov, Yahav; Danino, Matan; Shnerb, Nadav M.

2017-02-01

Neutral models, in which individual agents with equal fitness undergo a birth-death-mutation process, are very popular in population genetics and community ecology. Usually these models are applied to populations and communities with spatial structure, but the analytic results presented so far are limited to well-mixed or mainland-island scenarios. Here we combine analytic results and numerics to obtain an approximate solution for the species abundance distribution and the species richness for the neutral model on continuous landscape. We show how the regional diversity increases when the recruitment length decreases and the spatial segregation of species grows. Our results are supported by extensive numerical simulations and allow one to probe the numerically inaccessible regime of large-scale systems with extremely small mutation/speciation rates. Model predictions are compared with the findings of recent large-scale surveys of tropical trees across the Amazon basin, yielding new bounds for the species richness (between 13100 and 15000) and the number of singleton species (between 455 and 690).

2D modeling based comprehensive analysis of short channel effects in DMG strained VSTB FET

NASA Astrophysics Data System (ADS)

Saha, Priyanka; Banerjee, Pritha; Sarkar, Subir Kumar

2018-06-01

The paper aims to develop two dimensional analytical model of the proposed dual material (DM) Vertical Super Thin Body (VSTB) strained Field Effect Transistor (FET) with focus on its short channel behaviour in nanometer regime. Electrostatic potential across gate/channel and dielectric wall/channel interface is derived by solving 2D Poisson's equation with parabolic approximation method by applying appropriate boundary conditions. Threshold voltage is then calculated by using the criteria of minimum surface potential considering both gate and dielectric wall side potential. Performance analysis of the present structure is demonstrated in terms of potential, electric field, threshold voltage characteristics and subthreshold behaviour by varying various device parameters and applied biases. Effect of application of strain in channel is further explored to establish the superiority of the proposed device in comparison to conventional VSTB FET counterpart. All analytical results are compared with Silvaco ATLAS device simulated data to substantiate the accuracy of our derived model.

Linear Transformation of Electromagnetic Wave Beams of the Electron-Cyclotron Range in Toroidal Magnetic Configurations

NASA Astrophysics Data System (ADS)

Khusainov, T. A.; Shalashov, A. G.; Gospodchikov, E. D.

2018-05-01

The field structure of quasi-optical wave beams tunneled through the evanescence region in the vicinity of the plasma cutoff in a nonuniform magnetoactive plasma is analyzed. This problem is traditionally associated with the process of linear transformation of ordinary and extraordinary waves. An approximate analytical solution is constructed for a rather general magnetic configuration applicable to spherical tokamaks, optimized stellarators, and other magnetic confinement systems with a constant plasma density on magnetic surfaces. A general technique for calculating the transformation coefficient of a finite-aperture wave beam is proposed, and the physical conditions required for the most efficient transformation are analyzed.

Spacing distribution functions for the one-dimensional point-island model with irreversible attachment

NASA Astrophysics Data System (ADS)

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

2011-07-01

We study the configurational structure of the point-island model for epitaxial growth in one dimension. In particular, we calculate the island gap and capture zone distributions. Our model is based on an approximate description of nucleation inside the gaps. Nucleation is described by the joint probability density pnXY(x,y), which represents the probability density to have nucleation at position x within a gap of size y. Our proposed functional form for pnXY(x,y) describes excellently the statistical behavior of the system. We compare our analytical model with extensive numerical simulations. Our model retains the most relevant physical properties of the system.

Fundamental studies in X-ray astrophysics

NASA Technical Reports Server (NTRS)

Lamb, D. Q.; Lightman, A. P.

1982-01-01

An analytical model calculation of the ionization structure of matter accreting onto a degenerate dwarf was carried out. Self-consistent values of the various parameters are used. The possibility of nuclear burning of the accreting matter is included. We find the blackbody radiation emitted from the stellar surface keeps hydrogen and helium ionized out to distances much larger than a typical binary separation. Except for low mass stars or high accretion rates, the assumption of complete ionization of the elements heavier than helium is a good first approximation. For low mass stars or high accretion rates the validity of assuming complete ionization depends sensitivity on the distribution of matter in the binary system.

Donor-impurity-related optical response and electron Raman scattering in GaAs cone-like quantum dots

NASA Astrophysics Data System (ADS)

Gil-Corrales, A.; Morales, A. L.; Restrepo, R. L.; Mora-Ramos, M. E.; Duque, C. A.

2017-02-01

The donor-impurity-related optical absorption, relative refractive index changes, and Raman scattering in GaAs cone-like quantum dots are theoretically investigated. Calculations are performed within the effective mass and parabolic band approximations, using the variational procedure to include the electron-impurity correlation effects. The study involves 1 s -like, 2px-like, and 2pz-like states. The conical structure is chosen in such a way that the cone height is large enough in comparison with the base radius thus allowing the use a quasi-analytic solution of the uncorrelated Schrödinger-like electron states.

ICANT, a code for the self-consistent computation of ICRH antenna coupling

NASA Astrophysics Data System (ADS)

Pécoul, S.; Heuraux, S.; Koch, R.; Leclert, G.

1996-02-01

The code deals with 3D antenna structures (finite length antennae) that are used to launch electromagnetic waves into tokamak plasmas. The antenna radiation problem is solved using a finite boundary element technique combined with a spectral solution of the interior problem. The slab approximation is used, and periodicity in y and z directions is introduced to account for toroidal geometry. We present results for various types of antennae radiating in vacuum: antenna with a finite Faraday screen and ideal Faraday screen, antenna with side limiters and phased antenna arrays. The results (radiated power, current profile) obtained are very close to analytical solutions when available.

Continuous-variable quantum teleportation in bosonic structured environments

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

He Guangqiang; Zhang Jingtao; Zhu Jun

2011-09-15

The effects of dynamics of continuous-variable entanglement under the various kinds of environments on quantum teleportation are quantitatively investigated. Only under assumption of the weak system-reservoir interaction, the evolution of teleportation fidelity is analytically derived and is numerically plotted in terms of environment parameters including reservoir temperature and its spectral density, without Markovian and rotating wave approximations. We find that the fidelity of teleportation is a monotonically decreasing function for Markovian interaction in Ohmic-like environments, while it oscillates for non-Markovian ones. According to the dynamical laws of teleportation, teleportation with better performances can be implemented by selecting the appropriate time.

A method for the geometrically nonlinear analysis of compressively loaded prismatic composite structures

NASA Technical Reports Server (NTRS)

Stoll, Frederick; Gurdal, Zafer; Starnes, James H., Jr.

1991-01-01

A method was developed for the geometrically nonlinear analysis of the static response of thin-walled stiffened composite structures loaded in uniaxial or biaxial compression. The method is applicable to arbitrary prismatic configurations composed of linked plate strips, such as stiffened panels and thin-walled columns. The longitudinal ends of the structure are assumed to be simply supported, and geometric shape imperfections can be modeled. The method can predict the nonlinear phenomena of postbuckling strength and imperfection sensitivity which are exhibited by some buckling-dominated structures. The method is computer-based and is semi-analytic in nature, making it computationally economical in comparison to finite element methods. The method uses a perturbation approach based on the use of a series of buckling mode shapes to represent displacement contributions associated with nonlinear response. Displacement contributions which are of second order in the model amplitudes are incorported in addition to the buckling mode shapes. The principle of virtual work is applied using a finite basis of buckling modes, and terms through the third order in the model amplitudes are retained. A set of cubic nonlinear algebraic equations are obtained, from which approximate equilibrium solutions are determined. Buckling mode shapes for the general class of structure are obtained using the VIPASA analysis code within the PASCO stiffened-panel design code. Thus, subject to some additional restrictions in loading and plate anisotropy, structures which can be modeled with respect to buckling behavior by VIPASA can be analyzed with respect to nonlinear response using the new method. Results obtained using the method are compared with both experimental and analytical results in the literature. The configurations investigated include several different unstiffened and blade-stiffening panel configurations, featuring both homogeneous, isotropic materials, and laminated composite material.

