Sample records for linear response approximation

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

    PubMed

    Follmann, D; Wu, M

    1995-03-01

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

  2. Efficient Algorithms for Estimating the Absorption Spectrum within Linear Response TDDFT

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

    Brabec, Jiri; Lin, Lin; Shao, Meiyue

    We present two iterative algorithms for approximating the absorption spectrum of molecules within linear response of time-dependent density functional theory (TDDFT) framework. These methods do not attempt to compute eigenvalues or eigenvectors of the linear response matrix. They are designed to approximate the absorption spectrum as a function directly. They take advantage of the special structure of the linear response matrix. Neither method requires the linear response matrix to be constructed explicitly. They only require a procedure that performs the multiplication of the linear response matrix with a vector. These methods can also be easily modified to efficiently estimate themore » density of states (DOS) of the linear response matrix without computing the eigenvalues of this matrix. We show by computational experiments that the methods proposed in this paper can be much more efficient than methods that are based on the exact diagonalization of the linear response matrix. We show that they can also be more efficient than real-time TDDFT simulations. We compare the pros and cons of these methods in terms of their accuracy as well as their computational and storage cost.« less

  3. Thermal Density Functional Theory: Time-Dependent Linear Response and Approximate Functionals from the Fluctuation-Dissipation Theorem

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

    Pribram-Jones, Aurora; Grabowski, Paul E.; Burke, Kieron

    We present that the van Leeuwen proof of linear-response time-dependent density functional theory (TDDFT) is generalized to thermal ensembles. This allows generalization to finite temperatures of the Gross-Kohn relation, the exchange-correlation kernel of TDDFT, and fluctuation dissipation theorem for DFT. Finally, this produces a natural method for generating new thermal exchange-correlation approximations.

  4. Thermal Density Functional Theory: Time-Dependent Linear Response and Approximate Functionals from the Fluctuation-Dissipation Theorem

    DOE PAGES

    Pribram-Jones, Aurora; Grabowski, Paul E.; Burke, Kieron

    2016-06-08

    We present that the van Leeuwen proof of linear-response time-dependent density functional theory (TDDFT) is generalized to thermal ensembles. This allows generalization to finite temperatures of the Gross-Kohn relation, the exchange-correlation kernel of TDDFT, and fluctuation dissipation theorem for DFT. Finally, this produces a natural method for generating new thermal exchange-correlation approximations.

  5. Recursive Inversion By Finite-Impulse-Response Filters

    NASA Technical Reports Server (NTRS)

    Bach, Ralph E., Jr.; Baram, Yoram

    1991-01-01

    Recursive approximation gives least-squares best fit to exact response. Algorithm yields finite-impulse-response approximation of unknown single-input/single-output, causal, time-invariant, linear, real system, response of which is sequence of impulses. Applicable to such system-inversion problems as suppression of echoes and identification of target from its scatter response to incident impulse.

  6. Differential equation based method for accurate approximations in optimization

    NASA Technical Reports Server (NTRS)

    Pritchard, Jocelyn I.; Adelman, Howard M.

    1990-01-01

    This paper describes a method to efficiently and accurately approximate the effect of design changes on structural response. The key to this new method is to interpret sensitivity equations as differential equations that may be solved explicitly for closed form approximations, hence, the method is denoted the Differential Equation Based (DEB) method. Approximations were developed for vibration frequencies, mode shapes and static displacements. The DEB approximation method was applied to a cantilever beam and results compared with the commonly-used linear Taylor series approximations and exact solutions. The test calculations involved perturbing the height, width, cross-sectional area, tip mass, and bending inertia of the beam. The DEB method proved to be very accurate, and in msot cases, was more accurate than the linear Taylor series approximation. The method is applicable to simultaneous perturbation of several design variables. Also, the approximations may be used to calculate other system response quantities. For example, the approximations for displacement are used to approximate bending stresses.

  7. Differential equation based method for accurate approximations in optimization

    NASA Technical Reports Server (NTRS)

    Pritchard, Jocelyn I.; Adelman, Howard M.

    1990-01-01

    A method to efficiently and accurately approximate the effect of design changes on structural response is described. The key to this method is to interpret sensitivity equations as differential equations that may be solved explicitly for closed form approximations, hence, the method is denoted the Differential Equation Based (DEB) method. Approximations were developed for vibration frequencies, mode shapes and static displacements. The DEB approximation method was applied to a cantilever beam and results compared with the commonly-used linear Taylor series approximations and exact solutions. The test calculations involved perturbing the height, width, cross-sectional area, tip mass, and bending inertia of the beam. The DEB method proved to be very accurate, and in most cases, was more accurate than the linear Taylor series approximation. The method is applicable to simultaneous perturbation of several design variables. Also, the approximations may be used to calculate other system response quantities. For example, the approximations for displacements are used to approximate bending stresses.

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

    NASA Astrophysics Data System (ADS)

    Hsieh, Chang-Yu; Cao, Jianshu

    2018-01-01

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

  9. Derivative information recovery by a selective integration technique

    NASA Technical Reports Server (NTRS)

    Johnson, M. A.

    1974-01-01

    A nonlinear stationary homogeneous digital filter DIRSIT (derivative information recovery by a selective integration technique) is investigated. The spectrum of a quasi-linear discrete describing function (DDF) to DIRSIT is obtained by a digital measuring scheme. A finite impulse response (FIR) approximation to the quasi-linearization is then obtained. Finally, DIRSIT is compared with its quasi-linear approximation and with a standard digital differentiating technique. Results indicate the effects of DIRSIT on a wide variety of practical signals.

  10. Linear and nonlinear response in sheared soft spheres

    NASA Astrophysics Data System (ADS)

    Tighe, Brian

    2013-11-01

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

  11. Excited states with internally contracted multireference coupled-cluster linear response theory.

    PubMed

    Samanta, Pradipta Kumar; Mukherjee, Debashis; Hanauer, Matthias; Köhn, Andreas

    2014-04-07

    In this paper, the linear response (LR) theory for the variant of internally contracted multireference coupled cluster (ic-MRCC) theory described by Hanauer and Köhn [J. Chem. Phys. 134, 204211 (2011)] has been formulated and implemented for the computation of the excitation energies relative to a ground state of pronounced multireference character. We find that straightforward application of the linear-response formalism to the time-averaged ic-MRCC Lagrangian leads to unphysical second-order poles. However, the coupling matrix elements that cause this behavior are shown to be negligible whenever the internally contracted approximation as such is justified. Hence, for the numerical implementation of the method, we adopt a Tamm-Dancoff-type approximation and neglect these couplings. This approximation is also consistent with an equation-of-motion based derivation, which neglects these couplings right from the start. We have implemented the linear-response approach in the ic-MRCC singles-and-doubles framework and applied our method to calculate excitation energies for a number of molecules ranging from CH2 to p-benzyne and conjugated polyenes (up to octatetraene). The computed excitation energies are found to be very accurate, even for the notoriously difficult case of doubly excited states. The ic-MRCC-LR theory is also applicable to systems with open-shell ground-state wavefunctions and is by construction not biased towards a particular reference determinant. We have also compared the linear-response approach to the computation of energy differences by direct state-specific ic-MRCC calculations. We finally compare to Mk-MRCC-LR theory for which spurious roots have been reported [T.-C. Jagau and J. Gauss, J. Chem. Phys. 137, 044116 (2012)], being due to the use of sufficiency conditions to solve the Mk-MRCC equations. No such problem is present in ic-MRCC-LR theory.

  12. Linear-response time-dependent density-functional theory with pairing fields.

    PubMed

    Peng, Degao; van Aggelen, Helen; Yang, Yang; Yang, Weitao

    2014-05-14

    Recent development in particle-particle random phase approximation (pp-RPA) broadens the perspective on ground state correlation energies [H. van Aggelen, Y. Yang, and W. Yang, Phys. Rev. A 88, 030501 (2013), Y. Yang, H. van Aggelen, S. N. Steinmann, D. Peng, and W. Yang, J. Chem. Phys. 139, 174110 (2013); D. Peng, S. N. Steinmann, H. van Aggelen, and W. Yang, J. Chem. Phys. 139, 104112 (2013)] and N ± 2 excitation energies [Y. Yang, H. van Aggelen, and W. Yang, J. Chem. Phys. 139, 224105 (2013)]. So far Hartree-Fock and approximated density-functional orbitals have been utilized to evaluate the pp-RPA equation. In this paper, to further explore the fundamentals and the potential use of pairing matrix dependent functionals, we present the linear-response time-dependent density-functional theory with pairing fields with both adiabatic and frequency-dependent kernels. This theory is related to the density-functional theory and time-dependent density-functional theory for superconductors, but is applied to normal non-superconducting systems for our purpose. Due to the lack of the proof of the one-to-one mapping between the pairing matrix and the pairing field for time-dependent systems, the linear-response theory is established based on the representability assumption of the pairing matrix. The linear response theory justifies the use of approximated density-functionals in the pp-RPA equation. This work sets the fundamentals for future density-functional development to enhance the description of ground state correlation energies and N ± 2 excitation energies.

  13. Optimal Linear Responses for Markov Chains and Stochastically Perturbed Dynamical Systems

    NASA Astrophysics Data System (ADS)

    Antown, Fadi; Dragičević, Davor; Froyland, Gary

    2018-03-01

    The linear response of a dynamical system refers to changes to properties of the system when small external perturbations are applied. We consider the little-studied question of selecting an optimal perturbation so as to (i) maximise the linear response of the equilibrium distribution of the system, (ii) maximise the linear response of the expectation of a specified observable, and (iii) maximise the linear response of the rate of convergence of the system to the equilibrium distribution. We also consider the inhomogeneous, sequential, or time-dependent situation where the governing dynamics is not stationary and one wishes to select a sequence of small perturbations so as to maximise the overall linear response at some terminal time. We develop the theory for finite-state Markov chains, provide explicit solutions for some illustrative examples, and numerically apply our theory to stochastically perturbed dynamical systems, where the Markov chain is replaced by a matrix representation of an approximate annealed transfer operator for the random dynamical system.

  14. Recursive inversion of externally defined linear systems

    NASA Technical Reports Server (NTRS)

    Bach, Ralph E., Jr.; Baram, Yoram

    1988-01-01

    The approximate inversion of an internally unknown linear system, given by its impulse response sequence, by an inverse system having a finite impulse response, is considered. The recursive least squares procedure is shown to have an exact initialization, based on the triangular Toeplitz structure of the matrix involved. The proposed approach also suggests solutions to the problems of system identification and compensation.

  15. Recursive inversion of externally defined linear systems by FIR filters

    NASA Technical Reports Server (NTRS)

    Bach, Ralph E., Jr.; Baram, Yoram

    1989-01-01

    The approximate inversion of an internally unknown linear system, given by its impulse response sequence, by an inverse system having a finite impulse response, is considered. The recursive least-squares procedure is shown to have an exact initialization, based on the triangular Toeplitz structure of the matrix involved. The proposed approach also suggests solutions to the problem of system identification and compensation.

  16. Electrostatic Solvation Free Energy of Amino Acid Side Chain Analogs: Implications for the Validity of Electrostatic Linear Response in Water

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

    Lin, Bin; Pettitt, Bernard M.

    Electrostatic free energies of solvation for 15 neutral amino acid side chain analogs are computed. We compare three methods of varying computational complexity and accuracy for three force fields: free energy simulations, Poisson-Boltzmann (PB), and linear response approximation (LRA) using AMBER, CHARMM, and OPLSAA force fields. We find that deviations from simulation start at low charges for solutes. The approximate PB and LRA produce an overestimation of electrostatic solvation free energies for most of molecules studied here. These deviations are remarkably systematic. The variations among force fields are almost as large as the variations found among methods. Our study confirmsmore » that success of the approximate methods for electrostatic solvation free energies comes from their ability to evaluate free energy differences accurately.« less

  17. A new method to approximate load-displacement relationships of spinal motion segments for patient-specific multi-body models of scoliotic spine.

    PubMed

    Jalalian, Athena; Tay, Francis E H; Arastehfar, Soheil; Liu, Gabriel

    2017-06-01

    Load-displacement relationships of spinal motion segments are crucial factors in characterizing the stiffness of scoliotic spine models to mimic the spine responses to loads. Although nonlinear approach to approximation of the relationships can be superior to linear ones, little mention has been made to deriving personalized nonlinear load-displacement relationships in previous studies. A method is developed for nonlinear approximation of load-displacement relationships of spinal motion segments to assist characterizing in vivo the stiffness of spine models. We propose approximation by tangent functions and focus on rotational displacements in lateral direction. The tangent functions are characterized using lateral bending test. A multi-body model was characterized to 18 patients and utilized to simulate four spine positions; right bending, left bending, neutral, and traction. The same was done using linear functions to assess the performance of the proposed tangent function in comparison with the linear function. Root-mean-square error (RMSE) of the displacements estimated by the tangent functions was 44 % smaller than the linear functions. This shows the ability of our tangent function in approximation of the relationships for a range of infinitesimal to large displacements involved in the spine movement to the four positions. In addition, the models based on the tangent functions yielded 67, 55, and 39 % smaller RMSEs of Ferguson angles, locations of vertebrae, and orientations of vertebrae, respectively, implying better estimates of spine responses to loads. Overall, it can be concluded that our method for approximating load-displacement relationships of spinal motion segments can offer good estimates of scoliotic spine stiffness.

  18. A heteroscedastic generalized linear model with a non-normal speed factor for responses and response times.

    PubMed

    Molenaar, Dylan; Bolsinova, Maria

    2017-05-01

    In generalized linear modelling of responses and response times, the observed response time variables are commonly transformed to make their distribution approximately normal. A normal distribution for the transformed response times is desirable as it justifies the linearity and homoscedasticity assumptions in the underlying linear model. Past research has, however, shown that the transformed response times are not always normal. Models have been developed to accommodate this violation. In the present study, we propose a modelling approach for responses and response times to test and model non-normality in the transformed response times. Most importantly, we distinguish between non-normality due to heteroscedastic residual variances, and non-normality due to a skewed speed factor. In a simulation study, we establish parameter recovery and the power to separate both effects. In addition, we apply the model to a real data set. © 2017 The Authors. British Journal of Mathematical and Statistical Psychology published by John Wiley & Sons Ltd on behalf of British Psychological Society.

  19. Dynamics of Permanent-Magnet Biased Active Magnetic Bearings

    NASA Technical Reports Server (NTRS)

    Fukata, Satoru; Yutani, Kazuyuki

    1996-01-01

    Active magnetic radial bearings are constructed with a combination of permanent magnets to provide bias forces and electromagnets to generate control forces for the reduction of cost and the operating energy consumption. Ring-shaped permanent magnets with axial magnetization are attached to a shaft and share their magnet stators with the electromagnets. The magnet cores are made of solid iron for simplicity. A simplified magnetic circuit of the combined magnet system is analyzed with linear circuit theory by approximating the characteristics of permanent magnets with a linear relation. A linearized dynamical model of the control force is presented with the first-order approximation of the effects of eddy currents. Frequency responses of the rotor motion to disturbance inputs and the motion for impulsive forces are tested in the non-rotating state. The frequency responses are compared with numerical results. The decay of rotor speed due to magnetic braking is examined. The experimental results and the presented linearized model are similar to those of the all-electromagnetic design.

  20. Analysis of dynamic system response to product random processes

    NASA Technical Reports Server (NTRS)

    Sidwell, K.

    1978-01-01

    The response of dynamic systems to the product of two independent Gaussian random processes is developed by use of the Fokker-Planck and associated moment equations. The development is applied to the amplitude modulated process which is used to model atmospheric turbulence in aeronautical applications. The exact solution for the system response is compared with the solution obtained by the quasi-steady approximation which omits the dynamic properties of the random amplitude modulation. The quasi-steady approximation is valid as a limiting case of the exact solution for the dynamic response of linear systems to amplitude modulated processes. In the nonlimiting case the quasi-steady approximation can be invalid for dynamic systems with low damping.

  1. Exchange Energy Density Functionals that reproduce the Linear Response Function of the Free Electron Gas

    NASA Astrophysics Data System (ADS)

    García-Aldea, David; Alvarellos, J. E.

    2009-03-01

    We present several nonlocal exchange energy density functionals that reproduce the linear response function of the free electron gas. These nonlocal functionals are constructed following a similar procedure used previously for nonlocal kinetic energy density functionals by Chac'on-Alvarellos-Tarazona, Garc'ia-Gonz'alez et al., Wang-Govind-Carter and Garc'ia-Aldea-Alvarellos. The exchange response function is not known but we have used the approximate response function developed by Utsumi and Ichimaru, even we must remark that the same ansatz can be used to reproduce any other response function with the same scaling properties. We have developed two families of new nonlocal functionals: one is constructed with a mathematical structure based on the LDA approximation -- the Dirac functional for the exchange - and for the second one the structure of the second order gradient expansion approximation is took as a model. The functionals are constructed is such a way that they can be used in localized systems (using real space calculations) and in extended systems (using the momentum space, and achieving a quasilinear scaling with the system size if a constant reference electron density is defined).

  2. Linear and non-linear dynamic models of a geared rotor-bearing system

    NASA Technical Reports Server (NTRS)

    Kahraman, Ahmet; Singh, Rajendra

    1990-01-01

    A three degree of freedom non-linear model of a geared rotor-bearing system with gear backlash and radial clearances in rolling element bearings is proposed here. This reduced order model can be used to describe the transverse-torsional motion of the system. It is justified by comparing the eigen solutions yielded by corresponding linear model with the finite element method results. Nature of nonlinearities in bearings is examined and two approximate nonlinear stiffness functions are proposed. These approximate bearing models are verified by comparing their frequency responses with the results given by the exact form of nonlinearity. The proposed nonlinear dynamic model of the geared rotor-bearing system can be used to investigate the dynamic behavior and chaos.

  3. Note: A high dynamic range, linear response transimpedance amplifier.

    PubMed

    Eckel, S; Sushkov, A O; Lamoreaux, S K

    2012-02-01

    We have built a high dynamic range (nine decade) transimpedance amplifier with a linear response. The amplifier uses junction-gate field effect transistors (JFETs) to switch between three different resistors in the feedback of a low input bias current operational amplifier. This allows for the creation of multiple outputs, each with a linear response and a different transimpedance gain. The overall bandwidth of the transimpedance amplifier is set by the bandwidth of the most sensitive range. For our application, we demonstrate a three-stage amplifier with transimpedance gains of approximately 10(9)Ω, 3 × 10(7)Ω, and 10(4)Ω with a bandwidth of 100 Hz.

  4. Exponential approximations in optimal design

    NASA Technical Reports Server (NTRS)

    Belegundu, A. D.; Rajan, S. D.; Rajgopal, J.

    1990-01-01

    One-point and two-point exponential functions have been developed and proved to be very effective approximations of structural response. The exponential has been compared to the linear, reciprocal and quadratic fit methods. Four test problems in structural analysis have been selected. The use of such approximations is attractive in structural optimization to reduce the numbers of exact analyses which involve computationally expensive finite element analysis.

  5. Generation of linear dynamic models from a digital nonlinear simulation

    NASA Technical Reports Server (NTRS)

    Daniele, C. J.; Krosel, S. M.

    1979-01-01

    The results and methodology used to derive linear models from a nonlinear simulation are presented. It is shown that averaged positive and negative perturbations in the state variables can reduce numerical errors in finite difference, partial derivative approximations and, in the control inputs, can better approximate the system response in both directions about the operating point. Both explicit and implicit formulations are addressed. Linear models are derived for the F 100 engine, and comparisons of transients are made with the nonlinear simulation. The problem of startup transients in the nonlinear simulation in making these comparisons is addressed. Also, reduction of the linear models is investigated using the modal and normal techniques. Reduced-order models of the F 100 are derived and compared with the full-state models.

  6. Comparison of heaving buoy and oscillating flap wave energy converters

    NASA Astrophysics Data System (ADS)

    Abu Bakar, Mohd Aftar; Green, David A.; Metcalfe, Andrew V.; Najafian, G.

    2013-04-01

    Waves offer an attractive source of renewable energy, with relatively low environmental impact, for communities reasonably close to the sea. Two types of simple wave energy converters (WEC), the heaving buoy WEC and the oscillating flap WEC, are studied. Both WECs are considered as simple energy converters because they can be modelled, to a first approximation, as single degree of freedom linear dynamic systems. In this study, we estimate the response of both WECs to typical wave inputs; wave height for the buoy and corresponding wave surge for the flap, using spectral methods. A nonlinear model of the oscillating flap WEC that includes the drag force, modelled by the Morison equation is also considered. The response to a surge input is estimated by discrete time simulation (DTS), using central difference approximations to derivatives. This is compared with the response of the linear model obtained by DTS and also validated using the spectral method. Bendat's nonlinear system identification (BNLSI) technique was used to analyze the nonlinear dynamic system since the spectral analysis was only suitable for linear dynamic system. The effects of including the nonlinear term are quantified.

  7. Multiphysics modeling of non-linear laser-matter interactions for optically active semiconductors

    NASA Astrophysics Data System (ADS)

    Kraczek, Brent; Kanp, Jaroslaw

    Development of photonic devices for sensors and communications devices has been significantly enhanced by computational modeling. We present a new computational method for modelling laser propagation in optically-active semiconductors within the paraxial wave approximation (PWA). Light propagation is modeled using the Streamline-upwind/Petrov-Galerkin finite element method (FEM). Material response enters through the non-linear polarization, which serves as the right-hand side of the FEM calculation. Maxwell's equations for classical light propagation within the PWA can be written solely in terms of the electric field, producing a wave equation that is a form of the advection-diffusion-reaction equations (ADREs). This allows adaptation of the computational machinery developed for solving ADREs in fluid dynamics to light-propagation modeling. The non-linear polarization is incorporated using a flexible framework to enable the use of multiple methods for carrier-carrier interactions (e.g. relaxation-time-based or Monte Carlo) to enter through the non-linear polarization, as appropriate to the material type. We demonstrate using a simple carrier-carrier model approximating the response of GaN. Supported by ARL Materials Enterprise.

  8. Flapping response characteristics of hingeless rotor blades by a gereralized harmonic balance method

    NASA Technical Reports Server (NTRS)

    Peters, D. A.; Ormiston, R. A.

    1975-01-01

    Linearized equations of motion for the flapping response of flexible rotor blades in forward flight are derived in terms of generalized coordinates. The equations are solved using a matrix form of the method of linear harmonic balance, yielding response derivatives for each harmonic of the blade deformations and of the hub forces and moments. Numerical results and approximate closed-form expressions for rotor derivatives are used to illustrate the relationships between rotor parameters, modeling assumptions, and rotor response characteristics. Finally, basic hingeless rotor response derivatives are presented in tabular and graphical form for a wide range of configuration parameters and operating conditions.

  9. Trellis Coding of Non-coherent Multiple Symbol Full Response M-ary CPFSK with Modulation Index 1/M

    NASA Technical Reports Server (NTRS)

    Lee, H.; Divsalar, D.; Weber, C.

    1994-01-01

    This paper introduces a trellis coded modulation (TCM) scheme for non-coherent multiple full response M-ary CPFSK with modulation index 1/M. A proper branch metric for the trellis decoder is obtained by employing a simple approximation of the modified Bessel function for large signal to noise ratio (SNR). Pairwise error probability of coded sequences is evaluated by applying a linear approximation to the Rician random variable.

  10. Optimal clinical trial design based on a dichotomous Markov-chain mixed-effect sleep model.

    PubMed

    Steven Ernest, C; Nyberg, Joakim; Karlsson, Mats O; Hooker, Andrew C

    2014-12-01

    D-optimal designs for discrete-type responses have been derived using generalized linear mixed models, simulation based methods and analytical approximations for computing the fisher information matrix (FIM) of non-linear mixed effect models with homogeneous probabilities over time. In this work, D-optimal designs using an analytical approximation of the FIM for a dichotomous, non-homogeneous, Markov-chain phase advanced sleep non-linear mixed effect model was investigated. The non-linear mixed effect model consisted of transition probabilities of dichotomous sleep data estimated as logistic functions using piecewise linear functions. Theoretical linear and nonlinear dose effects were added to the transition probabilities to modify the probability of being in either sleep stage. D-optimal designs were computed by determining an analytical approximation the FIM for each Markov component (one where the previous state was awake and another where the previous state was asleep). Each Markov component FIM was weighted either equally or by the average probability of response being awake or asleep over the night and summed to derive the total FIM (FIM(total)). The reference designs were placebo, 0.1, 1-, 6-, 10- and 20-mg dosing for a 2- to 6-way crossover study in six dosing groups. Optimized design variables were dose and number of subjects in each dose group. The designs were validated using stochastic simulation/re-estimation (SSE). Contrary to expectations, the predicted parameter uncertainty obtained via FIM(total) was larger than the uncertainty in parameter estimates computed by SSE. Nevertheless, the D-optimal designs decreased the uncertainty of parameter estimates relative to the reference designs. Additionally, the improvement for the D-optimal designs were more pronounced using SSE than predicted via FIM(total). Through the use of an approximate analytic solution and weighting schemes, the FIM(total) for a non-homogeneous, dichotomous Markov-chain phase advanced sleep model was computed and provided more efficient trial designs and increased nonlinear mixed-effects modeling parameter precision.

  11. The Linear Bias in the Zeldovich Approximation and a Relation between the Number Density and the Linear Bias of Dark Halos

    NASA Astrophysics Data System (ADS)

    Fan, Zuhui

    2000-01-01

    The linear bias of the dark halos from a model under the Zeldovich approximation is derived and compared with the fitting formula of simulation results. While qualitatively similar to the Press-Schechter formula, this model gives a better description for the linear bias around the turnaround point. This advantage, however, may be compromised by the large uncertainty of the actual behavior of the linear bias near the turnaround point. For a broad class of structure formation models in the cold dark matter framework, a general relation exists between the number density and the linear bias of dark halos. This relation can be readily tested by numerical simulations. Thus, instead of laboriously checking these models one by one, numerical simulation studies can falsify a whole category of models. The general validity of this relation is important in identifying key physical processes responsible for the large-scale structure formation in the universe.

  12. Dependence of upper atmosphere photochemistry on the shape of the diurnal cycle of the photolysis rates

    NASA Astrophysics Data System (ADS)

    Montecinos, S.; Barrientos, P.

    2006-03-01

    A photochemical model of the atmosphere constitutes a non-linear, non-autonomous dynamical system, enforced by the Earth's rotation. Some studies have shown that the region of the mesopause tends towards non-linear responses such as period-doubling cascades and chaos. In these studies, simple go approximations for the diurnal variations of the photolysis rates are assumed. The goal of this article is to investigate what happens if the more realistic, calculated photolysis rates are introduced. It is found that, if the usual approximations-sinusoidal and step functions-are assumed, the responses of the system are similar: it converges to a 2-day periodic solution. If the more realistic, calculated diurnal cycle is introduced, a new 4-day subharmonic appear.

  13. 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.

  14. Dynamic Structure Factor: An Introduction

    NASA Astrophysics Data System (ADS)

    Sturm, K.

    1993-02-01

    The doubly differential cross-section for weak inelastic scattering of waves or particles by manybody systems is derived in Born approximation and expressed in terms of the dynamic structure factor according to van Hove. The application of this very general scheme to scattering of neutrons, x-rays and high-energy electrons is discussed briefly. The dynamic structure factor, which is the space and time Fourier transform of the density-density correlation function, is a property of the many-body system independent of the external probe and carries information on the excitation spectrum of the system. The relation of the electronic structure factor to the density-density response function defined in linear-response theory is shown using the fluctuation-dissipation theorem. This is important for calculations, since the response function can be calculated approximately from the independent-particle response function in self-consistent field approximations, such as the random-phase approximation or the local-density approximation of the density functional theory. Since the density-density response function also determines the dielectric function, the dynamic structure can be expressed by the dielectric function.

  15. On mathematical modelling of aeroelastic problems with finite element method

    NASA Astrophysics Data System (ADS)

    Sváček, Petr

    2018-06-01

    This paper is interested in solution of two-dimensional aeroelastic problems. Two mathematical models are compared for a benchmark problem. First, the classical approach of linearized aerodynamical forces is described to determine the aeroelastic instability and the aeroelastic response in terms of frequency and damping coefficient. This approach is compared to the coupled fluid-structure model solved with the aid of finite element method used for approximation of the incompressible Navier-Stokes equations. The finite element approximations are coupled to the non-linear motion equations of a flexibly supported airfoil. Both methods are first compared for the case of small displacement, where the linearized approach can be well adopted. The influence of nonlinearities for the case of post-critical regime is discussed.

  16. Accurate frequency domain measurement of the best linear time-invariant approximation of linear time-periodic systems including the quantification of the time-periodic distortions

    NASA Astrophysics Data System (ADS)

    Louarroudi, E.; Pintelon, R.; Lataire, J.

    2014-10-01

    Time-periodic (TP) phenomena occurring, for instance, in wind turbines, helicopters, anisotropic shaft-bearing systems, and cardiovascular/respiratory systems, are often not addressed when classical frequency response function (FRF) measurements are performed. As the traditional FRF concept is based on the linear time-invariant (LTI) system theory, it is only approximately valid for systems with varying dynamics. Accordingly, the quantification of any deviation from this ideal LTI framework is more than welcome. The “measure of deviation” allows us to define the notion of the best LTI (BLTI) approximation, which yields the best - in mean square sense - LTI description of a linear time-periodic LTP system. By taking into consideration the TP effects, it is shown in this paper that the variability of the BLTI measurement can be reduced significantly compared with that of classical FRF estimators. From a single experiment, the proposed identification methods can handle (non-)linear time-periodic [(N)LTP] systems in open-loop with a quantification of (i) the noise and/or the NL distortions, (ii) the TP distortions and (iii) the transient (leakage) errors. Besides, a geometrical interpretation of the BLTI approximation is provided, leading to a framework called vector FRF analysis. The theory presented is supported by numerical simulations as well as real measurements mimicking the well-known mechanical Mathieu oscillator.

  17. Linear response coupled cluster theory with the polarizable continuum model within the singles approximation for the solvent response.

    PubMed

    Caricato, Marco

    2018-04-07

    We report the theory and the implementation of the linear response function of the coupled cluster (CC) with the single and double excitations method combined with the polarizable continuum model of solvation, where the correlation solvent response is approximated with the perturbation theory with energy and singles density (PTES) scheme. The singles name is derived from retaining only the contribution of the CC single excitation amplitudes to the correlation density. We compare the PTES working equations with those of the full-density (PTED) method. We then test the PTES scheme on the evaluation of excitation energies and transition dipoles of solvated molecules, as well as of the isotropic polarizability and specific rotation. Our results show a negligible difference between the PTED and PTES schemes, while the latter affords a significantly reduced computational cost. This scheme is general and can be applied to any solvation model that includes mutual solute-solvent polarization, including explicit models. Therefore, the PTES scheme is a competitive approach to compute response properties of solvated systems using CC methods.

  18. Linear response coupled cluster theory with the polarizable continuum model within the singles approximation for the solvent response

    NASA Astrophysics Data System (ADS)

    Caricato, Marco

    2018-04-01

    We report the theory and the implementation of the linear response function of the coupled cluster (CC) with the single and double excitations method combined with the polarizable continuum model of solvation, where the correlation solvent response is approximated with the perturbation theory with energy and singles density (PTES) scheme. The singles name is derived from retaining only the contribution of the CC single excitation amplitudes to the correlation density. We compare the PTES working equations with those of the full-density (PTED) method. We then test the PTES scheme on the evaluation of excitation energies and transition dipoles of solvated molecules, as well as of the isotropic polarizability and specific rotation. Our results show a negligible difference between the PTED and PTES schemes, while the latter affords a significantly reduced computational cost. This scheme is general and can be applied to any solvation model that includes mutual solute-solvent polarization, including explicit models. Therefore, the PTES scheme is a competitive approach to compute response properties of solvated systems using CC methods.

  19. New model performance index for engineering design of control systems

    NASA Technical Reports Server (NTRS)

    1970-01-01

    Performance index includes a model representing linear control-system design specifications. Based on a geometric criterion for approximation of the model by the actual system, the index can be interpreted directly in terms of the desired system response model without actually having the model's time response.

  20. 40 CFR 86.884-11 - Instrument checks.

    Code of Federal Regulations, 2014 CFR

    2014-07-01

    ... equipment response of zero; (3) Calibrated neutral density filters having approximately 10, 20, and 40 percent opacity shall be employed to check the linearity of the instrument. The filter(s) shall be... beam of light from the light source emanates, and the recorder response shall be noted. Filters with...

  1. 40 CFR 92.122 - Smoke meter calibration.

    Code of Federal Regulations, 2014 CFR

    2014-07-01

    ... equipment response of zero; (b) Calibrated neutral density filters having approximately 10, 20, and 40 percent opacity shall be employed to check the linearity of the instrument. The filter(s) shall be... beam of light from the light source emanates, and the recorder response shall be noted. Filters with...

  2. Bounding solutions of geometrically nonlinear viscoelastic problems

    NASA Technical Reports Server (NTRS)

    Stubstad, J. M.; Simitses, G. J.

    1985-01-01

    Integral transform techniques, such as the Laplace transform, provide simple and direct methods for solving viscoelastic problems formulated within a context of linear material response and using linear measures for deformation. Application of the transform operator reduces the governing linear integro-differential equations to a set of algebraic relations between the transforms of the unknown functions, the viscoelastic operators, and the initial and boundary conditions. Inversion either directly or through the use of the appropriate convolution theorem, provides the time domain response once the unknown functions have been expressed in terms of sums, products or ratios of known transforms. When exact inversion is not possible approximate techniques may provide accurate results. The overall problem becomes substantially more complex when nonlinear effects must be included. Situations where a linear material constitutive law can still be productively employed but where the magnitude of the resulting time dependent deformations warrants the use of a nonlinear kinematic analysis are considered. The governing equations will be nonlinear integro-differential equations for this class of problems. Thus traditional as well as approximate techniques, such as cited above, cannot be employed since the transform of a nonlinear function is not explicitly expressible.

  3. Bounding solutions of geometrically nonlinear viscoelastic problems

    NASA Technical Reports Server (NTRS)

    Stubstad, J. M.; Simitses, G. J.

    1986-01-01

    Integral transform techniques, such as the Laplace transform, provide simple and direct methods for solving viscoelastic problems formulated within a context of linear material response and using linear measures for deformation. Application of the transform operator reduces the governing linear integro-differential equations to a set of algebraic relations between the transforms of the unknown functions, the viscoelastic operators, and the initial and boundary conditions. Inversion either directly or through the use of the appropriate convolution theorem, provides the time domain response once the unknown functions have been expressed in terms of sums, products or ratios of known transforms. When exact inversion is not possible approximate techniques may provide accurate results. The overall problem becomes substantially more complex when nonlinear effects must be included. Situations where a linear material constitutive law can still be productively employed but where the magnitude of the resulting time dependent deformations warrants the use of a nonlinear kinematic analysis are considered. The governing equations will be nonlinear integro-differential equations for this class of problems. Thus traditional as well as approximate techniques, such as cited above, cannot be employed since the transform of a nonlinear function is not explicitly expressible.

  4. Gauge invariance of excitonic linear and nonlinear optical response

    NASA Astrophysics Data System (ADS)

    Taghizadeh, Alireza; Pedersen, T. G.

    2018-05-01

    We study the equivalence of four different approaches to calculate the excitonic linear and nonlinear optical response of multiband semiconductors. These four methods derive from two choices of gauge, i.e., length and velocity gauges, and two ways of computing the current density, i.e., direct evaluation and evaluation via the time-derivative of the polarization density. The linear and quadratic response functions are obtained for all methods by employing a perturbative density-matrix approach within the mean-field approximation. The equivalence of all four methods is shown rigorously, when a correct interaction Hamiltonian is employed for the velocity gauge approaches. The correct interaction is written as a series of commutators containing the unperturbed Hamiltonian and position operators, which becomes equivalent to the conventional velocity gauge interaction in the limit of infinite Coulomb screening and infinitely many bands. As a case study, the theory is applied to hexagonal boron nitride monolayers, and the linear and nonlinear optical response found in different approaches are compared.

  5. Dynamics of a linear system coupled to a chain of light nonlinear oscillators analyzed through a continuous approximation

    NASA Astrophysics Data System (ADS)

    Charlemagne, S.; Ture Savadkoohi, A.; Lamarque, C.-H.

    2018-07-01

    The continuous approximation is used in this work to describe the dynamics of a nonlinear chain of light oscillators coupled to a linear main system. A general methodology is applied to an example where the chain has local nonlinear restoring forces. The slow invariant manifold is detected at fast time scale. At slow time scale, equilibrium and singular points are sought around this manifold in order to predict periodic regimes and strongly modulated responses of the system. Analytical predictions are in good accordance with numerical results and represent a potent tool for designing nonlinear chains for passive control purposes.

  6. Thermospheric dynamics - A system theory approach

    NASA Technical Reports Server (NTRS)

    Codrescu, M.; Forbes, J. M.; Roble, R. G.

    1990-01-01

    A system theory approach to thermospheric modeling is developed, based upon a linearization method which is capable of preserving nonlinear features of a dynamical system. The method is tested using a large, nonlinear, time-varying system, namely the thermospheric general circulation model (TGCM) of the National Center for Atmospheric Research. In the linearized version an equivalent system, defined for one of the desired TGCM output variables, is characterized by a set of response functions that is constructed from corresponding quasi-steady state and unit sample response functions. The linearized version of the system runs on a personal computer and produces an approximation of the desired TGCM output field height profile at a given geographic location.

  7. Implementing a Bayes Filter in a Neural Circuit: The Case of Unknown Stimulus Dynamics.

    PubMed

    Sokoloski, Sacha

    2017-09-01

    In order to interact intelligently with objects in the world, animals must first transform neural population responses into estimates of the dynamic, unknown stimuli that caused them. The Bayesian solution to this problem is known as a Bayes filter, which applies Bayes' rule to combine population responses with the predictions of an internal model. The internal model of the Bayes filter is based on the true stimulus dynamics, and in this note, we present a method for training a theoretical neural circuit to approximately implement a Bayes filter when the stimulus dynamics are unknown. To do this we use the inferential properties of linear probabilistic population codes to compute Bayes' rule and train a neural network to compute approximate predictions by the method of maximum likelihood. In particular, we perform stochastic gradient descent on the negative log-likelihood of the neural network parameters with a novel approximation of the gradient. We demonstrate our methods on a finite-state, a linear, and a nonlinear filtering problem and show how the hidden layer of the neural network develops tuning curves consistent with findings in experimental neuroscience.

  8. Pressure-coupled combustion response model for solid propellants based on Zeldovich-Novozhilov approach

    NASA Technical Reports Server (NTRS)

    Harstad, K. G.; Strand, L. D.

    1987-01-01

    An exact analytical solution is given to the problem of long-time propellant thermal response to a specified pressure oscillation. Coupling to the gas phase is made using the quasisteady Zeldovich-Novozhilov approximation. Explicit linear and lowest order (quadratic) nonlinear expressions for propellant response are obtained from the implicit nonlinear solutions. Using these expressions, response curves are presented for an ammonium perchlorate composite propellant and HMX monopropellant.

  9. Estimation of reflectance from camera responses by the regularized local linear model.

    PubMed

    Zhang, Wei-Feng; Tang, Gongguo; Dai, Dao-Qing; Nehorai, Arye

    2011-10-01

    Because of the limited approximation capability of using fixed basis functions, the performance of reflectance estimation obtained by traditional linear models will not be optimal. We propose an approach based on the regularized local linear model. Our approach performs efficiently and knowledge of the spectral power distribution of the illuminant and the spectral sensitivities of the camera is not needed. Experimental results show that the proposed method performs better than some well-known methods in terms of both reflectance error and colorimetric error. © 2011 Optical Society of America

  10. Modeling subharmonic response from contrast microbubbles as a function of ambient static pressure

    PubMed Central

    Katiyar, Amit; Sarkar, Kausik; Forsberg, Flemming

    2011-01-01

    Variation of subharmonic response from contrast microbubbles with ambient pressure is numerically investigated for non-invasive monitoring of organ-level blood pressure. Previously, several contrast microbubbles both in vitro and in vivo registered approximately linear (5–15 dB) subharmonic response reduction with 188 mm Hg change in ambient pressure. In contrast, simulated subharmonic response from a single microbubble is seen here to either increase or decrease with ambient pressure. This is shown using the code BUBBLESIM for encapsulated microbubbles, and then the underlying dynamics is investigated using a free bubble model. The ratio of the excitation frequency to the natural frequency of the bubble is the determining parameter—increasing ambient pressure increases natural frequency thereby changing this ratio. For frequency ratio below a lower critical value, increasing ambient pressure monotonically decreases subharmonic response. Above an upper critical value of the same ratio, increasing ambient pressure increases subharmonic response; in between, the subharmonic variation is non-monotonic. The precise values of frequency ratio for these three different trends depend on bubble radius and excitation amplitude. The modeled increase or decrease of subharmonic with ambient pressure, when one happens, is approximately linear only for certain range of excitation levels. Possible reasons for discrepancies between model and previous experiments are discussed. PMID:21476688

  11. Density response of the mesospheric sodium layer to gravity wave perturbations

    NASA Technical Reports Server (NTRS)

    Shelton, J. D.; Gardner, C. S.; Sechrist, C. F., Jr.

    1980-01-01

    Lidar observations of the mesospheric sodium layer often reveal wavelike features moving through the layer. It is often assumed that these features are a layer density response to gravity waves. Chiu and Ching (1978) described the approximate form of the linear response of atmospheric layers to gravity waves. In this paper, their results are used to predict the response of the sodium layer to gravity waves. These simulations are compared with experimental observations and a good correlation is found between the two. Because of the thickness of the sodium layer and the density gradients found in it, a linear model of the layer response is not always adequate to describe gravity wave-sodium layer interactions. Inclusion of nonlinearities in the layer response is briefly discussed. Experimental data is seen to contain features consistent with the predicted nonlinearities.

  12. Many-body perturbation theory and non-perturbative approaches: screened interaction as the key ingredient

    NASA Astrophysics Data System (ADS)

    Tarantino, Walter; Mendoza, Bernardo S.; Romaniello, Pina; Berger, J. A.; Reining, Lucia

    2018-04-01

    Many-body perturbation theory is often formulated in terms of an expansion in the dressed instead of the bare Green’s function, and in the screened instead of the bare Coulomb interaction. However, screening can be calculated on different levels of approximation, and it is important to define what is the most appropriate choice. We explore this question by studying a zero-dimensional model (so called ‘one-point model’) that retains the structure of the full equations. We study both linear and non-linear response approximations to the screening. We find that an expansion in terms of the screening in the random phase approximation is the most promising way for an application in real systems. Moreover, by making use of the nonperturbative features of the Kadanoff-Baym equation for the one-body Green’s function, we obtain an approximate solution in our model that is very promising, although its applicability to real systems has still to be explored.

  13. Analysis of the dynamic response of a supersonic inlet to flow-field perturbations upstream of the normal shock

    NASA Technical Reports Server (NTRS)

    Cole, G. L.; Willoh, R. G.

    1975-01-01

    A linearized mathematical analysis is presented for determining the response of normal shock position and subsonic duct pressures to flow-field perturbations upstream of the normal shock in mixed-compression supersonic inlets. The inlet duct cross-sectional area variation is approximated by constant-area sections; this approximation results in one-dimensional wave equations. A movable normal shock separates the supersonic and subsonic flow regions, and a choked exit is assumed for the inlet exit condition. The analysis leads to a closed-form matrix solution for the shock position and pressure transfer functions. Analytical frequency response results are compared with experimental data and a method of characteristics solution.

  14. The passage of an infinite swept airfoil through an oblique gust. [approximate solution for aerodynamic response

    NASA Technical Reports Server (NTRS)

    Adamczyk, J. L.

    1974-01-01

    An approximate solution is reported for the unsteady aerodynamic response of an infinite swept wing encountering a vertical oblique gust in a compressible stream. The approximate expressions are of closed form and do not require excessive computer storage or computation time, and further, they are in good agreement with the results of exact theory. This analysis is used to predict the unsteady aerodynamic response of a helicopter rotor blade encountering the trailing vortex from a previous blade. Significant effects of three dimensionality and compressibility are evident in the results obtained. In addition, an approximate solution for the unsteady aerodynamic forces associated with the pitching or plunging motion of a two dimensional airfoil in a subsonic stream is presented. The mathematical form of this solution approaches the incompressible solution as the Mach number vanishes, the linear transonic solution as the Mach number approaches one, and the solution predicted by piston theory as the reduced frequency becomes large.

  15. Spatiotemporal processing of linear acceleration: primary afferent and central vestibular neuron responses

    NASA Technical Reports Server (NTRS)

    Angelaki, D. E.; Dickman, J. D.

    2000-01-01

    Spatiotemporal convergence and two-dimensional (2-D) neural tuning have been proposed as a major neural mechanism in the signal processing of linear acceleration. To examine this hypothesis, we studied the firing properties of primary otolith afferents and central otolith neurons that respond exclusively to horizontal linear accelerations of the head (0.16-10 Hz) in alert rhesus monkeys. Unlike primary afferents, the majority of central otolith neurons exhibited 2-D spatial tuning to linear acceleration. As a result, central otolith dynamics vary as a function of movement direction. During movement along the maximum sensitivity direction, the dynamics of all central otolith neurons differed significantly from those observed for the primary afferent population. Specifically at low frequencies (

  16. Experimental Determination of Linear Dynamics of Two-Spool Turbojet Engines

    NASA Technical Reports Server (NTRS)

    Novik, David; Heppler, Herbert

    1954-01-01

    Transfer functions descriptive of the response of most engine variables were determined from transient data that were obtained from approximate step inputs in fuel flow and in exhaust-nozzle area. The speed responses of both spools to fuel flow and to turbine-inlet temperature appeared as identical first-order lags. Response to exhaust-nozzle area was characterized by a first-order lag response of the outer-spool speed, accompanied by virtually no change in inner-spool speed.

  17. Charge and pairing dynamics in the attractive Hubbard model: Mode coupling and the validity of linear-response theory

    NASA Astrophysics Data System (ADS)

    Bünemann, Jörg; Seibold, Götz

    2017-12-01

    Pump-probe experiments have turned out as a powerful tool in order to study the dynamics of competing orders in a large variety of materials. The corresponding analysis of the data often relies on standard linear-response theory generalized to nonequilibrium situations. Here we examine the validity of such an approach for the charge and pairing response of systems with charge-density wave and (or) superconducting (SC) order. Our investigations are based on the attractive Hubbard model which we study within the time-dependent Hartree-Fock approximation. In particular, we calculate the quench and pump-probe dynamics for SC and charge order parameters in order to analyze the frequency spectra and the coupling of the probe field to the specific excitations. Our calculations reveal that the "linear-response assumption" is justified for small to moderate nonequilibrium situations (i.e., pump pulses) in the case of a purely charge-ordered ground state. However, the pump-probe dynamics on top of a superconducting ground state is determined by phase and amplitude modes which get coupled far from the equilibrium state indicating the failure of the linear-response assumption.

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

    PubMed

    Gnecco, Giorgio; Kůrková, Věra; Sanguineti, Marcello

    2011-03-01

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

  19. Linear summation of outputs in a balanced network model of motor cortex.

    PubMed

    Capaday, Charles; van Vreeswijk, Carl

    2015-01-01

    Given the non-linearities of the neural circuitry's elements, we would expect cortical circuits to respond non-linearly when activated. Surprisingly, when two points in the motor cortex are activated simultaneously, the EMG responses are the linear sum of the responses evoked by each of the points activated separately. Additionally, the corticospinal transfer function is close to linear, implying that the synaptic interactions in motor cortex must be effectively linear. To account for this, here we develop a model of motor cortex composed of multiple interconnected points, each comprised of reciprocally connected excitatory and inhibitory neurons. We show how non-linearities in neuronal transfer functions are eschewed by strong synaptic interactions within each point. Consequently, the simultaneous activation of multiple points results in a linear summation of their respective outputs. We also consider the effects of reduction of inhibition at a cortical point when one or more surrounding points are active. The network response in this condition is linear over an approximately two- to three-fold decrease of inhibitory feedback strength. This result supports the idea that focal disinhibition allows linear coupling of motor cortical points to generate movement related muscle activation patterns; albeit with a limitation on gain control. The model also explains why neural activity does not spread as far out as the axonal connectivity allows, whilst also explaining why distant cortical points can be, nonetheless, functionally coupled by focal disinhibition. Finally, we discuss the advantages that linear interactions at the cortical level afford to motor command synthesis.

  20. Linearly exact parallel closures for slab geometry

    NASA Astrophysics Data System (ADS)

    Ji, Jeong-Young; Held, Eric D.; Jhang, Hogun

    2013-08-01

    Parallel closures are obtained by solving a linearized kinetic equation with a model collision operator using the Fourier transform method. The closures expressed in wave number space are exact for time-dependent linear problems to within the limits of the model collision operator. In the adiabatic, collisionless limit, an inverse Fourier transform is performed to obtain integral (nonlocal) parallel closures in real space; parallel heat flow and viscosity closures for density, temperature, and flow velocity equations replace Braginskii's parallel closure relations, and parallel flow velocity and heat flow closures for density and temperature equations replace Spitzer's parallel transport relations. It is verified that the closures reproduce the exact linear response function of Hammett and Perkins [Phys. Rev. Lett. 64, 3019 (1990)] for Landau damping given a temperature gradient. In contrast to their approximate closures where the vanishing viscosity coefficient numerically gives an exact response, our closures relate the heat flow and nonvanishing viscosity to temperature and flow velocity (gradients).

  1. Review of probabilistic analysis of dynamic response of systems with random parameters

    NASA Technical Reports Server (NTRS)

    Kozin, F.; Klosner, J. M.

    1989-01-01

    The various methods that have been studied in the past to allow probabilistic analysis of dynamic response for systems with random parameters are reviewed. Dynamic response may have been obtained deterministically if the variations about the nominal values were small; however, for space structures which require precise pointing, the variations about the nominal values of the structural details and of the environmental conditions are too large to be considered as negligible. These uncertainties are accounted for in terms of probability distributions about their nominal values. The quantities of concern for describing the response of the structure includes displacements, velocities, and the distributions of natural frequencies. The exact statistical characterization of the response would yield joint probability distributions for the response variables. Since the random quantities will appear as coefficients, determining the exact distributions will be difficult at best. Thus, certain approximations will have to be made. A number of techniques that are available are discussed, even in the nonlinear case. The methods that are described were: (1) Liouville's equation; (2) perturbation methods; (3) mean square approximate systems; and (4) nonlinear systems with approximation by linear systems.

  2. The matrix exponential in transient structural analysis

    NASA Technical Reports Server (NTRS)

    Minnetyan, Levon

    1987-01-01

    The primary usefulness of the presented theory is in the ability to represent the effects of high frequency linear response with accuracy, without requiring very small time steps in the analysis of dynamic response. The matrix exponential contains a series approximation to the dynamic model. However, unlike the usual analysis procedure which truncates the high frequency response, the approximation in the exponential matrix solution is in the time domain. By truncating the series solution to the matrix exponential short, the solution is made inaccurate after a certain time. Yet, up to that time the solution is extremely accurate, including all high frequency effects. By taking finite time increments, the exponential matrix solution can compute the response very accurately. Use of the exponential matrix in structural dynamics is demonstrated by simulating the free vibration response of multi degree of freedom models of cantilever beams.

  3. Comment on "Scaling regimes and linear/nonlinear responses of last millennium climate to volcanic and solar forcing" by S. Lovejoy and C. Varotsos (2016)

    NASA Astrophysics Data System (ADS)

    Rypdal, Kristoffer; Rypdal, Martin

    2016-07-01

    Lovejoy and Varotsos (2016) (L&V) analyse the temperature response to solar, volcanic, and solar plus volcanic forcing in the Zebiak-Cane (ZC) model, and to solar and solar plus volcanic forcing in the Goddard Institute for Space Studies (GISS) E2-R model. By using a simple wavelet filtering technique they conclude that the responses in the ZC model combine subadditively on timescales from 50 to 1000 years. Nonlinear response on shorter timescales is claimed by analysis of intermittencies in the forcing and the temperature signal for both models. The analysis of additivity in the ZC model suffers from a confusing presentation of results based on an invalid approximation, and from ignoring the effect of internal variability. We present tests without this approximation which are not able to detect nonlinearity in the response, even without accounting for internal variability. We also demonstrate that internal variability will appear as subadditivity if it is not accounted for. L&V's analysis of intermittencies is based on a mathematical result stating that the intermittencies of forcing and response are the same if the response is linear. We argue that there are at least three different factors that may invalidate the application of this result for these data. It is valid only for a power-law response function; it assumes power-law scaling of structure functions of forcing as well as temperature signal; and the internal variability, which is strong at least on the short timescales, will exert an influence on temperature intermittence which is independent of the forcing. We demonstrate by a synthetic example that the differences in intermittencies observed by L&V easily can be accounted for by these effects under the assumption of a linear response. Our conclusion is that the analysis performed by L&V does not present valid evidence for a detectable nonlinear response in the global temperature in these climate models.

  4. Exploiting symmetries in the modeling and analysis of tires

    NASA Technical Reports Server (NTRS)

    Noor, Ahmed K.; Andersen, Carl M.; Tanner, John A.

    1987-01-01

    A simple and efficient computational strategy for reducing both the size of a tire model and the cost of the analysis of tires in the presence of symmetry-breaking conditions (unsymmetry in the tire material, geometry, or loading) is presented. The strategy is based on approximating the unsymmetric response of the tire with a linear combination of symmetric and antisymmetric global approximation vectors (or modes). Details are presented for the three main elements of the computational strategy, which include: use of special three-field mixed finite-element models, use of operator splitting, and substantial reduction in the number of degrees of freedom. The proposed computational stategy is applied to three quasi-symmetric problems of tires: linear analysis of anisotropic tires, through use of semianalytic finite elements, nonlinear analysis of anisotropic tires through use of two-dimensional shell finite elements, and nonlinear analysis of orthotropic tires subjected to unsymmetric loading. Three basic types of symmetry (and their combinations) exhibited by the tire response are identified.

  5. Inductional Effects in a Halbach Magnet Motion Above Distributed Inductance

    NASA Astrophysics Data System (ADS)

    Tchatchoua, Yves; Conrow, Ary; Kim, Dong; Morgan, Daniel; Majewski, Walerian; Zafar, Zaeema

    2013-03-01

    We experimented with attempts to levitate a linear (bar) Halbach array of five 1'' Nd magnets above a linear inductive track. Next, in order to achieve a control over the relative velocity, we designed a different experiment. In it a large wheel with circumferentially positioned along its rim inducting coils rotates, while the magnet is suspended directly above the rim of the wheel on a force sensor. Faraday's Law with the Lenz's Rule is responsible for the lifting and drag forces on the magnet; the horizontal drag force is measured by another force sensor. Approximating the magnet's linear relative motion over inductors with a motion along a large circle, we may use formulas derived earlier in the literature for linear inductive levitation. We measured lift and drag forces as functions of relative velocity of the Halbach magnet and the inductive ``track,'' in an approximate agreement with the existing theory. We then vary the inductance and shape of the inductive elements to find the most beneficial choice for the lift/drag ratio at the lowest relative speed.

  6. 40 CFR 86.884-11 - Instrument checks.

    Code of Federal Regulations, 2010 CFR

    2010-07-01

    ... collection equipment response of zero; (3) Calibrated neutral density filters having approximately 10, 20, and 40 percent opacity shall be employed to check the linearity of the instrument. The filter(s) shall.... Filters with exposed filtering media should be checked for opacity every six months; all other filters...

  7. 40 CFR 92.122 - Smoke meter calibration.

    Code of Federal Regulations, 2010 CFR

    2010-07-01

    ... collection equipment response of zero; (b) Calibrated neutral density filters having approximately 10, 20, and 40 percent opacity shall be employed to check the linearity of the instrument. The filter(s) shall.... Filters with exposed filtering media should be checked for opacity every six months; all other filters...

  8. 40 CFR 86.884-11 - Instrument checks.

    Code of Federal Regulations, 2012 CFR

    2012-07-01

    ... collection equipment response of zero; (3) Calibrated neutral density filters having approximately 10, 20, and 40 percent opacity shall be employed to check the linearity of the instrument. The filter(s) shall.... Filters with exposed filtering media should be checked for opacity every six months; all other filters...

  9. 40 CFR 92.122 - Smoke meter calibration.

    Code of Federal Regulations, 2013 CFR

    2013-07-01

    ... collection equipment response of zero; (b) Calibrated neutral density filters having approximately 10, 20, and 40 percent opacity shall be employed to check the linearity of the instrument. The filter(s) shall.... Filters with exposed filtering media should be checked for opacity every six months; all other filters...

  10. 40 CFR 92.122 - Smoke meter calibration.

    Code of Federal Regulations, 2012 CFR

    2012-07-01

    ... collection equipment response of zero; (b) Calibrated neutral density filters having approximately 10, 20, and 40 percent opacity shall be employed to check the linearity of the instrument. The filter(s) shall.... Filters with exposed filtering media should be checked for opacity every six months; all other filters...

  11. 40 CFR 92.122 - Smoke meter calibration.

    Code of Federal Regulations, 2011 CFR

    2011-07-01

    ... collection equipment response of zero; (b) Calibrated neutral density filters having approximately 10, 20, and 40 percent opacity shall be employed to check the linearity of the instrument. The filter(s) shall.... Filters with exposed filtering media should be checked for opacity every six months; all other filters...

  12. 40 CFR 86.884-11 - Instrument checks.

    Code of Federal Regulations, 2011 CFR

    2011-07-01

    ... collection equipment response of zero; (3) Calibrated neutral density filters having approximately 10, 20, and 40 percent opacity shall be employed to check the linearity of the instrument. The filter(s) shall.... Filters with exposed filtering media should be checked for opacity every six months; all other filters...

  13. 40 CFR 86.884-11 - Instrument checks.

    Code of Federal Regulations, 2013 CFR

    2013-07-01

    ... collection equipment response of zero; (3) Calibrated neutral density filters having approximately 10, 20, and 40 percent opacity shall be employed to check the linearity of the instrument. The filter(s) shall.... Filters with exposed filtering media should be checked for opacity every six months; all other filters...

  14. Linear summation of outputs in a balanced network model of motor cortex

    PubMed Central

    Capaday, Charles; van Vreeswijk, Carl

    2015-01-01

    Given the non-linearities of the neural circuitry's elements, we would expect cortical circuits to respond non-linearly when activated. Surprisingly, when two points in the motor cortex are activated simultaneously, the EMG responses are the linear sum of the responses evoked by each of the points activated separately. Additionally, the corticospinal transfer function is close to linear, implying that the synaptic interactions in motor cortex must be effectively linear. To account for this, here we develop a model of motor cortex composed of multiple interconnected points, each comprised of reciprocally connected excitatory and inhibitory neurons. We show how non-linearities in neuronal transfer functions are eschewed by strong synaptic interactions within each point. Consequently, the simultaneous activation of multiple points results in a linear summation of their respective outputs. We also consider the effects of reduction of inhibition at a cortical point when one or more surrounding points are active. The network response in this condition is linear over an approximately two- to three-fold decrease of inhibitory feedback strength. This result supports the idea that focal disinhibition allows linear coupling of motor cortical points to generate movement related muscle activation patterns; albeit with a limitation on gain control. The model also explains why neural activity does not spread as far out as the axonal connectivity allows, whilst also explaining why distant cortical points can be, nonetheless, functionally coupled by focal disinhibition. Finally, we discuss the advantages that linear interactions at the cortical level afford to motor command synthesis. PMID:26097452

  15. Resolvent-based modeling of passive scalar dynamics in wall-bounded turbulence

    NASA Astrophysics Data System (ADS)

    Dawson, Scott; Saxton-Fox, Theresa; McKeon, Beverley

    2017-11-01

    The resolvent formulation of the Navier-Stokes equations expresses the system state as the output of a linear (resolvent) operator acting upon a nonlinear forcing. Previous studies have demonstrated that a low-rank approximation of this linear operator predicts many known features of incompressible wall-bounded turbulence. In this work, this resolvent model for wall-bounded turbulence is extended to include a passive scalar field. This formulation allows for a number of additional simplifications that reduce model complexity. Firstly, it is shown that the effect of changing scalar diffusivity can be approximated through a transformation of spatial wavenumbers and temporal frequencies. Secondly, passive scalar dynamics may be studied through the low-rank approximation of a passive scalar resolvent operator, which is decoupled from velocity response modes. Thirdly, this passive scalar resolvent operator is amenable to approximation by semi-analytic methods. We investigate the extent to which this resulting hierarchy of models can describe and predict passive scalar dynamics and statistics in wall-bounded turbulence. The support of AFOSR under Grant Numbers FA9550-16-1-0232 and FA9550-16-1-0361 is gratefully acknowledged.

  16. Piecewise linear approximation for hereditary control problems

    NASA Technical Reports Server (NTRS)

    Propst, Georg

    1987-01-01

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

  17. Development of FullWave : Hot Plasma RF Simulation Tool

    NASA Astrophysics Data System (ADS)

    Svidzinski, Vladimir; Kim, Jin-Soo; Spencer, J. Andrew; Zhao, Liangji; Galkin, Sergei

    2017-10-01

    Full wave simulation tool, modeling RF fields in hot inhomogeneous magnetized plasma, is being developed. The wave equations with linearized hot plasma dielectric response are solved in configuration space on adaptive cloud of computational points. The nonlocal hot plasma dielectric response is formulated in configuration space without limiting approximations by calculating the plasma conductivity kernel based on the solution of the linearized Vlasov equation in inhomogeneous magnetic field. This approach allows for better resolution of plasma resonances, antenna structures and complex boundaries. The formulation of FullWave and preliminary results will be presented: construction of the finite differences for approximation of derivatives on adaptive cloud of computational points; model and results of nonlocal conductivity kernel calculation in tokamak geometry; results of 2-D full wave simulations in the cold plasma model in tokamak geometry using the formulated approach; results of self-consistent calculations of hot plasma dielectric response and RF fields in 1-D mirror magnetic field; preliminary results of self-consistent simulations of 2-D RF fields in tokamak using the calculated hot plasma conductivity kernel; development of iterative solver for wave equations. Work is supported by the U.S. DOE SBIR program.

  18. Two Propositions on the Application of Point Elasticities to Finite Price Changes.

    ERIC Educational Resources Information Center

    Daskin, Alan J.

    1992-01-01

    Considers counterintuitive propositions about using point elasticities to estimate quantity changes in response to price changes. Suggests that elasticity increases with price along a linear demand curve, but falling quantity demand offsets it. Argues that point elasticity with finite percentage change in price only approximates percentage change…

  19. A Memory-Based Model of Hick's Law

    ERIC Educational Resources Information Center

    Schneider, Darryl W.; Anderson, John R.

    2011-01-01

    We propose and evaluate a memory-based model of Hick's law, the approximately linear increase in choice reaction time with the logarithm of set size (the number of stimulus-response alternatives). According to the model, Hick's law reflects a combination of associative interference during retrieval from declarative memory and occasional savings…

  20. Response analysis of a class of quasi-linear systems with fractional derivative excited by Poisson white noise

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

    Yang, Yongge; Xu, Wei, E-mail: weixu@nwpu.edu.cn; Yang, Guidong

    The Poisson white noise, as a typical non-Gaussian excitation, has attracted much attention recently. However, little work was referred to the study of stochastic systems with fractional derivative under Poisson white noise excitation. This paper investigates the stationary response of a class of quasi-linear systems with fractional derivative excited by Poisson white noise. The equivalent stochastic system of the original stochastic system is obtained. Then, approximate stationary solutions are obtained with the help of the perturbation method. Finally, two typical examples are discussed in detail to demonstrate the effectiveness of the proposed method. The analysis also shows that the fractionalmore » order and the fractional coefficient significantly affect the responses of the stochastic systems with fractional derivative.« less

  1. A molecular Debye-Hückel approach to the reorganization energy of electron transfer reactions in an electric cell

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

    Xiao, Tiejun; Department of Chemistry, Iowa State University, Ames, Iowa 50011; Song, Xueyu

    2014-10-07

    Electron transfer near an electrode immersed in ionic fluids is studied using the linear response approximation, namely, mean value of the vertical energy gap can be used to evaluate the reorganization energy, and hence any linear response model that can treat Coulomb interactions successfully can be used for the reorganization energy calculation. Specifically, a molecular Debye-Hückel theory is used to calculate the reorganization energy of electron transfer reactions in an electric cell. Applications to electron transfer near an electrode in molten salts show that the reorganization energies from our molecular Debye-Hückel theory agree well with the results from MD simulations.

  2. A linear chromatic mechanism drives the pupillary response.

    PubMed Central

    Tsujimura, S.; Wolffsohn, J. S.; Gilmartin, B.

    2001-01-01

    Previous studies have shown that a chromatic mechanism can drive pupil responses. The aim of this research was to clarify whether a linear or nonlinear chromatic mechanism drives pupillary responses by using test stimuli of various colours that are defined in cone contrast space. The pupil and accommodation responses evoked by these test stimuli were continuously and simultaneously objectively measured by photorefraction. The results with isochromatic and isoluminant stimuli showed that the accommodative level remained approximately constant (< 0.25 D change in mean level) even when the concurrent pupillary response was large (ca. 0.30 mm). The pupillary response to an isoluminant grating was sustained, delayed (by ca. 60 ms) and larger in amplitude than that for a isochromatic uniform stimulus, which supports previous work suggesting that the chromatic mechanism contributes to the pupillary response. In a second experiment, selected chromatic test gratings were used and isoresponse contours in cone contrast space were obtained. The results showed that the isoresponse contour in cone contrast space is well described (r(2) = 0.99) by a straight line with a positive slope. The results indicate that a /L - M/ linear chromatic mechanism, whereby a signal from the long wavelength cone is subtracted from that of the middle wavelength cone and vice versa, drives pupillary responses. PMID:11674867

  3. Linearization of Positional Response Curve of a Fiber-optic Displacement Sensor

    NASA Astrophysics Data System (ADS)

    Babaev, O. G.; Matyunin, S. A.; Paranin, V. D.

    2018-01-01

    Currently, the creation of optical measuring instruments and sensors for measuring linear displacement is one of the most relevant problems in the area of instrumentation. Fiber-optic contactless sensors based on the magneto-optical effect are of special interest. They are essentially contactless, non-electrical and have a closed optical channel not subject to contamination. The main problem of this type of sensors is the non-linearity of their positional response curve due to the hyperbolic nature of the magnetic field intensity variation induced by moving the magnetic source mounted on the controlled object relative to the sensing element. This paper discusses an algorithmic method of linearizing the positional response curve of fiber-optic displacement sensors in any selected range of the displacements to be measured. The method is divided into two stages: 1 - definition of the calibration function, 2 - measurement and linearization of the positional response curve (including its temperature stabilization). The algorithm under consideration significantly reduces the number of points of the calibration function, which is essential for the calibration of temperature dependence, due to the use of the points that randomly deviate from the grid points with uniform spacing. Subsequent interpolation of the deviating points and piecewise linear-plane approximation of the calibration function reduces the microcontroller storage capacity for storing the calibration function and the time required to process the measurement results. The paper also presents experimental results of testing real samples of fiber-optic displacement sensors.

  4. The nonlinear dynamics of a spacecraft coupled to the vibration of a contained fluid

    NASA Technical Reports Server (NTRS)

    Peterson, Lee D.; Crawley, Edward F.; Hansman, R. John

    1988-01-01

    The dynamics of a linear spacecraft mode coupled to a nonlinear low gravity slosh of a fluid in a cylindrical tank is investigated. Coupled, nonlinear equations of motion for the fluid-spacecraft dynamics are derived through an assumed mode Lagrangian method. Unlike linear fluid slosh models, this nonlinear slosh model retains two fundamental slosh modes and three secondary modes. An approximate perturbation solution of the equations of motion indicates that the nonlinear coupled system response involves fluid-spacecraft modal resonances not predicted by either a linear, or a nonlinear, uncoupled slosh analysis. Experimental results substantiate the analytical predictions.

  5. Linearizing an intermodulation radar transmitter by filtering switched tones

    NASA Astrophysics Data System (ADS)

    Mazzaro, Gregory J.; Sherbondy, Andrew J.; Ranney, Kenneth I.; Sherbondy, Kelly D.; Martone, Anthony F.

    2017-05-01

    For nonlinear radar, the transmit power required to measure a detectable response from a target is relatively high, and generating that high power is achieved at the cost of linearity. This paper applies the distortion mitigation technique Linearization by Time-Multiplexed Spectrum (LITMUS) to intermodulation radar, a type of nonlinear radar which receives spectral content produced by the mixing of multiple frequencies at a nonlinear target. By implementing LITMUS, an experimental detection system for an intermodulation radar achieves a signal-to-noise ratio up to 20 dB for a total transmit power of approximately 80 mW and nonlinear targets placed at a standoff distance of 2 meters.

  6. Compaction by impact of unconsolidated lunar fines

    NASA Technical Reports Server (NTRS)

    Ahrens, T. J.

    1975-01-01

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

  7. Dissociation of Self-Motion and Object Motion by Linear Population Decoding That Approximates Marginalization

    PubMed Central

    Sasaki, Ryo; Angelaki, Dora E.

    2017-01-01

    We use visual image motion to judge the movement of objects, as well as our own movements through the environment. Generally, image motion components caused by object motion and self-motion are confounded in the retinal image. Thus, to estimate heading, the brain would ideally marginalize out the effects of object motion (or vice versa), but little is known about how this is accomplished neurally. Behavioral studies suggest that vestibular signals play a role in dissociating object motion and self-motion, and recent computational work suggests that a linear decoder can approximate marginalization by taking advantage of diverse multisensory representations. By measuring responses of MSTd neurons in two male rhesus monkeys and by applying a recently-developed method to approximate marginalization by linear population decoding, we tested the hypothesis that vestibular signals help to dissociate self-motion and object motion. We show that vestibular signals stabilize tuning for heading in neurons with congruent visual and vestibular heading preferences, whereas they stabilize tuning for object motion in neurons with discrepant preferences. Thus, vestibular signals enhance the separability of joint tuning for object motion and self-motion. We further show that a linear decoder, designed to approximate marginalization, allows the population to represent either self-motion or object motion with good accuracy. Decoder weights are broadly consistent with a readout strategy, suggested by recent computational work, in which responses are decoded according to the vestibular preferences of multisensory neurons. These results demonstrate, at both single neuron and population levels, that vestibular signals help to dissociate self-motion and object motion. SIGNIFICANCE STATEMENT The brain often needs to estimate one property of a changing environment while ignoring others. This can be difficult because multiple properties of the environment may be confounded in sensory signals. The brain can solve this problem by marginalizing over irrelevant properties to estimate the property-of-interest. We explore this problem in the context of self-motion and object motion, which are inherently confounded in the retinal image. We examine how diversity in a population of multisensory neurons may be exploited to decode self-motion and object motion from the population activity of neurons in macaque area MSTd. PMID:29030435

  8. Utilization of Neurophysiological Protocols to Characterize Soldier Response to Irritant Gases. Phase 1.

    DTIC Science & Technology

    1990-02-15

    electrical activity mapping procedures. It is necessary to employ approximately 20 electrodes to conduct full- scale brain mapping procedures, using a...animal groups, likewise, showed no observable differences in the animal’s exploratory behavior, nuzzle response, lid-corneal and ear reflexes, pain ...SPECIFICATIONS FOR THE ENVIRONICS SERIES 100 GAS STANDARDS GENERATOR Accuracy of Flow 0.15 % of Full Scale Linearity 0.15 % of Full Scale Repeatability 0.10

  9. Low-Loss Coupler For Microwave Laser-Diode Modulation

    NASA Technical Reports Server (NTRS)

    Toda, Minoru

    1991-01-01

    Elimination of series resistor reduces loss of radio-frequency power. Quarter-wavelength matching section connected to transmission line eliminates need for resistor near laser diode and extends frequency response of system. Concept significantly extends relatively flat frequency response of laser diode or similar component, while simplifying design of its package, increasing amplitude of output signal, and reducing dissipation of heat by eliminating resistance. Phase characteristics approximately linear and any digital information transmitted not significantly altered.

  10. On optimal infinite impulse response edge detection filters

    NASA Technical Reports Server (NTRS)

    Sarkar, Sudeep; Boyer, Kim L.

    1991-01-01

    The authors outline the design of an optimal, computationally efficient, infinite impulse response edge detection filter. The optimal filter is computed based on Canny's high signal to noise ratio, good localization criteria, and a criterion on the spurious response of the filter to noise. An expression for the width of the filter, which is appropriate for infinite-length filters, is incorporated directly in the expression for spurious responses. The three criteria are maximized using the variational method and nonlinear constrained optimization. The optimal filter parameters are tabulated for various values of the filter performance criteria. A complete methodology for implementing the optimal filter using approximating recursive digital filtering is presented. The approximating recursive digital filter is separable into two linear filters operating in two orthogonal directions. The implementation is very simple and computationally efficient, has a constant time of execution for different sizes of the operator, and is readily amenable to real-time hardware implementation.

  11. Linear response and correlation of a self-propelled particle in the presence of external fields

    NASA Astrophysics Data System (ADS)

    Caprini, Lorenzo; Marini Bettolo Marconi, Umberto; Vulpiani, Angelo

    2018-03-01

    We study the non-equilibrium properties of non interacting active Ornstein-Uhlenbeck particles (AOUP) subject to an external nonuniform field using a Fokker-Planck approach with a focus on the linear response and time-correlation functions. In particular, we compare different methods to compute these functions including the unified colored noise approximation (UCNA). The AOUP model, described by the position of the particle and the active force acting on it, is usually mapped into a Markovian process, describing the motion of a fictitious passive particle in terms of its position and velocity, where the effect of the activity is transferred into a position-dependent friction. We show that the form of the response function of the AOUP depends on whether we put the perturbation on the position and keep unperturbed the active force in the original variables or perturb the position and maintain unperturbed the velocity in the transformed variables. Indeed, as a result of the change of variables the perturbation on the position becomes a perturbation both on the position and on the fictitious velocity. We test these predictions by considering the response for three types of convex potentials: quadratic, quartic and double-well potential. Moreover, by comparing the response of the AOUP model with the corresponding response of the UCNA model we conclude that although the stationary properties are fairly well approximated by the UCNA, the non equilibrium properties are not, an effect which is not negligible when the persistence time is large.

  12. Pilocarpine disposition and salivary flow responses following intravenous administration to dogs.

    PubMed

    Weaver, M L; Tanzer, J M; Kramer, P A

    1992-08-01

    Oral doses of pilocarpine increase salivary flow rates in patients afflicted with xerostomia (dry mouth). This study examined the pharmacokinetics of and a pharmacodynamic response (salivation) to intravenous pilocarpine nitrate administration in dogs. Disposition was linear over a dose range of 225-600 micrograms/kg; plasma concentrations were 10-120 micrograms/L. Elimination was rapid and generally biphasic, with a terminal elimination half-life of approximately 1.3 hr. The systemic clearance of pilocarpine was high (2.22 +/- 0.49 L/kg/hr) and its steady-state volume of distribution (2.30 +/- 0.64 L/kg) was comparable to that of many other basic drugs. All doses of pilocarpine induced measurable submaxillary and parotid salivary flow rates which could be maintained constant over time. Cumulative submaxillary saliva flow was linearly related to total pilocarpine dose. Plasma pilocarpine concentration was linearly related to both steady-state and postinfusion submaxillary salivary flow rates.

  13. Classical Testing in Functional Linear Models.

    PubMed

    Kong, Dehan; Staicu, Ana-Maria; Maity, Arnab

    2016-01-01

    We extend four tests common in classical regression - Wald, score, likelihood ratio and F tests - to functional linear regression, for testing the null hypothesis, that there is no association between a scalar response and a functional covariate. Using functional principal component analysis, we re-express the functional linear model as a standard linear model, where the effect of the functional covariate can be approximated by a finite linear combination of the functional principal component scores. In this setting, we consider application of the four traditional tests. The proposed testing procedures are investigated theoretically for densely observed functional covariates when the number of principal components diverges. Using the theoretical distribution of the tests under the alternative hypothesis, we develop a procedure for sample size calculation in the context of functional linear regression. The four tests are further compared numerically for both densely and sparsely observed noisy functional data in simulation experiments and using two real data applications.

  14. Classical Testing in Functional Linear Models

    PubMed Central

    Kong, Dehan; Staicu, Ana-Maria; Maity, Arnab

    2016-01-01

    We extend four tests common in classical regression - Wald, score, likelihood ratio and F tests - to functional linear regression, for testing the null hypothesis, that there is no association between a scalar response and a functional covariate. Using functional principal component analysis, we re-express the functional linear model as a standard linear model, where the effect of the functional covariate can be approximated by a finite linear combination of the functional principal component scores. In this setting, we consider application of the four traditional tests. The proposed testing procedures are investigated theoretically for densely observed functional covariates when the number of principal components diverges. Using the theoretical distribution of the tests under the alternative hypothesis, we develop a procedure for sample size calculation in the context of functional linear regression. The four tests are further compared numerically for both densely and sparsely observed noisy functional data in simulation experiments and using two real data applications. PMID:28955155

  15. Global hybrids from the semiclassical atom theory satisfying the local density linear response.

    PubMed

    Fabiano, Eduardo; Constantin, Lucian A; Cortona, Pietro; Della Sala, Fabio

    2015-01-13

    We propose global hybrid approximations of the exchange-correlation (XC) energy functional which reproduce well the modified fourth-order gradient expansion of the exchange energy in the semiclassical limit of many-electron neutral atoms and recover the full local density approximation (LDA) linear response. These XC functionals represent the hybrid versions of the APBE functional [Phys. Rev. Lett. 2011, 106, 186406] yet employing an additional correlation functional which uses the localization concept of the correlation energy density to improve the compatibility with the Hartree-Fock exchange as well as the coupling-constant-resolved XC potential energy. Broad energetic and structural testing, including thermochemistry and geometry, transition metal complexes, noncovalent interactions, gold clusters and small gold-molecule interfaces, as well as an analysis of the hybrid parameters, show that our construction is quite robust. In particular, our testing shows that the resulting hybrid, including 20% of Hartree-Fock exchange and named hAPBE, performs remarkably well for a broad palette of systems and properties, being generally better than popular hybrids (PBE0 and B3LYP). Semiempirical dispersion corrections are also provided.

  16. Performance of Al2O3:C optically stimulated luminescence dosimeters for clinical radiation therapy applications.

    PubMed

    Hu, B; Wang, Y; Zealey, W

    2009-12-01

    A commercial Optical Stimulated Luminescence (OSL) dosimetry system developed by Landauer was tested to analyse the possibility of using OSL dosimetry for external beam radiotherapy planning checks. Experiments were performed to determine signal sensitivity, dose response range, beam type/energy dependency, reproducibility and linearity. Optical annealing processes to test OSL material reusability were also studied. In each case the measurements were converted into absorbed dose. The experimental results show that OSL dosimetry provides a wide dose response range, good linearity and reproducibility for the doses up to 800cGy. The OSL output is linear with dose up to 600cGy range showing a maximum deviation from linearity of 2.0% for the doses above 600cGy. The standard deviation in response of 20 dosimeters was 3.0%. After optical annealing using incandescent light, the readout intensity decreased by approximately 98% in the first 30 minutes. The readout intensity, I, decreased after repeated optical annealing as a power law, given by I infinity t (-1.3). This study concludes that OSL dosimetry can provide an alternative dosimetry technique for use in in-vivo dosimetry if rigorous measurement protocols are established.

  17. Nonlinear Extraction of Independent Components of Natural Images Using Radial Gaussianization

    PubMed Central

    Lyu, Siwei; Simoncelli, Eero P.

    2011-01-01

    We consider the problem of efficiently encoding a signal by transforming it to a new representation whose components are statistically independent. A widely studied linear solution, known as independent component analysis (ICA), exists for the case when the signal is generated as a linear transformation of independent nongaussian sources. Here, we examine a complementary case, in which the source is nongaussian and elliptically symmetric. In this case, no invertible linear transform suffices to decompose the signal into independent components, but we show that a simple nonlinear transformation, which we call radial gaussianization (RG), is able to remove all dependencies. We then examine this methodology in the context of natural image statistics. We first show that distributions of spatially proximal bandpass filter responses are better described as elliptical than as linearly transformed independent sources. Consistent with this, we demonstrate that the reduction in dependency achieved by applying RG to either nearby pairs or blocks of bandpass filter responses is significantly greater than that achieved by ICA. Finally, we show that the RG transformation may be closely approximated by divisive normalization, which has been used to model the nonlinear response properties of visual neurons. PMID:19191599

  18. Revisiting the Landau fluid closure.

    NASA Astrophysics Data System (ADS)

    Hunana, P.; Zank, G. P.; Webb, G. M.; Adhikari, L.

    2017-12-01

    Advanced fluid models that are much closer to the full kinetic description than the usual magnetohydrodynamic description are a very useful tool for studying astrophysical plasmas and for interpreting solar wind observational data. The development of advanced fluid models that contain certain kinetic effects is complicated and has attracted much attention over the past years. Here we focus on fluid models that incorporate the simplest possible forms of Landau damping, derived from linear kinetic theory expanded about a leading-order (gyrotropic) bi-Maxwellian distribution function f_0, under the approximation that the perturbed distribution function f_1 is gyrotropic as well. Specifically, we focus on various Pade approximants to the usual plasma response function (and to the plasma dispersion function) and examine possibilities that lead to a closure of the linear kinetic hierarchy of fluid moments. We present re-examination of the simplest Landau fluid closures.

  19. Interaction function of oscillating coupled neurons

    PubMed Central

    Dodla, Ramana; Wilson, Charles J.

    2013-01-01

    Large scale simulations of electrically coupled neuronal oscillators often employ the phase coupled oscillator paradigm to understand and predict network behavior. We study the nature of the interaction between such coupled oscillators using weakly coupled oscillator theory. By employing piecewise linear approximations for phase response curves and voltage time courses, and parameterizing their shapes, we compute the interaction function for all such possible shapes and express it in terms of discrete Fourier modes. We find that reasonably good approximation is achieved with four Fourier modes that comprise of both sine and cosine terms. PMID:24229210

  20. 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.

  1. Ferroelectric hydration shells around proteins: electrostatics of the protein-water interface.

    PubMed

    LeBard, David N; Matyushov, Dmitry V

    2010-07-22

    Numerical simulations of hydrated proteins show that protein hydration shells are polarized into a ferroelectric layer with large values of the average dipole moment magnitude and the dipole moment variance. The emergence of the new polarized mesophase dramatically alters the statistics of electrostatic fluctuations at the protein-water interface. The linear response relation between the average electrostatic potential and its variance breaks down, with the breadth of the electrostatic fluctuations far exceeding the expectations of the linear response theories. The dynamics of these non-Gaussian electrostatic fluctuations are dominated by a slow (approximately = 1 ns) component that freezes in at the temperature of the dynamical transition of proteins. The ferroelectric shell propagates 3-5 water diameters into the bulk.

  2. Modelling the isometric force response to multiple pulse stimuli in locust skeletal muscle.

    PubMed

    Wilson, Emma; Rustighi, Emiliano; Mace, Brian R; Newland, Philip L

    2011-02-01

    An improved model of locust skeletal muscle will inform on the general behaviour of invertebrate and mammalian muscle with the eventual aim of improving biomedical models of human muscles, embracing prosthetic construction and muscle therapy. In this article, the isometric response of the locust hind leg extensor muscle to input pulse trains is investigated. Experimental data was collected by stimulating the muscle directly and measuring the force at the tibia. The responses to constant frequency stimulus trains of various frequencies and number of pulses were decomposed into the response to each individual stimulus. Each individual pulse response was then fitted to a model, it being assumed that the response to each pulse could be approximated as an impulse response and was linear, no assumption were made about the model order. When the interpulse frequency (IPF) was low and the number of pulses in the train small, a second-order model provided a good fit to each pulse. For moderate IPF or for long pulse trains a linear third-order model provided a better fit to the response to each pulse. The fit using a second-order model deteriorated with increasing IPF. When the input comprised higher IPFs with a large number of pulses the assumptions that the response was linear could not be confirmed. A generalised model is also presented. This model is second-order, and contains two nonlinear terms. The model is able to capture the force response to a range of inputs. This includes cases where the input comprised of higher frequency pulse trains and the assumption of quasi-linear behaviour could not be confirmed.

  3. A Fast Method to Calculate the Spatial Impulse Response for 1-D Linear Ultrasonic Phased Array Transducers

    PubMed Central

    Zou, Cheng; Sun, Zhenguo; Cai, Dong; Muhammad, Salman; Zhang, Wenzeng; Chen, Qiang

    2016-01-01

    A method is developed to accurately determine the spatial impulse response at the specifically discretized observation points in the radiated field of 1-D linear ultrasonic phased array transducers with great efficiency. In contrast, the previously adopted solutions only optimize the calculation procedure for a single rectangular transducer and required approximation considerations or nonlinear calculation. In this research, an algorithm that follows an alternative approach to expedite the calculation of the spatial impulse response of a rectangular linear array is presented. The key assumption for this algorithm is that the transducer apertures are identical and linearly distributed on an infinite rigid plane baffled with the same pitch. Two points in the observation field, which have the same position relative to two transducer apertures, share the same spatial impulse response that contributed from corresponding transducer, respectively. The observation field is discretized specifically to meet the relationship of equality. The analytical expressions of the proposed algorithm, based on the specific selection of the observation points, are derived to remove redundant calculations. In order to measure the proposed methodology, the simulation results obtained from the proposed method and the classical summation method are compared. The outcomes demonstrate that the proposed strategy can speed up the calculation procedure since it accelerates the speed-up ratio which relies upon the number of discrete points and the number of the array transducers. This development will be valuable in the development of advanced and faster linear ultrasonic phased array systems. PMID:27834799

  4. Beyond the electric-dipole approximation: A formulation and implementation of molecular response theory for the description of absorption of electromagnetic field radiation.

    PubMed

    List, Nanna Holmgaard; Kauczor, Joanna; Saue, Trond; Jensen, Hans Jørgen Aagaard; Norman, Patrick

    2015-06-28

    We present a formulation of molecular response theory for the description of a quantum mechanical molecular system in the presence of a weak, monochromatic, linearly polarized electromagnetic field without introducing truncated multipolar expansions. The presentation focuses on a description of linear absorption by adopting the energy-loss approach in combination with the complex polarization propagator formulation of response theory. Going beyond the electric-dipole approximation is essential whenever studying electric-dipole-forbidden transitions, and in general, non-dipolar effects become increasingly important when addressing spectroscopies involving higher-energy photons. These two aspects are examined by our study of the near K-edge X-ray absorption fine structure of the alkaline earth metals (Mg, Ca, Sr, Ba, and Ra) as well as the trans-polyenes. In following the series of alkaline earth metals, the sizes of non-dipolar effects are probed with respect to increasing photon energies and a detailed assessment of results is made in terms of studying the pertinent transition electron densities and in particular their spatial extension in comparison with the photon wavelength. Along the series of trans-polyenes, the sizes of non-dipolar effects are probed for X-ray spectroscopies on organic molecules with respect to the spatial extension of the chromophore.

  5. A refinement of the combination equations for evaporation

    USGS Publications Warehouse

    Milly, P.C.D.

    1991-01-01

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

  6. An equivalent frequency approach for determining non-linear effects on pre-tensioned-cable cross-braced structures

    NASA Astrophysics Data System (ADS)

    Giaccu, Gian Felice

    2018-05-01

    Pre-tensioned cable braces are widely used as bracing systems in various structural typologies. This technology is fundamentally utilized for stiffening purposes in the case of steel and timber structures. The pre-stressing force imparted to the braces provides to the system a remarkable increment of stiffness. On the other hand, the pre-tensioning force in the braces must be properly calibrated in order to satisfactorily meet both serviceability and ultimate limit states. Dynamic properties of these systems are however affected by non-linear behavior due to potential slackening of the pre-tensioned brace. In the recent years the author has been working on a similar problem regarding the non-linear response of cables in cable-stayed bridges and braced structures. In the present paper a displacement-based approach is used to examine the non-linear behavior of a building system. The methodology operates through linearization and allows obtaining an equivalent linearized frequency to approximately characterize, mode by mode, the dynamic behavior of the system. The equivalent frequency depends on both the mechanical characteristics of the system, the pre-tensioning level assigned to the braces and a characteristic vibration amplitude. The proposed approach can be used as a simplified technique, capable of linearizing the response of structural systems, characterized by non-linearity induced by the slackening of pre-tensioned braces.

  7. Systematic study of doping dependence on linear magnetoresistance in p-PbTe

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

    Schneider, J. M.; Chitta, V. A.; Oliveira, N. F.

    2014-10-20

    We report on a large linear magnetoresistance effect observed in doped p-PbTe films. While undoped p-PbTe reveals a sublinear magnetoresistance, p-PbTe films doped with BaF{sub 2} exhibit a transition to a nearly perfect linear magnetoresistance behaviour that is persistent up to 30 T. The linear magnetoresistance slope ΔR/ΔB is to a good approximation, independent of temperature. This is in agreement with the theory of Quantum Linear Magnetoresistance. We also performed magnetoresistance simulations using a classical model of linear magnetoresistance. We found that this model fails to explain the experimental data. A systematic study of the doping dependence reveals that the linearmore » magnetoresistance response has a maximum for small BaF{sub 2} doping levels and diminishes rapidly for increasing doping levels. Exploiting the huge impact of doping on the linear magnetoresistance signal could lead to new classes of devices with giant magnetoresistance behavior.« less

  8. Dose-response meta-analysis on coffee, tea and caffeine consumption with risk of Parkinson's disease.

    PubMed

    Qi, Hui; Li, Shixue

    2014-04-01

    A dose-response meta-analysis was carried out between Parkinson's disease (PD) risk, and coffee, tea and caffeine consumption. A comprehensive search was carried out to identify eligible studies. The fixed or random effect model was used based on heterogeneity test. The dose-response relationship was assessed by restricted cubic spline. A total of 13 articles involving 901 764 participants for coffee, eight articles involving 344 895 participants for tea and seven articles involving 492 724 participants for caffeine were included. A non-linear relationship was found between coffee consumption and PD risk overall, and the strength of protection reached the maximum at approximately 3 cups/day (smoking-adjusted relative risk: 0.72, 95% confidence interval 0.65-0.81). A linear relationship was found between tea and caffeine consumption, and PD risk overall, and the smoking-adjusted risk of PD decreased by 26% and 17% for every two cups/day and 200 mg/day increments, respectively. The association of coffee and tea consumption with PD risk was stronger for men than that for women, and the association of caffeine consumption with PD risk was stronger for ever users of hormones than that for never users of hormones among postmenopausal women. The aforementioned associations were weaker for USA relative to Europe or Asia. A linear dose-relationship for decreased PD risk with tea and caffeine consumption was found, whereas the strength of protection reached a maximum at approximately 3 cups/day for coffee consumption overall. Further studies are required to confirm the findings. © 2013 Japan Geriatrics Society.

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

    Moradi, Afshin, E-mail: a.moradi@kut.ac.ir

    We develop the Maxwell-Garnett theory for the effective medium approximation of composite materials with metallic nanoparticles by taking into account the quantum spatial dispersion effects in dielectric response of nanoparticles. We derive a quantum nonlocal generalization of the standard Maxwell-Garnett formula, by means the linearized quantum hydrodynamic theory in conjunction with the Poisson equation as well as the appropriate additional quantum boundary conditions.

  10. Lessons learned from the AIRS pre-flight radiometric calibration

    NASA Astrophysics Data System (ADS)

    Pagano, Thomas S.; Aumann, Hartmut H.; Weiler, Margie

    2013-09-01

    The Atmospheric Infrared Sounder (AIRS) instrument flies on the NASA Aqua satellite and measures the upwelling hyperspectral earth radiance in the spectral range of 3.7-15.4 μm with a nominal ground resolution at nadir of 13.5 km. The AIRS spectra are achieved using a temperature controlled grating spectrometer and HgCdTe infrared linear arrays providing 2378 channels with a nominal spectral resolution of approximately 1200. The AIRS pre-flight tests that impact the radiometric calibration include a full system radiometric response (linearity), polarization response, and response vs scan angle (RVS). We re-derive the AIRS instrument radiometric calibration coefficients from the pre-flight polarization measurements, the response vs scan (RVS) angle tests as well as the linearity tests, and a recent lunar roll test that allowed the AIRS to view the moon. The data and method for deriving the coefficients is discussed in detail and the resulting values compared amongst the different tests. Finally, we examine the residual errors in the reconstruction of the external calibrator blackbody radiances and the efficacy of a new radiometric uncertainty model. Results show the radiometric calibration of AIRS to be excellent and the radiometric uncertainty model does a reasonable job of characterizing the errors.

  11. Linear response to long wavelength fluctuations using curvature simulations

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

    Baldauf, Tobias; Zaldarriaga, Matias; Seljak, Uroš

    2016-09-01

    We study the local response to long wavelength fluctuations in cosmological N -body simulations, focusing on the matter and halo power spectra, halo abundance and non-linear transformations of the density field. The long wavelength mode is implemented using an effective curved cosmology and a mapping of time and distances. The method provides an alternative, more direct, way to measure the isotropic halo biases. Limiting ourselves to the linear case, we find generally good agreement between the biases obtained from the curvature method and the traditional power spectrum method at the level of a few percent. We also study the responsemore » of halo counts to changes in the variance of the field and find that the slope of the relation between the responses to density and variance differs from the naïve derivation assuming a universal mass function by approximately 8–20%. This has implications for measurements of the amplitude of local non-Gaussianity using scale dependent bias. We also analyze the halo power spectrum and halo-dark matter cross-spectrum response to long wavelength fluctuations and derive second order halo bias from it, as well as the super-sample variance contribution to the galaxy power spectrum covariance matrix.« less

  12. Full Wave Parallel Code for Modeling RF Fields in Hot Plasmas

    NASA Astrophysics Data System (ADS)

    Spencer, Joseph; Svidzinski, Vladimir; Evstatiev, Evstati; Galkin, Sergei; Kim, Jin-Soo

    2015-11-01

    FAR-TECH, Inc. is developing a suite of full wave RF codes in hot plasmas. It is based on a formulation in configuration space with grid adaptation capability. The conductivity kernel (which includes a nonlocal dielectric response) is calculated by integrating the linearized Vlasov equation along unperturbed test particle orbits. For Tokamak applications a 2-D version of the code is being developed. Progress of this work will be reported. This suite of codes has the following advantages over existing spectral codes: 1) It utilizes the localized nature of plasma dielectric response to the RF field and calculates this response numerically without approximations. 2) It uses an adaptive grid to better resolve resonances in plasma and antenna structures. 3) It uses an efficient sparse matrix solver to solve the formulated linear equations. The linear wave equation is formulated using two approaches: for cold plasmas the local cold plasma dielectric tensor is used (resolving resonances by particle collisions), while for hot plasmas the conductivity kernel is calculated. Work is supported by the U.S. DOE SBIR program.

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

    PubMed

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

    2018-05-23

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

  14. Towards time-dependent current-density-functional theory in the non-linear regime

    NASA Astrophysics Data System (ADS)

    Escartín, J. M.; Vincendon, M.; Romaniello, P.; Dinh, P. M.; Reinhard, P.-G.; Suraud, E.

    2015-02-01

    Time-Dependent Density-Functional Theory (TDDFT) is a well-established theoretical approach to describe and understand irradiation processes in clusters and molecules. However, within the so-called adiabatic local density approximation (ALDA) to the exchange-correlation (xc) potential, TDDFT can show insufficiencies, particularly in violently dynamical processes. This is because within ALDA the xc potential is instantaneous and is a local functional of the density, which means that this approximation neglects memory effects and long-range effects. A way to go beyond ALDA is to use Time-Dependent Current-Density-Functional Theory (TDCDFT), in which the basic quantity is the current density rather than the density as in TDDFT. This has been shown to offer an adequate account of dissipation in the linear domain when the Vignale-Kohn (VK) functional is used. Here, we go beyond the linear regime and we explore this formulation in the time domain. In this case, the equations become very involved making the computation out of reach; we hence propose an approximation to the VK functional which allows us to calculate the dynamics in real time and at the same time to keep most of the physics described by the VK functional. We apply this formulation to the calculation of the time-dependent dipole moment of Ca, Mg and Na2. Our results show trends similar to what was previously observed in model systems or within linear response. In the non-linear domain, our results show that relaxation times do not decrease with increasing deposited excitation energy, which sets some limitations to the practical use of TDCDFT in such a domain of excitations.

  15. Towards time-dependent current-density-functional theory in the non-linear regime.

    PubMed

    Escartín, J M; Vincendon, M; Romaniello, P; Dinh, P M; Reinhard, P-G; Suraud, E

    2015-02-28

    Time-Dependent Density-Functional Theory (TDDFT) is a well-established theoretical approach to describe and understand irradiation processes in clusters and molecules. However, within the so-called adiabatic local density approximation (ALDA) to the exchange-correlation (xc) potential, TDDFT can show insufficiencies, particularly in violently dynamical processes. This is because within ALDA the xc potential is instantaneous and is a local functional of the density, which means that this approximation neglects memory effects and long-range effects. A way to go beyond ALDA is to use Time-Dependent Current-Density-Functional Theory (TDCDFT), in which the basic quantity is the current density rather than the density as in TDDFT. This has been shown to offer an adequate account of dissipation in the linear domain when the Vignale-Kohn (VK) functional is used. Here, we go beyond the linear regime and we explore this formulation in the time domain. In this case, the equations become very involved making the computation out of reach; we hence propose an approximation to the VK functional which allows us to calculate the dynamics in real time and at the same time to keep most of the physics described by the VK functional. We apply this formulation to the calculation of the time-dependent dipole moment of Ca, Mg and Na2. Our results show trends similar to what was previously observed in model systems or within linear response. In the non-linear domain, our results show that relaxation times do not decrease with increasing deposited excitation energy, which sets some limitations to the practical use of TDCDFT in such a domain of excitations.

  16. Finite size and geometrical non-linear effects during crack pinning by heterogeneities: An analytical and experimental study

    NASA Astrophysics Data System (ADS)

    Vasoya, Manish; Unni, Aparna Beena; Leblond, Jean-Baptiste; Lazarus, Veronique; Ponson, Laurent

    2016-04-01

    Crack pinning by heterogeneities is a central toughening mechanism in the failure of brittle materials. So far, most analytical explorations of the crack front deformation arising from spatial variations of fracture properties have been restricted to weak toughness contrasts using first order approximation and to defects of small dimensions with respect to the sample size. In this work, we investigate the non-linear effects arising from larger toughness contrasts by extending the approximation to the second order, while taking into account the finite sample thickness. Our calculations predict the evolution of a planar crack lying on the mid-plane of a plate as a function of material parameters and loading conditions, especially in the case of a single infinitely elongated obstacle. Peeling experiments are presented which validate the approach and evidence that the second order term broadens its range of validity in terms of toughness contrast values. The work highlights the non-linear response of the crack front to strong defects and the central role played by the thickness of the specimen on the pinning process.

  17. An unsteady lifting surface method for single rotation propellers

    NASA Technical Reports Server (NTRS)

    Williams, Marc H.

    1990-01-01

    The mathematical formulation of a lifting surface method for evaluating the steady and unsteady loads induced on single rotation propellers by blade vibration and inflow distortion is described. The scheme is based on 3-D linearized compressible aerodynamics and presumes that all disturbances are simple harmonic in time. This approximation leads to a direct linear integral relation between the normal velocity on the blade (which is determined from the blade geometry and motion) and the distribution of pressure difference across the blade. This linear relation is discretized by breaking the blade up into subareas (panels) on which the pressure difference is treated as approximately constant, and constraining the normal velocity at one (control) point on each panel. The piece-wise constant loads can then be determined by Gaussian elimination. The resulting blade loads can be used in performance, stability and forced response predictions for the rotor. Mathematical and numerical aspects of the method are examined. A selection of results obtained from the method is presented. The appendices include various details of the derivation that were felt to be secondary to the main development in Section 1.

  18. Modelling the spatio-temporal modulation response of ganglion cells with difference-of-Gaussians receptive fields: relation to photoreceptor response kinetics.