Uniform analytic approximation of Wigner rotation matrices

NASA Astrophysics Data System (ADS)

Hoffmann, Scott E.

2018-02-01

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

An approximate analytical solution for describing surface runoff and sediment transport over hillslope

NASA Astrophysics Data System (ADS)

Tao, Wanghai; Wang, Quanjiu; Lin, Henry

2018-03-01

Soil and water loss from farmland causes land degradation and water pollution, thus continued efforts are needed to establish mathematical model for quantitative analysis of relevant processes and mechanisms. In this study, an approximate analytical solution has been developed for overland flow model and sediment transport model, offering a simple and effective means to predict overland flow and erosion under natural rainfall conditions. In the overland flow model, the flow regime was considered to be transitional with the value of parameter β (in the kinematic wave model) approximately two. The change rate of unit discharge with distance was assumed to be constant and equal to the runoff rate at the outlet of the plane. The excess rainfall was considered to be constant under uniform rainfall conditions. The overland flow model developed can be further applied to natural rainfall conditions by treating excess rainfall intensity as constant over a small time interval. For the sediment model, the recommended values of the runoff erosion calibration constant (cr) and the splash erosion calibration constant (cf) have been given in this study so that it is easier to use the model. These recommended values are 0.15 and 0.12, respectively. Comparisons with observed results were carried out to validate the proposed analytical solution. The results showed that the approximate analytical solution developed in this paper closely matches the observed data, thus providing an alternative method of predicting runoff generation and sediment yield, and offering a more convenient method of analyzing the quantitative relationships between variables. Furthermore, the model developed in this study can be used as a theoretical basis for developing runoff and erosion control methods.

Nanometric depth resolution from multi-focal images in microscopy.

PubMed

Dalgarno, Heather I C; Dalgarno, Paul A; Dada, Adetunmise C; Towers, Catherine E; Gibson, Gavin J; Parton, Richard M; Davis, Ilan; Warburton, Richard J; Greenaway, Alan H

2011-07-06

We describe a method for tracking the position of small features in three dimensions from images recorded on a standard microscope with an inexpensive attachment between the microscope and the camera. The depth-measurement accuracy of this method is tested experimentally on a wide-field, inverted microscope and is shown to give approximately 8 nm depth resolution, over a specimen depth of approximately 6 µm, when using a 12-bit charge-coupled device (CCD) camera and very bright but unresolved particles. To assess low-flux limitations a theoretical model is used to derive an analytical expression for the minimum variance bound. The approximations used in the analytical treatment are tested using numerical simulations. It is concluded that approximately 14 nm depth resolution is achievable with flux levels available when tracking fluorescent sources in three dimensions in live-cell biology and that the method is suitable for three-dimensional photo-activated localization microscopy resolution. Sub-nanometre resolution could be achieved with photon-counting techniques at high flux levels.

Nanometric depth resolution from multi-focal images in microscopy

PubMed Central

Dalgarno, Heather I. C.; Dalgarno, Paul A.; Dada, Adetunmise C.; Towers, Catherine E.; Gibson, Gavin J.; Parton, Richard M.; Davis, Ilan; Warburton, Richard J.; Greenaway, Alan H.

2011-01-01

We describe a method for tracking the position of small features in three dimensions from images recorded on a standard microscope with an inexpensive attachment between the microscope and the camera. The depth-measurement accuracy of this method is tested experimentally on a wide-field, inverted microscope and is shown to give approximately 8 nm depth resolution, over a specimen depth of approximately 6 µm, when using a 12-bit charge-coupled device (CCD) camera and very bright but unresolved particles. To assess low-flux limitations a theoretical model is used to derive an analytical expression for the minimum variance bound. The approximations used in the analytical treatment are tested using numerical simulations. It is concluded that approximately 14 nm depth resolution is achievable with flux levels available when tracking fluorescent sources in three dimensions in live-cell biology and that the method is suitable for three-dimensional photo-activated localization microscopy resolution. Sub-nanometre resolution could be achieved with photon-counting techniques at high flux levels. PMID:21247948

Structural Assessment of Advanced Composite Tow-Steered Shells

NASA Technical Reports Server (NTRS)

Wu, K. Chauncey; Stanford, Bret K.; Hrinda, Glenn A.; Wang, Zhuosong; Martin, Robert a.; Kim, H. Alicia

2013-01-01

The structural performance of two advanced composite tow-steered shells, manufactured using a fiber placement system, is assessed using both experimental and analytical methods. The fiber orientation angles vary continuously around the shell circumference from 10 degrees on the shell crown and keel, to 45 degrees on the shell sides. The two shells differ in that one shell has the full 24-tow course applied during each pass of the fiber placement system, while the second shell uses the fiber placement system s tow drop/add capability to achieve a more uniform shell wall thickness. The shells are tested in axial compression, and estimates of their prebuckling axial stiffnesses and bifurcation buckling loads are predicted using linear finite element analyses. These preliminary predictions compare well with the test results, with an average agreement of approximately 10 percent.

Theoretical approximation of focusing-wave induced load upon a large-scale vertical cylinder

NASA Astrophysics Data System (ADS)

Xue, Hong-xiang; Hu, Zhe; Tang, Wen-yong; Zhang, Xiao-ying; Wang, Kun-peng

2017-10-01

Until now, most researches into the rogue-wave-structure interaction have relied on experimental measurement and numerical simulation. Owing to the complexity of the physical mechanism of rogue waves, theoretical study on the wave-structure issue still makes little progress. In this paper, the rogue wave flow around a vertical cylinder is analytically studied within the scope of the potential theory. The rogue wave is modeled by the Gauss envelope, which is one particular case of the well-known focusing theory. The formulae of the wave-induced horizontal force and bending moment are proposed. For the convenience of engineering application, the derived formulae are simplified appropriately, and verified against numerical results. In addition, the influence of wave parameters, such as the energy focusing degree and the wave focusing position, is thoroughly investigated.

Study of modal coupling procedures for the shuttle: A matrix method for damping synthesis

NASA Technical Reports Server (NTRS)

Hasselman, T. K.

1972-01-01

The damping method was applied successfully to real structures as well as analytical models. It depends on the ability to determine an appropriate modal damping matrix for each substructure. In the past, modal damping matrices were assumed diagonal for lack of being able to determine the coupling terms which are significant in the general case of nonproportional damping. This problem was overcome by formulating the damped equations of motion as a linear perturbation of the undamped equations for light structural damping. Damped modes are defined as complex vectors derived from the complex frequency response vectors of each substructure and are obtained directly from sinusoidal vibration tests. The damped modes are used to compute first order approximations to the modal damping matrices. The perturbation approach avoids ever having to solve a complex eigenvalue problem.

Folding to Curved Surfaces: A Generalized Design Method and Mechanics of Origami-based Cylindrical Structures.

PubMed

Wang, Fei; Gong, Haoran; Chen, Xi; Chen, C Q

2016-09-14

Origami structures enrich the field of mechanical metamaterials with the ability to convert morphologically and systematically between two-dimensional (2D) thin sheets and three-dimensional (3D) spatial structures. In this study, an in-plane design method is proposed to approximate curved surfaces of interest with generalized Miura-ori units. Using this method, two combination types of crease lines are unified in one reprogrammable procedure, generating multiple types of cylindrical structures. Structural completeness conditions of the finite-thickness counterparts to the two types are also proposed. As an example of the design method, the kinematics and elastic properties of an origami-based circular cylindrical shell are analysed. The concept of Poisson's ratio is extended to the cylindrical structures, demonstrating their auxetic property. An analytical model of rigid plates linked by elastic hinges, consistent with numerical simulations, is employed to describe the mechanical response of the structures. Under particular load patterns, the circular shells display novel mechanical behaviour such as snap-through and limiting folding positions. By analysing the geometry and mechanics of the origami structures, we extend the design space of mechanical metamaterials and provide a basis for their practical applications in science and engineering.

Folding to Curved Surfaces: A Generalized Design Method and Mechanics of Origami-based Cylindrical Structures

NASA Astrophysics Data System (ADS)

Wang, Fei; Gong, Haoran; Chen, Xi; Chen, C. Q.