    PubMed

    Donner, K; Hemilä, S

    1996-01-01

    Difference-of-Gaussians (DOG) models for the receptive fields of retinal ganglion cells accurately predict linear responses to both periodic stimuli (typically moving sinusoidal gratings) and aperiodic stimuli (typically circular fields presented as square-wave pulses). While the relation of spatial organization to retinal anatomy has received considerable attention, temporal characteristics have been only loosely connected to retinal physiology. Here we integrate realistic photoreceptor response waveforms into the DOG model to clarify how far a single set of physiological parameters predict temporal aspects of linear responses to both periodic and aperiodic stimuli. Traditional filter-cascade models provide a useful first-order approximation of the single-photon response in photoreceptors. The absolute time scale of these, plus a time for retinal transmission, here construed as a fixed delay, are obtained from flash/step data. Using these values, we find that the DOG model predicts the main features of both the amplitude and phase response of linear cat ganglion cells to sinusoidal flicker. Where the simplest model formulation fails, it serves to reveal additional mechanisms. Unforeseen facts are the attenuation of low temporal frequencies even in pure center-type responses, and the phase advance of the response relative to the stimulus at low frequencies. Neither can be explained by any experimentally documented cone response waveform, but both would be explained by signal differentiation, e.g. in the retinal transmission pathway, as demonstrated at least in turtle retina.

  19. Input-output characterization of an ultrasonic testing system by digital signal analysis

    NASA Technical Reports Server (NTRS)

    Williams, J. H., Jr.; Lee, S. S.; Karagulle, H.

    1986-01-01

    Ultrasonic test system input-output characteristics were investigated by directly coupling the transmitting and receiving transducers face to face without a test specimen. Some of the fundamentals of digital signal processing were summarized. Input and output signals were digitized by using a digital oscilloscope, and the digitized data were processed in a microcomputer by using digital signal-processing techniques. The continuous-time test system was modeled as a discrete-time, linear, shift-invariant system. In estimating the unit-sample response and frequency response of the discrete-time system, it was necessary to use digital filtering to remove low-amplitude noise, which interfered with deconvolution calculations. A digital bandpass filter constructed with the assistance of a Blackman window and a rectangular time window were used. Approximations of the impulse response and the frequency response of the continuous-time test system were obtained by linearly interpolating the defining points of the unit-sample response and the frequency response of the discrete-time system. The test system behaved as a linear-phase bandpass filter in the frequency range 0.6 to 2.3 MHz. These frequencies were selected in accordance with the criterion that they were 6 dB below the maximum peak of the amplitude of the frequency response. The output of the system to various inputs was predicted and the results were compared with the corresponding measurements on the system.

  20. The Hindmarsh-Rose neuron model: bifurcation analysis and piecewise-linear approximations.

    PubMed

    Storace, Marco; Linaro, Daniele; de Lange, Enno

    2008-09-01

    This paper provides a global picture of the bifurcation scenario of the Hindmarsh-Rose model. A combination between simulations and numerical continuations is used to unfold the complex bifurcation structure. The bifurcation analysis is carried out by varying two bifurcation parameters and evidence is given that the structure that is found is universal and appears for all combinations of bifurcation parameters. The information about the organizing principles and bifurcation diagrams are then used to compare the dynamics of the model with that of a piecewise-linear approximation, customized for circuit implementation. A good match between the dynamical behaviors of the models is found. These results can be used both to design a circuit implementation of the Hindmarsh-Rose model mimicking the diversity of neural response and as guidelines to predict the behavior of the model as well as its circuit implementation as a function of parameters. (c) 2008 American Institute of Physics.

  1. Time dependent density functional calculation of plasmon response in clusters

    NASA Astrophysics Data System (ADS)

    Wang, Feng; Zhang, Feng-Shou; Eric, Suraud

    2003-02-01

    We have introduced a theoretical scheme for the efficient description of the optical response of a cluster based on the time-dependent density functional theory. The practical implementation is done by means of the fully fledged time-dependent local density approximation scheme, which is solved directly in the time domain without any linearization. As an example we consider the simple Na2 cluster and compute its surface plasmon photoabsorption cross section, which is in good agreement with the experiments.

  2. Stochastic resonance-enhanced laser-based particle detector.

    PubMed

    Dutta, A; Werner, C

    2009-01-01

    This paper presents a Laser-based particle detector whose response was enhanced by modulating the Laser diode with a white-noise generator. A Laser sheet was generated to cast a shadow of the object on a 200 dots per inch, 512 x 1 pixels linear sensor array. The Laser diode was modulated with a white-noise generator to achieve stochastic resonance. The white-noise generator essentially amplified the wide-bandwidth (several hundred MHz) noise produced by a reverse-biased zener diode operating in junction-breakdown mode. The gain in the amplifier in the white-noise generator was set such that the Receiver Operating Characteristics plot provided the best discriminability. A monofiber 40 AWG (approximately 80 microm) wire was detected with approximately 88% True Positive rate and approximately 19% False Positive rate in presence of white-noise modulation and with approximately 71% True Positive rate and approximately 15% False Positive rate in absence of white-noise modulation.

  3. An approximation theory for the identification of linear thermoelastic systems

    NASA Technical Reports Server (NTRS)

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

    1990-01-01

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

  4. Non-linear interactions between CO_2 radiative and physiological effects on Amazonian evapotranspiration in an Earth system model

    NASA Astrophysics Data System (ADS)

    Halladay, Kate; Good, Peter

    2017-10-01

    We present a detailed analysis of mechanisms underlying the evapotranspiration response to increased CO_2 in HadGEM2-ES, focussed on western Amazonia. We use three simulations from CMIP5 in which atmospheric CO_2 increases at 1% per year reaching approximately four times pre-industrial levels after 140 years. Using 3-hourly data, we found that evapotranspiration (ET) change was dominated by decreased stomatal conductance (g_s), and to a lesser extent by decreased canopy water and increased moisture gradient (specific humidity difference between surface and near-surface). There were large, non-linear decreases in ET in the simulation in which radiative and physiological forcings could interact. This non-linearity arises from non-linearity in the conductance term (includes aerodynamic and stomatal resistance and partitioning between the two, which is determined by canopy water availability), the moisture gradient, and negative correlation between these two terms. The conductance term is non-linear because GPP responds non-linearly to temperature and GPP is the dominant control on g_s in HadGEM2-ES. In addition, canopy water declines, mainly due to increases in potential evaporation, which further decrease the conductance term. The moisture gradient responds non-linearly owing to the non-linear response of temperature to CO_2 increases, which increases the Bowen ratio. Moisture gradient increases resulting from ET decline increase ET and thus constitute a negative feedback. This analysis highlights the importance of the g_s parametrisation in determining the ET response and the potential differences between offline and online simulations owing to feedbacks on ET via the atmosphere, some of which would not occur in an offline simulation.

  5. Numerical solution of distributed order fractional differential equations

    NASA Astrophysics Data System (ADS)

    Katsikadelis, John T.

    2014-02-01

    In this paper a method for the numerical solution of distributed order FDEs (fractional differential equations) of a general form is presented. The method applies to both linear and nonlinear equations. The Caputo type fractional derivative is employed. The distributed order FDE is approximated with a multi-term FDE, which is then solved by adjusting appropriately the numerical method developed for multi-term FDEs by Katsikadelis. Several example equations are solved and the response of mechanical systems described by such equations is studied. The convergence and the accuracy of the method for linear and nonlinear equations are demonstrated through well corroborated numerical results.

  6. Linear optical response of carbon nanotubes under axial magnetic field

    NASA Astrophysics Data System (ADS)

    Moradian, Rostam; Chegel, Raad; Behzad, Somayeh

    2010-04-01

    We considered single walled carbon naotubes (SWCNTs) as real three dimensional (3D) systems in a cylindrical coordinate. The optical matrix elements and linear susceptibility, χ(ω), in the tight binding approximation in terms of one-dimensional wave vector, kz and subband index, l are calculated. In an external axial magnetic field optical frequency dependence of linear susceptibility are investigated. We found that axial magnetic field has two effects on the imaginary part of the linear susceptibility spectrum, in agreement with experimental results. The first effect is broadening and the second, splitting. Also we found that for all metallic zigzag and armchair SWCNTs, the axial magnetic field leads to the creation of a peak with energy less than 1.5 eV, contrary to what is observed in the absence of a magnetic field.

  7. The exact thermal rotational spectrum of a two-dimensional rigid rotor obtained using Gaussian wave packet dynamics

    NASA Technical Reports Server (NTRS)

    Reimers, J. R.; Heller, E. J.

    1985-01-01

    The exact thermal rotational spectrum of a two-dimensional rigid rotor is obtained using Gaussian wave packet dynamics. The spectrum is obtained by propagating, without approximation, infinite sets of Gaussian wave packets. These sets are constructed so that collectively they have the correct periodicity, and indeed, are coherent states appropriate to this problem. Also, simple, almost classical, approximations to full wave packet dynamics are shown to give results which are either exact or very nearly exact. Advantages of the use of Gaussian wave packet dynamics over conventional linear response theory are discussed.

  8. Interfacial solvation thermodynamics

    NASA Astrophysics Data System (ADS)

    Ben-Amotz, Dor

    2016-10-01

    Previous studies have reached conflicting conclusions regarding the interplay of cavity formation, polarizability, desolvation, and surface capillary waves in driving the interfacial adsorptions of ions and molecules at air-water interfaces. Here we revisit these questions by combining exact potential distribution results with linear response theory and other physically motivated approximations. The results highlight both exact and approximate compensation relations pertaining to direct (solute-solvent) and indirect (solvent-solvent) contributions to adsorption thermodynamics, of relevance to solvation at air-water interfaces, as well as a broader class of processes linked to the mean force potential between ions, molecules, nanoparticles, proteins, and biological assemblies.

  9. Semiclassical Origin of Superdeformed Shell Structure in the Spheroidal Cavity Model

    NASA Astrophysics Data System (ADS)

    Arita, K.; Sugita, A.; Matsuyanagi, K.

    1998-12-01

    Classical periodic orbits responsible for emergence of the superdeformed shell structures of single-particle motion in spheroidal cavities are identified and their relative contributions to the shell structures are evaluated. Both prolate and oblate superdeformations (axis ratio approximately 2:1) as well as prolate hyperdeformation (axis ratio approximately 3:1) are investigated. Fourier transforms of quantum spectra clearly show that three-dimensional periodic orbits born out of bifurcations of planar orbits in the equatorial plane become predominant at large prolate deformations, while butterfly-shaped planar orbits bifurcated from linear orbits along the minor axis are important at large oblate deformations.

  10. Dissociation of Self-Motion and Object Motion by Linear Population Decoding That Approximates Marginalization.

    PubMed

    Sasaki, Ryo; Angelaki, Dora E; DeAngelis, Gregory C

    2017-11-15

    We use visual image motion to judge the movement of objects, as well as our own movements through the environment. Generally, image motion components caused by object motion and self-motion are confounded in the retinal image. Thus, to estimate heading, the brain would ideally marginalize out the effects of object motion (or vice versa), but little is known about how this is accomplished neurally. Behavioral studies suggest that vestibular signals play a role in dissociating object motion and self-motion, and recent computational work suggests that a linear decoder can approximate marginalization by taking advantage of diverse multisensory representations. By measuring responses of MSTd neurons in two male rhesus monkeys and by applying a recently-developed method to approximate marginalization by linear population decoding, we tested the hypothesis that vestibular signals help to dissociate self-motion and object motion. We show that vestibular signals stabilize tuning for heading in neurons with congruent visual and vestibular heading preferences, whereas they stabilize tuning for object motion in neurons with discrepant preferences. Thus, vestibular signals enhance the separability of joint tuning for object motion and self-motion. We further show that a linear decoder, designed to approximate marginalization, allows the population to represent either self-motion or object motion with good accuracy. Decoder weights are broadly consistent with a readout strategy, suggested by recent computational work, in which responses are decoded according to the vestibular preferences of multisensory neurons. These results demonstrate, at both single neuron and population levels, that vestibular signals help to dissociate self-motion and object motion. SIGNIFICANCE STATEMENT The brain often needs to estimate one property of a changing environment while ignoring others. This can be difficult because multiple properties of the environment may be confounded in sensory signals. The brain can solve this problem by marginalizing over irrelevant properties to estimate the property-of-interest. We explore this problem in the context of self-motion and object motion, which are inherently confounded in the retinal image. We examine how diversity in a population of multisensory neurons may be exploited to decode self-motion and object motion from the population activity of neurons in macaque area MSTd. Copyright © 2017 the authors 0270-6474/17/3711204-16$15.00/0.

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

    Woon Hyuk Chung

    Polyvinyl alcohol films containing congo red are useful as gamma and electron radiation dosimeters. Absorbed doses should not exceed 500 kGy. The dose response is rather linear in a higher range, e.g., 100 to 500 kGy. The film is relatively stable before and after irradiation for quite a long time against fading, for example, a change of [approximately]10% in 1 yr following irradiation at room temperature.

  12. Mechanical System Reliability and Cost Integration Using a Sequential Linear Approximation Method

    NASA Technical Reports Server (NTRS)

    Kowal, Michael T.

    1997-01-01

    The development of new products is dependent on product designs that incorporate high levels of reliability along with a design that meets predetermined levels of system cost. Additional constraints on the product include explicit and implicit performance requirements. Existing reliability and cost prediction methods result in no direct linkage between variables affecting these two dominant product attributes. A methodology to integrate reliability and cost estimates using a sequential linear approximation method is proposed. The sequential linear approximation method utilizes probability of failure sensitivities determined from probabilistic reliability methods as well a manufacturing cost sensitivities. The application of the sequential linear approximation method to a mechanical system is demonstrated.

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

    Escartín, J. M.; CNRS, UMR5152, F-31062 Toulouse Cedex; Theory of Condensed Matter Group, Cavendish Laboratory, University of Cambridge, J.J. Thomson Avenue, Cambridge CB3 0HE

    Time-Dependent Density-Functional Theory (TDDFT) is a well-established theoretical approach to describe and understand irradiation processes in clusters and molecules. However, within the so-called adiabatic local density approximation (ALDA) to the exchange-correlation (xc) potential, TDDFT can show insufficiencies, particularly in violently dynamical processes. This is because within ALDA the xc potential is instantaneous and is a local functional of the density, which means that this approximation neglects memory effects and long-range effects. A way to go beyond ALDA is to use Time-Dependent Current-Density-Functional Theory (TDCDFT), in which the basic quantity is the current density rather than the density as in TDDFT.more » This has been shown to offer an adequate account of dissipation in the linear domain when the Vignale-Kohn (VK) functional is used. Here, we go beyond the linear regime and we explore this formulation in the time domain. In this case, the equations become very involved making the computation out of reach; we hence propose an approximation to the VK functional which allows us to calculate the dynamics in real time and at the same time to keep most of the physics described by the VK functional. We apply this formulation to the calculation of the time-dependent dipole moment of Ca, Mg and Na{sub 2}. Our results show trends similar to what was previously observed in model systems or within linear response. In the non-linear domain, our results show that relaxation times do not decrease with increasing deposited excitation energy, which sets some limitations to the practical use of TDCDFT in such a domain of excitations.« less

  14. Use of a small overpotential approximation to analyze Geobacter sulfurreducens biofilm impedance

    NASA Astrophysics Data System (ADS)

    Babauta, Jerome T.; Beyenal, Haluk

    2017-07-01

    The electrochemical impedance of Geobacter sulfurreducens biofilms reflects the extracellular electron transfer mechanisms determining the rate of current output. Binned into two characteristic parameters, conductance and capacitance, biofilm impedance has received significant attention. The goal of this study was to evaluate a small overpotential approximation for extracellular electron transfer in G. sulfurreducens biofilms. Our motivation was to determine whether conductance over biofilm growth behaved linearly with respect to limiting current. Biofilm impedance was tracked during growth using electrochemical impedance spectroscopy (EIS) and electrochemical quartz crystal microbalance (eQCM). We showed that normalization of the biofilm impedance is useful for characterizing the changes during growth. When the conductance and capacitance were compared to the biofilm current, we found that: 1) conductance had a linear response and 2) constant phase elements (CPE) had a saturating response that coincided with the limiting current. We provided a framework using a simple iV relationship that predicted the conductance-current slope to be 9.57 V-1. CPEs showed more variability across biofilm replicates than conductance values. Although G. sulfurreducens biofilms were used here, other electrochemically active biofilms exhibiting catalytic waves could be studied using the same methods.

  15. A method for early determination of meat ultimate pH.

    PubMed

    Young, O A; West, J; Hart, A L; van Otterdijk, F F H

    2004-02-01

    A patented method of rapidly determining the ultimate pH from approximate glycolytic potential of muscles of slaughtered animals has been devised. The method is based on the rapid hydrolysis of muscle glycogen to glucose by the enzyme amyloglucosidase and subsequent measurement of the liberated glucose. In acetate buffer at pH 4.5, glucose concentration can be determined in 30 s with domestic meters for diabetes control. The meter response differed from that of glucose in blood, but was linear with concentration. In slurries comprising homogenised meat in acetate buffer and added glucose, a similar linear response was obtained. Amyloglucosidase was capable of rapidly hydrolysing glycogen to glucose in such slurries. In the 24 h following slaughter, a decrease in glycogen, as determined by glucose, occurred in parallel with the decline in pH. At the same time, lactate progressively accumulated as expected. Values for the approximate glycolytic potential and (by calibration) ultimate pH, were obtained on prerigor muscle within 7 min of muscle sampling in an industrial environment. The method is suitable for on-line application in beef abattoirs particularly those employing hot boning where ultimate must be known at the grading point.

  16. Materials and noncoplanar mesh designs for integrated circuits with linear elastic responses to extreme mechanical deformations.

    PubMed

    Kim, Dae-Hyeong; Song, Jizhou; Choi, Won Mook; Kim, Hoon-Sik; Kim, Rak-Hwan; Liu, Zhuangjian; Huang, Yonggang Y; Hwang, Keh-Chih; Zhang, Yong-wei; Rogers, John A

    2008-12-02

    Electronic systems that offer elastic mechanical responses to high-strain deformations are of growing interest because of their ability to enable new biomedical devices and other applications whose requirements are impossible to satisfy with conventional wafer-based technologies or even with those that offer simple bendability. This article introduces materials and mechanical design strategies for classes of electronic circuits that offer extremely high stretchability, enabling them to accommodate even demanding configurations such as corkscrew twists with tight pitch (e.g., 90 degrees in approximately 1 cm) and linear stretching to "rubber-band" levels of strain (e.g., up to approximately 140%). The use of single crystalline silicon nanomaterials for the semiconductor provides performance in stretchable complementary metal-oxide-semiconductor (CMOS) integrated circuits approaching that of conventional devices with comparable feature sizes formed on silicon wafers. Comprehensive theoretical studies of the mechanics reveal the way in which the structural designs enable these extreme mechanical properties without fracturing the intrinsically brittle active materials or even inducing significant changes in their electrical properties. The results, as demonstrated through electrical measurements of arrays of transistors, CMOS inverters, ring oscillators, and differential amplifiers, suggest a valuable route to high-performance stretchable electronics.

  17. Nonlinear ionic transport through microstructured solid electrolytes: homogenization estimates

    NASA Astrophysics Data System (ADS)

    Curto Sillamoni, Ignacio J.; Idiart, Martín I.

    2016-10-01

    We consider the transport of multiple ionic species by diffusion and migration through microstructured solid electrolytes in the presence of strong electric fields. The assumed constitutive relations for the constituent phases follow from convex energy and dissipation potentials which guarantee thermodynamic consistency. The effective response is heuristically deduced from a multi-scale convergence analysis of the relevant field equations. The resulting homogenized response involves an effective dissipation potential per species. Each potential is mathematically akin to that of a standard nonlinear heterogeneous conductor. A ‘linear-comparison’ homogenization technique is then used to generate estimates for these nonlinear potentials in terms of available estimates for corresponding linear conductors. By way of example, use is made of the Maxwell-Garnett and effective-medium linear approximations to generate estimates for two-phase systems with power-law dissipation. Explicit formulas are given for some limiting cases. In the case of threshold-type behavior, the estimates exhibit non-analytical dilute limits and seem to be consistent with fields localized in low energy paths.

  18. Nonlocal kinetic energy functional from the jellium-with-gap model: Applications to orbital-free density functional theory

    NASA Astrophysics Data System (ADS)

    Constantin, Lucian A.; Fabiano, Eduardo; Della Sala, Fabio

    2018-05-01

    Orbital-free density functional theory (OF-DFT) promises to describe the electronic structure of very large quantum systems, being its computational cost linear with the system size. However, the OF-DFT accuracy strongly depends on the approximation made for the kinetic energy (KE) functional. To date, the most accurate KE functionals are nonlocal functionals based on the linear-response kernel of the homogeneous electron gas, i.e., the jellium model. Here, we use the linear-response kernel of the jellium-with-gap model to construct a simple nonlocal KE functional (named KGAP) which depends on the band-gap energy. In the limit of vanishing energy gap (i.e., in the case of metals), the KGAP is equivalent to the Smargiassi-Madden (SM) functional, which is accurate for metals. For a series of semiconductors (with different energy gaps), the KGAP performs much better than SM, and results are close to the state-of-the-art functionals with sophisticated density-dependent kernels.

  19. Solution of linear systems by a singular perturbation technique

    NASA Technical Reports Server (NTRS)

    Ardema, M. D.

    1976-01-01

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

  20. Quasi-linear regime of gravitational instability: Implication to density-velocity relation

    NASA Technical Reports Server (NTRS)

    Shandarin, Sergei F.

    1993-01-01

    The well known linear relation between density and peculiar velocity distributions is a powerful tool for studying the large-scale structure in the Universe. Potentially it can test the gravitational instability theory and measure Omega. At present it is used in both ways: the velocity is reconstructed, provided the density is given, and vice versa. Reconstructing the density from the velocity field usually makes use of the Zel'dovich approximation. However, the standard linear approximation in Eulerian space is used when the velocity is reconstructed from the density distribution. I show that the linearized Zel'dovich approximation, in other words the linear approximation in the Lagrangian space, is more accurate for reconstructing velocity. In principle, a simple iteration technique can recover both the density and velocity distributions in Lagrangian space, but its practical application may need an additional study.

  1. Linear Approximation SAR Azimuth Processing Study

    NASA Technical Reports Server (NTRS)

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

    1979-01-01

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

  2. Legendre-tau approximation for functional differential equations. Part 2: The linear quadratic optimal control problem

    NASA Technical Reports Server (NTRS)

    Ito, K.; Teglas, R.

    1984-01-01

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

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

    NASA Technical Reports Server (NTRS)

    Ito, Kazufumi; Teglas, Russell

    1987-01-01

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

  4. Comparative evaluation of Kodak EDR2 and XV2 films for verification of intensity modulated radiation therapy.

    PubMed

    Dogan, Nesrin; Leybovich, Leonid B; Sethi, Anil

    2002-11-21

    Film dosimetry provides a convenient tool to determine dose distributions, especially for verification of IMRT plans. However, the film response to radiation shows a significant dependence on depth, energy and field size that compromise the accuracy of measurements. Kodak's XV2 film has a low saturation dose (approximately 100 cGy) and, consequently, a relatively short region of linear dose-response. The recently introduced Kodak extended range EDR2 film was reported to have a linear dose-response region extending to 500 cGy. This increased dose range may be particularly useful in the verification of IMRT plans. In this work, the dependence of Kodak EDR2 film's response on the depth, field size and energy was evaluated and compared with Kodak XV2 film. Co-60, 6 MV, 10 MV and 18 MV beams were used. Field sizes were 2 x 2, 6 x 6, 10 x 10, 14 x 14, 18 x 18 and 24 x 24 cm2. Doses for XV2 and EDR2 films were 80 cGy and 300 cGy, respectively. Optical density was converted to dose using depth-corrected sensitometric (Hurter and Driffield, or H&D) curves. For each field size, XV2 and EDR2 depth-dose curves were compared with ion chamber depth-dose curves. Both films demonstrated similar (within 1%) field size dependence. The deviation from the ion chamber for both films was small forthe fields ranging from 2 x 2 to 10 x 10 cm2: < or =2% for 6, 10 and 18 MV beams. No deviation was observed for the Co-60 beam. As the field size increased to 24 x 24 cm2, the deviation became significant for both films: approximately 7.5% for Co-60, approximately 5% for 6 MV and 10 MV, and approximately 6% for 18 MV. During the verification of IMRT plans, EDR2 film showed a better agreement with the calculated dose distributions than the XV2 film.

  5. Beyond the electric-dipole approximation: A formulation and implementation of molecular response theory for the description of absorption of electromagnetic field radiation

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

    List, Nanna Holmgaard, E-mail: nhl@sdu.dk; Jensen, Hans Jørgen Aagaard; Kauczor, Joanna

    2015-06-28

    We present a formulation of molecular response theory for the description of a quantum mechanical molecular system in the presence of a weak, monochromatic, linearly polarized electromagnetic field without introducing truncated multipolar expansions. The presentation focuses on a description of linear absorption by adopting the energy-loss approach in combination with the complex polarization propagator formulation of response theory. Going beyond the electric-dipole approximation is essential whenever studying electric-dipole-forbidden transitions, and in general, non-dipolar effects become increasingly important when addressing spectroscopies involving higher-energy photons. These two aspects are examined by our study of the near K-edge X-ray absorption fine structure ofmore » the alkaline earth metals (Mg, Ca, Sr, Ba, and Ra) as well as the trans-polyenes. In following the series of alkaline earth metals, the sizes of non-dipolar effects are probed with respect to increasing photon energies and a detailed assessment of results is made in terms of studying the pertinent transition electron densities and in particular their spatial extension in comparison with the photon wavelength. Along the series of trans-polyenes, the sizes of non-dipolar effects are probed for X-ray spectroscopies on organic molecules with respect to the spatial extension of the chromophore.« less

  6. The climate response to five trillion tonnes of carbon

    NASA Astrophysics Data System (ADS)

    Tokarska, Katarzyna B.; Gillett, Nathan P.; Weaver, Andrew J.; Arora, Vivek K.; Eby, Michael

    2016-09-01

    Concrete actions to curtail greenhouse gas emissions have so far been limited on a global scale, and therefore the ultimate magnitude of climate change in the absence of further mitigation is an important consideration for climate policy. Estimates of fossil fuel reserves and resources are highly uncertain, and the amount used under a business-as-usual scenario would depend on prevailing economic and technological conditions. In the absence of global mitigation actions, five trillion tonnes of carbon (5 EgC), corresponding to the lower end of the range of estimates of the total fossil fuel resource, is often cited as an estimate of total cumulative emissions. An approximately linear relationship between global warming and cumulative CO2 emissions is known to hold up to 2 EgC emissions on decadal to centennial timescales; however, in some simple climate models the predicted warming at higher cumulative emissions is less than that predicted by such a linear relationship. Here, using simulations from four comprehensive Earth system models, we demonstrate that CO2-attributable warming continues to increase approximately linearly up to 5 EgC emissions. These models simulate, in response to 5 EgC of CO2 emissions, global mean warming of 6.4-9.5 °C, mean Arctic warming of 14.7-19.5 °C, and mean regional precipitation increases by more than a factor of four. These results indicate that the unregulated exploitation of the fossil fuel resource could ultimately result in considerably more profound climate changes than previously suggested.

  7. Vestibular short latency responses to pulsed linear acceleration in unanesthetized animals

    NASA Technical Reports Server (NTRS)

    Jones, T. A.

    1992-01-01

    Linear acceleration transients were used to elicit vestibular compound action potentials in non-invasively prepared, unanesthetized animals for the first time (chicks, Gallus domesticus, n = 33). Responses were composed of a series of up to 8 dominant peaks occurring within 8 msec of the stimulus. Response amplitudes for 1.0 g stimulus ranged from 1 to 10 microV. A late, slow, triphasic, anesthesia-labile component was identified as a dominant response feature in unanesthetized animals. Amplitudes increased and latencies decreased as stimulus intensity was increased (MANOVA P less than 0.05). Linear regression slope ranges were: amplitudes = 1.0-5.0 microV/g; latencies = -300 to -1100 microseconds/g. Thresholds for single polarity stimuli (0.035 +/- 0.022 g, n = 11) were significantly lower than those of alternating polarity (0.074 +/- 0.028 g, n = 18, P less than 0.001). Bilateral labyrinthectomy eliminated responses whereas bilateral extirpation of cochleae did not significantly change response thresholds. Intense acoustic masking (100/104 dB SL) produced no effect in 2 animals, but did produce small to moderate effects on response amplitudes in 7 others. Changes were attributed to effects on vestibular end organs. Results of unilateral labyrinth blockade (tetrodotoxin) suggest that P1 and N1 preferentially reflect ipsilateral eighth nerve compound action potentials whereas components beyond approximately 2 msec reflect activity from vestibular neurons that depend on both labyrinths. The results demonstrate that short latency vestibular compound action potentials can be measured in unanesthetized, non-invasively prepared animals.

  8. Spline smoothing of histograms by linear programming

    NASA Technical Reports Server (NTRS)

    Bennett, J. O.

    1972-01-01

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

  9. Implementing Linear Algebra Related Algorithms on the TI-92+ Calculator.

    ERIC Educational Resources Information Center

    Alexopoulos, John; Abraham, Paul

    2001-01-01

    Demonstrates a less utilized feature of the TI-92+: its natural and powerful programming language. Shows how to implement several linear algebra related algorithms including the Gram-Schmidt process, Least Squares Approximations, Wronskians, Cholesky Decompositions, and Generalized Linear Least Square Approximations with QR Decompositions.…

  10. Numerical approximation for the infinite-dimensional discrete-time optimal linear-quadratic regulator problem

    NASA Technical Reports Server (NTRS)

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

    1986-01-01

    An abstract approximation framework is developed for the finite and infinite time horizon discrete-time linear-quadratic regulator problem for systems whose state dynamics are described by a linear semigroup of operators on an infinite dimensional Hilbert space. The schemes included the framework yield finite dimensional approximations to the linear state feedback gains which determine the optimal control law. Convergence arguments are given. Examples involving hereditary and parabolic systems and the vibration of a flexible beam are considered. Spline-based finite element schemes for these classes of problems, together with numerical results, are presented and discussed.

  11. Physics must join with biology in better assessing risk from low-dose irradiation.

    PubMed

    Feinendegen, L E; Neumann, R D

    2005-01-01

    This review summarises the complex response of mammalian cells and tissues to low doses of ionising radiation. This thesis encompasses induction of DNA damage, and adaptive protection against both renewed damage and against propagation of damage from the basic level of biological organisation to the clinical expression of detriment. The induction of DNA damage at low radiation doses apparently is proportional to absorbed dose at the physical/chemical level. However, any propagation of such damage to higher levels of biological organisation inherently follows a sigmoid function. Moreover, low-dose-induced inhibition of damage propagation is not linear, but instead follows a dose-effect function typical for adaptive protection, after an initial rapid rise it disappears at doses higher than approximately 0.1-0.2 Gy to cells. The particular biological response duality at low radiation doses precludes the validity of the linear-no-threshold hypothesis in the attempt to relate absorbed dose to cancer. In fact, theory and observation support not only a lower cancer incidence than expected from the linear-no-threshold hypothesis, but also a reduction of spontaneously occurring cancer, a hormetic response, in the healthy individual.

  12. Structural stability of nonlinear population dynamics.

    PubMed

    Cenci, Simone; Saavedra, Serguei

    2018-01-01

    In population dynamics, the concept of structural stability has been used to quantify the tolerance of a system to environmental perturbations. Yet, measuring the structural stability of nonlinear dynamical systems remains a challenging task. Focusing on the classic Lotka-Volterra dynamics, because of the linearity of the functional response, it has been possible to measure the conditions compatible with a structurally stable system. However, the functional response of biological communities is not always well approximated by deterministic linear functions. Thus, it is unclear the extent to which this linear approach can be generalized to other population dynamics models. Here, we show that the same approach used to investigate the classic Lotka-Volterra dynamics, which is called the structural approach, can be applied to a much larger class of nonlinear models. This class covers a large number of nonlinear functional responses that have been intensively investigated both theoretically and experimentally. We also investigate the applicability of the structural approach to stochastic dynamical systems and we provide a measure of structural stability for finite populations. Overall, we show that the structural approach can provide reliable and tractable information about the qualitative behavior of many nonlinear dynamical systems.

  13. Structural stability of nonlinear population dynamics

    NASA Astrophysics Data System (ADS)

    Cenci, Simone; Saavedra, Serguei

    2018-01-01

    In population dynamics, the concept of structural stability has been used to quantify the tolerance of a system to environmental perturbations. Yet, measuring the structural stability of nonlinear dynamical systems remains a challenging task. Focusing on the classic Lotka-Volterra dynamics, because of the linearity of the functional response, it has been possible to measure the conditions compatible with a structurally stable system. However, the functional response of biological communities is not always well approximated by deterministic linear functions. Thus, it is unclear the extent to which this linear approach can be generalized to other population dynamics models. Here, we show that the same approach used to investigate the classic Lotka-Volterra dynamics, which is called the structural approach, can be applied to a much larger class of nonlinear models. This class covers a large number of nonlinear functional responses that have been intensively investigated both theoretically and experimentally. We also investigate the applicability of the structural approach to stochastic dynamical systems and we provide a measure of structural stability for finite populations. Overall, we show that the structural approach can provide reliable and tractable information about the qualitative behavior of many nonlinear dynamical systems.

  14. Polarons and Mobile Impurities Near a Quantum Phase Transition

    NASA Astrophysics Data System (ADS)

    Shadkhoo, Shahriar

    This dissertation aims at improving the current understanding of the physics of mobile impurities in highly correlated liquid-like phases of matter. Impurity problems pose challenging and intricate questions in different realms of many-body physics. For instance, the problem of ''solvation'' of charged solutes in polar solvents, has been the subject of longstanding debates among chemical physicists. The significant role of quantum fluctuations of the solvent, as well as the break down of linear response theory, render the ordinary treatments intractable. Inspired by this complicated problem, we first attempt to understand the role of non-specific quantum fluctuations in the solvation process. To this end, we calculate the dynamic structure factor of a model polar liquid, using the classical Molecular Dynamics (MD) simulations. We verify the failure of linear response approximation in the vicinity of a hydrated electron, by comparing the outcomes of MD simulations with the predictions of linear response theory. This nonlinear behavior is associated with the pronounced peaks of the structure factor, which reflect the strong fluctuations of the local modes. A cavity picture is constructed based on heuristic arguments, which suggests that the electron, along with the surrounding polarization cloud, behave like a frozen sphere, for which the linear response theory is broken inside and valid outside. The inverse radius of the spherical region serves as a UV momentum cutoff for the linear response approximation to be applicable. The problem of mobile impurities in polar liquids can be also addressed in the framework of the ''polaron'' problem. Polaron is a quasiparticle that typically acquires an extended state at weak couplings, and crossovers to a self-trapped state at strong couplings. Using the analytical fits to the numerically obtained charge-charge structure factor, a phenomenological approach is proposed within the Leggett's influence functional formalism, which derives the effective Euclidean action from the classical equation of motion. We calculate the effective mass of the polaron in the model polar liquid at zero and finite temperatures. The self-trapping transition of this polaron turns out to be discontinuous in certain regions of the phase diagram. In order to systematically investigate the role of quantum fluctuations on the polaron properties, we adopt a quantum field theory which supports nearly-critical local modes: the quantum Landau-Brazovskii (QLB) model, which exhibits fluctuation-induced first order transition (weak crystallization). In the vicinity of the phase transition, the quantum fluctuations are strongly correlated; one can in principle tune the strength of these fluctuations, by adjusting the parameters close to or away from the transition point. Furthermore, sufficiently close to the transition, the theory accommodates "soliton'' solutions, signaling the nonlinear response of the system. Therefore, the model seems to be a promising candidate for studying the effects of strong quantum fluctuations and also failure of linear response theory, in the polaron problem. We observe that at zero temperature, and away from the Brazovskii transition where the linear response approximation is valid, the localization transition of the polaron is discontinuous. Upon enhancing fluctuations---of either thermal or quantum nature---the gap of the effective mass closes at distinct second-order critical points. Sufficiently close to the Brazovskii transition where the nonlinear contributions of the field are significantly large, a new state appears in addition to extended and self-trapped polarons: an impurity-induced soliton. We interpret this as the break-down of linear response, reminiscent of what we observe in a polar liquid. Quantum LB model has been proposed to be realizable in ultracold Bose gases in cavities. We thus discuss the experimental feasibility, and propose a setup which is believed to exhibit the aforementioned polaronic and solitonic states. We eventually generalize the polaron formalism to the case of impurities that couple quadratically to a nearly-critical field; hence called the ''quadratic polaron''. The Hertz-Millis field theory and its generalization to the case of magnetic transition in helimagnets, is taken as a toy model. The phase diagram of the bare model contains both second-order and fluctuation-induced first-order quantum phase transitions. We propose a semi-classical scenario in which the impurity and the field couple quadratically. The polaron properties in the vicinity of these transitions are calculated in different dimensions. We observe that the quadratic coupling in three dimensions, even in the absence of the critical modes with finite wavelength, leads to a jump-like localization of the polaron. In lower dimensions, the transition behavior remains qualitatively similar to those in the case of linear coupling, namely the critical modes must have a finite wavelength to localize the particle.

  15. Tunable band gap in Bi(Fe1-xMnx)O3 films

    NASA Astrophysics Data System (ADS)

    Xu, X. S.; Ihlefeld, J. F.; Lee, J. H.; Ezekoye, O. K.; Vlahos, E.; Ramesh, R.; Gopalan, V.; Pan, X. Q.; Schlom, D. G.; Musfeldt, J. L.

    2010-05-01

    In order to investigate band gap tunability in polar oxides, we measured the optical properties of a series of Bi(Fe1-xMnx)O3 thin films. The absorption response of the mixed metal solid solutions is approximately a linear combination of the characteristics of the two end members, a result that demonstrates straightforward band gap tunability in this system.

  16. General relationships between ultrasonic attenuation and dispersion

    NASA Technical Reports Server (NTRS)

    Odonnell, M.; Jaynes, E. T.; Miller, J. G.

    1978-01-01

    General relationships between the ultrasonic attenuation and dispersion are presented. The validity of these nonlocal relationships hinges only on the properties of causality and linearity, and does not depend upon details of the mechanism responsible for the attenuation and dispersion. Approximate, nearly local relationships are presented and are demonstrated to predict accurately the ultrasonic dispersion in solutions of hemoglobin from the results of attenuation measurements.

  17. An Evaluation of the Kernel Equating Method: A Special Study with Pseudotests Constructed from Real Test Data. Research Report. ETS RR-06-02

    ERIC Educational Resources Information Center

    von Davier, Alina A.; Holland, Paul W.; Livingston, Samuel A.; Casabianca, Jodi; Grant, Mary C.; Martin, Kathleen

    2006-01-01

    This study examines how closely the kernel equating (KE) method (von Davier, Holland, & Thayer, 2004a) approximates the results of other observed-score equating methods--equipercentile and linear equatings. The study used pseudotests constructed of item responses from a real test to simulate three equating designs: an equivalent groups (EG)…

  18. Separating the effects of interreinforcement time and number of interreinforcement responses1

    PubMed Central

    Neuringer, Allen J.; Schneider, Bruce A.

    1968-01-01

    The relative importance of interreinforcement time and interreinforcement responses was evaluated by varying each independently. To do this, a blackout was presented after each nonreinforced response under both fixed-ratio and fixed-interval schedules of reinforcement. Manipulating the blackout duration under the fixed-ratio schedule caused interreinforcement time to vary without affecting the number of interreinforcement responses. Pigeons' post-reinforcement and post-blackout response latencies were found to increase linearly with interreinforcement time. Under the fixed-interval schedule, the same blackout manipulations changed the number of interreinforcement responses without affecting interreinforcement time. Post-reinforcement and post-blackout response latencies under this condition were approximately constant. These results suggest that responding is controlled by interreinforcement time and is not influenced by the number of responses emitted between reinforcements. PMID:16811313

  19. A minimax technique for time-domain design of preset digital equalizers using linear programming

    NASA Technical Reports Server (NTRS)

    Vaughn, G. L.; Houts, R. C.

    1975-01-01

    A linear programming technique is presented for the design of a preset finite-impulse response (FIR) digital filter to equalize the intersymbol interference (ISI) present in a baseband channel with known impulse response. A minimax technique is used which minimizes the maximum absolute error between the actual received waveform and a specified raised-cosine waveform. Transversal and frequency-sampling FIR digital filters are compared as to the accuracy of the approximation, the resultant ISI and the transmitted energy required. The transversal designs typically have slightly better waveform accuracy for a given distortion; however, the frequency-sampling equalizer uses fewer multipliers and requires less transmitted energy. A restricted transversal design is shown to use the least number of multipliers at the cost of a significant increase in energy and loss of waveform accuracy at the receiver.

  20. Whole person-evoked fMRI activity patterns in human fusiform gyrus are accurately modeled by a linear combination of face- and body-evoked activity patterns

    PubMed Central

    Kaiser, Daniel; Strnad, Lukas; Seidl, Katharina N.; Kastner, Sabine

    2013-01-01

    Visual cues from the face and the body provide information about another's identity, emotional state, and intentions. Previous neuroimaging studies that investigated neural responses to (bodiless) faces and (headless) bodies have reported overlapping face- and body-selective brain regions in right fusiform gyrus (FG). In daily life, however, faces and bodies are typically perceived together and are effortlessly integrated into the percept of a whole person, raising the possibility that neural responses to whole persons are qualitatively different than responses to isolated faces and bodies. The present study used fMRI to examine how FG activity in response to a whole person relates to activity in response to the same face and body but presented in isolation. Using multivoxel pattern analysis, we modeled person-evoked response patterns in right FG through a linear combination of face- and body-evoked response patterns. We found that these synthetic patterns were able to accurately approximate the response patterns to whole persons, with face and body patterns each adding unique information to the response patterns evoked by whole person stimuli. These results suggest that whole person responses in FG primarily arise from the coactivation of independent face- and body-selective neural populations. PMID:24108794

  1. Three-dimensional organization of otolith-ocular reflexes in rhesus monkeys. III. Responses To translation

    NASA Technical Reports Server (NTRS)

    Angelaki, D. E.

    1998-01-01

    The three-dimensional (3-D) properties of the translational vestibulo-ocular reflexes (translational VORs) during lateral and fore-aft oscillations in complete darkness were studied in rhesus monkeys at frequencies between 0.16 and 25 Hz. In addition, constant velocity off-vertical axis rotations extended the frequency range to 0.02 Hz. During lateral motion, horizontal responses were in phase with linear velocity in the frequency range of 2-10 Hz. At both lower and higher frequencies, phase lags were introduced. Torsional response phase changed more than 180 degrees in the tested frequency range such that torsional eye movements, which could be regarded as compensatory to "an apparent roll tilt" at the lowest frequencies, became anticompensatory at all frequencies above approximately 1 Hz. These results suggest two functionally different frequency bandwidths for the translational VORs. In the low-frequency spectrum (<<0.5 Hz), horizontal responses compensatory to translation are small and high-pass-filtered whereas torsional response sensitivity is relatively frequency independent. At higher frequencies however, both horizontal and torsional response sensitivity and phase exhibit a similar frequency dependence, suggesting a common role during head translation. During up-down motion, vertical responses were in phase with translational velocity at 3-5 Hz but phase leads progressively increased for lower frequencies (>90 degrees at frequencies <0.2 Hz). No consistent dependence on static head orientation was observed for the vertical response components during up-down motion and the horizontal and torsional response components during lateral translation. The frequency response characteristics of the translational VORs were fitted by "periphery/brain stem" functions that related the linear acceleration input, transduced by primary otolith afferents, to the velocity signals providing the input to the velocity-to-position neural integrator and the oculomotor plant. The lowest-order, best-fit periphery/brain stem model that approximated the frequency dependence of the data consisted of a second order transfer function with two alternating poles (at 0.4 and 7.2 Hz) and zeros (at 0.035 and 3.4 Hz). In addition to clearly differentiator dynamics at low frequencies (less than approximately 0.5 Hz), there was no frequency bandwidth where the periphery/brain stem function could be approximated by an integrator, as previously suggested. In this scheme, the oculomotor plant dynamics are assumed to perform the necessary high-frequency integration as required by the reflex. The detailed frequency dependence of the data could only be precisely described by higher order functions with nonminimum phase characteristics that preclude simple filtering of afferent inputs and might be suggestive of distributed spatiotemporal processing of otolith signals in the translational VORs.

  2. Ab initio calculations of the elastic and thermodynamic properties of gold under pressure

    NASA Astrophysics Data System (ADS)

    Smirnov, N. A.

    2017-03-01

    The paper presents first-principles FP-LMTO calculations on the relative stability of fcc, bcc, hcp and dhcp gold under pressure. They were done in local density approximation (LDA), as well as in generalized gradient approximation (GGA) with and without spin-orbit interaction. Phonon spectra for the considered gold structures were obtained from LDA calculations within linear response theory and the contribution of lattice vibrations to the free energy of the system was determined in quasiharmonic approximation. Our thorough adjustment of FP-LMTO internal parameters (linearization and tail energies, the MT-sphere radius) helped us to obtain results that agree well with the available experimental phase relation Dubrovinsky et al (2007 Phys. Rev. Lett. 98 045503) between fcc and hcp structures of gold under pressure. The calculations suggest that gold compressed at room temperature successively undergoes the following structural changes: fcc\\to hcp\\to bcc . The paper also presents the calculated elastic constants of fcc, bcc and hcp Au, the principal Hugoniot and the melting curve. Calculated results were used to construct the PT-diagram which describes the relative stability of the gold structures under study up to 500 GPa.

  3. Ab initio calculations of the elastic and thermodynamic properties of gold under pressure.

    PubMed

    Smirnov, N A

    2017-03-15

    The paper presents first-principles FP-LMTO calculations on the relative stability of fcc, bcc, hcp and dhcp gold under pressure. They were done in local density approximation (LDA), as well as in generalized gradient approximation (GGA) with and without spin-orbit interaction. Phonon spectra for the considered gold structures were obtained from LDA calculations within linear response theory and the contribution of lattice vibrations to the free energy of the system was determined in quasiharmonic approximation. Our thorough adjustment of FP-LMTO internal parameters (linearization and tail energies, the MT-sphere radius) helped us to obtain results that agree well with the available experimental phase relation Dubrovinsky et al (2007 Phys. Rev. Lett. 98 045503) between fcc and hcp structures of gold under pressure. The calculations suggest that gold compressed at room temperature successively undergoes the following structural changes: [Formula: see text]. The paper also presents the calculated elastic constants of fcc, bcc and hcp Au, the principal Hugoniot and the melting curve. Calculated results were used to construct the PT-diagram which describes the relative stability of the gold structures under study up to 500 GPa.

  4. CONTRIBUTIONS TO RATIONAL APPROXIMATION,

    DTIC Science & Technology

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

  5. Photons in dense nuclear matter: Random-phase approximation

    NASA Astrophysics Data System (ADS)

    Stetina, Stephan; Rrapaj, Ermal; Reddy, Sanjay

    2018-04-01

    We present a comprehensive and pedagogic discussion of the properties of photons in cold and dense nuclear matter based on the resummed one-loop photon self-energy. Correlations among electrons, muons, protons, and neutrons in β equilibrium that arise as a result of electromagnetic and strong interactions are consistently taken into account within the random phase approximation. Screening effects, damping, and collective excitations are systematically studied in a fully relativistic setup. Our study is relevant to the linear response theory of dense nuclear matter, calculations of transport properties of cold dense matter, and investigations of the production and propagation of hypothetical vector bosons such as the dark photons.

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

    PubMed

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

    2015-11-28

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

  7. Reduced basis technique for evaluating the sensitivity coefficients of the nonlinear tire response

    NASA Technical Reports Server (NTRS)

    Noor, Ahmed K.; Tanner, John A.; Peters, Jeanne M.

    1992-01-01

    An efficient reduced-basis technique is proposed for calculating the sensitivity of nonlinear tire response to variations in the design variables. The tire is modeled using a 2-D, moderate rotation, laminated anisotropic shell theory, including the effects of variation in material and geometric parameters. The vector of structural response and its first-order and second-order sensitivity coefficients are each expressed as a linear combination of a small number of basis vectors. The effectiveness of the basis vectors used in approximating the sensitivity coefficients is demonstrated by a numerical example involving the Space Shuttle nose-gear tire, which is subjected to uniform inflation pressure.

  8. Response Functions for Neutron Skyshine Analyses

    NASA Astrophysics Data System (ADS)

    Gui, Ah Auu

    Neutron and associated secondary photon line-beam response functions (LBRFs) for point monodirectional neutron sources and related conical line-beam response functions (CBRFs) for azimuthally symmetric neutron sources are generated using the MCNP Monte Carlo code for use in neutron skyshine analyses employing the internal line-beam and integral conical-beam methods. The LBRFs are evaluated at 14 neutron source energies ranging from 0.01 to 14 MeV and at 18 emission angles from 1 to 170 degrees. The CBRFs are evaluated at 13 neutron source energies in the same energy range and at 13 source polar angles (1 to 89 degrees). The response functions are approximated by a three parameter formula that is continuous in source energy and angle using a double linear interpolation scheme. These response function approximations are available for a source-to-detector range up to 2450 m and for the first time, give dose equivalent responses which are required for modern radiological assessments. For the CBRF, ground correction factors for neutrons and photons are calculated and approximated by empirical formulas for use in air-over-ground neutron skyshine problems with azimuthal symmetry. In addition, a simple correction procedure for humidity effects on the neutron skyshine dose is also proposed. The approximate LBRFs are used with the integral line-beam method to analyze four neutron skyshine problems with simple geometries: (1) an open silo, (2) an infinite wall, (3) a roofless rectangular building, and (4) an infinite air medium. In addition, two simple neutron skyshine problems involving an open source silo are analyzed using the integral conical-beam method. The results obtained using the LBRFs and the CBRFs are then compared with MCNP results and results of previous studies.

  9. Methods And System Suppressing Clutter In A Gain-Block, Radar-Responsive Tag System

    DOEpatents

    Ormesher, Richard C.; Axline, Robert M.

    2006-04-18

    Methods and systems reduce clutter interference in a radar-responsive tag system. A radar transmits a series of linear-frequency-modulated pulses and receives echo pulses from nearby terrain and from radar-responsive tags that may be in the imaged scene. Tags in the vicinity of the radar are activated by the radar's pulses. The tags receive and remodulate the radar pulses. Tag processing reverses the direction, in time, of the received waveform's linear frequency modulation. The tag retransmits the remodulated pulses. The radar uses a reversed-chirp de-ramp pulse to process the tag's echo. The invention applies to radar systems compatible with coherent gain-block tags. The invention provides a marked reduction in the strength of residual clutter echoes on each and every echo pulse received by the radar. SAR receiver processing effectively whitens passive-clutter signatures across the range dimension. Clutter suppression of approximately 14 dB is achievable for a typical radar system.

  10. An efficient approach to ARMA modeling of biological systems with multiple inputs and delays

    NASA Technical Reports Server (NTRS)

    Perrott, M. H.; Cohen, R. J.

    1996-01-01

    This paper presents a new approach to AutoRegressive Moving Average (ARMA or ARX) modeling which automatically seeks the best model order to represent investigated linear, time invariant systems using their input/output data. The algorithm seeks the ARMA parameterization which accounts for variability in the output of the system due to input activity and contains the fewest number of parameters required to do so. The unique characteristics of the proposed system identification algorithm are its simplicity and efficiency in handling systems with delays and multiple inputs. We present results of applying the algorithm to simulated data and experimental biological data In addition, a technique for assessing the error associated with the impulse responses calculated from estimated ARMA parameterizations is presented. The mapping from ARMA coefficients to impulse response estimates is nonlinear, which complicates any effort to construct confidence bounds for the obtained impulse responses. Here a method for obtaining a linearization of this mapping is derived, which leads to a simple procedure to approximate the confidence bounds.

  11. Transition properties from the Hermitian formulation of the coupled cluster polarization propagator

    NASA Astrophysics Data System (ADS)

    Tucholska, Aleksandra M.; Modrzejewski, Marcin; Moszynski, Robert

    2014-09-01

    Theory of one-electron transition density matrices has been formulated within the time-independent coupled cluster method for the polarization propagator [R. Moszynski, P. S. Żuchowski, and B. Jeziorski, Coll. Czech. Chem. Commun. 70, 1109 (2005)]. Working expressions have been obtained and implemented with the coupled cluster method limited to single, double, and linear triple excitations (CC3). Selected dipole and quadrupole transition probabilities of the alkali earth atoms, computed with the new transition density matrices are compared to the experimental data. Good agreement between theory and experiment is found. The results obtained with the new approach are of the same quality as the results obtained with the linear response coupled cluster theory. The one-electron density matrices for the ground state in the CC3 approximation have also been implemented. The dipole moments for a few representative diatomic molecules have been computed with several variants of the new approach, and the results are discussed to choose the approximation with the best balance between the accuracy and computational efficiency.

  12. On conforming mixed finite element methods for incompressible viscous flow problems

    NASA Technical Reports Server (NTRS)

    Gunzburger, M. D; Nicolaides, R. A.; Peterson, J. S.

    1982-01-01

    The application of conforming mixed finite element methods to obtain approximate solutions of linearized Navier-Stokes equations is examined. Attention is given to the convergence rates of various finite element approximations of the pressure and the velocity field. The optimality of the convergence rates are addressed in terms of comparisons of the approximation convergence to a smooth solution in relation to the best approximation available for the finite element space used. Consideration is also devoted to techniques for efficient use of a Gaussian elimination algorithm to obtain a solution to a system of linear algebraic equations derived by finite element discretizations of linear partial differential equations.

  13. 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.

  14. A Reduced Dimension Static, Linearized Kalman Filter and Smoother

    NASA Technical Reports Server (NTRS)

    Fukumori, I.

    1995-01-01

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

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

    DOE PAGES

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

    2015-02-25

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

  16. The Shock and Vibration Bulletin. Part 3. Shock Testing, Shock Analysis

    DTIC Science & Technology

    1974-08-01

    APPROXIMATE TRANSFORMATION C.S. O’Hearne and J.W. Shipley, Martin Marietta Aerospace, Orlando, Florida LINEAR LUMPED-MASS MODELING TECHNIQUES FOR BLAST LOADED...Leppert, B.K. Wada, Jet Propulsion Laboratory, Pasadena, California, and R. Miyakawa, Martin - Marietta Aerospace, Denver, Colorado (assigned to the Jet...Wilmington, Delaware Vibration Testing and Analysis DEVELOPMENT OF SAM-D MISSILE RANDOM VIBRATION RESPONSE LOADS P.G. Hahn, Martin Marietta Aerospace

  17. Prospects of second generation artificial intelligence tools in calibration of chemical sensors.

    PubMed

    Braibanti, Antonio; Rao, Rupenaguntla Sambasiva; Ramam, Veluri Anantha; Rao, Gollapalli Nageswara; Rao, Vaddadi Venkata Panakala

    2005-05-01

    Multivariate data driven calibration models with neural networks (NNs) are developed for binary (Cu++ and Ca++) and quaternary (K+, Ca++, NO3- and Cl-) ion-selective electrode (ISE) data. The response profiles of ISEs with concentrations are non-linear and sub-Nernstian. This task represents function approximation of multi-variate, multi-response, correlated, non-linear data with unknown noise structure i.e. multi-component calibration/prediction in chemometric parlance. Radial distribution function (RBF) and Fuzzy-ARTMAP-NN models implemented in the software packages, TRAJAN and Professional II, are employed for the calibration. The optimum NN models reported are based on residuals in concentration space. Being a data driven information technology, NN does not require a model, prior- or posterior- distribution of data or noise structure. Missing information, spikes or newer trends in different concentration ranges can be modeled through novelty detection. Two simulated data sets generated from mathematical functions are modeled as a function of number of data points and network parameters like number of neurons and nearest neighbors. The success of RBF and Fuzzy-ARTMAP-NNs to develop adequate calibration models for experimental data and function approximation models for more complex simulated data sets ensures AI2 (artificial intelligence, 2nd generation) as a promising technology in quantitation.

  18. Nonlocal continuum analysis of a nonlinear uniaxial elastic lattice system under non-uniform axial load

    NASA Astrophysics Data System (ADS)

    Hérisson, Benjamin; Challamel, Noël; Picandet, Vincent; Perrot, Arnaud

    2016-09-01

    The static behavior of the Fermi-Pasta-Ulam (FPU) axial chain under distributed loading is examined. The FPU system examined in the paper is a nonlinear elastic lattice with linear and quadratic spring interaction. A dimensionless parameter controls the possible loss of convexity of the associated quadratic and cubic energy. Exact analytical solutions based on Hurwitz zeta functions are developed in presence of linear static loading. It is shown that this nonlinear lattice possesses scale effects and possible localization properties in the absence of energy convexity. A continuous approach is then developed to capture the main phenomena observed regarding the discrete axial problem. The associated continuum is built from a continualization procedure that is mainly based on the asymptotic expansion of the difference operators involved in the lattice problem. This associated continuum is an enriched gradient-based or nonlocal axial medium. A Taylor-based and a rational differential method are both considered in the continualization procedures to approximate the FPU lattice response. The Padé approximant used in the continualization procedure fits the response of the discrete system efficiently, even in the vicinity of the limit load when the non-convex FPU energy is examined. It is concluded that the FPU lattice system behaves as a nonlocal axial system in dynamic but also static loading.

  19. Intensity of hydrostimulation for the induction of root hydrotropism and its sensing by the root cap

    NASA Technical Reports Server (NTRS)

    Takahashi, H.; Scott, T. K.

    1993-01-01

    Roots of Pisum sativum L. and Zea mays L. were exposed to different moisture gradients established by placing both wet cheesecloth (hydrostimulant) and saturated aqueous solutions of various salts in a closed chamber. Atmospheric conditions with different relative humidity (RH) in a range between 98 and 86% RH were obtained at root level, 2 to 3mm from the water-saturated hydrostimulant. Roots of Silver Queen corn placed vertically with the tips down curved sideways toward the hydrostimulant in response to approximately 94% RH but did not respond positively to RH higher than approximately 95%. The positive hydrotropic response increased linearly as RH was lowered from 95 to 90%. A maximum response was observed at RH between 90 and 86%. However, RH required for the induction of hydrotropism as well as the responsiveness differed among plant species used; gravitropically sensitive roots appeared to require a somewhat greater moisture gradient for the induction of hydrotropism. Decapped roots of corn failed to curve hydrotropically, suggesting the root cap as a major site of hydrosensing.

  20. Consistency between hydrological models and field observations: Linking processes at the hillslope scale to hydrological responses at the watershed scale

    USGS Publications Warehouse

    Clark, M.P.; Rupp, D.E.; Woods, R.A.; Tromp-van, Meerveld; Peters, N.E.; Freer, J.E.

    2009-01-01

    The purpose of this paper is to identify simple connections between observations of hydrological processes at the hillslope scale and observations of the response of watersheds following rainfall, with a view to building a parsimonious model of catchment processes. The focus is on the well-studied Panola Mountain Research Watershed (PMRW), Georgia, USA. Recession analysis of discharge Q shows that while the relationship between dQ/dt and Q is approximately consistent with a linear reservoir for the hillslope, there is a deviation from linearity that becomes progressively larger with increasing spatial scale. To account for these scale differences conceptual models of streamflow recession are defined at both the hillslope scale and the watershed scale, and an assessment made as to whether models at the hillslope scale can be aggregated to be consistent with models at the watershed scale. Results from this study show that a model with parallel linear reservoirs provides the most plausible explanation (of those tested) for both the linear hillslope response to rainfall and non-linear recession behaviour observed at the watershed outlet. In this model each linear reservoir is associated with a landscape type. The parallel reservoir model is consistent with both geochemical analyses of hydrological flow paths and water balance estimates of bedrock recharge. Overall, this study demonstrates that standard approaches of using recession analysis to identify the functional form of storage-discharge relationships identify model structures that are inconsistent with field evidence, and that recession analysis at multiple spatial scales can provide useful insights into catchment behaviour. Copyright ?? 2008 John Wiley & Sons, Ltd.

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

    Dechant, Lawrence J.

    Wave packet analysis provides a connection between linear small disturbance theory and subsequent nonlinear turbulent spot flow behavior. The traditional association between linear stability analysis and nonlinear wave form is developed via the method of stationary phase whereby asymptotic (simplified) mean flow solutions are used to estimate dispersion behavior and stationary phase approximation are used to invert the associated Fourier transform. The resulting process typically requires nonlinear algebraic equations inversions that can be best performed numerically, which partially mitigates the value of the approximation as compared to a more complete, e.g. DNS or linear/nonlinear adjoint methods. To obtain a simpler,more » closed-form analytical result, the complete packet solution is modeled via approximate amplitude (linear convected kinematic wave initial value problem) and local sinusoidal (wave equation) expressions. Significantly, the initial value for the kinematic wave transport expression follows from a separable variable coefficient approximation to the linearized pressure fluctuation Poisson expression. The resulting amplitude solution, while approximate in nature, nonetheless, appears to mimic many of the global features, e.g. transitional flow intermittency and pressure fluctuation magnitude behavior. A low wave number wave packet models also recover meaningful auto-correlation and low frequency spectral behaviors.« less

  2. Effect of Initial Stress on the Dynamic Response of a Multi-Layered Plate-Strip Subjected to an Arbitrary Inclined Time-Harmonic Force

    NASA Astrophysics Data System (ADS)

    Daşdemir, A.

    2017-08-01

    The forced vibration of a multi-layered plate-strip with initial stress under the action of an arbitrary inclined time-harmonic force resting on a rigid foundation is considered. Within the framework of the piecewise homogeneous body model with the use of the three-dimensional linearized theory of elastic waves in initially stressed bodies (TLTEWISB), a mathematical modelling is presented in plane strain state. It is assumed that there exists the complete contact interaction at the interface between the layers and the materials of the layer are linearly elastic, homogeneous and isotropic. The governing system of the partial differential equations of motion for the considered problem is solved approximately by employing the Finite Element Method (FEM). Further, the influence of the initial stress parameter on the dynamic response of the plate-strip is presented.

  3. Oscillator strengths, first-order properties, and nuclear gradients for local ADC(2).

    PubMed

    Schütz, Martin

    2015-06-07

    We describe theory and implementation of oscillator strengths, orbital-relaxed first-order properties, and nuclear gradients for the local algebraic diagrammatic construction scheme through second order. The formalism is derived via time-dependent linear response theory based on a second-order unitary coupled cluster model. The implementation presented here is a modification of our previously developed algorithms for Laplace transform based local time-dependent coupled cluster linear response (CC2LR); the local approximations thus are state specific and adaptive. The symmetry of the Jacobian leads to considerable simplifications relative to the local CC2LR method; as a result, a gradient evaluation is about four times less expensive. Test calculations show that in geometry optimizations, usually very similar geometries are obtained as with the local CC2LR method (provided that a second-order method is applicable). As an exemplary application, we performed geometry optimizations on the low-lying singlet states of chlorophyllide a.

  4. Fields of an ultrashort tightly focused radially polarized laser pulse in a linear response plasma

    NASA Astrophysics Data System (ADS)

    Salamin, Yousef I.

    2017-10-01

    Analytical expressions for the fields of a radially polarized, ultrashort, and tightly focused laser pulse propagating in a linear-response plasma are derived and discussed. The fields are obtained from solving the inhomogeneous wave equations for the vector and scalar potentials, linked by the Lorenz gauge, in a plasma background. First, the scalar potential is eliminated using the gauge condition, then the vector potential is synthesized from Fourier components of an initial uniform distribution of wavenumbers, and the inverse Fourier transformation is carried out term-by-term in a truncated series (finite sum). The zeroth-order term in, for example, the axial electric field component is shown to model a pulse much better than its widely used paraxial approximation counterpart. Some of the propagation characteristics of the fields are discussed and all fields are shown to have manifested the expected limits for propagation in a vacuum.

  5. Combining global and local approximations

    NASA Technical Reports Server (NTRS)

    Haftka, Raphael T.

    1991-01-01

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

  6. The scotopic threshold response of the dark-adapted electroretinogram of the mouse.

    PubMed

    Saszik, Shannon M; Robson, John G; Frishman, Laura J

    2002-09-15

    The most sensitive response in the dark-adapted electroretinogram (ERG), the scotopic threshold response (STR) which originates from the proximal retina, has been identified in several mammals including humans, but previously not in the mouse. The current study established the presence and assessed the nature of the mouse STR. ERGs were recorded from adult wild-type C57/BL6 mice anaesthetized with ketamine (70 mg kg(-1)) and xylazine (7 mg kg(-1)). Recordings were between DTL fibres placed under contact lenses on the two eyes. Monocular test stimuli were brief flashes (lambda(max) 462 nm; -6.1 to +1.8 log scotopic Troland seconds(sc td s)) under fully dark-adapted conditions and in the presence of steady adapting backgrounds (-3.2 to -1.7 log sc td). For the weakest test stimuli, ERGs consisted of a slow negative potential maximal approximately 200 ms after the flash, with a small positive potential preceding it. The negative wave resembled the STR of other species. As intensity was increased, the negative potential saturated but the positive potential (maximal approximately 110 ms) continued to grow as the b-wave. For stimuli that saturated the b-wave, the a-wave emerged. For stimulus strengths up to those at which the a-wave emerged, ERG amplitudes measured at fixed times after the flash (110 and 200 ms) were fitted with a model assuming an initially linear rise of response amplitude with intensity, followed by saturation of five components of declining sensitivity: a negative STR (nSTR), a positive STR (pSTR), a positive scotopic response (pSR), PII (the bipolar cell component) and PIII (the photoreceptor component). The nSTR and pSTR were approximately 3 times more sensitive than the pSR, which was approximately 7 times more sensitive than PII. The sensitive positive components dominated the b-wave up to > 5 % of its saturated amplitude. Pharmacological agents that suppress proximal retinal activity (e.g. GABA) minimized the pSTR, nSTR and pSR, essentially isolating PII which rose linearly with intensity before showing hyperbolic saturation. The nSTR, pSTR and pSR were desensitized by weaker backgrounds than those desensitizing PII. In conclusion, ERG components of proximal retinal origin that are more sensitive to test flashes and adapting backgrounds than PII provide the 'threshold' negative and positive (b-wave) responses of the mouse dark-adapted ERG. These results support the use of the mouse ERG in studies of proximal retinal function.

  7. Converting conformational changes to electrostatic energy in molecular motors: The energetics of ATP synthase.

    PubMed

    Strajbl, Marek; Shurki, Avital; Warshel, Arieh

    2003-12-09

    F1-ATPase is the catalytic component of the ATP synthase molecular machine responsible for most of the uphill synthesis of ATP in living systems. The enormous advances in biochemical and structural studies of this machine provide an opportunity for detailed understanding of the nature of its rotary mechanism. However, further quantitative progress in this direction requires development of reliable ways of translating the observed structural changes to the corresponding energies. This requirement is particularly challenging because we are dealing with a large system that couples major structural changes with a chemical process. The present work provides such a structure-function correlation by using the linear response approximation to describe the rotary mechanism. This approach allows one to evaluate the energy of transitions between different conformational states by considering only the changes in the corresponding electrostatic energies of the ligands. The relevant energetics are also obtained by calculating the linear response approximation-based free energies of transferring the ligands from water to the different sites of F1-ATPase in their different conformational states. We also use the empirical valence bond approach to evaluate the actual free-energy profile for the ATP synthesis in the different conformational states of the system. Integrating the information from the different approaches provides a semiquantitative structure-function correlation for F1-ATPase. It is found that the conformational changes are converted to changes in the electrostatic interaction between the protein and its ligands, which drives the ATP synthesis.

  8. Mechanical Characterization of Hybrid Vesicles Based on Linear Poly(Dimethylsiloxane-b-Ethylene Oxide) and Poly(Butadiene-b-Ethylene Oxide) Block Copolymers

    PubMed Central

    Gaspard, Jeffery; Casey, Liam M.; Rozin, Matt; Munoz-Pinto, Dany J.; Silas, James A.; Hahn, Mariah S.

    2016-01-01

    Poly(dimethylsiloxane-ethylene oxide) (PDMS-PEO) and poly(butadiene-b-ethylene oxide) (PBd-PEO) are two block copolymers which separately form vesicles with disparate membrane permeabilities and fluidities. Thus, hybrid vesicles formed from both PDMS-PEO and PBd-PEO may ultimately allow for systematic, application-specific tuning of vesicle membrane fluidity and permeability. However, given the relatively low strength previously noted for comb-type PDMS-PEO vesicles, the mechanical robustness of the resulting hybrid vesicles must first be confirmed. Toward this end, we have characterized the mechanical behavior of vesicles formed from mixtures of linear PDMS-PEO and linear PBd-PEO using micropipette aspiration. Tension versus strain plots of pure PDMS12-PEO46 vesicles revealed a non-linear response in the high tension regime, in contrast to the approximately linear response of pure PBd33-PEO20 vesicles. Remarkably, the area expansion modulus, critical tension, and cohesive energy density of PDMS12-PEO46 vesicles were each significantly greater than for PBd33-PEO20 vesicles, although critical strain was not significantly different between these vesicle types. PDMS12-PEO46/PBd33-PEO20 hybrid vesicles generally displayed graded responses in between that of the pure component vesicles. Thus, the PDMS12-PEO46/PBd33-PEO20 hybrid vesicles retained or exceeded the strength and toughness characteristic of pure PBd-PEO vesicles, indicating that future assessment of the membrane permeability and fluidity of these hybrid vesicles may be warranted. PMID:26999148

  9. Multireference Density Functional Theory with Generalized Auxiliary Systems for Ground and Excited States.

    PubMed

    Chen, Zehua; Zhang, Du; Jin, Ye; Yang, Yang; Su, Neil Qiang; Yang, Weitao

    2017-09-21

    To describe static correlation, we develop a new approach to density functional theory (DFT), which uses a generalized auxiliary system that is of a different symmetry, such as particle number or spin, from that of the physical system. The total energy of the physical system consists of two parts: the energy of the auxiliary system, which is determined with a chosen density functional approximation (DFA), and the excitation energy from an approximate linear response theory that restores the symmetry to that of the physical system, thus rigorously leading to a multideterminant description of the physical system. The electron density of the physical system is different from that of the auxiliary system and is uniquely determined from the functional derivative of the total energy with respect to the external potential. Our energy functional is thus an implicit functional of the physical system density, but an explicit functional of the auxiliary system density. We show that the total energy minimum and stationary states, describing the ground and excited states of the physical system, can be obtained by a self-consistent optimization with respect to the explicit variable, the generalized Kohn-Sham noninteracting density matrix. We have developed the generalized optimized effective potential method for the self-consistent optimization. Among options of the auxiliary system and the associated linear response theory, reformulated versions of the particle-particle random phase approximation (pp-RPA) and the spin-flip time-dependent density functional theory (SF-TDDFT) are selected for illustration of principle. Numerical results show that our multireference DFT successfully describes static correlation in bond dissociation and double bond rotation.

  10. Semigroup theory and numerical approximation for equations in linear viscoelasticity

    NASA Technical Reports Server (NTRS)

    Fabiano, R. H.; Ito, K.

    1990-01-01

    A class of abstract integrodifferential equations used to model linear viscoelastic beams is investigated analytically, applying a Hilbert-space approach. The basic equation is rewritten as a Cauchy problem, and its well-posedness is demonstrated. Finite-dimensional subspaces of the state space and an estimate of the state operator are obtained; approximation schemes for the equations are constructed; and the convergence is proved using the Trotter-Kato theorem of linear semigroup theory. The actual convergence behavior of different approximations is demonstrated in numerical computations, and the results are presented in tables.

  11. Straightening Beta: Overdispersion of Lethal Chromosome Aberrations following Radiotherapeutic Doses Leads to Terminal Linearity in the Alpha–Beta Model

    PubMed Central

    Shuryak, Igor; Loucas, Bradford D.; Cornforth, Michael N.

    2017-01-01

    Recent technological advances allow precise radiation delivery to tumor targets. As opposed to more conventional radiotherapy—where multiple small fractions are given—in some cases, the preferred course of treatment may involve only a few (or even one) large dose(s) per fraction. Under these conditions, the choice of appropriate radiobiological model complicates the tasks of predicting radiotherapy outcomes and designing new treatment regimens. The most commonly used model for this purpose is the venerable linear-quadratic (LQ) formalism as it applies to cell survival. However, predictions based on the LQ model are frequently at odds with data following very high acute doses. In particular, although the LQ predicts a continuously bending dose–response relationship for the logarithm of cell survival, empirical evidence over the high-dose region suggests that the survival response is instead log-linear with dose. Here, we show that the distribution of lethal chromosomal lesions among individual human cells (lymphocytes and fibroblasts) exposed to gamma rays and X rays is somewhat overdispersed, compared with the Poisson distribution. Further, we show that such overdispersion affects the predicted dose response for cell survival (the fraction of cells with zero lethal lesions). This causes the dose response to approximate log-linear behavior at high doses, even when the mean number of lethal lesions per cell is well fitted by the continuously curving LQ model. Accounting for overdispersion of lethal lesions provides a novel, mechanistically based explanation for the observed shapes of cell survival dose responses that, in principle, may offer a tractable and clinically useful approach for modeling the effects of high doses per fraction. PMID:29312888

  12. THE DISTRIBUTION OF COOK’S D STATISTIC

    PubMed Central

    Muller, Keith E.; Mok, Mario Chen

    2013-01-01

    Cook (1977) proposed a diagnostic to quantify the impact of deleting an observation on the estimated regression coefficients of a General Linear Univariate Model (GLUM). Simulations of models with Gaussian response and predictors demonstrate that his suggestion of comparing the diagnostic to the median of the F for overall regression captures an erratically varying proportion of the values. We describe the exact distribution of Cook’s statistic for a GLUM with Gaussian predictors and response. We also present computational forms, simple approximations, and asymptotic results. A simulation supports the accuracy of the results. The methods allow accurate evaluation of a single value or the maximum value from a regression analysis. The approximations work well for a single value, but less well for the maximum. In contrast, the cut-point suggested by Cook provides widely varying tail probabilities. As with all diagnostics, the data analyst must use scientific judgment in deciding how to treat highlighted observations. PMID:24363487

  13. Using nonlinear forecasting to learn the magnitude and phasing of time-varying sediment suspension in the surf zone

    USGS Publications Warehouse

    Jaffe, B.E.; Rubin, D.M.

    1996-01-01

    The time-dependent response of sediment suspension to flow velocity was explored by modeling field measurements collected in the surf zone during a large storm. Linear and nonlinear models were created and tested using flow velocity as input and suspended-sediment concentration as output. A sequence of past velocities (velocity history), as well as velocity from the same instant as the suspended-sediment concentration, was used as input; this velocity history length was allowed to vary. The models also allowed for a lag between input (instantaneous velocity or end of velocity sequence) and output (suspended-sediment concentration). Predictions of concentration from instantaneous velocity or instantaneous velocity raised to a power (up to 8) using linear models were poor (correlation coefficients between predicted and observed concentrations were less than 0.10). Allowing a lag between velocity and concentration improved linear models (correlation coefficient of 0.30), with optimum lag time increasing with elevation above the seabed (from 1.5 s at 13 cm to 8.5 s at 60 cm). These lags are largely due to the time for an observed flow event to effect the bed and mix sediment upward. Using a velocity history further improved linear models (correlation coefficient of 0.43). The best linear model used 12.5 s of velocity history (approximately one wave period) to predict concentration. Nonlinear models gave better predictions than linear models, and, as with linear models, nonlinear models using a velocity history performed better than models using only instantaneous velocity as input. Including a lag time between the velocity and concentration also improved the predictions. The best model (correlation coefficient of 0.58) used 3 s (approximately a quarter wave period) of the cross-shore velocity squared, starting at 4.5 s before the observed concentration, to predict concentration. Using a velocity history increases the performance of the models by specifying a more complete description of the dynamical forcing of the flow (including accelerations and wave phase and shape) responsible for sediment suspension. Incorporating such a velocity history and a lag time into the formulation of the forcing for time-dependent models for sediment suspension in the surf zone will greatly increase our ability to predict suspended-sediment transport.

  14. Granular metamaterials for vibration mitigation

    NASA Astrophysics Data System (ADS)

    Gantzounis, G.; Serra-Garcia, M.; Homma, K.; Mendoza, J. M.; Daraio, C.

    2013-09-01

    Acoustic metamaterials that allow low-frequency band gaps are interesting for many practical engineering applications, where vibration control and sound insulation are necessary. In most prior studies, the mechanical response of these structures has been described using linear continuum approximations. In this work, we experimentally and theoretically address the formation of low-frequency band gaps in locally resonant granular crystals, where the dynamics of the system is governed by discrete equations. We investigate the quasi-linear behavior of such structures. The analysis shows that a stopband can be introduced at about one octave lower frequency than in materials without local resonances. Broadband and multi-frequency stopband characteristics can also be achieved by strategically tailoring the non-uniform local resonance parameters.

  15. The role of relativity in the optical response of gold within the time-dependent current-density-functional theory.

    PubMed

    Romaniello, P; de Boeij, P L

    2005-04-22

    We included relativistic effects in the formulation of the time-dependent current-density-functional theory for the calculation of linear response properties of metals [P. Romaniello and P. L. de Boeij, Phys. Rev. B (to be published)]. We treat the dominant scalar-relativistic effects using the zeroth-order regular approximation in the ground-state density-functional theory calculations, as well as in the time-dependent response calculations. The results for the dielectric function of gold calculated in the spectral range of 0-10 eV are compared with experimental data reported in literature and recent ellipsometric measurements. As well known, relativistic effects strongly influence the color of gold. We find that the onset of interband transitions is shifted from around 3.5 eV, obtained in a nonrelativistic calculation, to around 1.9 eV when relativity is included. With the inclusion of the scalar-relativistic effects there is an overall improvement of both real and imaginary parts of the dielectric function over the nonrelativistic ones. Nevertheless some important features in the absorption spectrum are not well reproduced, but can be explained in terms of spin-orbit coupling effects. The remaining deviations are attributed to the underestimation of the interband gap (5d-6sp band gap) in the local-density approximation and to the use of the adiabatic local-density approximation in the response calculation.

  16. 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.

  17. Polynomial compensation, inversion, and approximation of discrete time linear systems

    NASA Technical Reports Server (NTRS)

    Baram, Yoram

    1987-01-01

    The least-squares transformation of a discrete-time multivariable linear system into a desired one by convolving the first with a polynomial system yields optimal polynomial solutions to the problems of system compensation, inversion, and approximation. The polynomial coefficients are obtained from the solution to a so-called normal linear matrix equation, whose coefficients are shown to be the weighting patterns of certain linear systems. These, in turn, can be used in the recursive solution of the normal equation.

  18. Linear Approximation to Optimal Control Allocation for Rocket Nozzles with Elliptical Constraints

    NASA Technical Reports Server (NTRS)

    Orr, Jeb S.; Wall, Johnm W.

    2011-01-01

    In this paper we present a straightforward technique for assessing and realizing the maximum control moment effectiveness for a launch vehicle with multiple constrained rocket nozzles, where elliptical deflection limits in gimbal axes are expressed as an ensemble of independent quadratic constraints. A direct method of determining an approximating ellipsoid that inscribes the set of attainable angular accelerations is derived. In the case of a parameterized linear generalized inverse, the geometry of the attainable set is computationally expensive to obtain but can be approximated to a high degree of accuracy with the proposed method. A linear inverse can then be optimized to maximize the volume of the true attainable set by maximizing the volume of the approximating ellipsoid. The use of a linear inverse does not preclude the use of linear methods for stability analysis and control design, preferred in practice for assessing the stability characteristics of the inertial and servoelastic coupling appearing in large boosters. The present techniques are demonstrated via application to the control allocation scheme for a concept heavy-lift launch vehicle.

  19. Resistance thermometer has linear resistance-temperature coefficient at low temperatures

    NASA Technical Reports Server (NTRS)

    Kuzyk, W.

    1966-01-01

    Resistance thermometer incorporating a germanium resistance element with a platinum resistance element in a wheatstone bridge circuit has a linear temperature-resistance coefficient over a range from approximately minus 140 deg C to approximately minus 253 deg C.

  20. Assessment of time-dependent density functional theory with the restricted excitation space approximation for excited state calculations of large systems

    NASA Astrophysics Data System (ADS)

    Hanson-Heine, Magnus W. D.; George, Michael W.; Besley, Nicholas A.

    2018-06-01

    The restricted excitation subspace approximation is explored as a basis to reduce the memory storage required in linear response time-dependent density functional theory (TDDFT) calculations within the Tamm-Dancoff approximation. It is shown that excluding the core orbitals and up to 70% of the virtual orbitals in the construction of the excitation subspace does not result in significant changes in computed UV/vis spectra for large molecules. The reduced size of the excitation subspace greatly reduces the size of the subspace vectors that need to be stored when using the Davidson procedure to determine the eigenvalues of the TDDFT equations. Furthermore, additional screening of the two-electron integrals in combination with a reduction in the size of the numerical integration grid used in the TDDFT calculation leads to significant computational savings. The use of these approximations represents a simple approach to extend TDDFT to the study of large systems and make the calculations increasingly tractable using modest computing resources.

  1. Predicting Statistical Response and Extreme Events in Uncertainty Quantification through Reduced-Order Models

    NASA Astrophysics Data System (ADS)

    Qi, D.; Majda, A.

    2017-12-01

    A low-dimensional reduced-order statistical closure model is developed for quantifying the uncertainty in statistical sensitivity and intermittency in principal model directions with largest variability in high-dimensional turbulent system and turbulent transport models. Imperfect model sensitivity is improved through a recent mathematical strategy for calibrating model errors in a training phase, where information theory and linear statistical response theory are combined in a systematic fashion to achieve the optimal model performance. The idea in the reduced-order method is from a self-consistent mathematical framework for general systems with quadratic nonlinearity, where crucial high-order statistics are approximated by a systematic model calibration procedure. Model efficiency is improved through additional damping and noise corrections to replace the expensive energy-conserving nonlinear interactions. Model errors due to the imperfect nonlinear approximation are corrected by tuning the model parameters using linear response theory with an information metric in a training phase before prediction. A statistical energy principle is adopted to introduce a global scaling factor in characterizing the higher-order moments in a consistent way to improve model sensitivity. Stringent models of barotropic and baroclinic turbulence are used to display the feasibility of the reduced-order methods. Principal statistical responses in mean and variance can be captured by the reduced-order models with accuracy and efficiency. Besides, the reduced-order models are also used to capture crucial passive tracer field that is advected by the baroclinic turbulent flow. It is demonstrated that crucial principal statistical quantities like the tracer spectrum and fat-tails in the tracer probability density functions in the most important large scales can be captured efficiently with accuracy using the reduced-order tracer model in various dynamical regimes of the flow field with distinct statistical structures.

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

    NASA Technical Reports Server (NTRS)

    Futamase, Toshifumi; Sasaki, Misao

    1989-01-01

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

  3. Estimation of ion competition via correlated responsivity offset in linear ion trap mass spectrometry analysis: theory and practical use in the analysis of cyanobacterial hepatotoxin microcystin-LR in extracts of food additives.

    PubMed

    Urban, Jan; Hrouzek, Pavel; Stys, Dalibor; Martens, Harald

    2013-01-01

    Responsivity is a conversion qualification of a measurement device given by the functional dependence between the input and output quantities. A concentration-response-dependent calibration curve represents the most simple experiment for the measurement of responsivity in mass spectrometry. The cyanobacterial hepatotoxin microcystin-LR content in complex biological matrices of food additives was chosen as a model example of a typical problem. The calibration curves for pure microcystin and its mixtures with extracts of green alga and fish meat were reconstructed from the series of measurement. A novel approach for the quantitative estimation of ion competition in ESI is proposed in this paper. We define the correlated responsivity offset in the intensity values using the approximation of minimal correlation given by the matrix to the target mass values of the analyte. The estimation of the matrix influence enables the approximation of the position of a priori unknown responsivity and was easily evaluated using a simple algorithm. The method itself is directly derived from the basic attributes of the theory of measurements. There is sufficient agreement between the theoretical and experimental values. However, some theoretical issues are discussed to avoid misinterpretations and excessive expectations.

  4. Estimation of Ion Competition via Correlated Responsivity Offset in Linear Ion Trap Mass Spectrometry Analysis: Theory and Practical Use in the Analysis of Cyanobacterial Hepatotoxin Microcystin-LR in Extracts of Food Additives

    PubMed Central

    Hrouzek, Pavel; Štys, Dalibor; Martens, Harald

    2013-01-01

    Responsivity is a conversion qualification of a measurement device given by the functional dependence between the input and output quantities. A concentration-response-dependent calibration curve represents the most simple experiment for the measurement of responsivity in mass spectrometry. The cyanobacterial hepatotoxin microcystin-LR content in complex biological matrices of food additives was chosen as a model example of a typical problem. The calibration curves for pure microcystin and its mixtures with extracts of green alga and fish meat were reconstructed from the series of measurement. A novel approach for the quantitative estimation of ion competition in ESI is proposed in this paper. We define the correlated responsivity offset in the intensity values using the approximation of minimal correlation given by the matrix to the target mass values of the analyte. The estimation of the matrix influence enables the approximation of the position of a priori unknown responsivity and was easily evaluated using a simple algorithm. The method itself is directly derived from the basic attributes of the theory of measurements. There is sufficient agreement between the theoretical and experimental values. However, some theoretical issues are discussed to avoid misinterpretations and excessive expectations. PMID:23586036

  5. GMX approximation for the linear E ⊗ ɛ Jahn-Teller effect

    NASA Astrophysics Data System (ADS)

    Mancini, Jay D.; Fessatidis, Vassilios; Bowen, Samuel P.

    2006-02-01

    A newly developed generalized moments expansion (GMX) based on the t-expansion of Horn and Weinstein is applied to a linear E ⊗ ɛ Jahn-Teller system. Comparisons are made with other moments schemes as well a coupled cluster approximation.

  6. Discontinuous functional for linear-response time-dependent density-functional theory: The exact-exchange kernel and approximate forms

    NASA Astrophysics Data System (ADS)

    Hellgren, Maria; Gross, E. K. U.

    2013-11-01

    We present a detailed study of the exact-exchange (EXX) kernel of time-dependent density-functional theory with an emphasis on its discontinuity at integer particle numbers. It was recently found that this exact property leads to sharp peaks and step features in the kernel that diverge in the dissociation limit of diatomic systems [Hellgren and Gross, Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.85.022514 85, 022514 (2012)]. To further analyze the discontinuity of the kernel, we here make use of two different approximations to the EXX kernel: the Petersilka Gossmann Gross (PGG) approximation and a common energy denominator approximation (CEDA). It is demonstrated that whereas the PGG approximation neglects the discontinuity, the CEDA includes it explicitly. By studying model molecular systems it is shown that the so-called field-counteracting effect in the density-functional description of molecular chains can be viewed in terms of the discontinuity of the static kernel. The role of the frequency dependence is also investigated, highlighting its importance for long-range charge-transfer excitations as well as inner-shell excitations.

  7. Stresses and deformations in cross-ply composite tubes subjected to a uniform temperature change: Elasticity and Approximate Solutions

    NASA Technical Reports Server (NTRS)

    Hyer, M. W.; Cooper, D. E.; Cohen, D.

    1985-01-01

    The effects of a uniform temperature change on the stresses and deformations of composite tubes are investigated. The accuracy of an approximate solution based on the principle of complementary virtual work is determined. Interest centers on tube response away from the ends and so a planar elasticity approach is used. For the approximate solution a piecewise linear variation of stresses with the radial coordinate is assumed. The results from the approximate solution are compared with the elasticity solution. The stress predictions agree well, particularly peak interlaminar stresses. Surprisingly, the axial deformations also agree well. This, despite the fact that the deformations predicted by the approximate solution do not satisfy the interface displacement continuity conditions required by the elasticity solution. The study shows that the axial thermal expansion coefficient of tubes with a specific number of axial and circumferential layers depends on the stacking sequence. This is in contrast to classical lamination theory which predicts the expansion to be independent of the stacking arrangement. As expected, the sign and magnitude of the peak interlaminar stresses depends on stacking sequence.

  8. Subharmonic response of a single-degree-of-freedom nonlinear vibro-impact system to a narrow-band random excitation.

    PubMed

    Haiwu, Rong; Wang, Xiangdong; Xu, Wei; Fang, Tong

    2009-08-01

    The subharmonic response of single-degree-of-freedom nonlinear vibro-impact oscillator with a one-sided barrier to narrow-band random excitation is investigated. The narrow-band random excitation used here is a filtered Gaussian white noise. The analysis is based on a special Zhuravlev transformation, which reduces the system to one without impacts, or velocity jumps, thereby permitting the applications of asymptotic averaging over the "fast" variables. The averaged stochastic equations are solved exactly by the method of moments for the mean-square response amplitude for the case of linear system with zero offset. A perturbation-based moment closure scheme is proposed and the formula of the mean-square amplitude is obtained approximately for the case of linear system with nonzero offset. The perturbation-based moment closure scheme is used once again to obtain the algebra equation of the mean-square amplitude of the response for the case of nonlinear system. The effects of damping, detuning, nonlinear intensity, bandwidth, and magnitudes of random excitations are analyzed. The theoretical analyses are verified by numerical results. Theoretical analyses and numerical simulations show that the peak amplitudes may be strongly reduced at large detunings or large nonlinear intensity.

  9. Quantifying non-linear dynamics of mass-springs in series oscillators via asymptotic approach

    NASA Astrophysics Data System (ADS)

    Starosta, Roman; Sypniewska-Kamińska, Grażyna; Awrejcewicz, Jan

    2017-05-01

    Dynamical regular response of an oscillator with two serially connected springs with nonlinear characteristics of cubic type and governed by a set of differential-algebraic equations (DAEs) is studied. The classical approach of the multiple scales method (MSM) in time domain has been employed and appropriately modified to solve the governing DAEs of two systems, i.e. with one- and two degrees-of-freedom. The approximate analytical solutions have been verified by numerical simulations.

  10. Double-time correlation functions of two quantum operations in open systems

    NASA Astrophysics Data System (ADS)

    Ban, Masashi

    2017-10-01

    A double-time correlation function of arbitrary two quantum operations is studied for a nonstationary open quantum system which is in contact with a thermal reservoir. It includes a usual correlation function, a linear response function, and a weak value of an observable. Time evolution of the correlation function can be derived by means of the time-convolution and time-convolutionless projection operator techniques. For this purpose, a quasidensity operator accompanied by a fictitious field is introduced, which makes it possible to derive explicit formulas for calculating a double-time correlation function in the second-order approximation with respect to a system-reservoir interaction. The derived formula explicitly shows that the quantum regression theorem for calculating the double-time correlation function cannot be used if a thermal reservoir has a finite correlation time. Furthermore, the formula is applied for a pure dephasing process and a linear dissipative process. The quantum regression theorem and the the Leggett-Garg inequality are investigated for an open two-level system. The results are compared with those obtained by exact calculation to examine whether the formula is a good approximation.

  11. Sound waves and resonances in electron-hole plasma

    NASA Astrophysics Data System (ADS)

    Lucas, Andrew

    2016-06-01

    Inspired by the recent experimental signatures of relativistic hydrodynamics in graphene, we investigate theoretically the behavior of hydrodynamic sound modes in such quasirelativistic fluids near charge neutrality, within linear response. Locally driving an electron fluid at a resonant frequency to such a sound mode can lead to large increases in the electrical response at the edges of the sample, a signature, which cannot be explained using diffusive models of transport. We discuss the robustness of this signal to various effects, including electron-acoustic phonon coupling, disorder, and long-range Coulomb interactions. These long-range interactions convert the sound mode into a collective plasmonic mode at low frequencies unless the fluid is charge neutral. At the smallest frequencies, the response in a disordered fluid is quantitatively what is predicted by a "momentum relaxation time" approximation. However, this approximation fails at higher frequencies (which can be parametrically small), where the classical localization of sound waves cannot be neglected. Experimental observation of such resonances is a clear signature of relativistic hydrodynamics, and provides an upper bound on the viscosity of the electron-hole plasma.

  12. Global non-linear effect of temperature on economic production.

    PubMed

    Burke, Marshall; Hsiang, Solomon M; Miguel, Edward

    2015-11-12

    Growing evidence demonstrates that climatic conditions can have a profound impact on the functioning of modern human societies, but effects on economic activity appear inconsistent. Fundamental productive elements of modern economies, such as workers and crops, exhibit highly non-linear responses to local temperature even in wealthy countries. In contrast, aggregate macroeconomic productivity of entire wealthy countries is reported not to respond to temperature, while poor countries respond only linearly. Resolving this conflict between micro and macro observations is critical to understanding the role of wealth in coupled human-natural systems and to anticipating the global impact of climate change. Here we unify these seemingly contradictory results by accounting for non-linearity at the macro scale. We show that overall economic productivity is non-linear in temperature for all countries, with productivity peaking at an annual average temperature of 13 °C and declining strongly at higher temperatures. The relationship is globally generalizable, unchanged since 1960, and apparent for agricultural and non-agricultural activity in both rich and poor countries. These results provide the first evidence that economic activity in all regions is coupled to the global climate and establish a new empirical foundation for modelling economic loss in response to climate change, with important implications. If future adaptation mimics past adaptation, unmitigated warming is expected to reshape the global economy by reducing average global incomes roughly 23% by 2100 and widening global income inequality, relative to scenarios without climate change. In contrast to prior estimates, expected global losses are approximately linear in global mean temperature, with median losses many times larger than leading models indicate.

  13. Global non-linear effect of temperature on economic production

    NASA Astrophysics Data System (ADS)

    Burke, Marshall; Hsiang, Solomon M.; Miguel, Edward

    2015-11-01

    Growing evidence demonstrates that climatic conditions can have a profound impact on the functioning of modern human societies, but effects on economic activity appear inconsistent. Fundamental productive elements of modern economies, such as workers and crops, exhibit highly non-linear responses to local temperature even in wealthy countries. In contrast, aggregate macroeconomic productivity of entire wealthy countries is reported not to respond to temperature, while poor countries respond only linearly. Resolving this conflict between micro and macro observations is critical to understanding the role of wealth in coupled human-natural systems and to anticipating the global impact of climate change. Here we unify these seemingly contradictory results by accounting for non-linearity at the macro scale. We show that overall economic productivity is non-linear in temperature for all countries, with productivity peaking at an annual average temperature of 13 °C and declining strongly at higher temperatures. The relationship is globally generalizable, unchanged since 1960, and apparent for agricultural and non-agricultural activity in both rich and poor countries. These results provide the first evidence that economic activity in all regions is coupled to the global climate and establish a new empirical foundation for modelling economic loss in response to climate change, with important implications. If future adaptation mimics past adaptation, unmitigated warming is expected to reshape the global economy by reducing average global incomes roughly 23% by 2100 and widening global income inequality, relative to scenarios without climate change. In contrast to prior estimates, expected global losses are approximately linear in global mean temperature, with median losses many times larger than leading models indicate.

  14. LANDSAT-D MSS/TM tuned orbital jitter analysis model LDS900

    NASA Technical Reports Server (NTRS)

    Pollak, T. E.

    1981-01-01

    The final LANDSAT-D orbital dynamic math model (LSD900), comprised of all test validated substructures, was used to evaluate the jitter response of the MSS/TM experiments. A dynamic forced response analysis was performed at both the MSS and TM locations on all structural modes considered (thru 200 Hz). The analysis determined the roll angular response of the MSS/TM experiments to improve excitation generated by component operation. Cross axis and cross experiment responses were also calculated. The excitations were analytically represented by seven and nine term Fourier series approximations, for the MSS and TM experiment respectively, which enabled linear harmonic solution techniques to be applied to response calculations. Single worst case jitter was estimated by variations of the eigenvalue spectrum of model LSD 900. The probability of any worst case mode occurrence was investigated.

  15. Riding and handling qualities of light aircraft: A review and analysis

    NASA Technical Reports Server (NTRS)

    Smetana, F. O.; Summery, D. C.; Johnson, W. D.

    1972-01-01

    Design procedures and supporting data necessary for configuring light aircraft to obtain desired responses to pilot commands and gusts are presented. The procedures employ specializations of modern military and jet transport practice where these provide an improvement over earlier practice. General criteria for riding and handling qualities are discussed in terms of the airframe dynamics. Methods available in the literature for calculating the coefficients required for a linearized analysis of the airframe dynamics are reviewed in detail. The review also treats the relation of spin and stall to airframe geometry. Root locus analysis is used to indicate the sensitivity of airframe dynamics to variations in individual stability derivatives and to variations in geometric parameters. Computer programs are given for finding the frequencies, damping ratios, and time constants of all rigid body modes and for generating time histories of aircraft motions in response to control inputs. Appendices are included presenting the derivation of the linearized equations of motion; the stability derivatives; the transfer functions; approximate solutions for the frequency, damping ratio, and time constants; an indication of methods to be used when linear analysis is inadequate; sample calculations; and an explanation of the use of root locus diagrams and Bode plots.

  16. Many-body Green’s function theory for electron-phonon interactions: The Kadanoff-Baym approach to spectral properties of the Holstein dimer

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

    Säkkinen, Niko; Peng, Yang; Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, 14195 Berlin-Dahlem

    2015-12-21

    We present a Kadanoff-Baym formalism to study time-dependent phenomena for systems of interacting electrons and phonons in the framework of many-body perturbation theory. The formalism takes correctly into account effects of the initial preparation of an equilibrium state and allows for an explicit time-dependence of both the electronic and phononic degrees of freedom. The method is applied to investigate the charge neutral and non-neutral excitation spectra of a homogeneous, two-site, two-electron Holstein model. This is an extension of a previous study of the ground state properties in the Hartree (H), partially self-consistent Born (Gd) and fully self-consistent Born (GD) approximationsmore » published in Säkkinen et al. [J. Chem. Phys. 143, 234101 (2015)]. Here, the homogeneous ground state solution is shown to become unstable for a sufficiently strong interaction while a symmetry-broken ground state solution is shown to be stable in the Hartree approximation. Signatures of this instability are observed for the partially self-consistent Born approximation but are not found for the fully self-consistent Born approximation. By understanding the stability properties, we are able to study the linear response regime by calculating the density-density response function by time-propagation. This amounts to a solution of the Bethe-Salpeter equation with a sophisticated kernel. The results indicate that none of the approximations is able to describe the response function during or beyond the bipolaronic crossover for the parameters investigated. Overall, we provide an extensive discussion on when the approximations are valid and how they fail to describe the studied exact properties of the chosen model system.« less

  17. Indirect synthesis of multidegree-of-freedom transient systems

    NASA Technical Reports Server (NTRS)

    Chen, Y. H.; Pilkey, W. D.; Kalinowski, A. J.

    1976-01-01

    The indirect synthesis method is developed and shown to be capable of leading a near-optimal design of multidegree-of-freedom and multidesign-element transient nonlinear dynamical systems. The basis of the approach is to select the open design parameters such that the response of the portion of the system being designed approximates the limiting performances solution. The limiting performance problem can be formulated as one of linear programming by replacing all portions of the system subject to transient disturbances by control forces and supposing that the remaining portions are linear as are the overall kinematic constraints. One then selects the design parameters that respond most closely to the limiting performance solution, which can be achieved by unconstrained curve-fitting techniques.

  18. Interferometric Observations of the SiO High J Transition Maser associated with VY Canis Majoris with the Submillimeter Array

    NASA Astrophysics Data System (ADS)

    Shinnaga, H.; Moran, J. M.; Young, K. H.; Ho, P. T. P.

    2005-12-01

    We imaged the SiO maser emission of J=5-4 in the v=1 state associated with the peculiar red supergiant VY Canis Majoris using the partially completed Submillimeter Array. We identified seven maser components and measured the relative positions at sub-arcsecond scale in the high J transition for the first time. We have also measured the polarization of these maser components. The strongest maser feature has a linear polarization of ˜ 60%, and its direction of polarization is approximately aligned with the bipolar axis. Such a high degree of polarization suggests that radiative pumping is probably responsible for the maser inversion. Five of the other maser features have significant linear polarization.

  19. Updated Lagrangian finite element formulations of various biological soft tissue non-linear material models: a comprehensive procedure and review.

    PubMed

    Townsend, Molly T; Sarigul-Klijn, Nesrin

    2016-01-01

    Simplified material models are commonly used in computational simulation of biological soft tissue as an approximation of the complicated material response and to minimize computational resources. However, the simulation of complex loadings, such as long-duration tissue swelling, necessitates complex models that are not easy to formulate. This paper strives to offer the updated Lagrangian formulation comprehensive procedure of various non-linear material models for the application of finite element analysis of biological soft tissues including a definition of the Cauchy stress and the spatial tangential stiffness. The relationships between water content, osmotic pressure, ionic concentration and the pore pressure stress of the tissue are discussed with the merits of these models and their applications.