2016-09-01

Origami structures enrich the field of mechanical metamaterials with the ability to convert morphologically and systematically between two-dimensional (2D) thin sheets and three-dimensional (3D) spatial structures. In this study, an in-plane design method is proposed to approximate curved surfaces of interest with generalized Miura-ori units. Using this method, two combination types of crease lines are unified in one reprogrammable procedure, generating multiple types of cylindrical structures. Structural completeness conditions of the finite-thickness counterparts to the two types are also proposed. As an example of the design method, the kinematics and elastic properties of an origami-based circular cylindrical shell are analysed. The concept of Poisson’s ratio is extended to the cylindrical structures, demonstrating their auxetic property. An analytical model of rigid plates linked by elastic hinges, consistent with numerical simulations, is employed to describe the mechanical response of the structures. Under particular load patterns, the circular shells display novel mechanical behaviour such as snap-through and limiting folding positions. By analysing the geometry and mechanics of the origami structures, we extend the design space of mechanical metamaterials and provide a basis for their practical applications in science and engineering.

Folding to Curved Surfaces: A Generalized Design Method and Mechanics of Origami-based Cylindrical Structures

PubMed Central

Wang, Fei; Gong, Haoran; Chen, Xi; Chen, C. Q.

2016-01-01

Origami structures enrich the field of mechanical metamaterials with the ability to convert morphologically and systematically between two-dimensional (2D) thin sheets and three-dimensional (3D) spatial structures. In this study, an in-plane design method is proposed to approximate curved surfaces of interest with generalized Miura-ori units. Using this method, two combination types of crease lines are unified in one reprogrammable procedure, generating multiple types of cylindrical structures. Structural completeness conditions of the finite-thickness counterparts to the two types are also proposed. As an example of the design method, the kinematics and elastic properties of an origami-based circular cylindrical shell are analysed. The concept of Poisson’s ratio is extended to the cylindrical structures, demonstrating their auxetic property. An analytical model of rigid plates linked by elastic hinges, consistent with numerical simulations, is employed to describe the mechanical response of the structures. Under particular load patterns, the circular shells display novel mechanical behaviour such as snap-through and limiting folding positions. By analysing the geometry and mechanics of the origami structures, we extend the design space of mechanical metamaterials and provide a basis for their practical applications in science and engineering. PMID:27624892

Analytical solutions for coupling fractional partial differential equations with Dirichlet boundary conditions

NASA Astrophysics Data System (ADS)

Ding, Xiao-Li; Nieto, Juan J.

2017-11-01

In this paper, we consider the analytical solutions of coupling fractional partial differential equations (FPDEs) with Dirichlet boundary conditions on a finite domain. Firstly, the method of successive approximations is used to obtain the analytical solutions of coupling multi-term time fractional ordinary differential equations. Then, the technique of spectral representation of the fractional Laplacian operator is used to convert the coupling FPDEs to the coupling multi-term time fractional ordinary differential equations. By applying the obtained analytical solutions to the resulting multi-term time fractional ordinary differential equations, the desired analytical solutions of the coupling FPDEs are given. Our results are applied to derive the analytical solutions of some special cases to demonstrate their applicability.

Accurate modelling of anisotropic effects in austenitic stainless steel welds

NASA Astrophysics Data System (ADS)

Nowers, O. D.; Duxbury, D. J.; Drinkwater, B. W.

2014-02-01

The ultrasonic inspection of austenitic steel welds is challenging due to the formation of highly anisotropic and heterogeneous structures post-welding. This is due to the intrinsic crystallographic structure of austenitic steel, driving the formation of dendritic grain structures on cooling. The anisotropy is manifested as both a `steering' of the ultrasonic beam and the back-scatter of energy due to the macroscopic granular structure of the weld. However, the quantitative effects and relative impacts of these phenomena are not well-understood. A semi-analytical simulation framework has been developed to allow the study of anisotropic effects in austenitic stainless steel welds. Frequency-dependent scatterers are allocated to a weld-region to approximate the coarse grain-structures observed within austenitic welds and imaged using a simulated array. The simulated A-scans are compared against an equivalent experimental setup demonstrating excellent agreement of the Signal to Noise (S/N) ratio. Comparison of images of the simulated and experimental data generated using the Total Focusing Method (TFM) indicate a prominent layered effect in the simulated data. A superior grain allocation routine is required to improve upon this.

Structure and mechanical behavior of human hair.

PubMed

Yu, Yang; Yang, Wen; Wang, Bin; Meyers, Marc André

2017-04-01

The understanding of the mechanical behavior of hair under various conditions broadens our knowledge in biological materials science and contributes to the cosmetic industry. The hierarchical organization of hair is studied from the intermediate filament to the structural levels. The effects of strain rate, relative humidity, and temperature are evaluated. Hair exhibits a high tensile strength, 150-270MPa, which is significantly dependent on strain rate and humidity. The strain-rate sensitivity, approximately 0.06-0.1, is comparable to that of other keratinous materials and common synthetic polymers. The structures of the internal cortex and surface cuticle are affected by the large tensile extension. One distinguishing feature, the unwinding of the α-helix and the possible transformation to β-sheet structure of keratin under tension, which affects the ductility of hair, is analytically evaluated and incorporated into a constitutive equation. A good agreement with the experimental results is obtained. This model elucidates the tensile response of the α-keratin fibers. The contributions of elastic and plastic strains on reloading are evaluated and correlated to structural changes. Copyright © 2016 Elsevier B.V. All rights reserved.

Influence of large-scale motion on turbulent transport for confined coaxial jets. Volume 1: Analytical analysis of the experimental data using conditional sampling

NASA Technical Reports Server (NTRS)

Brondum, D. C.; Bennett, J. C.

1986-01-01

The existence of large scale coherent structures in turbulent shear flows has been well documented. Discrepancies between experimental and computational data suggest a necessity to understand the roles they play in mass and momentum transport. Using conditional sampling and averaging on coincident two component velocity and concentration velocity experimental data for swirling and nonswirling coaxial jets, triggers for identifying the structures were examined. Concentration fluctuation was found to be an adequate trigger or indicator for the concentration-velocity data, but no suitable detector was located for the two component velocity data. The large scale structures are found in the region where the largest discrepancies exist between model and experiment. The traditional gradient transport model does not fit in this region as a result of these structures. The large scale motion was found to be responsible for a large percentage downstream at approximately the mean velocity of the overall flow in the axial direction. The radial mean velocity of the structures was found to be substantially greater than that of the overall flow.

On the dynamics of approximating schemes for dissipative nonlinear equations

NASA Technical Reports Server (NTRS)

Jones, Donald A.

1993-01-01

Since one can rarely write down the analytical solutions to nonlinear dissipative partial differential equations (PDE's), it is important to understand whether, and in what sense, the behavior of approximating schemes to these equations reflects the true dynamics of the original equations. Further, because standard error estimates between approximations of the true solutions coming from spectral methods - finite difference or finite element schemes, for example - and the exact solutions grow exponentially in time, this analysis provides little value in understanding the infinite time behavior of a given approximating scheme. The notion of the global attractor has been useful in quantifying the infinite time behavior of dissipative PDEs, such as the Navier-Stokes equations. Loosely speaking, the global attractor is all that remains of a sufficiently large bounded set in phase space mapped infinitely forward in time under the evolution of the PDE. Though the attractor has been shown to have some nice properties - it is compact, connected, and finite dimensional, for example - it is in general quite complicated. Nevertheless, the global attractor gives a way to understand how the infinite time behavior of approximating schemes such as the ones coming from a finite difference, finite element, or spectral method relates to that of the original PDE. Indeed, one can often show that such approximations also have a global attractor. We therefore only need to understand how the structure of the attractor for the PDE behaves under approximation. This is by no means a trivial task. Several interesting results have been obtained in this direction. However, we will not go into the details. We mention here that approximations generally lose information about the system no matter how accurate they are. There are examples that show certain parts of the attractor may be lost by arbitrary small perturbations of the original equations.