  20. Linear score tests for variance components in linear mixed models and applications to genetic association studies.

    PubMed

    Qu, Long; Guennel, Tobias; Marshall, Scott L

    2013-12-01

    Following the rapid development of genome-scale genotyping technologies, genetic association mapping has become a popular tool to detect genomic regions responsible for certain (disease) phenotypes, especially in early-phase pharmacogenomic studies with limited sample size. In response to such applications, a good association test needs to be (1) applicable to a wide range of possible genetic models, including, but not limited to, the presence of gene-by-environment or gene-by-gene interactions and non-linearity of a group of marker effects, (2) accurate in small samples, fast to compute on the genomic scale, and amenable to large scale multiple testing corrections, and (3) reasonably powerful to locate causal genomic regions. The kernel machine method represented in linear mixed models provides a viable solution by transforming the problem into testing the nullity of variance components. In this study, we consider score-based tests by choosing a statistic linear in the score function. When the model under the null hypothesis has only one error variance parameter, our test is exact in finite samples. When the null model has more than one variance parameter, we develop a new moment-based approximation that performs well in simulations. Through simulations and analysis of real data, we demonstrate that the new test possesses most of the aforementioned characteristics, especially when compared to existing quadratic score tests or restricted likelihood ratio tests. © 2013, The International Biometric Society.

  1. Solvent effects in time-dependent self-consistent field methods. I. Optical response calculations

    DOE PAGES

    Bjorgaard, J. A.; Kuzmenko, V.; Velizhanin, K. A.; ...

    2015-01-22

    In this study, we implement and examine three excited state solvent models in time-dependent self-consistent field methods using a consistent formalism which unambiguously shows their relationship. These are the linear response, state specific, and vertical excitation solvent models. Their effects on energies calculated with the equivalent of COSMO/CIS/AM1 are given for a set of test molecules with varying excited state charge transfer character. The resulting solvent effects are explained qualitatively using a dipole approximation. It is shown that the fundamental differences between these solvent models are reflected by the character of the calculated excitations.

  2. Interpretability of Multivariate Brain Maps in Linear Brain Decoding: Definition, and Heuristic Quantification in Multivariate Analysis of MEG Time-Locked Effects.

    PubMed

    Kia, Seyed Mostafa; Vega Pons, Sandro; Weisz, Nathan; Passerini, Andrea

    2016-01-01

    Brain decoding is a popular multivariate approach for hypothesis testing in neuroimaging. Linear classifiers are widely employed in the brain decoding paradigm to discriminate among experimental conditions. Then, the derived linear weights are visualized in the form of multivariate brain maps to further study spatio-temporal patterns of underlying neural activities. It is well known that the brain maps derived from weights of linear classifiers are hard to interpret because of high correlations between predictors, low signal to noise ratios, and the high dimensionality of neuroimaging data. Therefore, improving the interpretability of brain decoding approaches is of primary interest in many neuroimaging studies. Despite extensive studies of this type, at present, there is no formal definition for interpretability of multivariate brain maps. As a consequence, there is no quantitative measure for evaluating the interpretability of different brain decoding methods. In this paper, first, we present a theoretical definition of interpretability in brain decoding; we show that the interpretability of multivariate brain maps can be decomposed into their reproducibility and representativeness. Second, as an application of the proposed definition, we exemplify a heuristic for approximating the interpretability in multivariate analysis of evoked magnetoencephalography (MEG) responses. Third, we propose to combine the approximated interpretability and the generalization performance of the brain decoding into a new multi-objective criterion for model selection. Our results, for the simulated and real MEG data, show that optimizing the hyper-parameters of the regularized linear classifier based on the proposed criterion results in more informative multivariate brain maps. More importantly, the presented definition provides the theoretical background for quantitative evaluation of interpretability, and hence, facilitates the development of more effective brain decoding algorithms in the future.

  3. Interpretability of Multivariate Brain Maps in Linear Brain Decoding: Definition, and Heuristic Quantification in Multivariate Analysis of MEG Time-Locked Effects

    PubMed Central

    Kia, Seyed Mostafa; Vega Pons, Sandro; Weisz, Nathan; Passerini, Andrea

    2017-01-01

    Brain decoding is a popular multivariate approach for hypothesis testing in neuroimaging. Linear classifiers are widely employed in the brain decoding paradigm to discriminate among experimental conditions. Then, the derived linear weights are visualized in the form of multivariate brain maps to further study spatio-temporal patterns of underlying neural activities. It is well known that the brain maps derived from weights of linear classifiers are hard to interpret because of high correlations between predictors, low signal to noise ratios, and the high dimensionality of neuroimaging data. Therefore, improving the interpretability of brain decoding approaches is of primary interest in many neuroimaging studies. Despite extensive studies of this type, at present, there is no formal definition for interpretability of multivariate brain maps. As a consequence, there is no quantitative measure for evaluating the interpretability of different brain decoding methods. In this paper, first, we present a theoretical definition of interpretability in brain decoding; we show that the interpretability of multivariate brain maps can be decomposed into their reproducibility and representativeness. Second, as an application of the proposed definition, we exemplify a heuristic for approximating the interpretability in multivariate analysis of evoked magnetoencephalography (MEG) responses. Third, we propose to combine the approximated interpretability and the generalization performance of the brain decoding into a new multi-objective criterion for model selection. Our results, for the simulated and real MEG data, show that optimizing the hyper-parameters of the regularized linear classifier based on the proposed criterion results in more informative multivariate brain maps. More importantly, the presented definition provides the theoretical background for quantitative evaluation of interpretability, and hence, facilitates the development of more effective brain decoding algorithms in the future. PMID:28167896

  4. Relationships between nonlinear normal modes and response to random inputs

    NASA Astrophysics Data System (ADS)

    Schoneman, Joseph D.; Allen, Matthew S.; Kuether, Robert J.

    2017-02-01

    The ability to model nonlinear structures subject to random excitation is of key importance in designing hypersonic aircraft and other advanced aerospace vehicles. When a structure is linear, superposition can be used to construct its response to a known spectrum in terms of its linear modes. Superposition does not hold for a nonlinear system, but several works have shown that a system's dynamics can still be understood qualitatively in terms of its nonlinear normal modes (NNMs). This work investigates the connection between a structure's undamped nonlinear normal modes and the spectrum of its response to high amplitude random forcing. Two examples are investigated: a spring-mass system and a clamped-clamped beam modeled within a geometrically nonlinear finite element package. In both cases, an intimate connection is observed between the smeared peaks in the response spectrum and the frequency-energy dependence of the nonlinear normal modes. In order to understand the role of coupling between the underlying linear modes, reduced order models with and without modal coupling terms are used to separate the effect of each NNM's backbone from the nonlinear couplings that give rise to internal resonances. In the cases shown here, uncoupled, single-degree-of-freedom nonlinear models are found to predict major features in the response with reasonable accuracy; a highly inexpensive approximation such as this could be useful in design and optimization studies. More importantly, the results show that a reduced order model can be expected to give accurate results only if it is also capable of accurately predicting the frequency-energy dependence of the nonlinear modes that are excited.

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

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

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

    2015-11-28

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

  6. Characterization of OSL dosimeters for use in dose assessment in Computed Tomography procedures.

    PubMed

    Giansante, Louise; Santos, Josilene C; Umisedo, Nancy K; Terini, Ricardo A; Costa, Paulo R

    2018-03-01

    This study describes the characterization of an Al 2 O 3 :C OSLD (Landauer's Luxel™ tape) for dose evaluation in Computed Tomography. The irradiations were conducted using both a constant potential X-ray equipment and a 64-slice clinical CT scanner, and the readouts were performed using a Risø TL/OSL reader. The following aspects were studied: batch homogeneity, energy response, linearity of dose response, reproducibility, reusability, and effect of uncertainties with the normalization of OSL signals per their response to beta radiation. A group of 330 dosimeters from the 452 irradiated with the same dose presented OSL signals within the interval of 4.7% from the average. The dosimeters presented energy-dependent response in good agreement with results found in the literature. The air kerma response of the OSL signal showed a linear trend for both the constant potential X-ray device and the clinical CT scanner, with differences in their slopes of approximately 10%. Reproducibility, reusability, and effect of beta normalization were analyzed by separating 72 dosimeters in 3 groups. The results obtained in this study together with those of previous works indicate that this type of dosimeter is adequate for dose evaluation in CT clinical applications. Copyright © 2018 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.

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

    PubMed

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

    2015-10-28

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

  8. Vestibulo-Ocular Responses to Vertical Translation using a Hand-Operated Chair as a Field Measure of Otolith Function

    NASA Technical Reports Server (NTRS)

    Wood, S. J.; Campbell, D. J.; Reschke, M. F.; Prather, L.; Clement, G.

    2016-01-01

    The translational Vestibulo-Ocular Reflex (tVOR) is an important otolith-mediated response to stabilize gaze during natural locomotion. One goal of this study was to develop a measure of the tVOR using a simple hand-operated chair that provided passive vertical motion. Binocular eye movements were recorded with a tight-fitting video mask in ten healthy subjects. Vertical motion was provided by a modified spring-powered chair (swopper.com) at approximately 2 Hz (+/- 2 cm displacement) to approximate the head motion during walking. Linear acceleration was measured with wireless inertial sensors (Xsens) mounted on the head and torso. Eye movements were recorded while subjects viewed near (0.5m) and far (approximately 4m) targets, and then imagined these targets in darkness. Subjects also provided perceptual estimates of target distances. Consistent with the kinematic properties shown in previous studies, the tVOR gain was greater with near targets, and greater with vision than in darkness. We conclude that this portable chair system can provide a field measure of otolith-ocular function at frequencies sufficient to elicit a robust tVOR.

  9. Quantitative model of diffuse speckle contrast analysis for flow measurement.

    PubMed

    Liu, Jialin; Zhang, Hongchao; Lu, Jian; Ni, Xiaowu; Shen, Zhonghua

    2017-07-01

    Diffuse speckle contrast analysis (DSCA) is a noninvasive optical technique capable of monitoring deep tissue blood flow. However, a detailed study of the speckle contrast model for DSCA has yet to be presented. We deduced the theoretical relationship between speckle contrast and exposure time and further simplified it to a linear approximation model. The feasibility of this linear model was validated by the liquid phantoms which demonstrated that the slope of this linear approximation was able to rapidly determine the Brownian diffusion coefficient of the turbid media at multiple distances using multiexposure speckle imaging. Furthermore, we have theoretically quantified the influence of optical property on the measurements of the Brownian diffusion coefficient which was a consequence of the fact that the slope of this linear approximation was demonstrated to be equal to the inverse of correlation time of the speckle.

  10. Optimal entrainment of circadian clocks in the presence of noise

    NASA Astrophysics Data System (ADS)

    Monti, Michele; Lubensky, David K.; ten Wolde, Pieter Rein

    2018-03-01

    Circadian clocks are biochemical oscillators that allow organisms to estimate the time of the day. These oscillators are inherently noisy due to the discrete nature of the reactants and the stochastic character of their interactions. To keep these oscillators in sync with the daily day-night rhythm in the presence of noise, circadian clocks must be coupled to the dark-light cycle. In this paper, we study the entrainment of phase oscillators as a function of the intrinsic noise in the system. Using stochastic simulations, we compute the optimal coupling strength, intrinsic frequency, and shape of the phase-response curve, that maximize the mutual information between the phase of the clock and time. We show that the optimal coupling strength and intrinsic frequency increase with the noise, but that the shape of the phase-response curve varies nonmonotonically with the noise: in the low-noise regime, it features a dead zone that increases in width as the noise increases, while in the high-noise regime, the width decreases with the noise. These results arise from a tradeoff between maximizing stability—noise suppression—and maximizing linearity of the input-output, i.e., time-phase, relation. We also show that three analytic approximations—the linear-noise approximation, the phase-averaging method, and linear-response theory—accurately describe different regimes of the coupling strength and the noise.

  11. Nonlinear Analysis of the Space Shuttle Superlightweight LO2 Tank. Part 2; Behavior Under 3g End-of-Flight Loads

    NASA Technical Reports Server (NTRS)

    Nemeth, Michael P.; Young, Richard D.; Collins, Timothy J.; Starnes, James H.,Jr.

    1998-01-01

    Results of linear bifurcation and nonlinear analyses of the Space Shuttle super lightweight (SLWT) external liquid-oxygen (LO2) tank are presented for an important end-of-flight loading condition. These results illustrate an important type of response mode for thin-walled shells, that are subjected to combined mechanical and thermal loads, that may be encountered in the design of other liquid-fuel launch vehicles. Linear bifurcation analyses are presented that predict several nearly equal eigenvalues that correspond to local buckling modes in the aft dome of the LO2 tank. In contrast, the nonlinear response phenomenon is shown to consist of a short-wavelength bending deformation in the aft elliptical dome of the LO2 tank that grows in amplitude in a stable manner with increasing load. Imperfection sensitivity analyses are presented that show that the presence of several nearly equal eigenvalues does not lead to a premature general instability mode for the aft dome. For the linear bifurcation and nonlinear analyses, the results show that accurate predictions of the response of the shell generally require a large-scale, high fidelity finite-element model. Results are also presented that show that the SLWT LO2 tank can support loads in excess of approximately 1.9 times the values of the operational loads considered.

  12. Convergence of linear acceleration and yaw rotation signals on non-eye movement neurons in the vestibular nucleus of macaques.

    PubMed

    Newlands, Shawn D; Abbatematteo, Ben; Wei, Min; Carney, Laurel H; Luan, Hongge

    2018-01-01

    Roughly half of all vestibular nucleus neurons without eye movement sensitivity respond to both angular rotation and linear acceleration. Linear acceleration signals arise from otolith organs, and rotation signals arise from semicircular canals. In the vestibular nerve, these signals are carried by different afferents. Vestibular nucleus neurons represent the first point of convergence for these distinct sensory signals. This study systematically evaluated how rotational and translational signals interact in single neurons in the vestibular nuclei: multisensory integration at the first opportunity for convergence between these two independent vestibular sensory signals. Single-unit recordings were made from the vestibular nuclei of awake macaques during yaw rotation, translation in the horizontal plane, and combinations of rotation and translation at different frequencies. The overall response magnitude of the combined translation and rotation was generally less than the sum of the magnitudes in responses to the stimuli applied independently. However, we found that under conditions in which the peaks of the rotational and translational responses were coincident these signals were approximately additive. With presentation of rotation and translation at different frequencies, rotation was attenuated more than translation, regardless of which was at a higher frequency. These data suggest a nonlinear interaction between these two sensory modalities in the vestibular nuclei, in which coincident peak responses are proportionally stronger than other, off-peak interactions. These results are similar to those reported for other forms of multisensory integration, such as audio-visual integration in the superior colliculus. NEW & NOTEWORTHY This is the first study to systematically explore the interaction of rotational and translational signals in the vestibular nuclei through independent manipulation. The results of this study demonstrate nonlinear integration leading to maximum response amplitude when the timing and direction of peak rotational and translational responses are coincident.

  13. Hugoniot equation of state of rock materials under shock compression

    PubMed Central

    Braithwaite, C. H.; Zhao, J.

    2017-01-01

    Two sets of shock compression tests (i.e. conventional and reverse impact) were conducted to determine the shock response of two rock materials using a plate impact facility. Embedded manganin stress gauges were used for the measurements of longitudinal stress and shock velocity. Photon Doppler velocimetry was used to capture the free surface velocity of the target. Experimental data were obtained on a fine-grained marble and a coarse-grained gabbro over a shock pressure range of approximately 1.5–12 GPa. Gabbro exhibited a linear Hugoniot equation of state (EOS) in the pressure–particle velocity (P–up) plane, while for marble a nonlinear response was observed. The EOS relations between shock velocity (US) and particle velocity (up) are linearly fitted as US = 2.62 + 3.319up and US = 5.4 85 + 1.038up for marble and gabbro, respectively. This article is part of the themed issue ‘Experimental testing and modelling of brittle materials at high strain rates’. PMID:27956506

  14. White noise analysis of Phycomyces light growth response system. I. Normal intensity range.

    PubMed Central

    Lipson, E D

    1975-01-01

    The Wiener-Lee-Schetzen method for the identification of a nonlinear system through white gaussian noise stimulation was applied to the transient light growth response of the sporangiophore of Phycomyces. In order to cover a moderate dynamic range of light intensity I, the imput variable was defined to be log I. The experiments were performed in the normal range of light intensity, centered about I0 = 10(-6) W/cm2. The kernels of the Wierner functionals were computed up to second order. Within the range of a few decades the system is reasonably linear with log I. The main nonlinear feature of the second-order kernel corresponds to the property of rectification. Power spectral analysis reveals that the slow dynamics of the system are of at least fifth order. The system can be represented approximately by a linear transfer function, including a first-order high-pass (adaptation) filter with a 4 min time constant and an underdamped fourth-order low-pass filter. Accordingly a linear electronic circuit was constructed to simulate the small scale response characteristics. In terms of the adaptation model of Delbrück and Reichardt (1956, in Cellular Mechanisms in Differentiation and Growth, Princeton University Press), kernels were deduced for the dynamic dependence of the growth velocity (output) on the "subjective intensity", a presumed internal variable. Finally the linear electronic simulator above was generalized to accommodate the large scale nonlinearity of the adaptation model and to serve as a tool for deeper test of the model. PMID:1203444

  15. Non-linear HRV indices under autonomic nervous system blockade.

    PubMed

    Bolea, Juan; Pueyo, Esther; Laguna, Pablo; Bailón, Raquel

    2014-01-01

    Heart rate variability (HRV) has been studied as a non-invasive technique to characterize the autonomic nervous system (ANS) regulation of the heart. Non-linear methods based on chaos theory have been used during the last decades as markers for risk stratification. However, interpretation of these nonlinear methods in terms of sympathetic and parasympathetic activity is not fully established. In this work we study linear and non-linear HRV indices during ANS blockades in order to assess their relation with sympathetic and parasympathetic activities. Power spectral content in low frequency (0.04-0.15 Hz) and high frequency (0.15-0.4 Hz) bands of HRV, as well as correlation dimension, sample and approximate entropies were computed in a database of subjects during single and dual ANS blockade with atropine and/or propranolol. Parasympathetic blockade caused a significant decrease in the low and high frequency power of HRV, as well as in correlation dimension and sample and approximate entropies. Sympathetic blockade caused a significant increase in approximate entropy. Sympathetic activation due to postural change from supine to standing caused a significant decrease in all the investigated non-linear indices and a significant increase in the normalized power in the low frequency band. The other investigated linear indices did not show significant changes. Results suggest that parasympathetic activity has a direct relation with sample and approximate entropies.

  16. The Shock and Vibration Bulletin. Part 2. Modal and Impedance Analysis, Human Response to Vibration and Shock, Isolation and Damping, Dynamic Analysis

    DTIC Science & Technology

    1979-09-01

    a " high performance fast timing" engine thrust with a mismatch between right and left SRfls...examine the dynamic behavior of a blade having a root geometry compatible with low frictional forces at high rotational speeds , somewhat like a "Christmas...Tree" root, but with a gap introduced which will close up only at high speed . Approximate non-linear equations of motion are derived and solved

  17. A mathematical study of a random process proposed as an atmospheric turbulence model

    NASA Technical Reports Server (NTRS)

    Sidwell, K.

    1977-01-01

    A random process is formed by the product of a local Gaussian process and a random amplitude process, and the sum of that product with an independent mean value process. The mathematical properties of the resulting process are developed, including the first and second order properties and the characteristic function of general order. An approximate method for the analysis of the response of linear dynamic systems to the process is developed. The transition properties of the process are also examined.

  18. FAST TRACK COMMUNICATION: Quantum anomalies and linear response theory

    NASA Astrophysics Data System (ADS)

    Sela, Itamar; Aisenberg, James; Kottos, Tsampikos; Cohen, Doron

    2010-08-01

    The analysis of diffusive energy spreading in quantized chaotic driven systems leads to a universal paradigm for the emergence of a quantum anomaly. In the classical approximation, a driven chaotic system exhibits stochastic-like diffusion in energy space with a coefficient D that is proportional to the intensity ɛ2 of the driving. In the corresponding quantized problem the coherent transitions are characterized by a generalized Wigner time tɛ, and a self-generated (intrinsic) dephasing process leads to nonlinear dependence of D on ɛ2.

  19. Failure of underground concrete structures subjected to blast loadings

    NASA Technical Reports Server (NTRS)

    Ross, C. A.; Nash, P. T.; Griner, G. R.

    1979-01-01

    The response and failure of two edges of free reinforced concrete slabs subjected to intermediate blast loadings are examined. The failure of the reinforced concrete structures is defined as a condition where actual separation or fracture of the reinforcing elements has occurred. Approximate theoretical methods using stationary and moving plastic hinge mechanisms with linearly varying and time dependent loadings are developed. Equations developed to predict deflection and failure of reinforced concrete beams are presented and compared with the experimental results.

  20. RESONANT AMPLIFICATION OF TURBULENCE BY THE BLAST WAVES

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

    Zankovich, A. M.; Kovalenko, I. G., E-mail: ilya.g.kovalenko@gmail.com

    2015-02-10

    We discuss the idea of whether spherical blast waves can amplify by a nonlocal resonant hydrodynamic mechanism inhomogeneities formed by turbulence or phase segregation in the interstellar medium. We consider the problem of a blast-wave-turbulence interaction in the Linear Interaction Approximation. Mathematically, this is an eigenvalue problem for finding the structure and amplitude of eigenfunctions describing the response of the shock-wave flow to forced oscillations by external perturbations in the ambient interstellar medium. Linear analysis shows that the blast wave can amplify density and vorticity perturbations for a wide range of length scales with amplification coefficients of up to 20,more » with increasing amplification the larger the length. There also exist resonant harmonics for which the gain becomes formally infinite in the linear approximation. Their orbital wavenumbers are within the range of macro- (l ∼ 1), meso- (l ∼ 20), and microscopic (l > 200) scales. Since the resonance width is narrow (typically, Δl < 1), resonance should select and amplify discrete isolated harmonics. We speculate on a possible explanation of an observed regular filamentary structure of regularly shaped round supernova remnants such as SNR 1572, 1006, or 0509-67.5. Resonant mesoscales found (l ≈ 18) are surprisingly close to the observed scales (l ≈ 15) of ripples in the shell's surface of SNR 0509-67.5.« less

  1. Consensual pupillary light response in the red-eared slider turtle (Trachemys scripta elegans).

    PubMed

    Dearworth, James R; Sipe, Grayson O; Cooper, Lori J; Brune, Erin E; Boyd, Angela L; Riegel, Rhae A L

    2010-03-17

    Purpose of this study was to determine if the turtle has a consensual pupillary light response (cPLR), and if so, to compare it to its direct pupillary light response (dPLR). One eye was illuminated with different intensities of light over a four log range while keeping the other eye in darkness. In the eye directly illuminated, pupil diameter was reduced by as much as approximately 31%. In the eye not stimulated by light, pupil diameter was also reduced but less to approximately 11%. When compared to the directly illuminated eye, this generated a ratio, cPLR-dPLR, equal to 0.35. Ratio of slopes for log/linear fits to plots of pupil changes versus retinal irradiance for non-illuminated (-1.27) to illuminated (-3.94) eyes closely matched at 0.32. cPLR had time constants ranging from 0.60 to 1.20min; however, they were comparable and not statistically different from those of the dPLR, which ranged from 1.41 to 2.00min. Application of mydriatic drugs to the directly illuminated eye also supported presence of a cPLR. Drugs reduced pupil constriction by approximately 9% for the dPLR and slowed its time constant to 9.58min while simultaneous enhancing constriction by approximately 6% for the cPLR. Time constant for the cPLR at 1.75min, however, was not changed. Results support that turtle possesses a cPLR although less strong than its dPLR. Copyright 2010 Elsevier Ltd. All rights reserved.

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

    PubMed

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

    2016-11-01

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

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

    NASA Technical Reports Server (NTRS)

    Rosen, I. G.

    1988-01-01

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

  4. Controlling Flexible Manipulators, an Experimental Investigation. Ph.D. Thesis

    NASA Technical Reports Server (NTRS)

    Hastings, Gordon Greene

    1986-01-01

    Lightweight, slender manipulators offer faster response and/or greater workspace range for the same size actuators than tradional manipulators. Lightweight construction of manipulator links results in increased structural flexibility. The increase flexibility must be considered in the design of control systems to properly account for the dynamic flexible vibrations and static deflections. Real time control of the flexible manipulator vibrations are experimentally investigated. Models intended for real-time control of distributed parameter system such as flexible manipulators rely on model approximation schemes. An linear model based on the application of Lagrangian dynamics to a rigid body mode and a series of separable flexible modes is examined with respect to model order requirements, and modal candidate selection. Balanced realizations are applied to the linear flexible model to obtain an estimate of appropriate order for a selected model. Describing the flexible deflections as a linear combination of modes results in measurements of beam state, which yield information about several modes. To realize the potential of linear systems theory, knowledge of each state must be available. State estimation is also accomplished by implementation of a Kalman Filter. State feedback control laws are implemented based upon linear quadratic regulator design.

  5. Dynamical heterogeneities and mechanical non-linearities: Modeling the onset of plasticity in polymer in the glass transition.

    PubMed

    Masurel, R J; Gelineau, P; Lequeux, F; Cantournet, S; Montes, H

    2017-12-27

    In this paper we focus on the role of dynamical heterogeneities on the non-linear response of polymers in the glass transition domain. We start from a simple coarse-grained model that assumes a random distribution of the initial local relaxation times and that quantitatively describes the linear viscoelasticity of a polymer in the glass transition regime. We extend this model to non-linear mechanics assuming a local Eyring stress dependence of the relaxation times. Implementing the model in a finite element mechanics code, we derive the mechanical properties and the local mechanical fields at the beginning of the non-linear regime. The model predicts a narrowing of distribution of relaxation times and the storage of a part of the mechanical energy --internal stress-- transferred to the material during stretching in this temperature range. We show that the stress field is not spatially correlated under and after loading and follows a Gaussian distribution. In addition the strain field exhibits shear bands, but the strain distribution is narrow. Hence, most of the mechanical quantities can be calculated analytically, in a very good approximation, with the simple assumption that the strain rate is constant.

  6. Distribution of Orientation Selectivity in Recurrent Networks of Spiking Neurons with Different Random Topologies

    PubMed Central

    Sadeh, Sadra; Rotter, Stefan

    2014-01-01

    Neurons in the primary visual cortex are more or less selective for the orientation of a light bar used for stimulation. A broad distribution of individual grades of orientation selectivity has in fact been reported in all species. A possible reason for emergence of broad distributions is the recurrent network within which the stimulus is being processed. Here we compute the distribution of orientation selectivity in randomly connected model networks that are equipped with different spatial patterns of connectivity. We show that, for a wide variety of connectivity patterns, a linear theory based on firing rates accurately approximates the outcome of direct numerical simulations of networks of spiking neurons. Distance dependent connectivity in networks with a more biologically realistic structure does not compromise our linear analysis, as long as the linearized dynamics, and hence the uniform asynchronous irregular activity state, remain stable. We conclude that linear mechanisms of stimulus processing are indeed responsible for the emergence of orientation selectivity and its distribution in recurrent networks with functionally heterogeneous synaptic connectivity. PMID:25469704

  7. Use of borated polyethylene to improve low energy response of a prompt gamma based neutron dosimeter

    NASA Astrophysics Data System (ADS)

    Priyada, P.; Ashwini, U.; Sarkar, P. K.

    2016-05-01

    The feasibility of using a combined sample of borated polyethylene and normal polyethylene to estimate neutron ambient dose equivalent from measured prompt gamma emissions is investigated theoretically to demonstrate improvements in low energy neutron dose response compared to only polyethylene. Monte Carlo simulations have been carried out using the FLUKA code to calculate the response of boron, hydrogen and carbon prompt gamma emissions to mono energetic neutrons. The weighted least square method is employed to arrive at the best linear combination of these responses that approximates the ICRP fluence to dose conversion coefficients well in the energy range of 10-8 MeV to 14 MeV. The configuration of the combined system is optimized through FLUKA simulations. The proposed method is validated theoretically with five different workplace neutron spectra with satisfactory outcome.

  8. Burgers approximation for two-dimensional flow past an ellipse

    NASA Technical Reports Server (NTRS)

    Dorrepaal, J. M.

    1982-01-01

    A linearization of the Navier-Stokes equation due to Burgers in which vorticity is transported by the velocity field corresponding to continuous potential flow is examined. The governing equations are solved exactly for the two dimensional steady flow past an ellipse of arbitrary aspect ratio. The requirement of no slip along the surface of the ellipse results in an infinite algebraic system of linear equations for coefficients appearing in the solution. The system is truncated at a point which gives reliable results for Reynolds numbers R in the range 0 R 5. Predictions of the Burgers approximation regarding separation, drag and boundary layer behavior are investigated. In particular, Burgers linearization gives drag coefficients which are closer to observed experimental values than those obtained from Oseen's approximation. In the special case of flow past a circular cylinder, Burgers approximation predicts a boundary layer whose thickness is roughly proportional to R-1/2.

  9. The vestibulo-ocular reflex of the squirrel monkey during eccentric rotation and roll tilt

    NASA Technical Reports Server (NTRS)

    Merfeld, D. M.; Young, L. R.

    1995-01-01

    The vestibulo-ocular reflexes (VOR) are determined not only by angular acceleration, but also by the presence of gravity and linear acceleration. This phenomenon was studied by measuring three-dimensional nystagmic eye movements, with implanted search coils, in six male squirrel monkeys during eccentric rotation. Monkeys were rotated in the dark at a constant velocity of 200 degrees/s (centrally or 79 cm off axis) with the axis of rotation always aligned with gravity and the spinal axis of the upright monkeys. The monkey's orientation (facing-motion or back-to-motion) had a dramatic influence on the VOR. These experiments show that: (a) the axis of eye rotation always shifted toward alignment with gravito-inertial force; (b) the peak value of horizontal slow phase eye velocity was greater with the monkey facing-motion than with back-to-motion; and (c) the time constant of horizontal eye movement decay was smaller with the monkey facing-motion than with back-to-motion. All of these findings were statistically significant and consistent across monkeys. In another set of tests, the same monkeys were rapidly tilted about their naso-occipital (roll) axis. Tilted orientations of 45 degrees and 90 degrees were maintained for 1 min. Other than a compensatory angular VOR during the angular rotation, no consistent eye velocity response was observed during or following the tilt for any of the six monkeys. The absence of any eye movement response following tilt weighs against the possibility that translational linear VOR responses are due to simple high-pass filtering of the otolith signals. The VOR response during eccentric rotation was divided into the more familiar angular VOR and linear VOR components. The angular component is known to depend upon semicircular canal dynamics and central influences. The linear component of the response decays rapidly with a mean duration of only 6.6 s, while the axis of eye rotation rapidly aligns (< 10 s) with gravito-inertial force. These results are consistent with the hypothesis that the measurement of gravito-inertial force by the otolith organs is resolved into central estimates of linear acceleration and gravity, such that the central estimate of gravitational force minus the central estimate of linear acceleration approximately equals the otolith measurement of gravito-inertial force.

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

    NASA Technical Reports Server (NTRS)

    Gibson, J. S.; Adamian, A.

    1988-01-01

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

  11. Comparisons of characteristic timescales and approximate models for Brownian magnetic nanoparticle rotations

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

    Reeves, Daniel B., E-mail: dbr@Dartmouth.edu; Weaver, John B.

    2015-06-21

    Magnetic nanoparticles are promising tools for a host of therapeutic and diagnostic medical applications. The dynamics of rotating magnetic nanoparticles in applied magnetic fields depend strongly on the type and strength of the field applied. There are two possible rotation mechanisms and the decision for the dominant mechanism is often made by comparing the equilibrium relaxation times. This is a problem when particles are driven with high-amplitude fields because they are not necessarily at equilibrium at all. Instead, it is more appropriate to consider the “characteristic timescales” that arise in various applied fields. Approximate forms for the characteristic time ofmore » Brownian particle rotations do exist and we show agreement between several analytical and phenomenological-fit models to simulated data from a stochastic Langevin equation approach. We also compare several approximate models with solutions of the Fokker-Planck equation to determine their range of validity for general fields and relaxation times. The effective field model is an excellent approximation, while the linear response solution is only useful for very low fields and frequencies for realistic Brownian particle rotations.« less

  12. Linear approximations of nonlinear systems

    NASA Technical Reports Server (NTRS)

    Hunt, L. R.; Su, R.

    1983-01-01

    The development of a method for designing an automatic flight controller for short and vertical take off aircraft is discussed. This technique involves transformations of nonlinear systems to controllable linear systems and takes into account the nonlinearities of the aircraft. In general, the transformations cannot always be given in closed form. Using partial differential equations, an approximate linear system called the modified tangent model was introduced. A linear transformation of this tangent model to Brunovsky canonical form can be constructed, and from this the linear part (about a state space point x sub 0) of an exact transformation for the nonlinear system can be found. It is shown that a canonical expansion in Lie brackets about the point x sub 0 yields the same modified tangent model.

  13. Oscillatory Reduction in Option Pricing Formula Using Shifted Poisson and Linear Approximation

    NASA Astrophysics Data System (ADS)

    Nur Rachmawati, Ro'fah; Irene; Budiharto, Widodo

    2014-03-01

    Option is one of derivative instruments that can help investors improve their expected return and minimize the risks. However, the Black-Scholes formula is generally used in determining the price of the option does not involve skewness factor and it is difficult to apply in computing process because it produces oscillation for the skewness values close to zero. In this paper, we construct option pricing formula that involve skewness by modified Black-Scholes formula using Shifted Poisson model and transformed it into the form of a Linear Approximation in the complete market to reduce the oscillation. The results are Linear Approximation formula can predict the price of an option with very accurate and successfully reduce the oscillations in the calculation processes.

  14. Gain in stochastic resonance: Precise numerics versus linear response theory beyond the two-mode approximation

    NASA Astrophysics Data System (ADS)

    Casado-Pascual, Jesús; Denk, Claus; Gómez-Ordóñez, José; Morillo, Manuel; Hänggi, Peter

    2003-03-01

    In the context of the phenomenon of stochastic resonance (SR), we study the correlation function, the signal-to-noise ratio (SNR), and the ratio of output over input SNR, i.e., the gain, which is associated to the nonlinear response of a bistable system driven by time-periodic forces and white Gaussian noise. These quantifiers for SR are evaluated using the techniques of linear response theory (LRT) beyond the usually employed two-mode approximation scheme. We analytically demonstrate within such an extended LRT description that the gain can indeed not exceed unity. We implement an efficient algorithm, based on work by Greenside and Helfand (detailed in the Appendix), to integrate the driven Langevin equation over a wide range of parameter values. The predictions of LRT are carefully tested against the results obtained from numerical solutions of the corresponding Langevin equation over a wide range of parameter values. We further present an accurate procedure to evaluate the distinct contributions of the coherent and incoherent parts of the correlation function to the SNR and the gain. As a main result we show for subthreshold driving that both the correlation function and the SNR can deviate substantially from the predictions of LRT and yet the gain can be either larger or smaller than unity. In particular, we find that the gain can exceed unity in the strongly nonlinear regime which is characterized by weak noise and very slow multifrequency subthreshold input signals with a small duty cycle. This latter result is in agreement with recent analog simulation results by Gingl et al. [ICNF 2001, edited by G. Bosman (World Scientific, Singapore, 2002), pp. 545 548; Fluct. Noise Lett. 1, L181 (2001)].

  15. Automated Dynamic Demand Response Implementation on a Micro-grid

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

    Kuppannagari, Sanmukh R.; Kannan, Rajgopal; Chelmis, Charalampos

    In this paper, we describe a system for real-time automated Dynamic and Sustainable Demand Response with sparse data consumption prediction implemented on the University of Southern California campus microgrid. Supply side approaches to resolving energy supply-load imbalance do not work at high levels of renewable energy penetration. Dynamic Demand Response (D 2R) is a widely used demand-side technique to dynamically adjust electricity consumption during peak load periods. Our D 2R system consists of accurate machine learning based energy consumption forecasting models that work with sparse data coupled with fast and sustainable load curtailment optimization algorithms that provide the ability tomore » dynamically adapt to changing supply-load imbalances in near real-time. Our Sustainable DR (SDR) algorithms attempt to distribute customer curtailment evenly across sub-intervals during a DR event and avoid expensive demand peaks during a few sub-intervals. It also ensures that each customer is penalized fairly in order to achieve the targeted curtailment. We develop near linear-time constant-factor approximation algorithms along with Polynomial Time Approximation Schemes (PTAS) for SDR curtailment that minimizes the curtailment error defined as the difference between the target and achieved curtailment values. Our SDR curtailment problem is formulated as an Integer Linear Program that optimally matches customers to curtailment strategies during a DR event while also explicitly accounting for customer strategy switching overhead as a constraint. We demonstrate the results of our D 2R system using real data from experiments performed on the USC smartgrid and show that 1) our prediction algorithms can very accurately predict energy consumption even with noisy or missing data and 2) our curtailment algorithms deliver DR with extremely low curtailment errors in the 0.01-0.05 kWh range.« less

  16. First-order symmetry-adapted perturbation theory for multiplet splittings.

    PubMed

    Patkowski, Konrad; Żuchowski, Piotr S; Smith, Daniel G A

    2018-04-28

    We present a symmetry-adapted perturbation theory (SAPT) for the interaction of two high-spin open-shell molecules (described by their restricted open-shell Hartree-Fock determinants) resulting in low-spin states of the complex. The previously available SAPT formalisms, except for some system-specific studies for few-electron complexes, were restricted to the high-spin state of the interacting system. Thus, the new approach provides, for the first time, a SAPT-based estimate of the splittings between different spin states of the complex. We have derived and implemented the lowest-order SAPT term responsible for these splittings, that is, the first-order exchange energy. We show that within the so-called S 2 approximation commonly used in SAPT (neglecting effects that vanish as fourth or higher powers of intermolecular overlap integrals), the first-order exchange energies for all multiplets are linear combinations of two matrix elements: a diagonal exchange term that determines the spin-averaged effect and a spin-flip term responsible for the splittings between the states. The numerical factors in this linear combination are determined solely by the Clebsch-Gordan coefficients: accordingly, the S 2 approximation implies a Heisenberg Hamiltonian picture with a single coupling strength parameter determining all the splittings. The new approach is cast into both molecular-orbital and atomic-orbital expressions: the latter enable an efficient density-fitted implementation. We test the newly developed formalism on several open-shell complexes ranging from diatomic systems (Li⋯H, Mn⋯Mn, …) to the phenalenyl dimer.

  17. First-order symmetry-adapted perturbation theory for multiplet splittings

    NASA Astrophysics Data System (ADS)

    Patkowski, Konrad; Żuchowski, Piotr S.; Smith, Daniel G. A.

    2018-04-01

    We present a symmetry-adapted perturbation theory (SAPT) for the interaction of two high-spin open-shell molecules (described by their restricted open-shell Hartree-Fock determinants) resulting in low-spin states of the complex. The previously available SAPT formalisms, except for some system-specific studies for few-electron complexes, were restricted to the high-spin state of the interacting system. Thus, the new approach provides, for the first time, a SAPT-based estimate of the splittings between different spin states of the complex. We have derived and implemented the lowest-order SAPT term responsible for these splittings, that is, the first-order exchange energy. We show that within the so-called S2 approximation commonly used in SAPT (neglecting effects that vanish as fourth or higher powers of intermolecular overlap integrals), the first-order exchange energies for all multiplets are linear combinations of two matrix elements: a diagonal exchange term that determines the spin-averaged effect and a spin-flip term responsible for the splittings between the states. The numerical factors in this linear combination are determined solely by the Clebsch-Gordan coefficients: accordingly, the S2 approximation implies a Heisenberg Hamiltonian picture with a single coupling strength parameter determining all the splittings. The new approach is cast into both molecular-orbital and atomic-orbital expressions: the latter enable an efficient density-fitted implementation. We test the newly developed formalism on several open-shell complexes ranging from diatomic systems (Li⋯H, Mn⋯Mn, …) to the phenalenyl dimer.

  18. Two-dimensional spatiotemporal coding of linear acceleration in vestibular nuclei neurons

    NASA Technical Reports Server (NTRS)

    Angelaki, D. E.; Bush, G. A.; Perachio, A. A.

    1993-01-01

    Response properties of vertical (VC) and horizontal (HC) canal/otolith-convergent vestibular nuclei neurons were studied in decerebrate rats during stimulation with sinusoidal linear accelerations (0.2-1.4 Hz) along different directions in the head horizontal plane. A novel characteristic of the majority of tested neurons was the nonzero response often elicited during stimulation along the "null" direction (i.e., the direction perpendicular to the maximum sensitivity vector, Smax). The tuning ratio (Smin gain/Smax gain), a measure of the two-dimensional spatial sensitivity, depended on stimulus frequency. For most vestibular nuclei neurons, the tuning ratio was small at the lowest stimulus frequencies and progressively increased with frequency. Specifically, HC neurons were characterized by a flat Smax gain and an approximately 10-fold increase of Smin gain per frequency decade. Thus, these neurons encode linear acceleration when stimulated along their maximum sensitivity direction, and the rate of change of linear acceleration (jerk) when stimulated along their minimum sensitivity direction. While the Smax vectors were distributed throughout the horizontal plane, the Smin vectors were concentrated mainly ipsilaterally with respect to head acceleration and clustered around the naso-occipital head axis. The properties of VC neurons were distinctly different from those of HC cells. The majority of VC cells showed decreasing Smax gains and small, relatively flat, Smin gains as a function of frequency. The Smax vectors were distributed ipsilaterally relative to the induced (apparent) head tilt. In type I anterior or posterior VC neurons, Smax vectors were clustered around the projection of the respective ipsilateral canal plane onto the horizontal head plane. These distinct spatial and temporal properties of HC and VC neurons during linear acceleration are compatible with the spatiotemporal organization of the horizontal and the vertical/torsional ocular responses, respectively, elicited in the rat during linear translation in the horizontal head plane. In addition, the data suggest a spatially and temporally specific and selective otolith/canal convergence. We propose that the central otolith system is organized in canal coordinates such that there is a close alignment between the plane of angular acceleration (canal) sensitivity and the plane of linear acceleration (otolith) sensitivity in otolith/canal-convergent vestibular nuclei neurons.

  19. Tight-binding approximations to time-dependent density functional theory — A fast approach for the calculation of electronically excited states

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

    Rüger, Robert, E-mail: rueger@scm.com; Department of Theoretical Chemistry, Vrije Universiteit Amsterdam, De Boelelaan 1083, 1081 HV Amsterdam; Wilhelm-Ostwald-Institut für Physikalische und Theoretische Chemie, Linnéstr. 2, 04103 Leipzig

    2016-05-14

    We propose a new method of calculating electronically excited states that combines a density functional theory based ground state calculation with a linear response treatment that employs approximations used in the time-dependent density functional based tight binding (TD-DFTB) approach. The new method termed time-dependent density functional theory TD-DFT+TB does not rely on the DFTB parametrization and is therefore applicable to systems involving all combinations of elements. We show that the new method yields UV/Vis absorption spectra that are in excellent agreement with computationally much more expensive TD-DFT calculations. Errors in vertical excitation energies are reduced by a factor of twomore » compared to TD-DFTB.« less

  20. Numerical Simulation Of Shock Response To Wall Changes In High Speed Intakes

    NASA Astrophysics Data System (ADS)

    Fincham, J.; Taylor, N. V.

    2011-05-01

    Hypersonic flight presents a number of challenges to the designer, one of which is the intake behaviour. Minimising drag requires careful positioning of the intake shock structure, while accurate understanding of the dynamic behaviour is required to allow minimisation of margins. In this paper, a two shock external compression intake derived from the Reaction Engines Limited SABRE engine is examined using inviscid axisymmetric CFD analysis to determine the response of the normal shockwave to axial motion of the intake centrebody. An approximately linear relationship between centrebody position and both the normal shock position and additive drag in steady flow is demonstrated. Initial results from an unsteady analysis are also given, which show complex behaviours may be triggered by rapid motion of the centrebody in response to control input.

  1. Asymptotic analysis of noisy fitness maximization, applied to metabolism & growth

    NASA Astrophysics Data System (ADS)

    De Martino, Daniele; Masoero, Davide

    2016-12-01

    We consider a population dynamics model coupling cell growth to a diffusion in the space of metabolic phenotypes as it can be obtained from realistic constraints-based modeling. In the asymptotic regime of slow diffusion, that coincides with the relevant experimental range, the resulting non-linear Fokker-Planck equation is solved for the steady state in the WKB approximation that maps it into the ground state of a quantum particle in an Airy potential plus a centrifugal term. We retrieve scaling laws for growth rate fluctuations and time response with respect to the distance from the maximum growth rate suggesting that suboptimal populations can have a faster response to perturbations.

  2. A Bayesian approach to identifying structural nonlinearity using free-decay response: Application to damage detection in composites

    USGS Publications Warehouse

    Nichols, J.M.; Link, W.A.; Murphy, K.D.; Olson, C.C.

    2010-01-01

    This work discusses a Bayesian approach to approximating the distribution of parameters governing nonlinear structural systems. Specifically, we use a Markov Chain Monte Carlo method for sampling the posterior parameter distributions thus producing both point and interval estimates for parameters. The method is first used to identify both linear and nonlinear parameters in a multiple degree-of-freedom structural systems using free-decay vibrations. The approach is then applied to the problem of identifying the location, size, and depth of delamination in a model composite beam. The influence of additive Gaussian noise on the response data is explored with respect to the quality of the resulting parameter estimates.

  3. Hall viscosity of a chiral two-orbital superconductor at finite temperatures

    NASA Astrophysics Data System (ADS)

    Yazdani-Hamid, Meghdad; Shahzamanian, Mohammad Ali

    2018-06-01

    The Hall viscosity known as the anti-symmetric part of the viscosity fourth-rank tensor. Such dissipationless response which appears for systems with broken time reversal symmetry. We calculate this non-dissipative quantity for a chiral two-orbital superconductor placed in a viscoelastic magnetic field using the linear response theory and apply our calculations to the putative multiband chiral superconductor Sr2RuO4. The chirality origin of a multiband superconductor arises from the interorbital coupling of the superconducting state. This feature leads to the robustness of the Hall viscosity against temperature and impurity effects. We study the temperature effect on the Hall viscosity at the one-loop approximation.

  4. Estuarine Response to River Flow and Sea-Level Rise under Future Climate Change and Human Development

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

    Yang, Zhaoqing; Wang, Taiping; Voisin, Nathalie

    Understanding the response of river flow and estuarine hydrodynamics to climate change, land-use/land-cover change (LULC), and sea-level rise is essential to managing water resources and stress on living organisms under these changing conditions. This paper presents a modeling study using a watershed hydrology model and an estuarine hydrodynamic model, in a one-way coupling, to investigate the estuarine hydrodynamic response to sea-level rise and change in river flow due to the effect of future climate and LULC changes in the Snohomish River estuary, Washington, USA. A set of hydrodynamic variables, including salinity intrusion points, average water depth, and salinity of themore » inundated area, were used to quantify the estuarine response to river flow and sea-level rise. Model results suggest that salinity intrusion points in the Snohomish River estuary and the average salinity of the inundated areas are a nonlinear function of river flow, although the average water depth in the inundated area is approximately linear with river flow. Future climate changes will shift salinity intrusion points further upstream under low flow conditions and further downstream under high flow conditions. In contrast, under the future LULC change scenario, the salinity intrusion point will shift downstream under both low and high flow conditions, compared to present conditions. The model results also suggest that the average water depth in the inundated areas increases linearly with sea-level rise but at a slower rate, and the average salinity in the inundated areas increases linearly with sea-level rise; however, the response of salinity intrusion points in the river to sea-level rise is strongly nonlinear.« less

  5. Relationships between nonlinear normal modes and response to random inputs

    DOE PAGES

    Schoneman, Joseph D.; Allen, Matthew S.; Kuether, Robert J.

    2016-07-25

    The ability to model nonlinear structures subject to random excitation is of key importance in designing hypersonic aircraft and other advanced aerospace vehicles. When a structure is linear, superposition can be used to construct its response to a known spectrum in terms of its linear modes. Superposition does not hold for a nonlinear system, but several works have shown that a system's dynamics can still be understood qualitatively in terms of its nonlinear normal modes (NNMs). Here, this work investigates the connection between a structure's undamped nonlinear normal modes and the spectrum of its response to high amplitude random forcing.more » Two examples are investigated: a spring-mass system and a clamped-clamped beam modeled within a geometrically nonlinear finite element package. In both cases, an intimate connection is observed between the smeared peaks in the response spectrum and the frequency-energy dependence of the nonlinear normal modes. In order to understand the role of coupling between the underlying linear modes, reduced order models with and without modal coupling terms are used to separate the effect of each NNM's backbone from the nonlinear couplings that give rise to internal resonances. In the cases shown here, uncoupled, single-degree-of-freedom nonlinear models are found to predict major features in the response with reasonable accuracy; a highly inexpensive approximation such as this could be useful in design and optimization studies. More importantly, the results show that a reduced order model can be expected to give accurate results only if it is also capable of accurately predicting the frequency-energy dependence of the nonlinear modes that are excited.« less

  6. Summary of the SeaRISE Project's Experiments on Modeled Ice-Sheet Contributions to Future Sea Level: Linearities and Non-linearities

    NASA Astrophysics Data System (ADS)

    Bindschadler, Robert

    2013-04-01

    The SeaRISE (Sea-level Response to Ice Sheet Evolution) project achieved ice-sheet model ensemble responses to a variety of prescribed changes to surface mass balance, basal sliding and ocean boundary melting. Greenland ice sheet models are more sensitive than Antarctic ice sheet models to likely atmospheric changes in surface mass balance, while Antarctic models are most sensitive to basal melting of its ice shelves. An experiment approximating the IPCC's RCP8.5 scenario produces first century contributions to sea level of 22.3 and 7.3 cm from Greenland and Antarctica, respectively, with a range among models of 62 and 17 cm, respectively. By 200 years, these projections increase to 53.2 and 23.4 cm, respectively, with ranges of 79 and 57 cm. The considerable range among models was not only in the magnitude of ice lost, but also in the spatial pattern of response to identical forcing. Despite this variation, the response of any single model to a large range in the forcing intensity was remarkably linear in most cases. Additionally, the results of sensitivity experiments to single types of forcing (i.e., only one of the surface mass balance, or basal sliding, or ocean boundary melting) could be summed to accurately predict any model's result for an experiment when multiple forcings were applied simultaneously. This suggests a limited amount of feedback through the ice sheet's internal dynamics between these types of forcing over the time scale of a few centuries (SeaRISE experiments lasted 500 years).

  7. Essential uncontrollability of discrete linear, time-invariant, dynamical systems

    NASA Technical Reports Server (NTRS)

    Cliff, E. M.

    1975-01-01

    The concept of a 'best approximating m-dimensional subspace' for a given set of vectors in n-dimensional whole space is introduced. Such a subspace is easily described in terms of the eigenvectors of an associated Gram matrix. This technique is used to approximate an achievable set for a discrete linear time-invariant dynamical system. This approximation characterizes the part of the state space that may be reached using modest levels of control. If the achievable set can be closely approximated by a proper subspace of the whole space then the system is 'essentially uncontrollable'. The notion finds application in studies of failure-tolerant systems, and in decoupling.

  8. Response Strength in Extreme Multiple Schedules

    PubMed Central

    McLean, Anthony P; Grace, Randolph C; Nevin, John A

    2012-01-01

    Four pigeons were trained in a series of two-component multiple schedules. Reinforcers were scheduled with random-interval schedules. The ratio of arranged reinforcer rates in the two components was varied over 4 log units, a much wider range than previously studied. When performance appeared stable, prefeeding tests were conducted to assess resistance to change. Contrary to the generalized matching law, logarithms of response ratios in the two components were not a linear function of log reinforcer ratios, implying a failure of parameter invariance. Over a 2 log unit range, the function appeared linear and indicated undermatching, but in conditions with more extreme reinforcer ratios, approximate matching was observed. A model suggested by McLean (1991), originally for local contrast, predicts these changes in sensitivity to reinforcer ratios somewhat better than models by Herrnstein (1970) and by Williams and Wixted (1986). Prefeeding tests of resistance to change were conducted at each reinforcer ratio, and relative resistance to change was also a nonlinear function of log reinforcer ratios, again contrary to conclusions from previous work. Instead, the function suggests that resistance to change in a component may be determined partly by the rate of reinforcement and partly by the ratio of reinforcers to responses. PMID:22287804

  9. Assessing direct analysis in real-time-mass spectrometry (DART-MS) for the rapid identification of additives in food packaging.

    PubMed

    Ackerman, L K; Noonan, G O; Begley, T H

    2009-12-01

    The ambient ionization technique direct analysis in real time (DART) was characterized and evaluated for the screening of food packaging for the presence of packaging additives using a benchtop mass spectrometer (MS). Approximate optimum conditions were determined for 13 common food-packaging additives, including plasticizers, anti-oxidants, colorants, grease-proofers, and ultraviolet light stabilizers. Method sensitivity and linearity were evaluated using solutions and characterized polymer samples. Additionally, the response of a model additive (di-ethyl-hexyl-phthalate) was examined across a range of sample positions, DART, and MS conditions (temperature, voltage and helium flow). Under optimal conditions, molecular ion (M+H+) was the major ion for most additives. Additive responses were highly sensitive to sample and DART source orientation, as well as to DART flow rates, temperatures, and MS inlet voltages, respectively. DART-MS response was neither consistently linear nor quantitative in this setting, and sensitivity varied by additive. All additives studied were rapidly identified in multiple food-packaging materials by DART-MS/MS, suggesting this technique can be used to screen food packaging rapidly. However, method sensitivity and quantitation requires further study and improvement.

  10. Data-driven discovery of Koopman eigenfunctions using deep learning

    NASA Astrophysics Data System (ADS)

    Lusch, Bethany; Brunton, Steven L.; Kutz, J. Nathan

    2017-11-01

    Koopman operator theory transforms any autonomous non-linear dynamical system into an infinite-dimensional linear system. Since linear systems are well-understood, a mapping of non-linear dynamics to linear dynamics provides a powerful approach to understanding and controlling fluid flows. However, finding the correct change of variables remains an open challenge. We present a strategy to discover an approximate mapping using deep learning. Our neural networks find this change of variables, its inverse, and a finite-dimensional linear dynamical system defined on the new variables. Our method is completely data-driven and only requires measurements of the system, i.e. it does not require derivatives or knowledge of the governing equations. We find a minimal set of approximate Koopman eigenfunctions that are sufficient to reconstruct and advance the system to future states. We demonstrate the method on several dynamical systems.

  11. A remote query magnetoelastic pH sensor.

    PubMed

    Cai, Q Y; Grimes, C A

    2000-11-15

    A remote query magnetoelastic pH sensor comprised of a magnetoelastic thick-film coated with a mass-changing pH-responsive polymer is described. In response to a magnetic query field the magnetoelastic sensor mechanically vibrates at a characteristic frequency that is inversely dependent upon the mass of the attached polymer layer. As the magnetoelastic sensor is magnetostrictive the mechanical vibrations of the sensor launch magnetic flux that can be detected remotely from the sensor using a pickup coil. The pH responsive copolymer is synthesized from 20 mol% of acrylic acid and 80 mol% of iso-octyl acrylate and then deposited onto a magnetoelastic film by dip-coating. For a 1 micrometer polymer coating upon a 30 micrometer thick Metglas [The Metglas alloys are a registered trademark of Honeywell Corporation. For product information see: http://www.electronicmaterials.com:80/businesses/sem/amorph/page5_1_2.htm.] alloy 2826MB magnetoelastic film between pH 5 and 9 the change in resonant frequency is linear, approximately 285 Hz/pH or 0.6%/pH. The addition of 10 mmol/l of KCl to the test solution decreases the sensitivity of the polymer approximately 4%. c2000 Elsevier Science B.V. All rights reserved.

  12. An analytical solution for the elastic response to surface loads imposed on a layered, transversely isotropic and self-gravitating Earth

    NASA Astrophysics Data System (ADS)

    Pan, E.; Chen, J. Y.; Bevis, M.; Bordoni, A.; Barletta, V. R.; Molavi Tabrizi, A.

    2015-12-01

    We present an analytical solution for the elastic deformation of an elastic, transversely isotropic, layered and self-gravitating Earth by surface loads. We first introduce the vector spherical harmonics to express the physical quantities in the layered Earth. This reduces the governing equations to a linear system of equations for the expansion coefficients. We then solve for the expansion coefficients analytically under the assumption (i.e. approximation) that in the mantle, the density in each layer varies as 1/r (where r is the radial coordinate) while the gravity is constant and that in the core the gravity in each layer varies linearly in r with constant density. These approximations dramatically simplify the subsequent mathematical analysis and render closed-form expressions for the expansion coefficients. We implement our solution in a MATLAB code and perform a benchmark which shows both the correctness of our solution and the implementation. We also calculate the load Love numbers (LLNs) of the PREM Earth for different degrees of the Legendre function for both isotropic and transversely isotropic, layered mantles with different core models, demonstrating for the first time the effect of Earth anisotropy on the LLNs.

  13. Ordinal probability effect measures for group comparisons in multinomial cumulative link models.

    PubMed

    Agresti, Alan; Kateri, Maria

    2017-03-01

    We consider simple ordinal model-based probability effect measures for comparing distributions of two groups, adjusted for explanatory variables. An "ordinal superiority" measure summarizes the probability that an observation from one distribution falls above an independent observation from the other distribution, adjusted for explanatory variables in a model. The measure applies directly to normal linear models and to a normal latent variable model for ordinal response variables. It equals Φ(β/2) for the corresponding ordinal model that applies a probit link function to cumulative multinomial probabilities, for standard normal cdf Φ and effect β that is the coefficient of the group indicator variable. For the more general latent variable model for ordinal responses that corresponds to a linear model with other possible error distributions and corresponding link functions for cumulative multinomial probabilities, the ordinal superiority measure equals exp(β)/[1+exp(β)] with the log-log link and equals approximately exp(β/2)/[1+exp(β/2)] with the logit link, where β is the group effect. Another ordinal superiority measure generalizes the difference of proportions from binary to ordinal responses. We also present related measures directly for ordinal models for the observed response that need not assume corresponding latent response models. We present confidence intervals for the measures and illustrate with an example. © 2016, The International Biometric Society.

  14. Stochastic Swift-Hohenberg Equation with Degenerate Linear Multiplicative Noise

    NASA Astrophysics Data System (ADS)

    Hernández, Marco; Ong, Kiah Wah

    2018-03-01

    We study the dynamic transition of the Swift-Hohenberg equation (SHE) when linear multiplicative noise acting on a finite set of modes of the dominant linear flow is introduced. Existence of a stochastic flow and a local stochastic invariant manifold for this stochastic form of SHE are both addressed in this work. We show that the approximate reduced system corresponding to the invariant manifold undergoes a stochastic pitchfork bifurcation, and obtain numerical evidence suggesting that this picture is a good approximation for the full system as well.

  15. How much would five trillion tonnes of carbon warm the climate?

    NASA Astrophysics Data System (ADS)

    Tokarska, Katarzyna Kasia; Gillett, Nathan P.; Weaver, Andrew J.; Arora, Vivek K.

    2016-04-01

    While estimates of fossil fuel reserves and resources are very uncertain, and the amount which could ultimately be burnt under a business as usual scenario would depend on prevailing economic and technological conditions, an amount of five trillion tonnes of carbon (5 EgC), corresponding to the lower end of the range of estimates of the total fossil fuel resource, is often cited as an estimate of total cumulative emissions in the absence of mitigation actions. The IPCC Fifth Assessment Report indicates that an approximately linear relationship between warming and cumulative carbon emissions holds only up to around 2 EgC emissions. It is typically assumed that at higher cumulative emissions the warming would tend to be less than that predicted by such a linear relationship, with the radiative saturation effect dominating the effects of positive carbon-climate feedbacks at high emissions, as predicted by simple carbon-climate models. We analyze simulations from four state-of-the-art Earth System Models (ESMs) from the Coupled Model Intercomparison Project Phase 5 (CMIP5) and seven Earth System Models of Intermediate Complexity (EMICs), driven by the Representative Concentration Pathway 8.5 Extension scenario (RCP 8.5 Ext), which represents a very high emission scenario of increasing greenhouse gas concentrations in absence of climate mitigation policies. Our results demonstrate that while terrestrial and ocean carbon storage varies between the models, the CO2-induced warming continues to increase approximately linearly with cumulative carbon emissions even for higher levels of cumulative emissions, in all four ESMs. Five of the seven EMICs considered simulate a similarly linear response, while two exhibit less warming at higher cumulative emissions for reasons we discuss. The ESMs simulate global mean warming of 6.6-11.0°C, mean Arctic warming of 15.3-19.7°C, and mean regional precipitation increases and decreases by more than a factor of four, in response to 5EgC, with smaller forcing contributions from other greenhouse gases. These results indicate that the unregulated exploitation of the fossil fuel resource would ultimately result in considerably more profound climate changes than previously suggested.

  16. On the importance of excited state dynamic response electron correlation in polarizable embedding methods.

    PubMed

    Eriksen, Janus J; Sauer, Stephan P A; Mikkelsen, Kurt V; Jensen, Hans J Aa; Kongsted, Jacob

    2012-09-30

    We investigate the effect of including a dynamic reaction field at the lowest possible ab inito wave function level of theory, namely the Hartree-Fock (HF) self-consistent field level within the polarizable embedding (PE) formalism. We formulate HF based PE within the linear response theory picture leading to the PE-random-phase approximation (PE-RPA) and bridge the expressions to a second-order polarization propagator approximation (SOPPA) frame such that dynamic reaction field contributions are included at the RPA level in addition to the static response described at the SOPPA level but with HF induced dipole moments. We conduct calculations on para-nitro-aniline and para-nitro-phenolate using said model in addition to dynamic PE-RPA and PE-CAM-B3LYP. We compare the results to recently published PE-CCSD data and demonstrate how the cost effective SOPPA-based model successfully recovers a great portion of the inherent PE-RPA error when the observable is the solvatochromic shift. We furthermore demonstrate that whenever the change in density resulting from the ground state-excited state electronic transition in the solute is not associated with a significant change in the electric field, dynamic response contributions formulated at the HF level of theory manage to capture the majority of the system response originating from derivative densities. Copyright © 2012 Wiley Periodicals, Inc.

  17. Finite-dimensional linear approximations of solutions to general irregular nonlinear operator equations and equations with quadratic operators

    NASA Astrophysics Data System (ADS)

    Kokurin, M. Yu.

    2010-11-01

    A general scheme for improving approximate solutions to irregular nonlinear operator equations in Hilbert spaces is proposed and analyzed in the presence of errors. A modification of this scheme designed for equations with quadratic operators is also examined. The technique of universal linear approximations of irregular equations is combined with the projection onto finite-dimensional subspaces of a special form. It is shown that, for finite-dimensional quadratic problems, the proposed scheme provides information about the global geometric properties of the intersections of quadrics.

  18. Bifurcations and Chaos of AN Immersed Cantilever Beam in a Fluid and Carrying AN Intermediate Mass

    NASA Astrophysics Data System (ADS)

    AL-QAISIA, A. A.; HAMDAN, M. N.

    2002-06-01

    The concern of this work is the local stability and period-doubling bifurcations of the response to a transverse harmonic excitation of a slender cantilever beam partially immersed in a fluid and carrying an intermediate lumped mass. The unimodal form of the non-linear dynamic model describing the beam-mass in-plane large-amplitude flexural vibration, which accounts for axial inertia, non-linear curvature and inextensibility condition, developed in Al-Qaisia et al. (2000Shock and Vibration7 , 179-194), is analyzed and studied for the resonance responses of the first three modes of vibration, using two-term harmonic balance method. Then a consistent second order stability analysis of the associated linearized variational equation is carried out using approximate methods to predict the zones of symmetry breaking leading to period-doubling bifurcation and chaos on the resonance response curves. The results of the present work are verified for selected physical system parameters by numerical simulations using methods of the qualitative theory, and good agreement was obtained between the analytical and numerical results. Also, analytical prediction of the period-doubling bifurcation and chaos boundaries obtained using a period-doubling bifurcation criterion proposed in Al-Qaisia and Hamdan (2001 Journal of Sound and Vibration244, 453-479) are compared with those of computer simulations. In addition, results of the effect of fluid density, fluid depth, mass ratio, mass position and damping on the period-doubling bifurcation diagrams are studies and presented.

  19. Estimating sub-surface dispersed oil concentration using acoustic backscatter response.

    PubMed

    Fuller, Christopher B; Bonner, James S; Islam, Mohammad S; Page, Cheryl; Ojo, Temitope; Kirkey, William

    2013-05-15

    The recent Deepwater Horizon disaster resulted in a dispersed oil plume at an approximate depth of 1000 m. Several methods were used to characterize this plume with respect to concentration and spatial extent including surface supported sampling and autonomous underwater vehicles with in situ instrument payloads. Additionally, echo sounders were used to track the plume location, demonstrating the potential for remote detection using acoustic backscatter (ABS). This study evaluated use of an Acoustic Doppler Current Profiler (ADCP) to quantitatively detect oil-droplet suspensions from the ABS response in a controlled laboratory setting. Results from this study showed log-linear ABS responses to oil-droplet volume concentration. However, the inability to reproduce ABS response factors suggests the difficultly in developing meaningful calibration factors for quantitative field analysis. Evaluation of theoretical ABS intensity derived from the particle size distribution provided insight regarding method sensitivity in the presence of interfering ambient particles. Copyright © 2013 Elsevier Ltd. All rights reserved.

  20. Assessment of the setup dependence of detector response functions for mega-voltage linear accelerators

    PubMed Central

    Fox, Christopher; Simon, Tom; Simon, Bill; Dempsey, James F.; Kahler, Darren; Palta, Jatinder R.; Liu, Chihray; Yan, Guanghua

    2010-01-01

    Purpose: Accurate modeling of beam profiles is important for precise treatment planning dosimetry. Calculated beam profiles need to precisely replicate profiles measured during machine commissioning. Finite detector size introduces perturbations into the measured profiles, which, in turn, impact the resulting modeled profiles. The authors investigate a method for extracting the unperturbed beam profiles from those measured during linear accelerator commissioning. Methods: In-plane and cross-plane data were collected for an Elekta Synergy linac at 6 MV using ionization chambers of volume 0.01, 0.04, 0.13, and 0.65 cm3 and a diode of surface area 0.64 mm2. The detectors were orientated with the stem perpendicular to the beam and pointing away from the gantry. Profiles were measured for a 10×10 cm2 field at depths ranging from 0.8 to 25.0 cm and SSDs from 90 to 110 cm. Shaping parameters of a Gaussian response function were obtained relative to the Edge detector. The Gaussian function was deconvolved from the measured ionization chamber data. The Edge detector profile was taken as an approximation to the true profile, to which deconvolved data were compared. Data were also collected with CC13 and Edge detectors for additional fields and energies on an Elekta Synergy, Varian Trilogy, and Siemens Oncor linear accelerator and response functions obtained. Response functions were compared as a function of depth, SSD, and detector scan direction. Variations in the shaping parameter were introduced and the effect on the resulting deconvolution profiles assessed. Results: Up to 10% setup dependence in the Gaussian shaping parameter occurred, for each detector for a particular plane. This translated to less than a ±0.7 mm variation in the 80%–20% penumbral width. For large volume ionization chambers such as the FC65 Farmer type, where the cavity length to diameter ratio is far from 1, the scan direction produced up to a 40% difference in the shaping parameter between in-plane and cross-plane measurements. This is primarily due to the directional difference in penumbral width measured by the FC65 chamber, which can more than double in profiles obtained with the detector stem parallel compared to perpendicular to the scan direction. For the more symmetric CC13 chamber the variation was only 3% between in-plane and cross-plane measurements. Conclusions: The authors have shown that the detector response varies with detector type, depth, SSD, and detector scan direction. In-plane vs cross-plane scanning can require calculation of a direction dependent response function. The effect of a 10% overall variation in the response function, for an ionization chamber, translates to a small deviation in the penumbra from that of the Edge detector measured profile when deconvolved. Due to the uncertainties introduced by deconvolution the Edge detector would be preferable in obtaining an approximation of the true profile, particularly for field sizes where the energy dependence of the diode can be neglected. However, an averaged response function could be utilized to provide a good approximation of the true profile for large ionization chambers and for larger fields for which diode detectors are not recommended. PMID:20229856

  1. Many-body problem

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

    Parry, W.E.

    1973-01-01

    An introduction is given to techniques used in the many-body problem, and a reference book is given for those techniques. Sevcral different formulations of the techniques, and their interrelations, are discussed, to prepare the reader for the published literature. Examples are taken mostly from the physics of solids, fluids and plasmas. Second quantization, perturbation theory, Green functions and correlation functions, examples in the use of diagrammatic perturbation theory, the equation of motion method, magnetism (the drone-fermion representation), linear response and transport processes, niany- body systems at zero temperature, the variational principle and pair-wave approximation. (UK)

  2. Neurobehavioral Effects of Carbon Monoxide (CO) Exposure in Humans: Elevated Carboxyhemoglobin (COHb) and Cerebrovascular Responses

    DTIC Science & Technology

    1989-05-19

    were (a) the dicrotic notch (see Figure 1) had to be present (b) no truncation or clipping could be present (c) the falling portion after the dichrotic... dicrotic notch or closing of the aortic valve (see Figure 1). The analog signal is fed to a delta z rebalancing circuit which has a maximum D.C. limit in... notch had to be relatively linear and (d) there could be only moderate baseline drift (maximum of approximately 30 degree baseline angle with respect

  3. Ultrasonic waves in classical gases

    NASA Astrophysics Data System (ADS)

    Magner, A. G.; Gorenstein, M. I.; Grygoriev, U. V.

    2017-12-01

    The velocity and absorption coefficient for the plane sound waves in a classical gas are obtained by solving the Boltzmann kinetic equation, which describes the reaction of the single-particle distribution function to a periodic external field. Within the linear response theory, the nonperturbative dispersion equation valid for all sound frequencies is derived and solved numerically. The results are in agreement with the approximate analytical solutions found for both the frequent- and rare-collision regimes. These results are also in qualitative agreement with the experimental data for ultrasonic waves in dilute gases.

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

    NASA Technical Reports Server (NTRS)

    Ito, Kazufumi

    1987-01-01

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

  5. 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.

  6. Linear Optical Response of Silicon Nanotubes Under Axial Magnetic Field

    NASA Astrophysics Data System (ADS)

    Chegel, Raad; Behzad, Somayeh

    2013-01-01

    We investigated the optical properties of silicon nanotubes (SiNTs) in the low energy region, E < 0.5 eV, and middle energy region, 1.8 eV < E < 2 eV. The dependence of optical matrix elements and linear susceptibility on radius and magnetic field, in terms of one-dimensional (1-d) wavevector and subband index, is calculated using the tight-binding approximation. It is found that, on increasing the nanotube diameter, the low-energy peaks show red-shift and their intensities are decreased. Also, we found that in the middle energy region all tubes have two distinct peaks, where the energy position of the second peak is approximately constant and independent of the nanotube diameter. Comparing the band structure of these tubes in different magnetic fields, several differences are clearly seen, such as splitting of degenerate bands, creation of additional band-edge states, and bandgap modification. It is found that applying the magnetic field leads to a phase transition in zigzag silicon hexagonal nanotubes (Si h-NTs), unlike in zigzag silicon gear-like nanotubes (Si g-NTs), which remain semiconducting in any magnetic field. We found that the axial magnetic field has two effects on the linear susceptibility spectrum, namely broadening and splitting. The axial magnetic field leads to the creation of a peak with energy less than 0.2 eV in metallic Si h-NTs, whereas in the absence of a magnetic field such a transition is not allowed.

  7. Ontogeny of vestibular compound action potentials in the domestic chicken

    NASA Technical Reports Server (NTRS)

    Jones, S. M.; Jones, T. A.

    2000-01-01

    Compound action potentials of the vestibular nerve were measured from the surface of the scalp in 148 chickens (Gallus domesticus). Ages ranged from incubation day 18 (E18) to 22 days posthatch (P22). Responses were elicited using linear acceleration cranial pulses. Response thresholds decreased at an average rate of -0.45 dB/day. The decrease was best fit by an exponential model with half-maturity time constant of 5.1 days and asymptote of approximately -25.9 dB re:1.0 g/ms. Mean threshold approached within 3 dB of the asymptote by ages P6-P9. Similarly, response latencies decreased exponentially to within 3% of mature values at ages beyond P9. The half-maturity time constant for peripheral response peak latencies P1, N1, and P2 was comparable to thresholds and ranged from approximately 4.6 to 6.2 days, whereas central peaks (N2, P3, and N3) ranged from 2.9 to 3.4 days. Latency-intensity slopes for P1, N1, and P2 tended to decrease with age, reaching mature values within approximately 100 hours of hatching. Amplitudes increased as a function of age with average growth rates for response peaks ranging from 0.04 to 0.09 microV/day. There was no obvious asymptote to the growth of amplitudes over the ages studied. Amplitude-intensity slopes also increased modestly with age. The results show that gravity receptors are responsive to transient cranial stimuli as early as E19 in the chicken embryo. The functional response of gravity receptors continues to develop for many days after all major morphological structures are in place. Distinct maturational processes can be identified in central and peripheral neural relays. Functional improvements during maturation may result from refinements in the receptor epithelia, improvements in central and peripheral synaptic transmission, increased neural myelination, as well as changes in the mechanical coupling between the cranium and receptor organ.

  8. Ontogeny of Vestibular Compound Action Potentials in the Domestic Chicken

    PubMed Central

    M. Jones, Sherri

    2000-01-01

    Compound action potentials of the vestibular nerve were measured from the surface of the scalp in 148 chickens (Gallus domesticus). Ages ranged from incubation day 18 (E18) to 22 days posthatch (P22). Responses were elicited using linear acceleration cranial pulses. Response thresholds decreased at an average rate of –0.45 dB/day. The decrease was best fit by an exponential model with half-maturity time constant of 5.1 days and asymptote of approximately –25.9 dB re:1.0 g/ms. Mean threshold approached within 3 dB of the asymptote by ages P6–P9. Similarly, response latencies decreased exponentially to within 3% of mature values at ages beyond P9. The half-maturity time constant for peripheral response peak latencies P1, N1, and P2 was comparable to thresholds and ranged from approximately 4.6 to 6.2 days, whereas central peaks (N2, P3, and N3) ranged from 2.9 to 3.4 days. Latency-intensity slopes for P1, N1, and P2 tended to decrease with age, reaching mature values within approximately 100 hours of hatching. Amplitudes increased as a function of age with average growth rates for response peaks ranging from 0.04 to 0.09 μV/day. There was no obvious asymptote to the growth of amplitudes over the ages studied. Amplitude-intensity slopes also increased modestly with age. The results show that gravity receptors are responsive to transient cranial stimuli as early as E19 in the chicken embryo. The functional response of gravity receptors continues to develop for many days after all major morphological structures are in place. Distinct maturational processes can be identified in central and peripheral neural relays. Functional improvements during maturation may result from refinements in the receptor epithelia, improvements in central and peripheral synaptic transmission, increased neural myelination, as well as changes in the mechanical coupling between the cranium and receptor organ. PMID:11545229

  9. Fall with Linear Drag and Wien's Displacement Law: Approximate Solution and Lambert Function

    ERIC Educational Resources Information Center

    Vial, Alexandre

    2012-01-01

    We present an approximate solution for the downward time of travel in the case of a mass falling with a linear drag force. We show how a quasi-analytical solution implying the Lambert function can be found. We also show that solving the previous problem is equivalent to the search for Wien's displacement law. These results can be of interest for…

  10. A Galerkin approximation for linear elastic shallow shells

    NASA Astrophysics Data System (ADS)

    Figueiredo, I. N.; Trabucho, L.

    1992-03-01

    This work is a generalization to shallow shell models of previous results for plates by B. Miara (1989). Using the same basis functions as in the plate case, we construct a Galerkin approximation of the three-dimensional linearized elasticity problem, and establish some error estimates as a function of the thickness, the curvature, the geometry of the shell, the forces and the Lamé costants.

  11. Approximating a nonlinear advanced-delayed equation from acoustics

    NASA Astrophysics Data System (ADS)

    Teodoro, M. Filomena

    2016-10-01

    We approximate the solution of a particular non-linear mixed type functional differential equation from physiology, the mucosal wave model of the vocal oscillation during phonation. The mathematical equation models a superficial wave propagating through the tissues. The numerical scheme is adapted from the work presented in [1, 2, 3], using homotopy analysis method (HAM) to solve the non linear mixed type equation under study.

  12. An implicit-iterative solution of the heat conduction equation with a radiation boundary condition

    NASA Technical Reports Server (NTRS)

    Williams, S. D.; Curry, D. M.

    1977-01-01

    For the problem of predicting one-dimensional heat transfer between conducting and radiating mediums by an implicit finite difference method, four different formulations were used to approximate the surface radiation boundary condition while retaining an implicit formulation for the interior temperature nodes. These formulations are an explicit boundary condition, a linearized boundary condition, an iterative boundary condition, and a semi-iterative boundary method. The results of these methods in predicting surface temperature on the space shuttle orbiter thermal protection system model under a variety of heating rates were compared. The iterative technique caused the surface temperature to be bounded at each step. While the linearized and explicit methods were generally more efficient, the iterative and semi-iterative techniques provided a realistic surface temperature response without requiring step size control techniques.

  13. Dynamical discrete/continuum linear response shells theory of solvation: convergence test for NH4+ and OH- ions in water solution using DFT and DFTB methods.

    PubMed

    de Lima, Guilherme Ferreira; Duarte, Hélio Anderson; Pliego, Josefredo R

    2010-12-09

    A new dynamical discrete/continuum solvation model was tested for NH(4)(+) and OH(-) ions in water solvent. The method is similar to continuum solvation models in a sense that the linear response approximation is used. However, different from pure continuum models, explicit solvent molecules are included in the inner shell, which allows adequate treatment of specific solute-solvent interactions present in the first solvation shell, the main drawback of continuum models. Molecular dynamics calculations coupled with SCC-DFTB method are used to generate the configurations of the solute in a box with 64 water molecules, while the interaction energies are calculated at the DFT level. We have tested the convergence of the method using a variable number of explicit water molecules and it was found that even a small number of waters (as low as 14) are able to produce converged values. Our results also point out that the Born model, often used for long-range correction, is not reliable and our method should be applied for more accurate calculations.

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

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

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

    2014-03-14

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

  15. Efficient block preconditioned eigensolvers for linear response time-dependent density functional theory

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

    Vecharynski, Eugene; Brabec, Jiri; Shao, Meiyue

    We present two efficient iterative algorithms for solving the linear response eigen- value problem arising from the time dependent density functional theory. Although the matrix to be diagonalized is nonsymmetric, it has a special structure that can be exploited to save both memory and floating point operations. In particular, the nonsymmetric eigenvalue problem can be transformed into a product eigenvalue problem that is self-adjoint with respect to a K-inner product. This product eigenvalue problem can be solved efficiently by a modified Davidson algorithm and a modified locally optimal block preconditioned conjugate gradient (LOBPCG) algorithm that make use of the K-innermore » product. The solution of the product eigenvalue problem yields one component of the eigenvector associated with the original eigenvalue problem. However, the other component of the eigenvector can be easily recovered in a postprocessing procedure. Therefore, the algorithms we present here are more efficient than existing algorithms that try to approximate both components of the eigenvectors simultaneously. The efficiency of the new algorithms is demonstrated by numerical examples.« less

  16. Nanoscale linear permittivity imaging based on scanning nonlinear dielectric microscopy

    NASA Astrophysics Data System (ADS)

    Hiranaga, Yoshiomi; Chinone, Norimichi; Cho, Yasuo

    2018-05-01

    A nanoscale linear permittivity imaging method based on scanning nonlinear dielectric microscopy (SNDM) was developed. The ∂C/∂z-mode SNDM (∂C/∂z-SNDM) technique described herein employs probe-height modulation to suppress disturbances originating from stray capacitance and to improve measurement stability. This method allows local permittivity distributions to be examined with extremely low noise levels (approximately 0.01 aF) by virtue of the highly sensitive probe. A cross-section of a multilayer oxide film was visualized using ∂C/∂z-SNDM as a demonstration, and numerical simulations of the response signals were conducted to gain additional insights. The experimental signal intensities were found to be in a good agreement with the theoretical values, with the exception of the background components, demonstrating that absolute sample permittivity values could be determined. The signal profiles near the boundaries between different dielectrics were calculated using various vibration amplitudes and the boundary transition widths were obtained. The beneficial aspects of higher-harmonic response imaging are discussed herein, taking into account assessments of spatial resolution and quantitation.

  17. Lattice dynamic properties of Rh2XAl (X=Fe and Y) alloys

    NASA Astrophysics Data System (ADS)

    Al, Selgin; Arikan, Nihat; Demir, Süleyman; Iyigör, Ahmet

    2018-02-01

    The electronic band structure, elastic and vibrational spectra of Rh2FeAl and Rh2YAl alloys were computed in detail by employing an ab-initio pseudopotential method and a linear-response technique based on the density-functional theory (DFT) scheme within a generalized gradient approximation (GGA). Computed lattice constants, bulk modulus and elastic constants were compared. Rh2YAl exhibited higher ability to resist volume change than Rh2FeAl. The elastic constants, shear modulus, Young modulus, Poisson's ratio, B/G ratio electronic band structure, total and partial density of states, and total magnetic moment of alloys were also presented. Rh2FeAl showed spin up and spin down states whereas Rh2YAl showed none due to being non-magnetic. The calculated total densities of states for both materials suggest that both alloys are metallic in nature. Full phonon spectra of Rh2FeAl and Rh2YA1 alloys in the L21 phase were collected using the ab-initio linear response method. The obtained phonon frequencies were in the positive region indicating that both alloys are dynamically stable.

  18. Nanoscale linear permittivity imaging based on scanning nonlinear dielectric microscopy.

    PubMed

    Hiranaga, Yoshiomi; Chinone, Norimichi; Cho, Yasuo

    2018-05-18

    A nanoscale linear permittivity imaging method based on scanning nonlinear dielectric microscopy (SNDM) was developed. The ∂C/∂z-mode SNDM (∂C/∂z-SNDM) technique described herein employs probe-height modulation to suppress disturbances originating from stray capacitance and to improve measurement stability. This method allows local permittivity distributions to be examined with extremely low noise levels (approximately 0.01 aF) by virtue of the highly sensitive probe. A cross-section of a multilayer oxide film was visualized using ∂C/∂z-SNDM as a demonstration, and numerical simulations of the response signals were conducted to gain additional insights. The experimental signal intensities were found to be in a good agreement with the theoretical values, with the exception of the background components, demonstrating that absolute sample permittivity values could be determined. The signal profiles near the boundaries between different dielectrics were calculated using various vibration amplitudes and the boundary transition widths were obtained. The beneficial aspects of higher-harmonic response imaging are discussed herein, taking into account assessments of spatial resolution and quantitation.

  19. Response of two identical seven-story structures to the San Fernando earthquake of February 9, 1971

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

    Freeman, S.A.; Honda, K.K.

    1973-10-01

    The results of the structural dynamic investigation of two sevenstory reinforced concrete frame structures are presented here. The structures are both Holiday Inn rnotor hotels that are essentially identical: one is locrted about 13 miles and the other about 26 miles from the epicenter of the February 9, 1971, San Fernando earthquake. Appreciable nonstructural damage as well as some structural damage was observed. Strong-motion seismic records were obtained for the roof, intermediate story, and ground floor of each structure. The analyses are based on data from the structural drawings, architectural drawings, photographs, engineering reports, and seisrnogram records obtained before, during,more » and after the San Fernando earthquake. Both structures experienced motion well beyond the limits of the building code design criteria. A change in fundamental period was observed for each structure after several seconds of response to the earthquake, which indicated nonlinear response. The analyses indicated that the elastic capacity of some structural members was exceeded. Idealized linear models were constructed to approximate response at various time segments. A method for approximating the nonlinear response of each structure is presented. The effects of nonstructural elements, yielding beams, and column capacities are illustrated. Comparisons of the two buildings are made for ductility factors, dynarnic response characteristics, and damage. Conclusions are drawn concerning the effects of the earthquake on the structures and the future capacities of the structures. (auth)« less

  20. Meta-Regression Approximations to Reduce Publication Selection Bias

    ERIC Educational Resources Information Center

    Stanley, T. D.; Doucouliagos, Hristos

    2014-01-01

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

  1. Estimating large numbers.

    PubMed

    Landy, David; Silbert, Noah; Goldin, Aleah

    2013-07-01

    Despite their importance in public discourse, numbers in the range of 1 million to 1 trillion are notoriously difficult to understand. We examine magnitude estimation by adult Americans when placing large numbers on a number line and when qualitatively evaluating descriptions of imaginary geopolitical scenarios. Prior theoretical conceptions predict a log-to-linear shift: People will either place numbers linearly or will place numbers according to a compressive logarithmic or power-shaped function (Barth & Paladino, ; Siegler & Opfer, ). While about half of people did estimate numbers linearly over this range, nearly all the remaining participants placed 1 million approximately halfway between 1 thousand and 1 billion, but placed numbers linearly across each half, as though they believed that the number words "thousand, million, billion, trillion" constitute a uniformly spaced count list. Participants in this group also tended to be optimistic in evaluations of largely ineffective political strategies, relative to linear number-line placers. The results indicate that the surface structure of number words can heavily influence processes for dealing with numbers in this range, and it can amplify the possibility that analogous surface regularities are partially responsible for parallel phenomena in children. In addition, these results have direct implications for lawmakers and scientists hoping to communicate effectively with the public. Copyright © 2013 Cognitive Science Society, Inc.

  2. Sensitivity of the human circadian pacemaker to nocturnal light: melatonin phase resetting and suppression

    NASA Technical Reports Server (NTRS)

    Zeitzer, J. M.; Dijk, D. J.; Kronauer, R.; Brown, E.; Czeisler, C.

    2000-01-01

    Ocular exposure to early morning room light can significantly advance the timing of the human circadian pacemaker. The resetting response to such light has a non-linear relationship to illuminance. The dose-response relationship of the human circadian pacemaker to late evening light of dim to moderate intensity has not been well established. Twenty-three healthy young male and female volunteers took part in a 9 day protocol in which a single experimental light exposure6.5 h in duration was given in the early biological night. The effects of the light exposure on the endogenous circadian phase of the melatonin rhythm and the acute effects of the light exposure on plasma melatonin concentration were calculated. We demonstrate that humans are highly responsive to the phase-delaying effects of light during the early biological night and that both the phase resetting response to light and the acute suppressive effects of light on plasma melatonin follow a logistic dose-response curve, as do many circadian responses to light in mammals. Contrary to expectations, we found that half of the maximal phase-delaying response achieved in response to a single episode of evening bright light ( approximately 9000 lux (lx)) can be obtained with just over 1 % of this light (dim room light of approximately 100 lx). The same held true for the acute suppressive effects of light on plasma melatonin concentrations. This indicates that even small changes in ordinary light exposure during the late evening hours can significantly affect both plasma melatonin concentrations and the entrained phase of the human circadian pacemaker.

  3. Method and apparatus for measuring web material wound on a reel

    NASA Technical Reports Server (NTRS)

    Muller, R. M. (Inventor)

    1977-01-01

    The method and apparatus for measuring the number of layers of a web material of known thickness wound on a storage or take-up reel is presented. The method and apparatus are based on the principle that, at a relatively large radius, the loci of layers of a thin web wound on the reel approximate a family of concentric circles having radii respectively successively increasing by a length equal to the web thickness. Tachometer pulses are generated in response to linear movement of the web and reset pulses are generated in response to rotation of the reel. A digital circuit, responsive to the tachometer and reset pulses, generates data indicative of the layer number of any layer of the web and of position of the web within the layer without requiring numerical interpolation.

  4. Direct differentiation of the quasi-incompressible fluid formulation of fluid-structure interaction using the PFEM

    NASA Astrophysics Data System (ADS)

    Zhu, Minjie; Scott, Michael H.

    2017-07-01

    Accurate and efficient response sensitivities for fluid-structure interaction (FSI) simulations are important for assessing the uncertain response of coastal and off-shore structures to hydrodynamic loading. To compute gradients efficiently via the direct differentiation method (DDM) for the fully incompressible fluid formulation, approximations of the sensitivity equations are necessary, leading to inaccuracies of the computed gradients when the geometry of the fluid mesh changes rapidly between successive time steps or the fluid viscosity is nonzero. To maintain accuracy of the sensitivity computations, a quasi-incompressible fluid is assumed for the response analysis of FSI using the particle finite element method and DDM is applied to this formulation, resulting in linearized equations for the response sensitivity that are consistent with those used to compute the response. Both the response and the response sensitivity can be solved using the same unified fractional step method. FSI simulations show that although the response using the quasi-incompressible and incompressible fluid formulations is similar, only the quasi-incompressible approach gives accurate response sensitivity for viscous, turbulent flows regardless of time step size.

  5. An update on modeling dose-response relationships: Accounting for correlated data structure and heterogeneous error variance in linear and nonlinear mixed models.

    PubMed

    Gonçalves, M A D; Bello, N M; Dritz, S S; Tokach, M D; DeRouchey, J M; Woodworth, J C; Goodband, R D

    2016-05-01

    Advanced methods for dose-response assessments are used to estimate the minimum concentrations of a nutrient that maximizes a given outcome of interest, thereby determining nutritional requirements for optimal performance. Contrary to standard modeling assumptions, experimental data often present a design structure that includes correlations between observations (i.e., blocking, nesting, etc.) as well as heterogeneity of error variances; either can mislead inference if disregarded. Our objective is to demonstrate practical implementation of linear and nonlinear mixed models for dose-response relationships accounting for correlated data structure and heterogeneous error variances. To illustrate, we modeled data from a randomized complete block design study to evaluate the standardized ileal digestible (SID) Trp:Lys ratio dose-response on G:F of nursery pigs. A base linear mixed model was fitted to explore the functional form of G:F relative to Trp:Lys ratios and assess model assumptions. Next, we fitted 3 competing dose-response mixed models to G:F, namely a quadratic polynomial (QP) model, a broken-line linear (BLL) ascending model, and a broken-line quadratic (BLQ) ascending model, all of which included heteroskedastic specifications, as dictated by the base model. The GLIMMIX procedure of SAS (version 9.4) was used to fit the base and QP models and the NLMIXED procedure was used to fit the BLL and BLQ models. We further illustrated the use of a grid search of initial parameter values to facilitate convergence and parameter estimation in nonlinear mixed models. Fit between competing dose-response models was compared using a maximum likelihood-based Bayesian information criterion (BIC). The QP, BLL, and BLQ models fitted on G:F of nursery pigs yielded BIC values of 353.7, 343.4, and 345.2, respectively, thus indicating a better fit of the BLL model. The BLL breakpoint estimate of the SID Trp:Lys ratio was 16.5% (95% confidence interval [16.1, 17.0]). Problems with the estimation process rendered results from the BLQ model questionable. Importantly, accounting for heterogeneous variance enhanced inferential precision as the breadth of the confidence interval for the mean breakpoint decreased by approximately 44%. In summary, the article illustrates the use of linear and nonlinear mixed models for dose-response relationships accounting for heterogeneous residual variances, discusses important diagnostics and their implications for inference, and provides practical recommendations for computational troubleshooting.

  6. Solving the Problem of Linear Viscoelasticity for Piecewise-Homogeneous Anisotropic Plates

    NASA Astrophysics Data System (ADS)

    Kaloerov, S. A.; Koshkin, A. A.

    2017-11-01

    An approximate method for solving the problem of linear viscoelasticity for thin anisotropic plates subject to transverse bending is proposed. The method of small parameter is used to reduce the problem to a sequence of boundary problems of applied theory of bending of plates solved using complex potentials. The general form of complex potentials in approximations and the boundary conditions for determining them are obtained. Problems for a plate with elliptic elastic inclusions are solved as an example. The numerical results for a plate with one, two elliptical (circular), and linear inclusions are analyzed.

  7. Conduction cooling systems for linear accelerator cavities

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

    Kephart, Robert

    A conduction cooling system for linear accelerator cavities. The system conducts heat from the cavities to a refrigeration unit using at least one cavity cooler interconnected with a cooling connector. The cavity cooler and cooling connector are both made from solid material having a very high thermal conductivity of approximately 1.times.10.sup.4 W m.sup.-1 K.sup.-1 at temperatures of approximately 4 degrees K. This allows for very simple and effective conduction of waste heat from the linear accelerator cavities to the cavity cooler, along the cooling connector, and thence to the refrigeration unit.

  8. A joint modeling and estimation method for multivariate longitudinal data with mixed types of responses to analyze physical activity data generated by accelerometers.

    PubMed

    Li, Haocheng; Zhang, Yukun; Carroll, Raymond J; Keadle, Sarah Kozey; Sampson, Joshua N; Matthews, Charles E

    2017-11-10

    A mixed effect model is proposed to jointly analyze multivariate longitudinal data with continuous, proportion, count, and binary responses. The association of the variables is modeled through the correlation of random effects. We use a quasi-likelihood type approximation for nonlinear variables and transform the proposed model into a multivariate linear mixed model framework for estimation and inference. Via an extension to the EM approach, an efficient algorithm is developed to fit the model. The method is applied to physical activity data, which uses a wearable accelerometer device to measure daily movement and energy expenditure information. Our approach is also evaluated by a simulation study. Copyright © 2017 John Wiley & Sons, Ltd.

  9. An Optical Actuation System and Curvature Sensor for a MR-compatible Active Needle

    PubMed Central

    Ryu, Seok Chang; Quek, Zhan Fan; Renaud, Pierre; Black, Richard J.; Daniel, Bruce L.; Cutkosky, Mark R.

    2015-01-01

    A side optical actuation method is presented for a slender MR-compatible active needle. The needle includes an active region with a shape memory alloy (SMA) wire actuator, where the wire generates a contraction force when optically heated by a laser delivered though optical fibers, producing needle tip bending. A prototype, with multiple side heating spots, demonstrates twice as fast an initial response compared to fiber tip heating when 0.8 W of optical power is applied. A single-ended optical sensor with a gold reflector is also presented to measure the curvature as a function of optical transmission loss. Preliminary tests with the sensor prototype demonstrate approximately linear response and a repeatable signal, independent of the bending history. PMID:26509099

  10. Linear approximations of global behaviors in nonlinear systems with moderate or strong noise

    NASA Astrophysics Data System (ADS)

    Liang, Junhao; Din, Anwarud; Zhou, Tianshou

    2018-03-01

    While many physical or chemical systems can be modeled by nonlinear Langevin equations (LEs), dynamical analysis of these systems is challenging in the cases of moderate and strong noise. Here we develop a linear approximation scheme, which can transform an often intractable LE into a linear set of binomial moment equations (BMEs). This scheme provides a feasible way to capture nonlinear behaviors in the sense of probability distribution and is effective even when the noise is moderate or big. Based on BMEs, we further develop a noise reduction technique, which can effectively handle tough cases where traditional small-noise theories are inapplicable. The overall method not only provides an approximation-based paradigm to analysis of the local and global behaviors of nonlinear noisy systems but also has a wide range of applications.

  11. Wavelength Dependence of Solar Irradiance Enhancement During X-class Flares and Its Influence on the Upper Atmosphere

    NASA Technical Reports Server (NTRS)

    Huang, Yanshi; Richmond, A. D.

    2013-01-01

    The wavelength dependence of solar irradiance enhancement during flare events is one of the important factors in determining how the Thermosphere-Ionosphere (TI) system responds to flares. To investigate the wavelength dependence of flare enhancement, the Flare Irradiance Spectral Model (FISM) was run for 61X-class flares. The absolute and the percentage increases of solar irradiance at flare peaks, compared to pre-flare conditions, have clear wavelength dependences. The 0-4 nm irradiance increases much more ((is) approximately 680 on average) than that in the 14-25 nm waveband ((is) approximately 65 on average), except at 24 nm ( (is) approximately 220). The average percentage increases for the 25-105 nm and 122-190 nm wave bands are approximately 120 and approximately 35, respectively. The influence of 6 different wavebands (0-14 nm, 14-25 nm, 25-105 nm, 105-120 nm, 121.56 nm,and122-175 nm) on the thermosphere was examined for the October 28th, 2003 flare (X17-class) event by coupling FISM with the National Center for Atmospheric Research (NCAR) Thermosphere-Ionosphere-Electrodynamics General Circulation Model(TIE-GCM) under geomagnetically quiet conditions (Kp=1). While the enhancement in the0-14nm waveband caused the largest enhancement of the globally integrated solar heating, the impact of solar irradiance enhancement on the thermosphere at 400 km is largest for the 25-105 nm waveband (EUV), which accounts for about 33 K of the total 45 K temperature enhancement, and approximately 7.4% of the total approximately 11.5% neutral density enhancement. The effect of 122-175 nm flare radiation on the thermosphere is rather small. The study also illustrates that the high-altitude thermospheric response to the flare radiation at 0-175 nm is almost a linear combination of the responses to the individual wavebands. The upper thermospheric temperature and density enhancements peaked 3-5 h after the maximum flare radiation.

  12. An approximation of herd effect due to vaccinating children against seasonal influenza - a potential solution to the incorporation of indirect effects into static models.

    PubMed

    Van Vlaenderen, Ilse; Van Bellinghen, Laure-Anne; Meier, Genevieve; Nautrup, Barbara Poulsen

    2013-01-22

    Indirect herd effect from vaccination of children offers potential for improving the effectiveness of influenza prevention in the remaining unvaccinated population. Static models used in cost-effectiveness analyses cannot dynamically capture herd effects. The objective of this study was to develop a methodology to allow herd effect associated with vaccinating children against seasonal influenza to be incorporated into static models evaluating the cost-effectiveness of influenza vaccination. Two previously published linear equations for approximation of herd effects in general were compared with the results of a structured literature review undertaken using PubMed searches to identify data on herd effects specific to influenza vaccination. A linear function was fitted to point estimates from the literature using the sum of squared residuals. The literature review identified 21 publications on 20 studies for inclusion. Six studies provided data on a mathematical relationship between effective vaccine coverage in subgroups and reduction of influenza infection in a larger unvaccinated population. These supported a linear relationship when effective vaccine coverage in a subgroup population was between 20% and 80%. Three studies evaluating herd effect at a community level, specifically induced by vaccinating children, provided point estimates for fitting linear equations. The fitted linear equation for herd protection in the target population for vaccination (children) was slightly less conservative than a previously published equation for herd effects in general. The fitted linear equation for herd protection in the non-target population was considerably less conservative than the previously published equation. This method of approximating herd effect requires simple adjustments to the annual baseline risk of influenza in static models: (1) for the age group targeted by the childhood vaccination strategy (i.e. children); and (2) for other age groups not targeted (e.g. adults and/or elderly). Two approximations provide a linear relationship between effective coverage and reduction in the risk of infection. The first is a conservative approximation, recommended as a base-case for cost-effectiveness evaluations. The second, fitted to data extracted from a structured literature review, provides a less conservative estimate of herd effect, recommended for sensitivity analyses.

  13. Nonlinear Time Domain Seismic Soil-Structure Interaction (SSI) Deep Soil Site Methodology Development

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

    Spears, Robert Edward; Coleman, Justin Leigh

    Currently the Department of Energy (DOE) and the nuclear industry perform seismic soil-structure interaction (SSI) analysis using equivalent linear numerical analysis tools. For lower levels of ground motion, these tools should produce reasonable in-structure response values for evaluation of existing and new facilities. For larger levels of ground motion these tools likely overestimate the in-structure response (and therefore structural demand) since they do not consider geometric nonlinearities (such as gaping and sliding between the soil and structure) and are limited in the ability to model nonlinear soil behavior. The current equivalent linear SSI (SASSI) analysis approach either joins the soilmore » and structure together in both tension and compression or releases the soil from the structure for both tension and compression. It also makes linear approximations for material nonlinearities and generalizes energy absorption with viscous damping. This produces the potential for inaccurately establishing where the structural concerns exist and/or inaccurately establishing the amplitude of the in-structure responses. Seismic hazard curves at nuclear facilities have continued to increase over the years as more information has been developed on seismic sources (i.e. faults), additional information gathered on seismic events, and additional research performed to determine local site effects. Seismic hazard curves are used to develop design basis earthquakes (DBE) that are used to evaluate nuclear facility response. As the seismic hazard curves increase, the input ground motions (DBE’s) used to numerically evaluation nuclear facility response increase causing larger in-structure response. As ground motions increase so does the importance of including nonlinear effects in numerical SSI models. To include material nonlinearity in the soil and geometric nonlinearity using contact (gaping and sliding) it is necessary to develop a nonlinear time domain methodology. This methodology will be known as, NonLinear Soil-Structure Interaction (NLSSI). In general NLSSI analysis should provide a more accurate representation of the seismic demands on nuclear facilities their systems and components. INL, in collaboration with a Nuclear Power Plant Vender (NPP-V), will develop a generic Nuclear Power Plant (NPP) structural design to be used in development of the methodology and for comparison with SASSI. This generic NPP design has been evaluated for the INL soil site because of the ease of access and quality of the site specific data. It is now being evaluated for a second site at Vogtle which is located approximately 15 miles East-Northeast of Waynesboro, Georgia and adjacent to Savanna River. The Vogtle site consists of many soil layers spanning down to a depth of 1058 feet. The reason that two soil sites are chosen is to demonstrate the methodology across multiple soil sites. The project will drive the models (soil and structure) using successively increasing acceleration time histories with amplitudes. The models will be run in time domain codes such as ABAQUS, LS-DYNA, and/or ESSI and compared with the same models run in SASSI. The project is focused on developing and documenting a method for performing time domain, non-linear seismic soil structure interaction (SSI) analysis. Development of this method will provide the Department of Energy (DOE) and industry with another tool to perform seismic SSI analysis.« less

  14. Applications of nonlinear systems theory to control design

    NASA Technical Reports Server (NTRS)

    Hunt, L. R.; Villarreal, Ramiro

    1988-01-01

    For most applications in the control area, the standard practice is to approximate a nonlinear mathematical model by a linear system. Since the feedback linearizable systems contain linear systems as a subclass, the procedure of approximating a nonlinear system by a feedback linearizable one is examined. Because many physical plants (e.g., aircraft at the NASA Ames Research Center) have mathematical models which are close to feedback linearizable systems, such approximations are certainly justified. Results and techniques are introduced for measuring the gap between the model and its truncated linearizable part. The topic of pure feedback systems is important to the study.