Analytic Approximations to the Free Boundary and Multi-dimensional Problems in Financial Derivatives Pricing

NASA Astrophysics Data System (ADS)

Lau, Chun Sing

This thesis studies two types of problems in financial derivatives pricing. The first type is the free boundary problem, which can be formulated as a partial differential equation (PDE) subject to a set of free boundary condition. Although the functional form of the free boundary condition is given explicitly, the location of the free boundary is unknown and can only be determined implicitly by imposing continuity conditions on the solution. Two specific problems are studied in details, namely the valuation of fixed-rate mortgages and CEV American options. The second type is the multi-dimensional problem, which involves multiple correlated stochastic variables and their governing PDE. One typical problem we focus on is the valuation of basket-spread options, whose underlying asset prices are driven by correlated geometric Brownian motions (GBMs). Analytic approximate solutions are derived for each of these three problems. For each of the two free boundary problems, we propose a parametric moving boundary to approximate the unknown free boundary, so that the original problem transforms into a moving boundary problem which can be solved analytically. The governing parameter of the moving boundary is determined by imposing the first derivative continuity condition on the solution. The analytic form of the solution allows the price and the hedging parameters to be computed very efficiently. When compared against the benchmark finite-difference method, the computational time is significantly reduced without compromising the accuracy. The multi-stage scheme further allows the approximate results to systematically converge to the benchmark results as one recasts the moving boundary into a piecewise smooth continuous function. For the multi-dimensional problem, we generalize the Kirk (1995) approximate two-asset spread option formula to the case of multi-asset basket-spread option. Since the final formula is in closed form, all the hedging parameters can also be derived in closed form. Numerical examples demonstrate that the pricing and hedging errors are in general less than 1% relative to the benchmark prices obtained by numerical integration or Monte Carlo simulation. By exploiting an explicit relationship between the option price and the underlying probability distribution, we further derive an approximate distribution function for the general basket-spread variable. It can be used to approximate the transition probability distribution of any linear combination of correlated GBMs. Finally, an implicit perturbation is applied to reduce the pricing errors by factors of up to 100. When compared against the existing methods, the basket-spread option formula coupled with the implicit perturbation turns out to be one of the most robust and accurate approximation methods.

Analytical solution for the diffusion of a capacitor discharge generated magnetic field pulse in a conductor

NASA Astrophysics Data System (ADS)

Grants, Ilmārs; Bojarevičs, Andris; Gerbeth, Gunter

2016-06-01

Powerful forces arise when a pulse of a magnetic field in the order of a few tesla diffuses into a conductor. Such pulses are used in electromagnetic forming, impact welding of dissimilar materials and grain refinement of solidifying alloys. Strong magnetic field pulses are generated by the discharge current of a capacitor bank. We consider analytically the penetration of such pulse into a conducting half-space. Besides the exact solution we obtain two simple self-similar approximate solutions for two sequential stages of the initial transient. Furthermore, a general solution is provided for the external field given as a power series of time. Each term of this solution represents a self-similar function for which we obtain an explicit expression. The validity range of various approximate analytical solutions is evaluated by comparison to the exact solution.

Interaction and charge transfer between dielectric spheres: Exact and approximate analytical solutions.

PubMed

Lindén, Fredrik; Cederquist, Henrik; Zettergren, Henning

2016-11-21

We present exact analytical solutions for charge transfer reactions between two arbitrarily charged hard dielectric spheres. These solutions, and the corresponding exact ones for sphere-sphere interaction energies, include sums that describe polarization effects to infinite orders in the inverse of the distance between the sphere centers. In addition, we show that these exact solutions may be approximated by much simpler analytical expressions that are useful for many practical applications. This is exemplified through calculations of Langevin type cross sections for forming a compound system of two colliding spheres and through calculations of electron transfer cross sections. We find that it is important to account for dielectric properties and finite sphere sizes in such calculations, which for example may be useful for describing the evolution, growth, and dynamics of nanometer sized dielectric objects such as molecular clusters or dust grains in different environments including astrophysical ones.

Determination of the aerosol size distribution by analytic inversion of the extinction spectrum in the complex anomalous diffraction approximation.

PubMed

Franssens, G; De Maziére, M; Fonteyn, D

2000-08-20

A new derivation is presented for the analytical inversion of aerosol spectral extinction data to size distributions. It is based on the complex analytic extension of the anomalous diffraction approximation (ADA). We derive inverse formulas that are applicable to homogeneous nonabsorbing and absorbing spherical particles. Our method simplifies, generalizes, and unifies a number of results obtained previously in the literature. In particular, we clarify the connection between the ADA transform and the Fourier and Laplace transforms. Also, the effect of the particle refractive-index dispersion on the inversion is examined. It is shown that, when Lorentz's model is used for this dispersion, the continuous ADA inverse transform is mathematically well posed, whereas with a constant refractive index it is ill posed. Further, a condition is given, in terms of Lorentz parameters, for which the continuous inverse operator does not amplify the error.

Viscous damping and spring force in periodic perforated planar microstructures when the Reynolds’ equation cannot be applied

PubMed Central

Homentcovschi, Dorel; Miles, Ronald N.

2010-01-01

A model of squeeze-film behavior is developed based on Stokes’ equations for viscous, compressible isothermal flows. The flow domain is an axisymmetrical, unit cell approximation of a planar, periodic, perforated microstructure. The model is developed for cases when the lubrication approximation cannot be applied. The complex force generated by vibrations of the diaphragm driving the flow has two components: the damping force and the spring force. While for large frequencies the spring force dominates, at low (acoustical) frequencies the damping force is the most important part. The analytical approach developed here yields an explicit formula for both forces. In addition, using a finite element software package, the damping force is also obtained numerically. A comparison is made between the analytic result, numerical solution, and some experimental data found in the literature, which validates the analytic formula and provides compelling arguments about its value in designing microelectomechanical devices. PMID:20329828

Spectrum Evolution of Accelerating or Slowing down Soliton at its Propagation in a Medium with Gold Nanorods

NASA Astrophysics Data System (ADS)

Trofimov, Vyacheslav A.; Lysak, Tatiana M.

2018-04-01

We investigate both numerically and analytically the spectrum evolution of a novel type soliton - nonlinear chirped accelerating or decelerating soliton - at a femtosecond pulse propagation in a medium containing noble nanoparticles. In our consideration, we take into account one- or two-photon absorption of laser radiation by nanorods, and time-dependent nanorod aspect ratio changing due to their melting or reshaping because of laser energy absorption. The chirped solitons are formed due to the trapping of laser radiation by the nanorods reshaping fronts, if a positive or negative phase-amplitude grating is induced by laser radiation. Accelerating or slowing down chirped soliton formation is accompanied by the soliton spectrum blue or red shift. To prove our numerical results, we derived the approximate analytical law for the spectrum maximum intensity evolution along the propagation coordinate, based on earlier developed approximate analytical solutions for accelerating and decelerating solitons.

A simple method for estimating frequency response corrections for eddy covariance systems

Treesearch

W. J. Massman

2000-01-01

A simple analytical formula is developed for estimating the frequency attenuation of eddy covariance fluxes due to sensor response, path-length averaging, sensor separation, signal processing, and flux averaging periods. Although it is an approximation based on flat terrain cospectra, this analytical formula should have broader applicability than just flat-terrain...

Point spread functions and deconvolution of ultrasonic images.

PubMed

Dalitz, Christoph; Pohle-Fröhlich, Regina; Michalk, Thorsten

2015-03-01

This article investigates the restoration of ultrasonic pulse-echo C-scan images by means of deconvolution with a point spread function (PSF). The deconvolution concept from linear system theory (LST) is linked to the wave equation formulation of the imaging process, and an analytic formula for the PSF of planar transducers is derived. For this analytic expression, different numerical and analytic approximation schemes for evaluating the PSF are presented. By comparing simulated images with measured C-scan images, we demonstrate that the assumptions of LST in combination with our formula for the PSF are a good model for the pulse-echo imaging process. To reconstruct the object from a C-scan image, we compare different deconvolution schemes: the Wiener filter, the ForWaRD algorithm, and the Richardson-Lucy algorithm. The best results are obtained with the Richardson-Lucy algorithm with total variation regularization. For distances greater or equal twice the near field distance, our experiments show that the numerically computed PSF can be replaced with a simple closed analytic term based on a far field approximation.