  15. Triangle based TVD schemes for hyperbolic conservation laws

    NASA Technical Reports Server (NTRS)

    Durlofsky, Louis J.; Osher, Stanley; Engquist, Bjorn

    1990-01-01

    A triangle based total variation diminishing (TVD) scheme for the numerical approximation of hyperbolic conservation laws in two space dimensions is constructed. The novelty of the scheme lies in the nature of the preprocessing of the cell averaged data, which is accomplished via a nearest neighbor linear interpolation followed by a slope limiting procedures. Two such limiting procedures are suggested. The resulting method is considerably more simple than other triangle based non-oscillatory approximations which, like this scheme, approximate the flux up to second order accuracy. Numerical results for linear advection and Burgers' equation are presented.

  16. Congruence Approximations for Entrophy Endowed Hyperbolic Systems

    NASA Technical Reports Server (NTRS)

    Barth, Timothy J.; Saini, Subhash (Technical Monitor)

    1998-01-01

    Building upon the standard symmetrization theory for hyperbolic systems of conservation laws, congruence properties of the symmetrized system are explored. These congruence properties suggest variants of several stabilized numerical discretization procedures for hyperbolic equations (upwind finite-volume, Galerkin least-squares, discontinuous Galerkin) that benefit computationally from congruence approximation. Specifically, it becomes straightforward to construct the spatial discretization and Jacobian linearization for these schemes (given a small amount of derivative information) for possible use in Newton's method, discrete optimization, homotopy algorithms, etc. Some examples will be given for the compressible Euler equations and the nonrelativistic MHD equations using linear and quadratic spatial approximation.

  17. Implementation of an approximate self-energy correction scheme in the orthogonalized linear combination of atomic orbitals method of band-structure calculations

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

    Gu, Z.; Ching, W.Y.

    Based on the Sterne-Inkson model for the self-energy correction to the single-particle energy in the local-density approximation (LDA), we have implemented an approximate energy-dependent and [bold k]-dependent [ital GW] correction scheme to the orthogonalized linear combination of atomic orbital-based local-density calculation for insulators. In contrast to the approach of Jenkins, Srivastava, and Inkson, we evaluate the on-site exchange integrals using the LDA Bloch functions throughout the Brillouin zone. By using a [bold k]-weighted band gap [ital E][sub [ital g

  18. AESOP- INTERACTIVE DESIGN OF LINEAR QUADRATIC REGULATORS AND KALMAN FILTERS

    NASA Technical Reports Server (NTRS)

    Lehtinen, B.

    1994-01-01

    AESOP was developed to solve a number of problems associated with the design of controls and state estimators for linear time-invariant systems. The systems considered are modeled in state-variable form by a set of linear differential and algebraic equations with constant coefficients. Two key problems solved by AESOP are the linear quadratic regulator (LQR) design problem and the steady-state Kalman filter design problem. AESOP is designed to be used in an interactive manner. The user can solve design problems and analyze the solutions in a single interactive session. Both numerical and graphical information are available to the user during the session. The AESOP program is structured around a list of predefined functions. Each function performs a single computation associated with control, estimation, or system response determination. AESOP contains over sixty functions and permits the easy inclusion of user defined functions. The user accesses these functions either by inputting a list of desired functions in the order they are to be performed, or by specifying a single function to be performed. The latter case is used when the choice of function and function order depends on the results of previous functions. The available AESOP functions are divided into several general areas including: 1) program control, 2) matrix input and revision, 3) matrix formation, 4) open-loop system analysis, 5) frequency response, 6) transient response, 7) transient function zeros, 8) LQR and Kalman filter design, 9) eigenvalues and eigenvectors, 10) covariances, and 11) user-defined functions. The most important functions are those that design linear quadratic regulators and Kalman filters. The user interacts with AESOP when using these functions by inputting design weighting parameters and by viewing displays of designed system response. Support functions obtain system transient and frequency responses, transfer functions, and covariance matrices. AESOP can also provide the user with open-loop system information including stability, controllability, and observability. The AESOP program is written in FORTRAN IV for interactive execution and has been implemented on an IBM 3033 computer using TSS 370. As currently configured, AESOP has a central memory requirement of approximately 2 Megs of 8 bit bytes. Memory requirements can be reduced by redimensioning arrays in the AESOP program. Graphical output requires adaptation of the AESOP plot routines to whatever device is available. The AESOP program was developed in 1984.

  19. Algorithms for sorting unsigned linear genomes by the DCJ operations.

    PubMed

    Jiang, Haitao; Zhu, Binhai; Zhu, Daming

    2011-02-01

    The double cut and join operation (abbreviated as DCJ) has been extensively used for genomic rearrangement. Although the DCJ distance between signed genomes with both linear and circular (uni- and multi-) chromosomes is well studied, the only known result for the NP-complete unsigned DCJ distance problem is an approximation algorithm for unsigned linear unichromosomal genomes. In this article, we study the problem of computing the DCJ distance on two unsigned linear multichromosomal genomes (abbreviated as UDCJ). We devise a 1.5-approximation algorithm for UDCJ by exploiting the distance formula for signed genomes. In addition, we show that UDCJ admits a weak kernel of size 2k and hence an FPT algorithm running in O(2(2k)n) time.

  20. Prediction of the Main Engine Power of a New Container Ship at the Preliminary Design Stage

    NASA Astrophysics Data System (ADS)

    Cepowski, Tomasz

    2017-06-01

    The paper presents mathematical relationships that allow us to forecast the estimated main engine power of new container ships, based on data concerning vessels built in 2005-2015. The presented approximations allow us to estimate the engine power based on the length between perpendiculars and the number of containers the ship will carry. The approximations were developed using simple linear regression and multivariate linear regression analysis. The presented relations have practical application for estimation of container ship engine power needed in preliminary parametric design of the ship. It follows from the above that the use of multiple linear regression to predict the main engine power of a container ship brings more accurate solutions than simple linear regression.

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

    PubMed

    Hasegawa, Chihiro; Duffull, Stephen B

    2018-02-01

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

  2. Criterion for estimation of stress-deformed state of SD-materials

    NASA Astrophysics Data System (ADS)

    Orekhov, Andrey V.

    2018-05-01

    A criterion is proposed that determines the moment when the growth pattern of the monotonic numerical sequence varies from the linear to the parabolic one. The criterion is based on the comparison of squares of errors for the linear and the incomplete quadratic approximation. The approximating functions are constructed locally, only at those points that are located near a possible change in nature of the increase in the sequence.

  3. Photogrammetric Processing of Planetary Linear Pushbroom Images Based on Approximate Orthophotos

    NASA Astrophysics Data System (ADS)

    Geng, X.; Xu, Q.; Xing, S.; Hou, Y. F.; Lan, C. Z.; Zhang, J. J.

    2018-04-01

    It is still a great challenging task to efficiently produce planetary mapping products from orbital remote sensing images. There are many disadvantages in photogrammetric processing of planetary stereo images, such as lacking ground control information and informative features. Among which, image matching is the most difficult job in planetary photogrammetry. This paper designs a photogrammetric processing framework for planetary remote sensing images based on approximate orthophotos. Both tie points extraction for bundle adjustment and dense image matching for generating digital terrain model (DTM) are performed on approximate orthophotos. Since most of planetary remote sensing images are acquired by linear scanner cameras, we mainly deal with linear pushbroom images. In order to improve the computational efficiency of orthophotos generation and coordinates transformation, a fast back-projection algorithm of linear pushbroom images is introduced. Moreover, an iteratively refined DTM and orthophotos scheme was adopted in the DTM generation process, which is helpful to reduce search space of image matching and improve matching accuracy of conjugate points. With the advantages of approximate orthophotos, the matching results of planetary remote sensing images can be greatly improved. We tested the proposed approach with Mars Express (MEX) High Resolution Stereo Camera (HRSC) and Lunar Reconnaissance Orbiter (LRO) Narrow Angle Camera (NAC) images. The preliminary experimental results demonstrate the feasibility of the proposed approach.

  4. Approximate reduction of linear population models governed by stochastic differential equations: application to multiregional models.

    PubMed

    Sanz, Luis; Alonso, Juan Antonio

    2017-12-01

    In this work we develop approximate aggregation techniques in the context of slow-fast linear population models governed by stochastic differential equations and apply the results to the treatment of populations with spatial heterogeneity. Approximate aggregation techniques allow one to transform a complex system involving many coupled variables and in which there are processes with different time scales, by a simpler reduced model with a fewer number of 'global' variables, in such a way that the dynamics of the former can be approximated by that of the latter. In our model we contemplate a linear fast deterministic process together with a linear slow process in which the parameters are affected by additive noise, and give conditions for the solutions corresponding to positive initial conditions to remain positive for all times. By letting the fast process reach equilibrium we build a reduced system with a lesser number of variables, and provide results relating the asymptotic behaviour of the first- and second-order moments of the population vector for the original and the reduced system. The general technique is illustrated by analysing a multiregional stochastic system in which dispersal is deterministic and the rate growth of the populations in each patch is affected by additive noise.

  5. Dose-response relationship between sleep duration and human psychomotor vigilance and subjective alertness

    NASA Technical Reports Server (NTRS)

    Jewett, M. E.; Dijk, D. J.; Kronauer, R. E.; Dinges, D. F.

    1999-01-01

    Although it has been well documented that sleep is required for human performance and alertness to recover from low levels after prolonged periods of wakefulness, it remains unclear whether they increase in a linear or asymptotic manner during sleep. It has been postulated that there is a relation between the rate of improvement in neurobehavioral functioning and rate of decline of slow-wave sleep and/or slow-wave activity (SWS/SWA) during sleep, but this has not been verified. Thus, a cross-study comparison was conducted in which dose-response curves (DRCs) were constructed for Stanford Sleepiness Scale (SSS) and Psychomotor Vigilance Task (PVT) tests taken at 1000 hours by subjects who had been allowed to sleep 0 hours, 2 hours, 5 hours or 8 hours the previous night. We found that the DRCs to each PVT metric improved in a saturating exponential manner, with recovery rates that were similar [time constant (T) approximately 2.14 hours] for all the metrics. This recovery rate was slightly faster than, though not statistically significantly different from, the reported rate of SWS/SWA decline (T approximately 2.7 hours). The DRC to the SSS improved much more slowly than psychomotor vigilance, so that it could be fit equally well by a linear function (slope = -0.26) or a saturating exponential function (T = 9.09 hours). We conclude that although SWS/SWA, subjective alertness, and a wide variety of psychomotor vigilance metrics may all change asymptotically during sleep, it remains to be determined whether the underlying physiologic processes governing their expression are different.

  6. Importance of Vibronic Effects in the UV-Vis Spectrum of the 7,7,8,8-Tetracyanoquinodimethane Anion.

    PubMed

    Tapavicza, Enrico; Furche, Filipp; Sundholm, Dage

    2016-10-11

    We present a computational method for simulating vibronic absorption spectra in the ultraviolet-visible (UV-vis) range and apply it to the 7,7,8,8-tetracyanoquinodimethane anion (TCNQ - ), which has been used as a ligand in black absorbers. Gaussian broadening of vertical electronic excitation energies of TCNQ - from linear-response time-dependent density functional theory produces only one band, which is qualitatively incorrect. Thus, the harmonic vibrational modes of the two lowest doublet states were computed, and the vibronic UV-vis spectrum was simulated using the displaced harmonic oscillator approximation, the frequency-shifted harmonic oscillator approximation, and the full Duschinsky formalism. An efficient real-time generating function method was implemented to avoid the exponential complexity of conventional Franck-Condon approaches to vibronic spectra. The obtained UV-vis spectra for TCNQ - agree well with experiment; the Duschinsky rotation is found to have only a minor effect on the spectrum. Born-Oppenheimer molecular dynamics simulations combined with calculations of the electronic excitation energies for a large number of molecular structures were also used for simulating the UV-vis spectrum. The Born-Oppenheimer molecular dynamics simulations yield a broadening of the energetically lowest peak in the absorption spectrum, but additional vibrational bands present in the experimental and simulated quantum harmonic oscillator spectra are not observed in the molecular dynamics simulations. Our results underline the importance of vibronic effects for the UV-vis spectrum of TCNQ - , and they establish an efficient method for obtaining vibronic spectra using a combination of linear-response time-dependent density functional theory and a real-time generating function approach.

  7. Will intra-specific differences in transpiration efficiency in wheat be maintained in a high CO₂ world? A FACE study.

    PubMed

    Tausz-Posch, Sabine; Norton, Robert M; Seneweera, Saman; Fitzgerald, Glenn J; Tausz, Michael

    2013-06-01

    This study evaluates whether the target breeding trait of superior leaf level transpiration efficiency is still appropriate under increasing carbon dioxide levels of a future climate using a semi-arid cropping system as a model. Specifically, we investigated whether physiological traits governing leaf level transpiration efficiency, such as net assimilation rates (A(net)), stomatal conductance (g(s)) or stomatal sensitivity were affected differently between two Triticum aestivum L. cultivars differing in transpiration efficiency (cv. Drysdale, superior; cv. Hartog, low). Plants were grown under Free Air Carbon dioxide Enrichment (FACE, approximately 550 µmol mol⁻¹ or ambient CO₂ concentrations (approximately 390 µmol mol⁻¹). Mean A(net) (approximately 15% increase) and gs (approximately 25% decrease) were less affected by elevated [CO₂] than previously found in FACE-grown wheat (approximately 25% increase and approximately 32% decrease, respectively), potentially reflecting growth in a dry-land cropping system. In contrast to previous FACE studies, analyses of the Ball et al. model revealed an elevated [CO₂] effect on the slope of the linear regression by 12% indicating a decrease in stomatal sensitivity to the combination of [CO₂], photosynthesis rate and humidity. Differences between cultivars indicated greater transpiration efficiency for Drysdale with growth under elevated [CO₂] potentially increasing the response of this trait. This knowledge adds valuable information for crop germplasm improvement for future climates. Copyright © Physiologia Plantarum 2012.

  8. Stresses and deformations in cross-ply composite tubes subjected to a uniform temperature change

    NASA Technical Reports Server (NTRS)

    Hyer, M. W.; Cooper, D. E.; Cohen, D.

    1986-01-01

    This study investigates the effects of a uniform temperature change on the stresses and deformations of composite tubes and determines the accuracy of an approximate solution based on the principle of complementary virtual work. Interest centers on tube response away from the ends and so a planar elasticity approach is used. For the approximate solution a piecewise linear variation of stresses with the radial coordinate is assumed. The results from the approximate solution are compared with the elasticity solution. The stress predictions agree well, particularly peak interlaminar stresses. Surprisingly, the axial deformations also agree well, despite the fact that the deformations predicted by the approximate solution do not satisfy the interface displacement continuity conditions required by the elasticity solution. The study shows that the axial thermal expansion coefficient of tubes with a specific number of axial and circumferential layers depends on the stacking sequence. This is in contrast to classical lamination theory, which predicts that the expansion will be independent of the stacking arrangement. As expected, the sign and magnitude of the peak interlaminar stresses depend on stacking sequence. For tubes with a specific number of axial and circumferential layers, thermally induced interlaminar stresses can be controlled by altering stacking arrangement.

  9. Three-dimensional inversion of multisource array electromagnetic data

    NASA Astrophysics Data System (ADS)

    Tartaras, Efthimios

    Three-dimensional (3-D) inversion is increasingly important for the correct interpretation of geophysical data sets in complex environments. To this effect, several approximate solutions have been developed that allow the construction of relatively fast inversion schemes. One such method that is fast and provides satisfactory accuracy is the quasi-linear (QL) approximation. It has, however, the drawback that it is source-dependent and, therefore, impractical in situations where multiple transmitters in different positions are employed. I have, therefore, developed a localized form of the QL approximation that is source-independent. This so-called localized quasi-linear (LQL) approximation can have a scalar, a diagonal, or a full tensor form. Numerical examples of its comparison with the full integral equation solution, the Born approximation, and the original QL approximation are given. The objective behind developing this approximation is to use it in a fast 3-D inversion scheme appropriate for multisource array data such as those collected in airborne surveys, cross-well logging, and other similar geophysical applications. I have developed such an inversion scheme using the scalar and diagonal LQL approximation. It reduces the original nonlinear inverse electromagnetic (EM) problem to three linear inverse problems. The first of these problems is solved using a weighted regularized linear conjugate gradient method, whereas the last two are solved in the least squares sense. The algorithm I developed provides the option of obtaining either smooth or focused inversion images. I have applied the 3-D LQL inversion to synthetic 3-D EM data that simulate a helicopter-borne survey over different earth models. The results demonstrate the stability and efficiency of the method and show that the LQL approximation can be a practical solution to the problem of 3-D inversion of multisource array frequency-domain EM data. I have also applied the method to helicopter-borne EM data collected by INCO Exploration over the Voisey's Bay area in Labrador, Canada. The results of the 3-D inversion successfully delineate the shallow massive sulfides and show that the method can produce reasonable results even in areas of complex geology and large resistivity contrasts.

  10. Lateralization and Binaural Interaction of Middle-Latency and Late-Brainstem Components of the Auditory Evoked Response.

    PubMed

    Dykstra, Andrew R; Burchard, Daniel; Starzynski, Christian; Riedel, Helmut; Rupp, Andre; Gutschalk, Alexander

    2016-08-01

    We used magnetoencephalography to examine lateralization and binaural interaction of the middle-latency and late-brainstem components of the auditory evoked response (the MLR and SN10, respectively). Click stimuli were presented either monaurally, or binaurally with left- or right-leading interaural time differences (ITDs). While early MLR components, including the N19 and P30, were larger for monaural stimuli presented contralaterally (by approximately 30 and 36 % in the left and right hemispheres, respectively), later components, including the N40 and P50, were larger ipsilaterally. In contrast, MLRs elicited by binaural clicks with left- or right-leading ITDs did not differ. Depending on filter settings, weak binaural interaction could be observed as early as the P13 but was clearly much larger for later components, beginning at the P30, indicating some degree of binaural linearity up to early stages of cortical processing. The SN10, an obscure late-brainstem component, was observed consistently in individuals and showed linear binaural additivity. The results indicate that while the MLR is lateralized in response to monaural stimuli-and not ITDs-this lateralization reverses from primarily contralateral to primarily ipsilateral as early as 40 ms post stimulus and is never as large as that seen with fMRI.

  11. Asymptotic aspect of derivations in Banach algebras.

    PubMed

    Roh, Jaiok; Chang, Ick-Soon

    2017-01-01

    We prove that every approximate linear left derivation on a semisimple Banach algebra is continuous. Also, we consider linear derivations on Banach algebras and we first study the conditions for a linear derivation on a Banach algebra. Then we examine the functional inequalities related to a linear derivation and their stability. We finally take central linear derivations with radical ranges on semiprime Banach algebras and a continuous linear generalized left derivation on a semisimple Banach algebra.

  12. Strain accumulation in bituminous binders under repeated creep-recovery loading predicted from small-amplitude oscillatory shear (SAOS) experiments

    NASA Astrophysics Data System (ADS)

    Laukkanen, Olli-Ville; Winter, H. Henning

    2017-11-01

    The creep-recovery (CR) test starts out with a period of shearing at constant stress (creep) and is followed by a period of zero-shear stress where some of the accumulated shear strain gets reversed. Linear viscoelasticity (LVE) allows one to predict the strain response to repeated creep-recovery (RCR) loading from measured small-amplitude oscillatory shear (SAOS) data. Only the relaxation and retardation time spectra of a material need to be known and these can be determined from SAOS data. In an application of the Boltzmann superposition principle (BSP), the strain response to RCR loading can be obtained as a linear superposition of the strain response to many single creep-recovery tests. SAOS and RCR data were collected for several unmodified and modified bituminous binders, and the measured and predicted RCR responses were compared. Generally good agreement was found between the measured and predicted strain accumulation under RCR loading. However, in the case of modified binders, the strain accumulation was slightly overestimated (≤20% relative error) due to the insufficient SAOS information at long relaxation times. Our analysis also demonstrates that the evolution in the strain response under RCR loading, caused by incomplete recovery, can be reasonably well predicted by the presented methodology. It was also shown that the outlined modeling framework can be used, as a first approximation, to estimate the rutting resistance of bituminous binders by predicting the values of the Multiple Stress Creep Recovery (MSCR) test parameters.

  13. STRONG ORACLE OPTIMALITY OF FOLDED CONCAVE PENALIZED ESTIMATION.

    PubMed

    Fan, Jianqing; Xue, Lingzhou; Zou, Hui

    2014-06-01

    Folded concave penalization methods have been shown to enjoy the strong oracle property for high-dimensional sparse estimation. However, a folded concave penalization problem usually has multiple local solutions and the oracle property is established only for one of the unknown local solutions. A challenging fundamental issue still remains that it is not clear whether the local optimum computed by a given optimization algorithm possesses those nice theoretical properties. To close this important theoretical gap in over a decade, we provide a unified theory to show explicitly how to obtain the oracle solution via the local linear approximation algorithm. For a folded concave penalized estimation problem, we show that as long as the problem is localizable and the oracle estimator is well behaved, we can obtain the oracle estimator by using the one-step local linear approximation. In addition, once the oracle estimator is obtained, the local linear approximation algorithm converges, namely it produces the same estimator in the next iteration. The general theory is demonstrated by using four classical sparse estimation problems, i.e., sparse linear regression, sparse logistic regression, sparse precision matrix estimation and sparse quantile regression.

  14. STRONG ORACLE OPTIMALITY OF FOLDED CONCAVE PENALIZED ESTIMATION

    PubMed Central

    Fan, Jianqing; Xue, Lingzhou; Zou, Hui

    2014-01-01

    Folded concave penalization methods have been shown to enjoy the strong oracle property for high-dimensional sparse estimation. However, a folded concave penalization problem usually has multiple local solutions and the oracle property is established only for one of the unknown local solutions. A challenging fundamental issue still remains that it is not clear whether the local optimum computed by a given optimization algorithm possesses those nice theoretical properties. To close this important theoretical gap in over a decade, we provide a unified theory to show explicitly how to obtain the oracle solution via the local linear approximation algorithm. For a folded concave penalized estimation problem, we show that as long as the problem is localizable and the oracle estimator is well behaved, we can obtain the oracle estimator by using the one-step local linear approximation. In addition, once the oracle estimator is obtained, the local linear approximation algorithm converges, namely it produces the same estimator in the next iteration. The general theory is demonstrated by using four classical sparse estimation problems, i.e., sparse linear regression, sparse logistic regression, sparse precision matrix estimation and sparse quantile regression. PMID:25598560

  15. 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.

  16. A Lyapunov and Sacker–Sell spectral stability theory for one-step methods

    DOE PAGES

    Steyer, Andrew J.; Van Vleck, Erik S.

    2018-04-13

    Approximation theory for Lyapunov and Sacker–Sell spectra based upon QR techniques is used to analyze the stability of a one-step method solving a time-dependent (nonautonomous) linear ordinary differential equation (ODE) initial value problem in terms of the local error. Integral separation is used to characterize the conditioning of stability spectra calculations. The stability of the numerical solution by a one-step method of a nonautonomous linear ODE using real-valued, scalar, nonautonomous linear test equations is justified. This analysis is used to approximate exponential growth/decay rates on finite and infinite time intervals and establish global error bounds for one-step methods approximating uniformly,more » exponentially stable trajectories of nonautonomous and nonlinear ODEs. A time-dependent stiffness indicator and a one-step method that switches between explicit and implicit Runge–Kutta methods based upon time-dependent stiffness are developed based upon the theoretical results.« less

  17. A Lyapunov and Sacker–Sell spectral stability theory for one-step methods

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

    Steyer, Andrew J.; Van Vleck, Erik S.

    Approximation theory for Lyapunov and Sacker–Sell spectra based upon QR techniques is used to analyze the stability of a one-step method solving a time-dependent (nonautonomous) linear ordinary differential equation (ODE) initial value problem in terms of the local error. Integral separation is used to characterize the conditioning of stability spectra calculations. The stability of the numerical solution by a one-step method of a nonautonomous linear ODE using real-valued, scalar, nonautonomous linear test equations is justified. This analysis is used to approximate exponential growth/decay rates on finite and infinite time intervals and establish global error bounds for one-step methods approximating uniformly,more » exponentially stable trajectories of nonautonomous and nonlinear ODEs. A time-dependent stiffness indicator and a one-step method that switches between explicit and implicit Runge–Kutta methods based upon time-dependent stiffness are developed based upon the theoretical results.« less

  18. 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.

  19. Assessing the Utility of Compound Trait Estimates of Narrow Personality Traits.

    PubMed

    Credé, Marcus; Harms, Peter D; Blacksmith, Nikki; Wood, Dustin

    2016-01-01

    It has been argued that approximations of narrow traits can be made through linear combinations of broad traits such as the Big Five personality traits. Indeed, Hough and Ones ( 2001 ) used a qualitative analysis of scale content to arrive at a taxonomy of how Big Five traits might be combined to approximate various narrow traits. However, the utility of such compound trait approximations has yet to be established beyond specific cases such as integrity and customer service orientation. Using data from the Eugene-Springfield Community Sample (Goldberg, 2008 ), we explore the ability of linear composites of scores on Big Five traits to approximate scores on 127 narrow trait measures from 5 well-known non-Big-Five omnibus measures of personality. Our findings indicate that individuals' standing on more than 30 narrow traits can be well estimated from 3 different types of linear composites of scores on Big Five traits without a substantial sacrifice in criterion validity. We discuss theoretical accounts for why such relationships exist as well as the theoretical and practical implications of these findings for researchers and practitioners.

  20. Mode instability in one-dimensional anharmonic lattices: Variational equation approach

    NASA Astrophysics Data System (ADS)

    Yoshimura, K.

    1999-03-01

    The stability of normal mode oscillations has been studied in detail under the single-mode excitation condition for the Fermi-Pasta-Ulam-β lattice. Numerical experiments indicate that the mode stability depends strongly on k/N, where k is the wave number of the initially excited mode and N is the number of degrees of freedom in the system. It has been found that this feature does not change when N increases. We propose an average variational equation - approximate version of the variational equation - as a theoretical tool to facilitate a linear stability analysis. It is shown that this strong k/N dependence of the mode stability can be explained from the view point of the linear stability of the relevant orbits. We introduce a low-dimensional approximation of the average variational equation, which approximately describes the time evolution of variations in four normal mode amplitudes. The linear stability analysis based on this four-mode approximation demonstrates that the parametric instability mechanism plays a crucial role in the strong k/N dependence of the mode stability.

  1. Nonlinear identification of the total baroreflex arc.

    PubMed

    Moslehpour, Mohsen; Kawada, Toru; Sunagawa, Kenji; Sugimachi, Masaru; Mukkamala, Ramakrishna

    2015-12-15

    The total baroreflex arc [the open-loop system relating carotid sinus pressure (CSP) to arterial pressure (AP)] is known to exhibit nonlinear behaviors. However, few studies have quantitatively characterized its nonlinear dynamics. The aim of this study was to develop a nonlinear model of the sympathetically mediated total arc without assuming any model form. Normal rats were studied under anesthesia. The vagal and aortic depressor nerves were sectioned, the carotid sinus regions were isolated and attached to a servo-controlled piston pump, and the AP and sympathetic nerve activity (SNA) were measured. CSP was perturbed using a Gaussian white noise signal. A second-order Volterra model was developed by applying nonparametric identification to the measurements. The second-order kernel was mainly diagonal, but the diagonal differed in shape from the first-order kernel. Hence, a reduced second-order model was similarly developed comprising a linear dynamic system in parallel with a squaring system in cascade with a slower linear dynamic system. This "Uryson" model predicted AP changes 12% better (P < 0.01) than a linear model in response to new Gaussian white noise CSP. The model also predicted nonlinear behaviors, including thresholding and mean responses to CSP changes about the mean. Models of the neural arc (the system relating CSP to SNA) and peripheral arc (the system relating SNA to AP) were likewise developed and tested. However, these models of subsystems of the total arc showed approximately linear behaviors. In conclusion, the validated nonlinear model of the total arc revealed that the system takes on an Uryson structure. Copyright © 2015 the American Physiological Society.

  2. Nonlinear identification of the total baroreflex arc

    PubMed Central

    Moslehpour, Mohsen; Kawada, Toru; Sunagawa, Kenji; Sugimachi, Masaru

    2015-01-01

    The total baroreflex arc [the open-loop system relating carotid sinus pressure (CSP) to arterial pressure (AP)] is known to exhibit nonlinear behaviors. However, few studies have quantitatively characterized its nonlinear dynamics. The aim of this study was to develop a nonlinear model of the sympathetically mediated total arc without assuming any model form. Normal rats were studied under anesthesia. The vagal and aortic depressor nerves were sectioned, the carotid sinus regions were isolated and attached to a servo-controlled piston pump, and the AP and sympathetic nerve activity (SNA) were measured. CSP was perturbed using a Gaussian white noise signal. A second-order Volterra model was developed by applying nonparametric identification to the measurements. The second-order kernel was mainly diagonal, but the diagonal differed in shape from the first-order kernel. Hence, a reduced second-order model was similarly developed comprising a linear dynamic system in parallel with a squaring system in cascade with a slower linear dynamic system. This “Uryson” model predicted AP changes 12% better (P < 0.01) than a linear model in response to new Gaussian white noise CSP. The model also predicted nonlinear behaviors, including thresholding and mean responses to CSP changes about the mean. Models of the neural arc (the system relating CSP to SNA) and peripheral arc (the system relating SNA to AP) were likewise developed and tested. However, these models of subsystems of the total arc showed approximately linear behaviors. In conclusion, the validated nonlinear model of the total arc revealed that the system takes on an Uryson structure. PMID:26354845

  3. Testing of next-generation nonlinear calibration based non-uniformity correction techniques using SWIR devices

    NASA Astrophysics Data System (ADS)

    Lovejoy, McKenna R.; Wickert, Mark A.

    2017-05-01

    A known problem with infrared imaging devices is their non-uniformity. This non-uniformity is the result of dark current, amplifier mismatch as well as the individual photo response of the detectors. To improve performance, non-uniformity correction (NUC) techniques are applied. Standard calibration techniques use linear, or piecewise linear models to approximate the non-uniform gain and off set characteristics as well as the nonlinear response. Piecewise linear models perform better than the one and two-point models, but in many cases require storing an unmanageable number of correction coefficients. Most nonlinear NUC algorithms use a second order polynomial to improve performance and allow for a minimal number of stored coefficients. However, advances in technology now make higher order polynomial NUC algorithms feasible. This study comprehensively tests higher order polynomial NUC algorithms targeted at short wave infrared (SWIR) imagers. Using data collected from actual SWIR cameras, the nonlinear techniques and corresponding performance metrics are compared with current linear methods including the standard one and two-point algorithms. Machine learning, including principal component analysis, is explored for identifying and replacing bad pixels. The data sets are analyzed and the impact of hardware implementation is discussed. Average floating point results show 30% less non-uniformity, in post-corrected data, when using a third order polynomial correction algorithm rather than a second order algorithm. To maximize overall performance, a trade off analysis on polynomial order and coefficient precision is performed. Comprehensive testing, across multiple data sets, provides next generation model validation and performance benchmarks for higher order polynomial NUC methods.

  4. Reduction of Radiometric Miscalibration—Applications to Pushbroom Sensors

    PubMed Central

    Rogaß, Christian; Spengler, Daniel; Bochow, Mathias; Segl, Karl; Lausch, Angela; Doktor, Daniel; Roessner, Sigrid; Behling, Robert; Wetzel, Hans-Ulrich; Kaufmann, Hermann

    2011-01-01

    The analysis of hyperspectral images is an important task in Remote Sensing. Foregoing radiometric calibration results in the assignment of incident electromagnetic radiation to digital numbers and reduces the striping caused by slightly different responses of the pixel detectors. However, due to uncertainties in the calibration some striping remains. This publication presents a new reduction framework that efficiently reduces linear and nonlinear miscalibrations by an image-driven, radiometric recalibration and rescaling. The proposed framework—Reduction Of Miscalibration Effects (ROME)—considering spectral and spatial probability distributions, is constrained by specific minimisation and maximisation principles and incorporates image processing techniques such as Minkowski metrics and convolution. To objectively evaluate the performance of the new approach, the technique was applied to a variety of commonly used image examples and to one simulated and miscalibrated EnMAP (Environmental Mapping and Analysis Program) scene. Other examples consist of miscalibrated AISA/Eagle VNIR (Visible and Near Infrared) and Hawk SWIR (Short Wave Infrared) scenes of rural areas of the region Fichtwald in Germany and Hyperion scenes of the Jalal-Abad district in Southern Kyrgyzstan. Recovery rates of approximately 97% for linear and approximately 94% for nonlinear miscalibrated data were achieved, clearly demonstrating the benefits of the new approach and its potential for broad applicability to miscalibrated pushbroom sensor data. PMID:22163960

  5. Estimation of time- and state-dependent delays and other parameters in functional differential equations

    NASA Technical Reports Server (NTRS)

    Murphy, K. A.

    1988-01-01

    A parameter estimation algorithm is developed which can be used to estimate unknown time- or state-dependent delays and other parameters (e.g., initial condition) appearing within a nonlinear nonautonomous functional differential equation. The original infinite dimensional differential equation is approximated using linear splines, which are allowed to move with the variable delay. The variable delays are approximated using linear splines as well. The approximation scheme produces a system of ordinary differential equations with nice computational properties. The unknown parameters are estimated within the approximating systems by minimizing a least-squares fit-to-data criterion. Convergence theorems are proved for time-dependent delays and state-dependent delays within two classes, which say essentially that fitting the data by using approximations will, in the limit, provide a fit to the data using the original system. Numerical test examples are presented which illustrate the method for all types of delay.

  6. An approximation theory for the identification of nonlinear distributed parameter systems

    NASA Technical Reports Server (NTRS)

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

    1988-01-01

    An abstract approximation framework for the identification of nonlinear distributed parameter systems is developed. Inverse problems for nonlinear systems governed by strongly maximal monotone operators (satisfying a mild continuous dependence condition with respect to the unknown parameters to be identified) are treated. Convergence of Galerkin approximations and the corresponding solutions of finite dimensional approximating identification problems to a solution of the original finite dimensional identification problem is demonstrated using the theory of nonlinear evolution systems and a nonlinear analog of the Trotter-Kato approximation result for semigroups of bounded linear operators. The nonlinear theory developed here is shown to subsume an existing linear theory as a special case. It is also shown to be applicable to a broad class of nonlinear elliptic operators and the corresponding nonlinear parabolic partial differential equations to which they lead. An application of the theory to a quasilinear model for heat conduction or mass transfer is discussed.

  7. A Numerical Approximation Framework for the Stochastic Linear Quadratic Regulator on Hilbert Spaces

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

    Levajković, Tijana, E-mail: tijana.levajkovic@uibk.ac.at, E-mail: t.levajkovic@sf.bg.ac.rs; Mena, Hermann, E-mail: hermann.mena@uibk.ac.at; Tuffaha, Amjad, E-mail: atufaha@aus.edu

    We present an approximation framework for computing the solution of the stochastic linear quadratic control problem on Hilbert spaces. We focus on the finite horizon case and the related differential Riccati equations (DREs). Our approximation framework is concerned with the so-called “singular estimate control systems” (Lasiecka in Optimal control problems and Riccati equations for systems with unbounded controls and partially analytic generators: applications to boundary and point control problems, 2004) which model certain coupled systems of parabolic/hyperbolic mixed partial differential equations with boundary or point control. We prove that the solutions of the approximate finite-dimensional DREs converge to the solutionmore » of the infinite-dimensional DRE. In addition, we prove that the optimal state and control of the approximate finite-dimensional problem converge to the optimal state and control of the corresponding infinite-dimensional problem.« less

  8. Estimation of time- and state-dependent delays and other parameters in functional differential equations

    NASA Technical Reports Server (NTRS)

    Murphy, K. A.

    1990-01-01

    A parameter estimation algorithm is developed which can be used to estimate unknown time- or state-dependent delays and other parameters (e.g., initial condition) appearing within a nonlinear nonautonomous functional differential equation. The original infinite dimensional differential equation is approximated using linear splines, which are allowed to move with the variable delay. The variable delays are approximated using linear splines as well. The approximation scheme produces a system of ordinary differential equations with nice computational properties. The unknown parameters are estimated within the approximating systems by minimizing a least-squares fit-to-data criterion. Convergence theorems are proved for time-dependent delays and state-dependent delays within two classes, which say essentially that fitting the data by using approximations will, in the limit, provide a fit to the data using the original system. Numerical test examples are presented which illustrate the method for all types of delay.

  9. Remarks on Hierarchic Control for a Linearized Micropolar Fluids System in Moving Domains

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

    Jesus, Isaías Pereira de, E-mail: isaias@ufpi.edu.br

    We study a Stackelberg strategy subject to the evolutionary linearized micropolar fluids equations in domains with moving boundaries, considering a Nash multi-objective equilibrium (non necessarily cooperative) for the “follower players” (as is called in the economy field) and an optimal problem for the leader player with approximate controllability objective. We will obtain the following main results: the existence and uniqueness of Nash equilibrium and its characterization, the approximate controllability of the linearized micropolar system with respect to the leader control and the existence and uniqueness of the Stackelberg–Nash problem, where the optimality system for the leader is given.

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

    ERIC Educational Resources Information Center

    Oud, Johan H. L.; Folmer, Henk

    2011-01-01

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

  11. Metaheuristic optimisation methods for approximate solving of singular boundary value problems

    NASA Astrophysics Data System (ADS)

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

    2017-07-01

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

  12. Fourth order Douglas implicit scheme for solving three dimension reaction diffusion equation with non-linear source term

    NASA Astrophysics Data System (ADS)

    Hasnain, Shahid; Saqib, Muhammad; Mashat, Daoud Suleiman

    2017-07-01

    This research paper represents a numerical approximation to non-linear three dimension reaction diffusion equation with non-linear source term from population genetics. Since various initial and boundary value problems exist in three dimension reaction diffusion phenomena, which are studied numerically by different numerical methods, here we use finite difference schemes (Alternating Direction Implicit and Fourth Order Douglas Implicit) to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with analytical results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. Numerical results showed that Fourth Order Douglas Implicit scheme is very efficient and reliable for solving 3-D non-linear reaction diffusion equation.

  13. A computational algorithm for spacecraft control and momentum management

    NASA Technical Reports Server (NTRS)

    Dzielski, John; Bergmann, Edward; Paradiso, Joseph

    1990-01-01

    Developments in the area of nonlinear control theory have shown how coordinate changes in the state and input spaces of a dynamical system can be used to transform certain nonlinear differential equations into equivalent linear equations. These techniques are applied to the control of a spacecraft equipped with momentum exchange devices. An optimal control problem is formulated that incorporates a nonlinear spacecraft model. An algorithm is developed for solving the optimization problem using feedback linearization to transform to an equivalent problem involving a linear dynamical constraint and a functional approximation technique to solve for the linear dynamics in terms of the control. The original problem is transformed into an unconstrained nonlinear quadratic program that yields an approximate solution to the original problem. Two examples are presented to illustrate the results.

  14. An Efficient Finite Element Framework to Assess Flexibility Performances of SMA Self-Expandable Carotid Artery Stents

    PubMed Central

    Ferraro, Mauro; Auricchio, Ferdinando; Boatti, Elisa; Scalet, Giulia; Conti, Michele; Morganti, Simone; Reali, Alessandro

    2015-01-01

    Computer-based simulations are nowadays widely exploited for the prediction of the mechanical behavior of different biomedical devices. In this aspect, structural finite element analyses (FEA) are currently the preferred computational tool to evaluate the stent response under bending. This work aims at developing a computational framework based on linear and higher order FEA to evaluate the flexibility of self-expandable carotid artery stents. In particular, numerical simulations involving large deformations and inelastic shape memory alloy constitutive modeling are performed, and the results suggest that the employment of higher order FEA allows accurately representing the computational domain and getting a better approximation of the solution with a widely-reduced number of degrees of freedom with respect to linear FEA. Moreover, when buckling phenomena occur, higher order FEA presents a superior capability of reproducing the nonlinear local effects related to buckling phenomena. PMID:26184329

  15. Quantifying relative importance: Computing standardized effects in models with binary outcomes

    USGS Publications Warehouse

    Grace, James B.; Johnson, Darren; Lefcheck, Jonathan S.; Byrnes, Jarrett E.K.

    2018-01-01

    Results from simulation studies show that both the LT and OE methods of standardization support a similarly-broad range of coefficient comparisons. The LT method estimates effects that reflect underlying latent-linear propensities, while the OE method computes a linear approximation for the effects of predictors on binary responses. The contrast between assumptions for the two methods is reflected in persistently weaker standardized effects associated with OE standardization. Reliance on standard deviations for standardization (the traditional approach) is critically examined and shown to introduce substantial biases when predictors are non-Gaussian. The use of relevant ranges in place of standard deviations has the capacity to place LT and OE standardized coefficients on a more comparable scale. As ecologists address increasingly complex hypotheses, especially those that involve comparing the influences of different controlling factors (e.g., top-down versus bottom-up or biotic versus abiotic controls), comparable coefficients become a necessary component for evaluations.

  16. Nonlinear Dynamic Behavior of Impact Damage in a Composite Skin-Stiffener Structure

    NASA Technical Reports Server (NTRS)

    Ooijevaar, T. H.; Rogge, M. D.; Loendersloot, R.; Warnet, L.; Akkerman, R.; deBoer, A.

    2013-01-01

    One of the key issues in composite structures for aircraft applications is the early identification of damage. Often, service induced damage does not involve visible plastic deformation, but internal matrix related damage, like delaminations. A wide range of technologies, comprising global vibration and local wave propagation methods can be employed for health monitoring purposes. Traditional low frequency modal analysis based methods are linear methods. The effectiveness of these methods is often limited since they rely on a stationary and linear approximation of the system. The nonlinear interaction between a low frequency wave field and a local impact induced skin-stiffener failure is experimentally demonstrated in this paper. The different mechanisms that are responsible for the nonlinearities (opening, closing and contact) of the distorted harmonic waveforms are separated with the help of phase portraits. A basic analytical model is employed to support the observations.

  17. Aptamer-Based Paper Strip Sensor for Detecting Vibrio fischeri.

    PubMed

    Shin, Woo-Ri; Sekhon, Simranjeet Singh; Rhee, Sung-Keun; Ko, Jung Ho; Ahn, Ji-Young; Min, Jiho; Kim, Yang-Hoon

    2018-05-14

    Aptamer-based paper strip sensor for detecting Vibrio fischeri was developed. Our method was based on the aptamer sandwich assay between whole live cells, V. fischeri and DNA aptamer probes. Following 9 rounds of Cell-SELEX and one of the negative-SELEX, V. fischeri Cell Aptamer (VFCA)-02 and -03 were isolated, with the former showing approximately 10-fold greater avidity (in the subnanomolar range) for the target cells when arrayed on a surface. The colorimetric response of a paper sensor based on VFCA-02 was linear in the range of 4 × 10 1 to 4 × 10 5 CFU/mL of target cell by using scanning reader. The linear regression correlation coefficient ( R 2 ) was 0.9809. This system shows promise for use in aptamer-conjugated gold nanoparticle probes in paper strip format for in-field detection of marine bioindicating bacteria.

  18. On-line estimation of nonlinear physical systems

    USGS Publications Warehouse

    Christakos, G.

    1988-01-01

    Recursive algorithms for estimating states of nonlinear physical systems are presented. Orthogonality properties are rediscovered and the associated polynomials are used to linearize state and observation models of the underlying random processes. This requires some key hypotheses regarding the structure of these processes, which may then take account of a wide range of applications. The latter include streamflow forecasting, flood estimation, environmental protection, earthquake engineering, and mine planning. The proposed estimation algorithm may be compared favorably to Taylor series-type filters, nonlinear filters which approximate the probability density by Edgeworth or Gram-Charlier series, as well as to conventional statistical linearization-type estimators. Moreover, the method has several advantages over nonrecursive estimators like disjunctive kriging. To link theory with practice, some numerical results for a simulated system are presented, in which responses from the proposed and extended Kalman algorithms are compared. ?? 1988 International Association for Mathematical Geology.

  19. Exponential convergence through linear finite element discretization of stratified subdomains

    NASA Astrophysics Data System (ADS)

    Guddati, Murthy N.; Druskin, Vladimir; Vaziri Astaneh, Ali

    2016-10-01

    Motivated by problems where the response is needed at select localized regions in a large computational domain, we devise a novel finite element discretization that results in exponential convergence at pre-selected points. The key features of the discretization are (a) use of midpoint integration to evaluate the contribution matrices, and (b) an unconventional mapping of the mesh into complex space. Named complex-length finite element method (CFEM), the technique is linked to Padé approximants that provide exponential convergence of the Dirichlet-to-Neumann maps and thus the solution at specified points in the domain. Exponential convergence facilitates drastic reduction in the number of elements. This, combined with sparse computation associated with linear finite elements, results in significant reduction in the computational cost. The paper presents the basic ideas of the method as well as illustration of its effectiveness for a variety of problems involving Laplace, Helmholtz and elastodynamics equations.

  20. On the analytical modeling of the nonlinear vibrations of pretensioned space structures

    NASA Technical Reports Server (NTRS)

    Housner, J. M.; Belvin, W. K.

    1983-01-01

    Pretensioned structures are receiving considerable attention as candidate large space structures. A typical example is a hoop-column antenna. The large number of preloaded members requires efficient analytical methods for concept validation and design. Validation through analyses is especially important since ground testing may be limited due to gravity effects and structural size. The present investigation has the objective to present an examination of the analytical modeling of pretensioned members undergoing nonlinear vibrations. Two approximate nonlinear analysis are developed to model general structural arrangements which include beam-columns and pretensioned cables attached to a common nucleus, such as may occur at a joint of a pretensioned structure. Attention is given to structures undergoing nonlinear steady-state oscillations due to sinusoidal excitation forces. Three analyses, linear, quasi-linear, and nonlinear are conducted and applied to study the response of a relatively simple cable stiffened structure.

  1. An invariant asymptotic formula for solutions of second-order linear ODE's

    NASA Technical Reports Server (NTRS)

    Gingold, H.

    1988-01-01

    An invariant-matrix technique for the approximate solution of second-order ordinary differential equations (ODEs) of form y-double-prime = phi(x)y is developed analytically and demonstrated. A set of linear transformations for the companion matrix differential system is proposed; the diagonalization procedure employed in the final stage of the asymptotic decomposition is explained; and a scalar formulation of solutions for the ODEs is obtained. Several typical ODEs are analyzed, and it is shown that the Liouville-Green or WKB approximation is a special case of the present formula, which provides an approximation which is valid for the entire interval (0, infinity).

  2. zeldovich-PLT: Zel'dovich approximation initial conditions generator

    NASA Astrophysics Data System (ADS)

    Eisenstein, Daniel; Garrison, Lehman

    2016-05-01

    zeldovich-PLT generates Zel'dovich approximation (ZA) initial conditions (i.e. first-order Lagrangian perturbation theory) for cosmological N-body simulations, optionally applying particle linear theory (PLT) corrections.

  3. Smooth function approximation using neural networks.

    PubMed

    Ferrari, Silvia; Stengel, Robert F

    2005-01-01

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

  4. Contact position sensor using constant contact force control system

    NASA Technical Reports Server (NTRS)

    Sturdevant, Jay (Inventor)

    1995-01-01

    A force control system (50) and method are provided for controlling a position contact sensor (10) so as to produce a constant controlled contact force therewith. The system (50) includes a contact position sensor (10) which has a contact probe (12) for contacting the surface of a target to be measured and an output signal (V.sub.o) for providing a position indication thereof. An actuator (30) is provided for controllably driving the contact position sensor (10) in response to an actuation control signal (I). A controller (52) receives the position indication signal (V.sub.o) and generates in response thereto the actuation control signal (I) so as to provide a substantially constant selective force (F) exerted by the contact probe (12). The actuation drive signal (I) is generated further in response to substantially linear approximation curves based on predetermined force and position data attained from the sensor (10) and the actuator (30).

  5. Nonreciprocal quantum Hall devices with driven edge magnetoplasmons in two-dimensional materials

    NASA Astrophysics Data System (ADS)

    Bosco, S.; DiVincenzo, D. P.

    2017-05-01

    We develop a theory that describes the response of nonreciprocal devices employing two-dimensional materials in the quantum Hall regime capacitively coupled to external electrodes. As the conduction in these devices is understood to be associated to the edge magnetoplasmons (EMPs), we first investigate the EMP problem by using the linear response theory in the random phase approximation. Our model can incorporate several cases that were often treated on different grounds in literature. In particular, we analyze plasmonic excitations supported by a smooth and sharp confining potential in a two-dimensional electron gas, and in monolayer graphene, and we point out the similarities and differences in these materials. We also account for a general time-dependent external drive applied to the system. Finally, we describe the behavior of a nonreciprocal quantum Hall device: the response contains additional resonant features, which were not foreseen from previous models.

  6. Adjoints and Low-rank Covariance Representation

    NASA Technical Reports Server (NTRS)

    Tippett, Michael K.; Cohn, Stephen E.