Capillary-wave dynamics and interface structure modulation in binary Bose-Einstein condensate mixtures

NASA Astrophysics Data System (ADS)

Indekeu, Joseph O.; Van Thu, Nguyen; Lin, Chang-You; Phat, Tran Huu

2018-04-01

The localized low-energy interfacial excitations, or interfacial Nambu-Goldstone modes, of phase-segregated binary mixtures of Bose-Einstein condensates are investigated analytically. To this end a double-parabola approximation (DPA) is performed on the Lagrangian density in Gross-Pitaevskii theory for a system in a uniform potential. This DPA entails a model in which analytic expressions are obtained for the excitations underlying capillary waves or ripplons for arbitrary strength K (>1 ) of the phase segregation. The dispersion relation ω (k ) ∝k3 /2 is derived directly from the Bogoliubov-de Gennes equations in the limit that the wavelength 2 π /k is much larger than the interface width. The proportionality constant in the dispersion relation provides the static interfacial tension. A correction term in ω (k ) of order k5 /2 is calculated analytically within the DPA model. The combined result is tested against numerical diagonalization of the exact Bogoliubov-de Gennes equations. Satisfactory agreement is obtained in the range of physically relevant wavelengths. The ripplon dispersion relation is relevant to state-of-the-art experiments using (quasi)uniform optical-box traps. Furthermore, within the DPA model explicit expressions are obtained for the structural deformation of the interface due to the passing of the capillary wave. It is found that the amplitude of the wave is enhanced by an amount that is quadratic in the ratio of the phase velocity ω /k to the sound velocity c . For generic mixtures consisting of condensates with unequal healing lengths, an additional modulation is predicted of the common value of the condensate densities at the interface.

Accurate Estimate of Some Propagation Characteristics for the First Higher Order Mode in Graded Index Fiber with Simple Analytic Chebyshev Method

NASA Astrophysics Data System (ADS)

Dutta, Ivy; Chowdhury, Anirban Roy; Kumbhakar, Dharmadas

2013-03-01

Using Chebyshev power series approach, accurate description for the first higher order (LP11) mode of graded index fibers having three different profile shape functions are presented in this paper and applied to predict their propagation characteristics. These characteristics include fractional power guided through the core, excitation efficiency and Petermann I and II spot sizes with their approximate analytic formulations. We have shown that where two and three Chebyshev points in LP11 mode approximation present fairly accurate results, the values based on our calculations involving four Chebyshev points match excellently with available exact numerical results.

A generalized analytical model for radiative transfer in vacuum thermal insulation of space vehicles

NASA Astrophysics Data System (ADS)

Krainova, Irina V.; Dombrovsky, Leonid A.; Nenarokomov, Aleksey V.; Budnik, Sergey A.; Titov, Dmitry M.; Alifanov, Oleg M.

2017-08-01

The previously developed spectral model for radiative transfer in vacuum thermal insulation of space vehicles is generalized to take into account possible thermal contact between a fibrous spacer and one of the neighboring aluminum foil layers. An approximate analytical solution based on slightly modified two-flux approximation for radiative transfer in a semi-transparent fibrous spacer is derived. It was shown that thermal contact between the spacer and adjacent foil may decrease significantly the quality of thermal insulation because of an increase in radiative flux to/from the opposite aluminum foil. Theoretical predictions are confirmed by comparison with new results of laboratory experiments.

Monitoring by forward scatter radar techniques: an improved second-order analytical model

NASA Astrophysics Data System (ADS)

Falconi, Marta Tecla; Comite, Davide; Galli, Alessandro; Marzano, Frank S.; Pastina, Debora; Lombardo, Pierfrancesco

2017-10-01

In this work, a second-order phase approximation is introduced to provide an improved analytical model of the signal received in forward scatter radar systems. A typical configuration with a rectangular metallic object illuminated while crossing the baseline, in far- or near-field conditions, is considered. An improved second-order model is compared with a simplified one already proposed by the authors and based on a paraxial approximation. A phase error analysis is carried out to investigate benefits and limitations of the second-order modeling. The results are validated by developing full-wave numerical simulations implementing the relevant scattering problem on a commercial tool.

Stress generation in thermally grown oxide films. [oxide scale spalling from superalloy substrates

NASA Technical Reports Server (NTRS)

Kumnick, A. J.; Ebert, L. J.

1981-01-01

A three dimensional finite element analysis was conducted, using the ANSYS computer program, of the stress state in a thin oxide film thermally formed on a rectangular piece of NiCrAl alloy. The analytical results indicate a very high compressive stress in the lateral directions of the film (approximately 6200 MPa), and tensile stresses in the metal substrate that ranged from essentially zero to about 55 MPa. It was found further that the intensity of the analytically determined average stresses could be approximated reasonably well by the modification of an equation developed previously by Oxx for stresses induced into bodies by thermal gradients.

Brownian systems with spatially inhomogeneous activity

NASA Astrophysics Data System (ADS)

Sharma, A.; Brader, J. M.

2017-09-01

We generalize the Green-Kubo approach, previously applied to bulk systems of spherically symmetric active particles [J. Chem. Phys. 145, 161101 (2016), 10.1063/1.4966153], to include spatially inhomogeneous activity. The method is applied to predict the spatial dependence of the average orientation per particle and the density. The average orientation is given by an integral over the self part of the Van Hove function and a simple Gaussian approximation to this quantity yields an accurate analytical expression. Taking this analytical result as input to a dynamic density functional theory approximates the spatial dependence of the density in good agreement with simulation data. All theoretical predictions are validated using Brownian dynamics simulations.

The Potential-Well Distortion Effect and Coherent Instabilities of Electron Bunches in Storage Rings

NASA Astrophysics Data System (ADS)

Korchuganov, V. N.; Smygacheva, A. S.; Fomin, E. A.

2018-05-01

The effect of electromagnetic interaction between electron bunches and the vacuum chamber of a storage ring on the longitudinal motion of bunches is studied. Specifically, the potential-well distortion effect and the so-called coherent instabilities of coupled bunches are considered. An approximate analytical solution for the frequencies of incoherent oscillations of bunches distributed arbitrarily within the ring is obtained for a distorted potential well. A new approach to determining frequencies of coherent oscillations and an approximate analytical relation for estimating the stability of a system of bunches as a function of their distribution in the accelerator orbit are presented.

Solar neutrino masses and mixing from bilinear R-parity broken supersymmetry: Analytical versus numerical results

NASA Astrophysics Data System (ADS)

Díaz, M.; Hirsch, M.; Porod, W.; Romão, J.; Valle, J.

2003-07-01

We give an analytical calculation of solar neutrino masses and mixing at one-loop order within bilinear R-parity breaking supersymmetry, and compare our results to the exact numerical calculation. Our method is based on a systematic perturbative expansion of R-parity violating vertices to leading order. We find in general quite good agreement between the approximate and full numerical calculations, but the approximate expressions are much simpler to implement. Our formalism works especially well for the case of the large mixing angle Mikheyev-Smirnov-Wolfenstein solution, now strongly favored by the recent KamLAND reactor neutrino data.

Evolution of Hyperbolic-Secant Pulses Towards Cross-Phase Modulation Induced Optical Wave Breaking and Soliton or Soliton Trains Generation in Quintic Nonlinear Fibers

NASA Astrophysics Data System (ADS)

Zhong, Xian-Qiong; Zhang, Xiao-Xia; Du, Xian-Tong; Liu, Yong; Cheng, Ke

2015-10-01

The approximate analytical frequency chirps and the critical distances for cross-phase modulation induced optical wave breaking (OWB) of the initial hyperbolic-secant optical pulses propagating in optical fibers with quintic nonlinearity (QN) are presented. The pulse evolutions in terms of the frequency chirps, shapes and spectra are numerically calculated in the normal dispersion regime. The results reveal that, depending on different QN parameters, the traditional OWB or soliton or soliton pulse trains may occur. The approximate analytical critical distances are found to be in good agreement with the numerical ones only for the traditional OWB whereas the approximate analytical frequency chirps accords well with the numerical ones at the initial evolution stages of the pulses. Supported by the Postdoctoral Fund of China under Grant No. 2011M501402, the Key Project of Chinese Ministry of Education under Grant No. 210186, the Major Project of Natural Science Supported by the Educational Department of Sichuan Province under Grant No. 13ZA0081, the Key Project of National Natural Science Foundation of China under Grant No 61435010, and the National Natural Science Foundation of China under Grant No. 61275039

Comparison of Three Methods for Wind Turbine Capacity Factor Estimation

PubMed Central

Ditkovich, Y.; Kuperman, A.

2014-01-01

Three approaches to calculating capacity factor of fixed speed wind turbines are reviewed and compared using a case study. The first “quasiexact” approach utilizes discrete wind raw data (in the histogram form) and manufacturer-provided turbine power curve (also in discrete form) to numerically calculate the capacity factor. On the other hand, the second “analytic” approach employs a continuous probability distribution function, fitted to the wind data as well as continuous turbine power curve, resulting from double polynomial fitting of manufacturer-provided power curve data. The latter approach, while being an approximation, can be solved analytically thus providing a valuable insight into aspects, affecting the capacity factor. Moreover, several other merits of wind turbine performance may be derived based on the analytical approach. The third “approximate” approach, valid in case of Rayleigh winds only, employs a nonlinear approximation of the capacity factor versus average wind speed curve, only requiring rated power and rotor diameter of the turbine. It is shown that the results obtained by employing the three approaches are very close, enforcing the validity of the analytically derived approximations, which may be used for wind turbine performance evaluation. PMID:24587755

Approximate analytical solution for induction heating of solid cylinders

DOE PAGES

Jankowski, Todd Andrew; Pawley, Norma Helen; Gonzales, Lindsey Michal; ...

2015-10-20

An approximate solution to the mathematical model for induction heating of a solid cylinder in a cylindrical induction coil is presented here. The coupled multiphysics model includes equations describing the electromagnetic field in the heated object, a heat transfer simulation to determine temperature of the heated object, and an AC circuit simulation of the induction heating power supply. A multiple-scale perturbation method is used to solve the multiphysics model. The approximate analytical solution yields simple closed-form expressions for the electromagnetic field and heat generation rate in the solid cylinder, for the equivalent impedance of the associated tank circuit, and formore » the frequency response of a variable frequency power supply driving the tank circuit. The solution developed here is validated by comparing predicted power supply frequency to both experimental measurements and calculated values from finite element analysis for heating of graphite cylinders in an induction furnace. The simple expressions from the analytical solution clearly show the functional dependence of the power supply frequency on the material properties of the load and the geometrical characteristics of the furnace installation. In conclusion, the expressions developed here provide physical insight into observations made during load signature analysis of induction heating.« less

Rapid perfusion quantification using Welch-Satterthwaite approximation and analytical spectral filtering

NASA Astrophysics Data System (ADS)

Krishnan, Karthik; Reddy, Kasireddy V.; Ajani, Bhavya; Yalavarthy, Phaneendra K.

2017-02-01

CT and MR perfusion weighted imaging (PWI) enable quantification of perfusion parameters in stroke studies. These parameters are calculated from the residual impulse response function (IRF) based on a physiological model for tissue perfusion. The standard approach for estimating the IRF is deconvolution using oscillatory-limited singular value decomposition (oSVD) or Frequency Domain Deconvolution (FDD). FDD is widely recognized as the fastest approach currently available for deconvolution of CT Perfusion/MR PWI. In this work, three faster methods are proposed. The first is a direct (model based) crude approximation to the final perfusion quantities (Blood flow, Blood volume, Mean Transit Time and Delay) using the Welch-Satterthwaite approximation for gamma fitted concentration time curves (CTC). The second method is a fast accurate deconvolution method, we call Analytical Fourier Filtering (AFF). The third is another fast accurate deconvolution technique using Showalter's method, we call Analytical Showalter's Spectral Filtering (ASSF). Through systematic evaluation on phantom and clinical data, the proposed methods are shown to be computationally more than twice as fast as FDD. The two deconvolution based methods, AFF and ASSF, are also shown to be quantitatively accurate compared to FDD and oSVD.

S-curve networks and an approximate method for estimating degree distributions of complex networks

NASA Astrophysics Data System (ADS)

Guo, Jin-Li

2010-12-01

In the study of complex networks almost all theoretical models have the property of infinite growth, but the size of actual networks is finite. According to statistics from the China Internet IPv4 (Internet Protocol version 4) addresses, this paper proposes a forecasting model by using S curve (logistic curve). The growing trend of IPv4 addresses in China is forecasted. There are some reference values for optimizing the distribution of IPv4 address resource and the development of IPv6. Based on the laws of IPv4 growth, that is, the bulk growth and the finitely growing limit, it proposes a finite network model with a bulk growth. The model is said to be an S-curve network. Analysis demonstrates that the analytic method based on uniform distributions (i.e., Barabási-Albert method) is not suitable for the network. It develops an approximate method to predict the growth dynamics of the individual nodes, and uses this to calculate analytically the degree distribution and the scaling exponents. The analytical result agrees with the simulation well, obeying an approximately power-law form. This method can overcome a shortcoming of Barabási-Albert method commonly used in current network research.

Self-consistent approximation beyond the CPA: Part II

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

Kaplan, T.; Gray, L.J.

1981-08-01

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

Understanding cooperative behavior in structurally disordered populations

NASA Astrophysics Data System (ADS)

Xu, C.; Zhang, W.; Du, P.; Choi, C. W.; Hui, P. M.

2016-06-01

The effects of an inhomogeneous competing environment on the extent of cooperation are studied within the context of a site-diluted evolutionary snowdrift game on a square lattice, with the occupied sites representing the players, both numerically and analytically. The frequency of cooperation ℱ C generally shows a non-monotonic dependence on the fraction of occupied sites ρ, for different values of the payoff parameter r. Slightly diluting a lattice leads to a lower cooperation for small and high values of r. For a range of r, however, dilution leads to an enhanced cooperation. An analytic treatment is developed for ℱC I + ℱC II, with ℱC I emphasizing the importance of the small clusters of players especially for ℱC II from the other players is shown to be inadequate. A local configuration approximation (LCA) that treats the local competing configurations as the variables and amounts to include spatial correlation up to the neighborhood of a player's neighbors is developed. Results of ℱ C ( ρ) and the number of different local configurations from LCA are in good agreement with simulation results. A transparent physical picture of the dynamics stemming from LCA is also presented. The theoretical approach provides a framework that can be readily applied to competing agent-based models in structurally ordered and disordered populations.

An analytical platform for mass spectrometry-based identification and chemical analysis of RNA in ribonucleoprotein complexes.

PubMed

Taoka, Masato; Yamauchi, Yoshio; Nobe, Yuko; Masaki, Shunpei; Nakayama, Hiroshi; Ishikawa, Hideaki; Takahashi, Nobuhiro; Isobe, Toshiaki

2009-11-01

We describe here a mass spectrometry (MS)-based analytical platform of RNA, which combines direct nano-flow reversed-phase liquid chromatography (RPLC) on a spray tip column and a high-resolution LTQ-Orbitrap mass spectrometer. Operating RPLC under a very low flow rate with volatile solvents and MS in the negative mode, we could estimate highly accurate mass values sufficient to predict the nucleotide composition of a approximately 21-nucleotide small interfering RNA, detect post-transcriptional modifications in yeast tRNA, and perform collision-induced dissociation/tandem MS-based structural analysis of nucleolytic fragments of RNA at a sub-femtomole level. Importantly, the method allowed the identification and chemical analysis of small RNAs in ribonucleoprotein (RNP) complex, such as the pre-spliceosomal RNP complex, which was pulled down from cultured cells with a tagged protein cofactor as bait. We have recently developed a unique genome-oriented database search engine, Ariadne, which allows tandem MS-based identification of RNAs in biological samples. Thus, the method presented here has broad potential for automated analysis of RNA; it complements conventional molecular biology-based techniques and is particularly suited for simultaneous analysis of the composition, structure, interaction, and dynamics of RNA and protein components in various cellular RNP complexes.

Towards precision constraints on gravity with the Effective Field Theory of Large-Scale Structure

NASA Astrophysics Data System (ADS)

Bose, Benjamin; Koyama, Kazuya; Lewandowski, Matthew; Vernizzi, Filippo; Winther, Hans A.

2018-04-01

We compare analytical computations with numerical simulations for dark-matter clustering, in general relativity and in the normal branch of DGP gravity (nDGP). Our analytical frameword is the Effective Field Theory of Large-Scale Structure (EFTofLSS), which we use to compute the one-loop dark-matter power spectrum, including the resummation of infrared bulk displacement effects. We compare this to a set of 20 COLA simulations at redshifts z = 0, z = 0.5, and z = 1, and fit the free parameter of the EFTofLSS, called the speed of sound, in both ΛCDM and nDGP at each redshift. At one-loop at z = 0, the reach of the EFTofLSS is kreach ≈ 0.14 Mpc‑1 for both ΛCDM and nDGP. Along the way, we compare two different infrared resummation schemes and two different treatments of the time dependence of the perturbative expansion, concluding that they agree to approximately 1% over the scales of interest. Finally, we use the ratio of the COLA power spectra to make a precision measurement of the difference between the speeds of sound in ΛCDM and nDGP, and verify that this is proportional to the modification of the linear coupling constant of the Poisson equation.

A novel nonlinear damage resonance intermodulation effect for structural health monitoring

NASA Astrophysics Data System (ADS)

Ciampa, Francesco; Scarselli, Gennaro; Meo, Michele

2017-04-01

This paper is aimed at developing a theoretical model able to predict the generation of nonlinear elastic effects associated to the interaction of ultrasonic waves with the steady-state nonlinear response of local defect resonance (LDR). The LDR effect is used in nonlinear elastic wave spectroscopy to enhance the excitation of the material damage at its local resonance, thus to dramatically increase the vibrational amplitude of material nonlinear phenomena. The main result of this work is to prove both analytically and experimentally the generation of novel nonlinear elastic wave effects, here named as nonlinear damage resonance intermodulation, which correspond to a nonlinear intermodulation between the driving frequency and the LDR one. Beside this intermodulation effect, other nonlinear elastic wave phenomena such as higher harmonics of the input frequency and superharmonics of LDR frequency were found. The analytical model relies on solving the nonlinear equation of motion governing bending displacement under the assumption of both quadratic and cubic nonlinear defect approximation. Experimental tests on a damaged composite laminate confirmed and validated these predictions and showed that using continuous periodic excitation, the nonlinear structural phenomena associated to LDR could also be featured at locations different from the damage resonance. These findings will provide new opportunities for material damage detection using nonlinear ultrasounds.

Evolution of individual versus social learning on social networks

PubMed Central

Tamura, Kohei; Kobayashi, Yutaka; Ihara, Yasuo

2015-01-01

A number of studies have investigated the roles played by individual and social learning in cultural phenomena and the relative advantages of the two learning strategies in variable environments. Because social learning involves the acquisition of behaviours from others, its utility depends on the availability of ‘cultural models’ exhibiting adaptive behaviours. This indicates that social networks play an essential role in the evolution of learning. However, possible effects of social structure on the evolution of learning have not been fully explored. Here, we develop a mathematical model to explore the evolutionary dynamics of learning strategies on social networks. We first derive the condition under which social learners (SLs) are selectively favoured over individual learners in a broad range of social network. We then obtain an analytical approximation of the long-term average frequency of SLs in homogeneous networks, from which we specify the condition, in terms of three relatedness measures, for social structure to facilitate the long-term evolution of social learning. Finally, we evaluate our approximation by Monte Carlo simulations in complete graphs, regular random graphs and scale-free networks. We formally show that whether social structure favours the evolution of social learning is determined by the relative magnitudes of two effects of social structure: localization in competition, by which competition between learning strategies is evaded, and localization in cultural transmission, which slows down the spread of adaptive traits. In addition, our estimates of the relatedness measures suggest that social structure disfavours the evolution of social learning when selection is weak. PMID:25631568

Evolution of individual versus social learning on social networks.

PubMed

Tamura, Kohei; Kobayashi, Yutaka; Ihara, Yasuo

2015-03-06

A number of studies have investigated the roles played by individual and social learning in cultural phenomena and the relative advantages of the two learning strategies in variable environments. Because social learning involves the acquisition of behaviours from others, its utility depends on the availability of 'cultural models' exhibiting adaptive behaviours. This indicates that social networks play an essential role in the evolution of learning. However, possible effects of social structure on the evolution of learning have not been fully explored. Here, we develop a mathematical model to explore the evolutionary dynamics of learning strategies on social networks. We first derive the condition under which social learners (SLs) are selectively favoured over individual learners in a broad range of social network. We then obtain an analytical approximation of the long-term average frequency of SLs in homogeneous networks, from which we specify the condition, in terms of three relatedness measures, for social structure to facilitate the long-term evolution of social learning. Finally, we evaluate our approximation by Monte Carlo simulations in complete graphs, regular random graphs and scale-free networks. We formally show that whether social structure favours the evolution of social learning is determined by the relative magnitudes of two effects of social structure: localization in competition, by which competition between learning strategies is evaded, and localization in cultural transmission, which slows down the spread of adaptive traits. In addition, our estimates of the relatedness measures suggest that social structure disfavours the evolution of social learning when selection is weak. © 2015 The Author(s) Published by the Royal Society. All rights reserved.

Analysis of packing microstructure and wall effects in a narrow-bore ultrahigh pressure liquid chromatography column using focused ion-beam scanning electron microscopy.

PubMed

Reising, Arved E; Schlabach, Sabine; Baranau, Vasili; Stoeckel, Daniela; Tallarek, Ulrich

2017-09-01

Column wall effects are well recognized as major limiting factor in achieving high separation efficiency in HPLC. This is especially important for modern analytical columns packed with small particles, where wall effects dominate the band broadening. Detailed knowledge about the packing microstructure of packed analytical columns has so far not been acquired. Here, we present the first three-dimensional reconstruction protocol for these columns utilizing focused ion-beam scanning electron microscopy (FIB-SEM) on a commercial 2.1mm inner diameter×50mm length narrow-bore analytical column packed with 1.7μm bridged-ethyl hybrid silica particles. Two sections from the packed bed are chosen for reconstruction by FIB-SEM: one from the bulk packing region of the column and one from its critical wall region. This allows quantification of structural differences between the wall region and the center of the bed due to effects induced by the hard, confining column wall. Consequences of these effects on local flow velocity in the column are analyzed with flow simulations utilizing the lattice-Boltzmann method. The reconstructions of the bed structures reveal significant structural differences in the wall region (extending radially over approximately 62 particle diameters) compared to the center of the column. It includes the local reduction of the external porosity by up to 10% and an increase of the mean particle diameter by up to 3%, resulting in a decrease of the local flow velocity by up to 23%. In addition, four (more ordered) layers of particles in the direct vicinity of the column wall induce local velocity fluctuations by up to a factor of three regarding the involved velocity amplitudes. These observations highlight the impact of radial variations in packing microstructure on band migration and column performance. This knowledge on morphological peculiarities of column wall effects helps guiding us towards further optimization of the packing process for analytical HPLC columns. Copyright © 2017 Elsevier B.V. All rights reserved.

Loglinear Approximate Solutions to Real-Business-Cycle Models: Some Observations

ERIC Educational Resources Information Center

Lau, Sau-Him Paul; Ng, Philip Hoi-Tak

2007-01-01

Following the analytical approach suggested in Campbell, the authors consider a baseline real-business-cycle (RBC) model with endogenous labor supply. They observe that the coefficients in the loglinear approximation of the dynamic equations characterizing the equilibrium are related to the fundamental parameters in a relatively simple manner.…

Towards comprehensive structural motif mining for better fold annotation in the "twilight zone" of sequence dissimilarity

PubMed Central

Jia, Yi; Huan, Jun; Buhr, Vincent; Zhang, Jintao; Carayannopoulos, Leonidas N

2009-01-01

Background Automatic identification of structure fingerprints from a group of diverse protein structures is challenging, especially for proteins whose divergent amino acid sequences may fall into the "twilight-" or "midnight-" zones where pair-wise sequence identities to known sequences fall below 25% and sequence-based functional annotations often fail. Results Here we report a novel graph database mining method and demonstrate its application to protein structure pattern identification and structure classification. The biologic motivation of our study is to recognize common structure patterns in "immunoevasins", proteins mediating virus evasion of host immune defense. Our experimental study, using both viral and non-viral proteins, demonstrates the efficiency and efficacy of the proposed method. Conclusion We present a theoretic framework, offer a practical software implementation for incorporating prior domain knowledge, such as substitution matrices as studied here, and devise an efficient algorithm to identify approximate matched frequent subgraphs. By doing so, we significantly expanded the analytical power of sophisticated data mining algorithms in dealing with large volume of complicated and noisy protein structure data. And without loss of generality, choice of appropriate compatibility matrices allows our method to be easily employed in domains where subgraph labels have some uncertainty. PMID:19208148

Double power series method for approximating cosmological perturbations

NASA Astrophysics Data System (ADS)

Wren, Andrew J.; Malik, Karim A.

2017-04-01

We introduce a double power series method for finding approximate analytical solutions for systems of differential equations commonly found in cosmological perturbation theory. The method was set out, in a noncosmological context, by Feshchenko, Shkil' and Nikolenko (FSN) in 1966, and is applicable to cases where perturbations are on subhorizon scales. The FSN method is essentially an extension of the well known Wentzel-Kramers-Brillouin (WKB) method for finding approximate analytical solutions for ordinary differential equations. The FSN method we use is applicable well beyond perturbation theory to solve systems of ordinary differential equations, linear in the derivatives, that also depend on a small parameter, which here we take to be related to the inverse wave-number. We use the FSN method to find new approximate oscillating solutions in linear order cosmological perturbation theory for a flat radiation-matter universe. Together with this model's well-known growing and decaying Mészáros solutions, these oscillating modes provide a complete set of subhorizon approximations for the metric potential, radiation and matter perturbations. Comparison with numerical solutions of the perturbation equations shows that our approximations can be made accurate to within a typical error of 1%, or better. We also set out a heuristic method for error estimation. A Mathematica notebook which implements the double power series method is made available online.

A new concept of pencil beam dose calculation for 40-200 keV photons using analytical dose kernels.

PubMed

Bartzsch, Stefan; Oelfke, Uwe

2013-11-01

The advent of widespread kV-cone beam computer tomography in image guided radiation therapy and special therapeutic application of keV photons, e.g., in microbeam radiation therapy (MRT) require accurate and fast dose calculations for photon beams with energies between 40 and 200 keV. Multiple photon scattering originating from Compton scattering and the strong dependence of the photoelectric cross section on the atomic number of the interacting tissue render these dose calculations by far more challenging than the ones established for corresponding MeV beams. That is why so far developed analytical models of kV photon dose calculations fail to provide the required accuracy and one has to rely on time consuming Monte Carlo simulation techniques. In this paper, the authors introduce a novel analytical approach for kV photon dose calculations with an accuracy that is almost comparable to the one of Monte Carlo simulations. First, analytical point dose and pencil beam kernels are derived for homogeneous media and compared to Monte Carlo simulations performed with the Geant4 toolkit. The dose contributions are systematically separated into contributions from the relevant orders of multiple photon scattering. Moreover, approximate scaling laws for the extension of the algorithm to inhomogeneous media are derived. The comparison of the analytically derived dose kernels in water showed an excellent agreement with the Monte Carlo method. Calculated values deviate less than 5% from Monte Carlo derived dose values, for doses above 1% of the maximum dose. The analytical structure of the kernels allows adaption to arbitrary materials and photon spectra in the given energy range of 40-200 keV. The presented analytical methods can be employed in a fast treatment planning system for MRT. In convolution based algorithms dose calculation times can be reduced to a few minutes.

The H i-to-H{sub 2} Transition in a Turbulent Medium

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

Bialy, Shmuel; Sternberg, Amiel; Burkhart, Blakesley, E-mail: shmuelbi@mail.tau.ac.il

2017-07-10

We study the effect of density fluctuations induced by turbulence on the H i/H{sub 2} structure in photodissociation regions (PDRs) both analytically and numerically. We perform magnetohydrodynamic numerical simulations for both subsonic and supersonic turbulent gas and chemical H i/H{sub 2} balance calculations. We derive atomic-to-molecular density profiles and the H i column density probability density function (PDF) assuming chemical equilibrium. We find that, while the H i/H{sub 2} density profiles are strongly perturbed in turbulent gas, the mean H i column density is well approximated by the uniform-density analytic formula of Sternberg et al. The PDF width depends onmore » (a) the radiation intensity–to–mean density ratio, (b) the sonic Mach number, and (c) the turbulence decorrelation scale, or driving scale. We derive an analytic model for the H i PDF and demonstrate how our model, combined with 21 cm observations, can be used to constrain the Mach number and driving scale of turbulent gas. As an example, we apply our model to observations of H i in the Perseus molecular cloud. We show that a narrow observed H i PDF may imply small-scale decorrelation, pointing to the potential importance of subcloud-scale turbulence driving.« less

Dimensional transitions in thermodynamic properties of ideal Maxwell-Boltzmann gases

NASA Astrophysics Data System (ADS)

Aydin, Alhun; Sisman, Altug

2015-04-01

An ideal Maxwell-Boltzmann gas confined in various rectangular nanodomains is considered under quantum size effects. Thermodynamic quantities are calculated from their relations with the partition function, which consists of triple infinite summations over momentum states in each direction. To obtain analytical expressions, summations are converted to integrals for macrosystems by a continuum approximation, which fails at the nanoscale. To avoid both the numerical calculation of summations and the failure of their integral approximations at the nanoscale, a method which gives an analytical expression for a single particle partition function (SPPF) is proposed. It is shown that a dimensional transition in momentum space occurs at a certain magnitude of confinement. Therefore, to represent the SPPF by lower-dimensional analytical expressions becomes possible, rather than numerical calculation of summations. Considering rectangular domains with different aspect ratios, a comparison of the results of derived expressions with those of summation forms of the SPPF is made. It is shown that analytical expressions for the SPPF give very precise results with maximum relative errors of around 1%, 2% and 3% at exactly the transition point for single, double and triple transitions, respectively. Based on dimensional transitions, expressions for free energy, entropy, internal energy, chemical potential, heat capacity and pressure are given analytically valid for any scale.

An analytical approach to the CMB polarization in a spatially closed background

NASA Astrophysics Data System (ADS)

Niazy, Pedram; Abbassi, Amir H.

2018-03-01

The scalar mode polarization of the cosmic microwave background is derived in a spatially closed universe from the Boltzmann equation using the line of sight integral method. The EE and TE multipole coefficients have been extracted analytically by considering some tolerable approximations such as considering the evolution of perturbation hydrodynamically and sudden transition from opacity to transparency at the time of last scattering. As the major advantage of analytic expressions, CEE,ℓS and CTE,ℓ explicitly show the dependencies on baryon density ΩB, matter density ΩM, curvature ΩK, primordial spectral index ns, primordial power spectrum amplitude As, Optical depth τreion, recombination width σt and recombination time tL. Using a realistic set of cosmological parameters taken from a fit to data from Planck, the closed universe EE and TE power spectrums in the scalar mode are compared with numerical results from the CAMB code and also latest observational data. The analytic results agree with the numerical ones on the big and moderate scales. The peak positions are in good agreement with the numerical result on these scales while the peak heights agree with that to within 20% due to the approximations have been considered for these derivations. Also, several interesting properties of CMB polarization are revealed by the analytic spectra.