    2000-01-01

    Quantitative measures of the uncertainty of Earth System estimates can be as important as the estimates themselves. Second moments of estimation errors are described by the covariance matrix, whose direct calculation is impractical when the number of degrees of freedom of the system state is large. Ensemble and reduced-state approaches to prediction and data assimilation replace full estimation error covariance matrices by low-rank approximations. The appropriateness of such approximations depends on the spectrum of the full error covariance matrix, whose calculation is also often impractical. Here we examine the situation where the error covariance is a linear transformation of a forcing error covariance. We use operator norms and adjoints to relate the appropriateness of low-rank representations to the conditioning of this transformation. The analysis is used to investigate low-rank representations of the steady-state response to random forcing of an idealized discrete-time dynamical system.

  7. Electronic excitation of molecules in solution calculated using the symmetry-adapted cluster–configuration interaction method in the polarizable continuum model

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

    Fukuda, Ryoichi, E-mail: fukuda@ims.ac.jp; Ehara, Masahiro; Elements Strategy Initiative for Catalysts and Batteries

    2015-12-31

    The effects from solvent environment are specific to the electronic states; therefore, a computational scheme for solvent effects consistent with the electronic states is necessary to discuss electronic excitation of molecules in solution. The PCM (polarizable continuum model) SAC (symmetry-adapted cluster) and SAC-CI (configuration interaction) methods are developed for such purposes. The PCM SAC-CI adopts the state-specific (SS) solvation scheme where solvent effects are self-consistently considered for every ground and excited states. For efficient computations of many excited states, we develop a perturbative approximation for the PCM SAC-CI method, which is called corrected linear response (cLR) scheme. Our test calculationsmore » show that the cLR PCM SAC-CI is a very good approximation of the SS PCM SAC-CI method for polar and nonpolar solvents.« less

  8. Noise Suppression and Surplus Synchrony by Coincidence Detection

    PubMed Central

    Schultze-Kraft, Matthias; Diesmann, Markus; Grün, Sonja; Helias, Moritz

    2013-01-01

    The functional significance of correlations between action potentials of neurons is still a matter of vivid debate. In particular, it is presently unclear how much synchrony is caused by afferent synchronized events and how much is intrinsic due to the connectivity structure of cortex. The available analytical approaches based on the diffusion approximation do not allow to model spike synchrony, preventing a thorough analysis. Here we theoretically investigate to what extent common synaptic afferents and synchronized inputs each contribute to correlated spiking on a fine temporal scale between pairs of neurons. We employ direct simulation and extend earlier analytical methods based on the diffusion approximation to pulse-coupling, allowing us to introduce precisely timed correlations in the spiking activity of the synaptic afferents. We investigate the transmission of correlated synaptic input currents by pairs of integrate-and-fire model neurons, so that the same input covariance can be realized by common inputs or by spiking synchrony. We identify two distinct regimes: In the limit of low correlation linear perturbation theory accurately determines the correlation transmission coefficient, which is typically smaller than unity, but increases sensitively even for weakly synchronous inputs. In the limit of high input correlation, in the presence of synchrony, a qualitatively new picture arises. As the non-linear neuronal response becomes dominant, the output correlation becomes higher than the total correlation in the input. This transmission coefficient larger unity is a direct consequence of non-linear neural processing in the presence of noise, elucidating how synchrony-coded signals benefit from these generic properties present in cortical networks. PMID:23592953

  9. Discriminant analysis for fast multiclass data classification through regularized kernel function approximation.

    PubMed

    Ghorai, Santanu; Mukherjee, Anirban; Dutta, Pranab K

    2010-06-01

    In this brief we have proposed the multiclass data classification by computationally inexpensive discriminant analysis through vector-valued regularized kernel function approximation (VVRKFA). VVRKFA being an extension of fast regularized kernel function approximation (FRKFA), provides the vector-valued response at single step. The VVRKFA finds a linear operator and a bias vector by using a reduced kernel that maps a pattern from feature space into the low dimensional label space. The classification of patterns is carried out in this low dimensional label subspace. A test pattern is classified depending on its proximity to class centroids. The effectiveness of the proposed method is experimentally verified and compared with multiclass support vector machine (SVM) on several benchmark data sets as well as on gene microarray data for multi-category cancer classification. The results indicate the significant improvement in both training and testing time compared to that of multiclass SVM with comparable testing accuracy principally in large data sets. Experiments in this brief also serve as comparison of performance of VVRKFA with stratified random sampling and sub-sampling.

  10. A Bidirectional Brain-Machine Interface Algorithm That Approximates Arbitrary Force-Fields

    PubMed Central

    Semprini, Marianna; Mussa-Ivaldi, Ferdinando A.; Panzeri, Stefano

    2014-01-01

    We examine bidirectional brain-machine interfaces that control external devices in a closed loop by decoding motor cortical activity to command the device and by encoding the state of the device by delivering electrical stimuli to sensory areas. Although it is possible to design this artificial sensory-motor interaction while maintaining two independent channels of communication, here we propose a rule that closes the loop between flows of sensory and motor information in a way that approximates a desired dynamical policy expressed as a field of forces acting upon the controlled external device. We previously developed a first implementation of this approach based on linear decoding of neural activity recorded from the motor cortex into a set of forces (a force field) applied to a point mass, and on encoding of position of the point mass into patterns of electrical stimuli delivered to somatosensory areas. However, this previous algorithm had the limitation that it only worked in situations when the position-to-force map to be implemented is invertible. Here we overcome this limitation by developing a new non-linear form of the bidirectional interface that can approximate a virtually unlimited family of continuous fields. The new algorithm bases both the encoding of position information and the decoding of motor cortical activity on an explicit map between spike trains and the state space of the device computed with Multi-Dimensional-Scaling. We present a detailed computational analysis of the performance of the interface and a validation of its robustness by using synthetic neural responses in a simulated sensory-motor loop. PMID:24626393

  11. Bayesian feature selection for high-dimensional linear regression via the Ising approximation with applications to genomics.

    PubMed

    Fisher, Charles K; Mehta, Pankaj

    2015-06-01

    Feature selection, identifying a subset of variables that are relevant for predicting a response, is an important and challenging component of many methods in statistics and machine learning. Feature selection is especially difficult and computationally intensive when the number of variables approaches or exceeds the number of samples, as is often the case for many genomic datasets. Here, we introduce a new approach--the Bayesian Ising Approximation (BIA)-to rapidly calculate posterior probabilities for feature relevance in L2 penalized linear regression. In the regime where the regression problem is strongly regularized by the prior, we show that computing the marginal posterior probabilities for features is equivalent to computing the magnetizations of an Ising model with weak couplings. Using a mean field approximation, we show it is possible to rapidly compute the feature selection path described by the posterior probabilities as a function of the L2 penalty. We present simulations and analytical results illustrating the accuracy of the BIA on some simple regression problems. Finally, we demonstrate the applicability of the BIA to high-dimensional regression by analyzing a gene expression dataset with nearly 30 000 features. These results also highlight the impact of correlations between features on Bayesian feature selection. An implementation of the BIA in C++, along with data for reproducing our gene expression analyses, are freely available at http://physics.bu.edu/∼pankajm/BIACode. © The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

  12. Born approximation in linear-time invariant system

    NASA Astrophysics Data System (ADS)

    Gumjudpai, Burin

    2017-09-01

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

  13. An h-p Taylor-Galerkin finite element method for compressible Euler equations

    NASA Technical Reports Server (NTRS)

    Demkowicz, L.; Oden, J. T.; Rachowicz, W.; Hardy, O.

    1991-01-01

    An extension of the familiar Taylor-Galerkin method to arbitrary h-p spatial approximations is proposed. Boundary conditions are analyzed, and a linear stability result for arbitrary meshes is given, showing the unconditional stability for the parameter of implicitness alpha not less than 0.5. The wedge and blunt body problems are solved with both linear, quadratic, and cubic elements and h-adaptivity, showing the feasibility of higher orders of approximation for problems with shocks.

  14. Dosimetric evaluation of a new OneDose MOSFET for Ir-192 energy.

    PubMed

    Kinhikar, Rajesh A; Sharma, Pramod K; Tambe, Chandrashekhar M; Deshpande, Deepak D

    2006-03-07

    The purpose of this study was to investigate dosimetry (reproducibility, energy correction, relative response with distance from source, linearity with threshold dose, rate of fading, temperature and angular dependence) of a newly designed OneDosetrade mark MOSFET patient dosimetry system for use in HDR brachytherapy with Ir-192 energy. All measurements were performed with a MicroSelectron HDR unit and OneDose MOSFET detectors. All dosimeters were normalized to 3 min post-irradiation to minimize fading effects. All dosimeters gave reproducible readings with mean deviation of 1.8% (SD 0.4) and 2.4% (SD 0.6) for 0 degrees and 180 degrees incidences, respectively. The mean energy correction factor was found to be 1.1 (range 1.06-1.12). Overall, there was 60% and 40% mean response of the MOSFET at 2 and 3 cm, respectively, from the source. MOSFET results showed good agreement with TLD and parallel plate ion chamber. Linear dose response with threshold voltage shift was observed with applied doses of 0.3 Gy-5 Gy with Ir-192 energy. Linearity (R2 = 1) was observed in the MOSFET signal with the applied dose range of 0.3 Gy-5 Gy with Ir-192 energy. Fading effects were less than 1% after 10 min and the MOSFET detectors stayed stable (within 5%) over a period of 1 month. The MOSFET response was found to be decreased by approximately 1.5% at 37 degrees C compared to 20 degrees C. The isotropic response of the MOSFET was found to be within +/-6%. A maximum deviation of 5.5% was obtained between 0 degrees and 180 degrees for both the axes and this should be considered in clinical applications. The small size, cable-less, instant readout, permanent storage of dose and ease of use make the MOSFET a novel dosimeter and beneficial to patients for skin dose measurements with HDRBT using an Ir-192 source compared to the labour demanding and time-consuming TLDs.

  15. Design of a high-speed optical dark-soliton detector using a phase-shifted waveguide Bragg grating in reflection.

    PubMed

    Ngo, Nam Quoc

    2007-12-01

    A theoretical study of a new application of a simple pi-phase-shifted waveguide Bragg grating (PSWBG) in reflection mode as a high-speed optical dark-soliton detector is presented. The PSWBG consists of two concatenated identical uniform waveguide Bragg gratings with a pi phase shift between them. The reflective PSWBG, with grating reflectivities equal to 0.9, a free spectral range of 1.91 THz, and a nonlinear phase response, can convert a 40 Gbit/s noisy dark-soliton signal into a high-quality 40 Gbit/s return-to-zero signal with a peak power level of approximately 17.5 dB greater than that by the existing Mach-Zehnder interferometer with free spectral range of 1.91 THz and a linear phase response.

  16. Dielectric response of Anderson and pseudogapped insulators

    NASA Astrophysics Data System (ADS)

    Feigel’man, M. V.; Ivanov, D. A.; Cuevas, E.

    2018-05-01

    Using a combination of analytic and numerical methods, we study the polarizability of a (non-interacting) Anderson insulator in one-, two-, and three-dimensions and demonstrate that, in a wide range of parameters, it scales proportionally to the square of the localization length, contrary to earlier claims based on the effective-medium approximation. We further analyze the effect of electron–electron interactions on the dielectric constant in quasi-1D, quasi-2D and 3D materials with large localization length, including both Coulomb repulsion and phonon-mediated attraction. The phonon-mediated attraction (in the pseudogapped state on the insulating side of the superconductor-insulator transition) produces a correction to the dielectric constant, which may be detected from a linear response of a dielectric constant to an external magnetic field.

  17. Simulation-based decision support framework for dynamic ambulance redeployment in Singapore.

    PubMed

    Lam, Sean Shao Wei; Ng, Clarence Boon Liang; Nguyen, Francis Ngoc Hoang Long; Ng, Yih Yng; Ong, Marcus Eng Hock

    2017-10-01

    Dynamic ambulance redeployment policies tend to introduce much more flexibilities in improving ambulance resource allocation by capitalizing on the definite geospatial-temporal variations in ambulance demand patterns over the time-of-the-day and day-of-the-week effects. A novel modelling framework based on the Approximate Dynamic Programming (ADP) approach leveraging on a Discrete Events Simulation (DES) model for dynamic ambulance redeployment in Singapore is proposed in this paper. The study was based on the Singapore's national Emergency Medical Services (EMS) system. Based on a dataset comprising 216,973 valid incidents over a continuous two-years study period from 1 January 2011-31 December 2012, a DES model for the EMS system was developed. An ADP model based on linear value function approximations was then evaluated using the DES model via the temporal difference (TD) learning family of algorithms. The objective of the ADP model is to derive approximate optimal dynamic redeployment policies based on the primary outcome of ambulance coverage. Considering an 8min response time threshold, an estimated 5% reduction in the proportion of calls that cannot be reached within the threshold (equivalent to approximately 8000 dispatches) was observed from the computational experiments. The study also revealed that the redeployment policies which are restricted within the same operational division could potentially result in a more promising response time performance. Furthermore, the best policy involved the combination of redeploying ambulances whenever they are released from service and that of relocating ambulances that are idle in bases. This study demonstrated the successful application of an approximate modelling framework based on ADP that leverages upon a detailed DES model of the Singapore's EMS system to generate approximate optimal dynamic redeployment plans. Various policies and scenarios relevant to the Singapore EMS system were evaluated. Copyright © 2017 Elsevier B.V. All rights reserved.

  18. Stability Analysis of Finite Difference Schemes for Hyperbolic Systems, and Problems in Applied and Computational Linear Algebra.

    DTIC Science & Technology

    FINITE DIFFERENCE THEORY, * LINEAR ALGEBRA , APPLIED MATHEMATICS, APPROXIMATION(MATHEMATICS), BOUNDARY VALUE PROBLEMS, COMPUTATIONS, HYPERBOLAS, MATHEMATICAL MODELS, NUMERICAL ANALYSIS, PARTIAL DIFFERENTIAL EQUATIONS, STABILITY.

  19. Chemical association in simple models of molecular and ionic fluids. III. The cavity function

    NASA Astrophysics Data System (ADS)

    Zhou, Yaoqi; Stell, George

    1992-01-01

    Exact equations which relate the cavity function to excess solvation free energies and equilibrium association constants are rederived by using a thermodynamic cycle. A zeroth-order approximation, derived previously by us as a simple interpolation scheme, is found to be very accurate if the associative bonding occurs on or near the surface of the repulsive core of the interaction potential. If the bonding radius is substantially less than the core radius, the approximation overestimates the association degree and the association constant. For binary association, the zeroth-order approximation is equivalent to the first-order thermodynamic perturbation theory (TPT) of Wertheim. For n-particle association, the combination of the zeroth-order approximation with a ``linear'' approximation (for n-particle distribution functions in terms of the two-particle function) yields the first-order TPT result. Using our exact equations to go beyond TPT, near-exact analytic results for binary hard-sphere association are obtained. Solvent effects on binary hard-sphere association and ionic association are also investigated. A new rule which generalizes Le Chatelier's principle is used to describe the three distinct forms of behaviors involving solvent effects that we find. The replacement of the dielectric-continuum solvent model by a dipolar hard-sphere model leads to improved agreement with an experimental observation. Finally, equation of state for an n-particle flexible linear-chain fluid is derived on the basis of a one-parameter approximation that interpolates between the generalized Kirkwood superposition approximation and the linear approximation. A value of the parameter that appears to be near optimal in the context of this application is obtained from comparison with computer-simulation data.

  20. An approximation of herd effect due to vaccinating children against seasonal influenza – a potential solution to the incorporation of indirect effects into static models

    PubMed Central

    2013-01-01

    Background Indirect herd effect from vaccination of children offers potential for improving the effectiveness of influenza prevention in the remaining unvaccinated population. Static models used in cost-effectiveness analyses cannot dynamically capture herd effects. The objective of this study was to develop a methodology to allow herd effect associated with vaccinating children against seasonal influenza to be incorporated into static models evaluating the cost-effectiveness of influenza vaccination. Methods Two previously published linear equations for approximation of herd effects in general were compared with the results of a structured literature review undertaken using PubMed searches to identify data on herd effects specific to influenza vaccination. A linear function was fitted to point estimates from the literature using the sum of squared residuals. Results The literature review identified 21 publications on 20 studies for inclusion. Six studies provided data on a mathematical relationship between effective vaccine coverage in subgroups and reduction of influenza infection in a larger unvaccinated population. These supported a linear relationship when effective vaccine coverage in a subgroup population was between 20% and 80%. Three studies evaluating herd effect at a community level, specifically induced by vaccinating children, provided point estimates for fitting linear equations. The fitted linear equation for herd protection in the target population for vaccination (children) was slightly less conservative than a previously published equation for herd effects in general. The fitted linear equation for herd protection in the non-target population was considerably less conservative than the previously published equation. Conclusions This method of approximating herd effect requires simple adjustments to the annual baseline risk of influenza in static models: (1) for the age group targeted by the childhood vaccination strategy (i.e. children); and (2) for other age groups not targeted (e.g. adults and/or elderly). Two approximations provide a linear relationship between effective coverage and reduction in the risk of infection. The first is a conservative approximation, recommended as a base-case for cost-effectiveness evaluations. The second, fitted to data extracted from a structured literature review, provides a less conservative estimate of herd effect, recommended for sensitivity analyses. PMID:23339290

  1. Unruh effect for general trajectories

    NASA Astrophysics Data System (ADS)

    Obadia, N.; Milgrom, M.

    2007-03-01

    We consider two-level detectors coupled to a scalar field and moving on arbitrary trajectories in Minkowski space-time. We first derive a generic expression for the response function using a (novel) regularization procedure based on the Feynman prescription that is explicitly causal, and we compare it to other expressions used in the literature. We then use this expression to study, analytically and numerically, the time dependence of the response function in various nonstationarity situations. We show that, generically, the response function decreases like a power in the detector’s level spacing, E, for high E. It is only for stationary worldlines that the response function decays faster than any power law, in keeping with the known exponential behavior for some stationary cases. Under some conditions the (time-dependent) response function for a nonstationary worldline is well approximated by the value of the response function for a stationary worldline having the same instantaneous acceleration, torsion, and hypertorsion. While we cannot offer general conditions for this to apply, we discuss special cases; in particular, the low-energy limit for linear space trajectories.

  2. Proprioceptive influence on the optokinetic nystagmus.

    PubMed

    Botti, F; Anastasopoulos, D; Kostadima, V; Bambagioni, D; Pettorossi, V E

    2001-01-01

    The influence of neck and leg proprioceptive inputs on optokinetic-induced quick phases was studied in humans. Ten subjects received unidirectional horizontal optokinetic stimulation (10-20%/s) during sinusoidal neck, leg and combined neck + leg proprioceptive stimulation. The optokinetic reflex was measured by electro-oculography. Neck stimulation induced a shift in the nystagmus beating field in the opposite direction to body movement (gain 0.3 0.4, phase 140-180 degrees). The beating field shift resulted totally from the amplitude and frequency modulation of optokinetic quick phases, as slow phases were not affected. Leg proprioceptive stimulation induced a similar effect, but the phase of the response lagged by approximately 90 degrees compared with that of neck response. With combined neck + leg stimulation, the amplitude of the effect was a sum of the separate effects, but the phase coincided with that of the leg response. This suggests that neck and leg proprioceptive signals do not add linearly and that the leg signal determines the time of the response.

  3. Local Laplacian Coding From Theoretical Analysis of Local Coding Schemes for Locally Linear Classification.

    PubMed

    Pang, Junbiao; Qin, Lei; Zhang, Chunjie; Zhang, Weigang; Huang, Qingming; Yin, Baocai

    2015-12-01

    Local coordinate coding (LCC) is a framework to approximate a Lipschitz smooth function by combining linear functions into a nonlinear one. For locally linear classification, LCC requires a coding scheme that heavily determines the nonlinear approximation ability, posing two main challenges: 1) the locality making faraway anchors have smaller influences on current data and 2) the flexibility balancing well between the reconstruction of current data and the locality. In this paper, we address the problem from the theoretical analysis of the simplest local coding schemes, i.e., local Gaussian coding and local student coding, and propose local Laplacian coding (LPC) to achieve the locality and the flexibility. We apply LPC into locally linear classifiers to solve diverse classification tasks. The comparable or exceeded performances of state-of-the-art methods demonstrate the effectiveness of the proposed method.

  4. Non-linear principal component analysis applied to Lorenz models and to North Atlantic SLP

    NASA Astrophysics Data System (ADS)

    Russo, A.; Trigo, R. M.

    2003-04-01

    A non-linear generalisation of Principal Component Analysis (PCA), denoted Non-Linear Principal Component Analysis (NLPCA), is introduced and applied to the analysis of three data sets. Non-Linear Principal Component Analysis allows for the detection and characterisation of low-dimensional non-linear structure in multivariate data sets. This method is implemented using a 5-layer feed-forward neural network introduced originally in the chemical engineering literature (Kramer, 1991). The method is described and details of its implementation are addressed. Non-Linear Principal Component Analysis is first applied to a data set sampled from the Lorenz attractor (1963). It is found that the NLPCA approximations are more representative of the data than are the corresponding PCA approximations. The same methodology was applied to the less known Lorenz attractor (1984). However, the results obtained weren't as good as those attained with the famous 'Butterfly' attractor. Further work with this model is underway in order to assess if NLPCA techniques can be more representative of the data characteristics than are the corresponding PCA approximations. The application of NLPCA to relatively 'simple' dynamical systems, such as those proposed by Lorenz, is well understood. However, the application of NLPCA to a large climatic data set is much more challenging. Here, we have applied NLPCA to the sea level pressure (SLP) field for the entire North Atlantic area and the results show a slight imcrement of explained variance associated. Finally, directions for future work are presented.%}

  5. Efficient Algorithms for Estimating the Absorption Spectrum within Linear Response TDDFT

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

    Brabec, Jiri; Lin, Lin; Shao, Meiyue

    We present a special symmetric Lanczos algorithm and a kernel polynomial method (KPM) for approximating the absorption spectrum of molecules within the linear response time-dependent density functional theory (TDDFT) framework in the product form. In contrast to existing algorithms, the new algorithms are based on reformulating the original non-Hermitian eigenvalue problem as a product eigenvalue problem and the observation that the product eigenvalue problem is self-adjoint with respect to an appropriately chosen inner product. This allows a simple symmetric Lanczos algorithm to be used to compute the desired absorption spectrum. The use of a symmetric Lanczos algorithm only requires halfmore » of the memory compared with the nonsymmetric variant of the Lanczos algorithm. The symmetric Lanczos algorithm is also numerically more stable than the nonsymmetric version. The KPM algorithm is also presented as a low-memory alternative to the Lanczos approach, but the algorithm may require more matrix-vector multiplications in practice. We discuss the pros and cons of these methods in terms of their accuracy as well as their computational and storage cost. Applications to a set of small and medium-sized molecules are also presented.« less

  6. Efficient Algorithms for Estimating the Absorption Spectrum within Linear Response TDDFT

    DOE PAGES

    Brabec, Jiri; Lin, Lin; Shao, Meiyue; ...

    2015-10-06

    We present a special symmetric Lanczos algorithm and a kernel polynomial method (KPM) for approximating the absorption spectrum of molecules within the linear response time-dependent density functional theory (TDDFT) framework in the product form. In contrast to existing algorithms, the new algorithms are based on reformulating the original non-Hermitian eigenvalue problem as a product eigenvalue problem and the observation that the product eigenvalue problem is self-adjoint with respect to an appropriately chosen inner product. This allows a simple symmetric Lanczos algorithm to be used to compute the desired absorption spectrum. The use of a symmetric Lanczos algorithm only requires halfmore » of the memory compared with the nonsymmetric variant of the Lanczos algorithm. The symmetric Lanczos algorithm is also numerically more stable than the nonsymmetric version. The KPM algorithm is also presented as a low-memory alternative to the Lanczos approach, but the algorithm may require more matrix-vector multiplications in practice. We discuss the pros and cons of these methods in terms of their accuracy as well as their computational and storage cost. Applications to a set of small and medium-sized molecules are also presented.« less

  7. Effects of Hydrostatic Pressure and Electric Field on the Electron-Related Optical Properties in GaAs Multiple Quantum Well.

    PubMed

    Ospina, D A; Mora-Ramos, M E; Duque, C A

    2017-02-01

    The properties of the electronic structure of a finite-barrier semiconductor multiple quantum well are investigated taking into account the effects of the application of a static electric field and hydrostatic pressure. With the information of the allowed quasi-stationary energy states, the coefficients of linear and nonlinear optical absorption and of the relative refractive index change associated to transitions between allowed subbands are calculated with the use of a two-level scheme for the density matrix equation of motion and the rotating wave approximation. It is noticed that the hydrostatic pressure enhances the amplitude of the nonlinear contribution to the optical response of the multiple quantum well, whilst the linear one becomes reduced. Besides, the calculated coefficients are blueshifted due to the increasing of the applied electric field, and shows systematically dependence upon the hydrostatic pressure. The comparison of these results with those related with the consideration of a stationary spectrum of states in the heterostructure-obtained by placing infinite confining barriers at a conveniently far distance-shows essential differences in the pressure-induced effects in the sense of resonant frequency shifting as well as in the variation of the amplitudes of the optical responses.

  8. Approximating the linear quadratic optimal control law for hereditary systems with delays in the control

    NASA Technical Reports Server (NTRS)

    Milman, Mark H.

    1987-01-01

    The fundamental control synthesis issue of establishing a priori convergence rates of approximation schemes for feedback controllers for a class of distributed parameter systems is addressed within the context of hereditary systems. Specifically, a factorization approach is presented for deriving approximations to the optimal feedback gains for the linear regulator-quadratic cost problem associated with time-varying functional differential equations with control delays. The approach is based on a discretization of the state penalty which leads to a simple structure for the feedback control law. General properties of the Volterra factors of Hilbert-Schmidt operators are then used to obtain convergence results for the controls, trajectories and feedback kernels. Two algorithms are derived from the basic approximation scheme, including a fast algorithm, in the time-invariant case. A numerical example is also considered.

  9. Approximating the linear quadratic optimal control law for hereditary systems with delays in the control

    NASA Technical Reports Server (NTRS)

    Milman, Mark H.

    1988-01-01

    The fundamental control synthesis issue of establishing a priori convergence rates of approximation schemes for feedback controllers for a class of distributed parameter systems is addressed within the context of hereditary schemes. Specifically, a factorization approach is presented for deriving approximations to the optimal feedback gains for the linear regulator-quadratic cost problem associated with time-varying functional differential equations with control delays. The approach is based on a discretization of the state penalty which leads to a simple structure for the feedback control law. General properties of the Volterra factors of Hilbert-Schmidt operators are then used to obtain convergence results for the controls, trajectories and feedback kernels. Two algorithms are derived from the basic approximation scheme, including a fast algorithm, in the time-invariant case. A numerical example is also considered.

  10. Displacement analysis of diagnostic ultrasound backscatter: A methodology for characterizing, modeling, and monitoring high intensity focused ultrasound therapy

    PubMed Central

    Speyer, Gavriel; Kaczkowski, Peter J.; Brayman, Andrew A.; Crum, Lawrence A.

    2010-01-01

    Accurate monitoring of high intensity focused ultrasound (HIFU) therapy is critical for widespread clinical use. Pulse-echo diagnostic ultrasound (DU) is known to exhibit temperature sensitivity through relative changes in time-of-flight between two sets of radio frequency (RF) backscatter measurements, one acquired before and one after therapy. These relative displacements, combined with knowledge of the exposure protocol, material properties, heat transfer, and measurement noise statistics, provide a natural framework for estimating the administered heating, and thereby therapy. The proposed method, termed displacement analysis, identifies the relative displacements using linearly independent displacement patterns, or modes, each induced by a particular time-varying heating applied during the exposure interval. These heating modes are themselves linearly independent. This relationship implies that a linear combination of displacement modes aligning the DU measurements is the response to an identical linear combination of heating modes, providing the heating estimate. Furthermore, the accuracy of coefficient estimates in this approximation is determined a priori, characterizing heating, thermal dose, and temperature estimates for any given protocol. Predicted performance is validated using simulations and experiments in alginate gel phantoms. Evidence for a spatially distributed interaction between temperature and time-of-flight changes is presented. PMID:20649206

  11. A new Newton-like method for solving nonlinear equations.

    PubMed

    Saheya, B; Chen, Guo-Qing; Sui, Yun-Kang; Wu, Cai-Ying

    2016-01-01

    This paper presents an iterative scheme for solving nonline ar equations. We establish a new rational approximation model with linear numerator and denominator which has generalizes the local linear model. We then employ the new approximation for nonlinear equations and propose an improved Newton's method to solve it. The new method revises the Jacobian matrix by a rank one matrix each iteration and obtains the quadratic convergence property. The numerical performance and comparison show that the proposed method is efficient.

  12. A new approach to approximating the linear quadratic optimal control law for hereditary systems with control delays

    NASA Technical Reports Server (NTRS)

    Milman, M. H.

    1985-01-01

    A factorization approach is presented for deriving approximations to the optimal feedback gain for the linear regulator-quadratic cost problem associated with time-varying functional differential equations with control delays. The approach is based on a discretization of the state penalty which leads to a simple structure for the feedback control law. General properties of the Volterra factors of Hilbert-Schmidt operators are then used to obtain convergence results for the feedback kernels.

  13. Time domain convergence properties of Lyapunov stable penalty methods

    NASA Technical Reports Server (NTRS)

    Kurdila, A. J.; Sunkel, John

    1991-01-01

    Linear hyperbolic partial differential equations are analyzed using standard techniques to show that a sequence of solutions generated by the Liapunov stable penalty equations approaches the solution of the differential-algebraic equations governing the dynamics of multibody problems arising in linear vibrations. The analysis does not require that the system be conservative and does not impose any specific integration scheme. Variational statements are derived which bound the error in approximation by the norm of the constraint violation obtained in the approximate solutions.

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

    PubMed

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

    2015-02-01

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

  15. Migration of scattered teleseismic body waves

    NASA Astrophysics Data System (ADS)

    Bostock, M. G.; Rondenay, S.

    1999-06-01

    The retrieval of near-receiver mantle structure from scattered waves associated with teleseismic P and S and recorded on three-component, linear seismic arrays is considered in the context of inverse scattering theory. A Ray + Born formulation is proposed which admits linearization of the forward problem and economy in the computation of the elastic wave Green's function. The high-frequency approximation further simplifies the problem by enabling (1) the use of an earth-flattened, 1-D reference model, (2) a reduction in computations to 2-D through the assumption of 2.5-D experimental geometry, and (3) band-diagonalization of the Hessian matrix in the inverse formulation. The final expressions are in a form reminiscent of the classical diffraction stack of seismic migration. Implementation of this procedure demands an accurate estimate of the scattered wave contribution to the impulse response, and thus requires the removal of both the reference wavefield and the source time signature from the raw record sections. An approximate separation of direct and scattered waves is achieved through application of the inverse free-surface transfer operator to individual station records and a Karhunen-Loeve transform to the resulting record sections. This procedure takes the full displacement field to a wave vector space wherein the first principal component of the incident wave-type section is identified with the direct wave and is used as an estimate of the source time function. The scattered displacement field is reconstituted from the remaining principal components using the forward free-surface transfer operator, and may be reduced to a scattering impulse response upon deconvolution of the source estimate. An example employing pseudo-spectral synthetic seismograms demonstrates an application of the methodology.

  16. Pattern analysis of total item score and item response of the Kessler Screening Scale for Psychological Distress (K6) in a nationally representative sample of US adults

    PubMed Central

    Kawasaki, Yohei; Ide, Kazuki; Akutagawa, Maiko; Yamada, Hiroshi; Yutaka, Ono; Furukawa, Toshiaki A.

    2017-01-01

    Background Several recent studies have shown that total scores on depressive symptom measures in a general population approximate an exponential pattern except for the lower end of the distribution. Furthermore, we confirmed that the exponential pattern is present for the individual item responses on the Center for Epidemiologic Studies Depression Scale (CES-D). To confirm the reproducibility of such findings, we investigated the total score distribution and item responses of the Kessler Screening Scale for Psychological Distress (K6) in a nationally representative study. Methods Data were drawn from the National Survey of Midlife Development in the United States (MIDUS), which comprises four subsamples: (1) a national random digit dialing (RDD) sample, (2) oversamples from five metropolitan areas, (3) siblings of individuals from the RDD sample, and (4) a national RDD sample of twin pairs. K6 items are scored using a 5-point scale: “none of the time,” “a little of the time,” “some of the time,” “most of the time,” and “all of the time.” The pattern of total score distribution and item responses were analyzed using graphical analysis and exponential regression model. Results The total score distributions of the four subsamples exhibited an exponential pattern with similar rate parameters. The item responses of the K6 approximated a linear pattern from “a little of the time” to “all of the time” on log-normal scales, while “none of the time” response was not related to this exponential pattern. Discussion The total score distribution and item responses of the K6 showed exponential patterns, consistent with other depressive symptom scales. PMID:28289560

  17. Pattern and polarization measurements of integrated-circuit spiral antennas at 10-μm wavelength

    NASA Astrophysics Data System (ADS)

    MacDonald, Michael E.; Grossman, Erich N.

    1996-12-01

    Radiation patterns are presented for planar equiangular spiral antennas at wavelengths of approximately 10 micrometers . These antennas are fabricated using integrated-circuit processes on silicon substrates and are coupled through dielectric lenses. Patterns are presented over a full 2D scan for orthogonal linear polarizations, and for left- circular (LCP) and right-circular (RCP) polarizations. The antennas respond preferentially to left-circularly polarized radiation, as expected for the left-handed sense of the spiral arms. Cross-polarization ratios as large as 10 dB in circular polarization are obtained, corresponding to an axial ratio of 1.2. No difference in response between horizontally and vertically polarized radiation is observed, as expected for circularly polarized antennas. Directivities as large as 14 dB in left-circular polarization have been obtained. The cross-polarized directivity is considerably lower than the co-polarized directivity. All patterns are approximately circularly symmetric about the (theta) equals 0 axis. The cross-polarization ratio and pattern symmetry strongly depend on the alignment of the antenna and detector response is antenna coupled, even at radiation wavelength of the same order of magnitude as the resolution limit of the optical lithography used to define the antenna geometry.

  18. Introduction to the Treatment of Non-Linear Effects Using a Gravitational Pendulum

    ERIC Educational Resources Information Center

    Weltner, Klaus; Esperidiao, Antonio Sergio C.; Miranda, Paulo

    2004-01-01

    We show that the treatment of pendulum movement, other than the linear approximation,may be an instructive experimentally based introduction to the physics of non-linear effects. Firstly the natural frequency of a gravitational pendulum is measured as function of its amplitude. Secondly forced oscillations of a gravitational pendulum are…

  19. PV Degradation Curves: Non-Linearities and Failure Modes

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

    Jordan, Dirk C.; Silverman, Timothy J.; Sekulic, Bill

    Photovoltaic (PV) reliability and durability have seen increased interest in recent years. Historically, and as a preliminarily reasonable approximation, linear degradation rates have been used to quantify long-term module and system performance. The underlying assumption of linearity can be violated at the beginning of the life, as has been well documented, especially for thin-film technology. Additionally, non-linearities in the wear-out phase can have significant economic impact and appear to be linked to different failure modes. In addition, associating specific degradation and failure modes with specific time series behavior will aid in duplicating these degradation modes in accelerated tests and, eventually,more » in service life prediction. In this paper, we discuss different degradation modes and how some of these may cause approximately linear degradation within the measurement uncertainty (e.g., modules that were mainly affected by encapsulant discoloration) while other degradation modes lead to distinctly non-linear degradation (e.g., hot spots caused by cracked cells or solder bond failures and corrosion). The various behaviors are summarized with the goal of aiding in predictions of what may be seen in other systems.« less

  20. Relationship between depolarization-induced force responses and Ca2+ content in skeletal muscle fibres of rat and toad.

    PubMed

    Owen, V J; Lamb, G D; Stephenson, D G; Fryer, M W

    1997-02-01

    1. The relationship between the total Ca2+ content of a muscle fibre and the magnitude of the force response to depolarization was examined in mechanically skinned fibres from the iliofibularis muscle of the toad and the extensor digitorum longus muscle of the rat. The response to depolarization in each skinned fibre was assessed either at the endogenous level of Ca2+ content or after depleting the fibre of Ca2+ to some degree. Ca2+ content was determined by a fibre lysing technique. 2. In both muscle types, the total Ca2+ content could be reduced from the endogenous level of approximately 1.3 mmol l-1 (expressed relative to intact fibre volume) to approximately 0.25 mmol l-1 by either depolarization or caffeine application in the presence of Ca2+ chelators, showing that the great majority of the Ca2+ was stored in the sarcoplasmic reticulum (SR). Chelation of Ca2+ in the transverse tubular (T-) system, either by exposure of fibres to EGTA before skinning or by permeabilizing the T-system with saponin after skinning, reduced the lower limit of Ca2+ content to < or = 0.12 mmol l-1, indicating that 10-20% of the total fibre Ca2+ resided in the T-system. 3. In toad fibres, both the peak and the area (i.e. time integral) of the force response to depolarization were reduced by any reduction in SR Ca2+ content, with both decreasing to zero in an approximately linear manner as the SR Ca2+ content was reduced to < 15% of the endogenous level. In rat fibres, the peak size of the force response was less affected by small decreases in SR content, but both the peak and area of the response decreased to zero with greater depletion. In partially depleted toad fibres, inhibition of SR Ca2+ uptake potentiated the force response to depolarization almost 2-fold. 4. The results show that in this skinned fibre preparation: (a) T-system depolarization and caffeine application can each virtually fully deplete the SR of Ca2+, irrespective of any putative inhibitory effect of SR depletion on channel activation; (b) all of the endogenous level of SR Ca2+ must be released in order to produce a maximal response to depolarization; and (c) a substantial part (approximately 40%) of the Ca2+ released by a depolarization is normally taken back into the SR before it can contribute to force production.

  1. Relationship between depolarization-induced force responses and Ca2+ content in skeletal muscle fibres of rat and toad.

    PubMed Central

    Owen, V J; Lamb, G D; Stephenson, D G; Fryer, M W

    1997-01-01

    1. The relationship between the total Ca2+ content of a muscle fibre and the magnitude of the force response to depolarization was examined in mechanically skinned fibres from the iliofibularis muscle of the toad and the extensor digitorum longus muscle of the rat. The response to depolarization in each skinned fibre was assessed either at the endogenous level of Ca2+ content or after depleting the fibre of Ca2+ to some degree. Ca2+ content was determined by a fibre lysing technique. 2. In both muscle types, the total Ca2+ content could be reduced from the endogenous level of approximately 1.3 mmol l-1 (expressed relative to intact fibre volume) to approximately 0.25 mmol l-1 by either depolarization or caffeine application in the presence of Ca2+ chelators, showing that the great majority of the Ca2+ was stored in the sarcoplasmic reticulum (SR). Chelation of Ca2+ in the transverse tubular (T-) system, either by exposure of fibres to EGTA before skinning or by permeabilizing the T-system with saponin after skinning, reduced the lower limit of Ca2+ content to < or = 0.12 mmol l-1, indicating that 10-20% of the total fibre Ca2+ resided in the T-system. 3. In toad fibres, both the peak and the area (i.e. time integral) of the force response to depolarization were reduced by any reduction in SR Ca2+ content, with both decreasing to zero in an approximately linear manner as the SR Ca2+ content was reduced to < 15% of the endogenous level. In rat fibres, the peak size of the force response was less affected by small decreases in SR content, but both the peak and area of the response decreased to zero with greater depletion. In partially depleted toad fibres, inhibition of SR Ca2+ uptake potentiated the force response to depolarization almost 2-fold. 4. The results show that in this skinned fibre preparation: (a) T-system depolarization and caffeine application can each virtually fully deplete the SR of Ca2+, irrespective of any putative inhibitory effect of SR depletion on channel activation; (b) all of the endogenous level of SR Ca2+ must be released in order to produce a maximal response to depolarization; and (c) a substantial part (approximately 40%) of the Ca2+ released by a depolarization is normally taken back into the SR before it can contribute to force production. PMID:9051571

  2. ANNIT - An Efficient Inversion Algorithm based on Prediction Principles

    NASA Astrophysics Data System (ADS)

    Růžek, B.; Kolář, P.

    2009-04-01

    Solution of inverse problems represents meaningful job in geophysics. The amount of data is continuously increasing, methods of modeling are being improved and the computer facilities are also advancing great technical progress. Therefore the development of new and efficient algorithms and computer codes for both forward and inverse modeling is still up to date. ANNIT is contributing to this stream since it is a tool for efficient solution of a set of non-linear equations. Typical geophysical problems are based on parametric approach. The system is characterized by a vector of parameters p, the response of the system is characterized by a vector of data d. The forward problem is usually represented by unique mapping F(p)=d. The inverse problem is much more complex and the inverse mapping p=G(d) is available in an analytical or closed form only exceptionally and generally it may not exist at all. Technically, both forward and inverse mapping F and G are sets of non-linear equations. ANNIT solves such situation as follows: (i) joint subspaces {pD, pM} of original data and model spaces D, M, resp. are searched for, within which the forward mapping F is sufficiently smooth that the inverse mapping G does exist, (ii) numerical approximation of G in subspaces {pD, pM} is found, (iii) candidate solution is predicted by using this numerical approximation. ANNIT is working in an iterative way in cycles. The subspaces {pD, pM} are searched for by generating suitable populations of individuals (models) covering data and model spaces. The approximation of the inverse mapping is made by using three methods: (a) linear regression, (b) Radial Basis Function Network technique, (c) linear prediction (also known as "Kriging"). The ANNIT algorithm has built in also an archive of already evaluated models. Archive models are re-used in a suitable way and thus the number of forward evaluations is minimized. ANNIT is now implemented both in MATLAB and SCILAB. Numerical tests show good performance of the algorithm. Both versions and documentation are available on Internet and anybody can download them. The goal of this presentation is to offer the algorithm and computer codes for anybody interested in the solution to inverse problems.

  3. Land Surface Reflectance Retrieval from Hyperspectral Data Collected by an Unmanned Aerial Vehicle over the Baotou Test Site

    PubMed Central

    Duan, Si-Bo; Li, Zhao-Liang; Tang, Bo-Hui; Wu, Hua; Ma, Lingling; Zhao, Enyu; Li, Chuanrong

    2013-01-01

    To evaluate the in-flight performance of a new hyperspectral sensor onboard an unmanned aerial vehicle (UAV-HYPER), a comprehensive field campaign was conducted over the Baotou test site in China on 3 September 2011. Several portable reference reflectance targets were deployed across the test site. The radiometric performance of the UAV-HYPER sensor was assessed in terms of signal-to-noise ratio (SNR) and the calibration accuracy. The SNR of the different bands of the UAV-HYPER sensor was estimated to be between approximately 5 and 120 over the homogeneous targets, and the linear response of the apparent reflectance ranged from approximately 0.05 to 0.45. The uniform and non-uniform Lambertian land surface reflectance was retrieved and validated using in situ measurements, with root mean square error (RMSE) of approximately 0.01–0.07 and relative RMSE of approximately 5%–12%. There were small discrepancies between the retrieved uniform and non-uniform Lambertian land surface reflectance over the homogeneous targets and under low aerosol optical depth (AOD) conditions (AOD = 0.18). However, these discrepancies must be taken into account when adjacent pixels had large land surface reflectance contrast and under high AOD conditions (e.g. AOD = 1.0). PMID:23785513

  4. Effects of the approximations of light propagation on quantitative photoacoustic tomography using two-dimensional photon diffusion equation and linearization

    NASA Astrophysics Data System (ADS)

    Okawa, Shinpei; Hirasawa, Takeshi; Kushibiki, Toshihiro; Ishihara, Miya

    2017-12-01

    Quantitative photoacoustic tomography (QPAT) employing a light propagation model will play an important role in medical diagnoses by quantifying the concentration of hemoglobin or a contrast agent. However, QPAT by the light propagation model with the three-dimensional (3D) radiative transfer equation (RTE) requires a huge computational load in the iterative forward calculations involved in the updating process to reconstruct the absorption coefficient. The approximations of the light propagation improve the efficiency of the image reconstruction for the QPAT. In this study, we compared the 3D/two-dimensional (2D) photon diffusion equation (PDE) approximating 3D RTE with the Monte Carlo simulation based on 3D RTE. Then, the errors in a 2D PDE-based linearized image reconstruction caused by the approximations were quantitatively demonstrated and discussed in the numerical simulations. It was clearly observed that the approximations affected the reconstructed absorption coefficient. The 2D PDE-based linearized algorithm succeeded in the image reconstruction of the region with a large absorption coefficient in the 3D phantom. The value reconstructed in the phantom experiment agreed with that in the numerical simulation, so that it was validated that the numerical simulation of the image reconstruction predicted the relationship between the true absorption coefficient of the target in the 3D medium and the reconstructed value with the 2D PDE-based linearized algorithm. Moreover, the the true absorption coefficient in 3D medium was estimated from the 2D reconstructed image on the basis of the prediction by the numerical simulation. The estimation was successful in the phantom experiment, although some limitations were revealed.

  5. Pleiotropy Analysis of Quantitative Traits at Gene Level by Multivariate Functional Linear Models

    PubMed Central

    Wang, Yifan; Liu, Aiyi; Mills, James L.; Boehnke, Michael; Wilson, Alexander F.; Bailey-Wilson, Joan E.; Xiong, Momiao; Wu, Colin O.; Fan, Ruzong

    2015-01-01

    In genetics, pleiotropy describes the genetic effect of a single gene on multiple phenotypic traits. A common approach is to analyze the phenotypic traits separately using univariate analyses and combine the test results through multiple comparisons. This approach may lead to low power. Multivariate functional linear models are developed to connect genetic variant data to multiple quantitative traits adjusting for covariates for a unified analysis. Three types of approximate F-distribution tests based on Pillai–Bartlett trace, Hotelling–Lawley trace, and Wilks’s Lambda are introduced to test for association between multiple quantitative traits and multiple genetic variants in one genetic region. The approximate F-distribution tests provide much more significant results than those of F-tests of univariate analysis and optimal sequence kernel association test (SKAT-O). Extensive simulations were performed to evaluate the false positive rates and power performance of the proposed models and tests. We show that the approximate F-distribution tests control the type I error rates very well. Overall, simultaneous analysis of multiple traits can increase power performance compared to an individual test of each trait. The proposed methods were applied to analyze (1) four lipid traits in eight European cohorts, and (2) three biochemical traits in the Trinity Students Study. The approximate F-distribution tests provide much more significant results than those of F-tests of univariate analysis and SKAT-O for the three biochemical traits. The approximate F-distribution tests of the proposed functional linear models are more sensitive than those of the traditional multivariate linear models that in turn are more sensitive than SKAT-O in the univariate case. The analysis of the four lipid traits and the three biochemical traits detects more association than SKAT-O in the univariate case. PMID:25809955

  6. Pleiotropy analysis of quantitative traits at gene level by multivariate functional linear models.

    PubMed

    Wang, Yifan; Liu, Aiyi; Mills, James L; Boehnke, Michael; Wilson, Alexander F; Bailey-Wilson, Joan E; Xiong, Momiao; Wu, Colin O; Fan, Ruzong

    2015-05-01

    In genetics, pleiotropy describes the genetic effect of a single gene on multiple phenotypic traits. A common approach is to analyze the phenotypic traits separately using univariate analyses and combine the test results through multiple comparisons. This approach may lead to low power. Multivariate functional linear models are developed to connect genetic variant data to multiple quantitative traits adjusting for covariates for a unified analysis. Three types of approximate F-distribution tests based on Pillai-Bartlett trace, Hotelling-Lawley trace, and Wilks's Lambda are introduced to test for association between multiple quantitative traits and multiple genetic variants in one genetic region. The approximate F-distribution tests provide much more significant results than those of F-tests of univariate analysis and optimal sequence kernel association test (SKAT-O). Extensive simulations were performed to evaluate the false positive rates and power performance of the proposed models and tests. We show that the approximate F-distribution tests control the type I error rates very well. Overall, simultaneous analysis of multiple traits can increase power performance compared to an individual test of each trait. The proposed methods were applied to analyze (1) four lipid traits in eight European cohorts, and (2) three biochemical traits in the Trinity Students Study. The approximate F-distribution tests provide much more significant results than those of F-tests of univariate analysis and SKAT-O for the three biochemical traits. The approximate F-distribution tests of the proposed functional linear models are more sensitive than those of the traditional multivariate linear models that in turn are more sensitive than SKAT-O in the univariate case. The analysis of the four lipid traits and the three biochemical traits detects more association than SKAT-O in the univariate case. © 2015 WILEY PERIODICALS, INC.

  7. Laminar and orientation-dependent characteristics of spatial nonlinearities: implications for the computational architecture of visual cortex.

    PubMed

    Victor, Jonathan D; Mechler, Ferenc; Ohiorhenuan, Ifije; Schmid, Anita M; Purpura, Keith P

    2009-12-01

    A full understanding of the computations performed in primary visual cortex is an important yet elusive goal. Receptive field models consisting of cascades of linear filters and static nonlinearities may be adequate to account for responses to simple stimuli such as gratings and random checkerboards, but their predictions of responses to complex stimuli such as natural scenes are only approximately correct. It is unclear whether these discrepancies are limited to quantitative inaccuracies that reflect well-recognized mechanisms such as response normalization, gain controls, and cross-orientation suppression or, alternatively, imply additional qualitative features of the underlying computations. To address this question, we examined responses of V1 and V2 neurons in the monkey and area 17 neurons in the cat to two-dimensional Hermite functions (TDHs). TDHs are intermediate in complexity between traditional analytic stimuli and natural scenes and have mathematical properties that facilitate their use to test candidate models. By exploiting these properties, along with the laminar organization of V1, we identify qualitative aspects of neural computations beyond those anticipated from the above-cited model framework. Specifically, we find that V1 neurons receive signals from orientation-selective mechanisms that are highly nonlinear: they are sensitive to phase correlations, not just spatial frequency content. That is, the behavior of V1 neurons departs from that of linear-nonlinear cascades with standard modulatory mechanisms in a qualitative manner: even relatively simple stimuli evoke responses that imply complex spatial nonlinearities. The presence of these findings in the input layers suggests that these nonlinearities act in a feedback fashion.

  8. DQM: Decentralized Quadratically Approximated Alternating Direction Method of Multipliers

    NASA Astrophysics Data System (ADS)

    Mokhtari, Aryan; Shi, Wei; Ling, Qing; Ribeiro, Alejandro

    2016-10-01

    This paper considers decentralized consensus optimization problems where nodes of a network have access to different summands of a global objective function. Nodes cooperate to minimize the global objective by exchanging information with neighbors only. A decentralized version of the alternating directions method of multipliers (DADMM) is a common method for solving this category of problems. DADMM exhibits linear convergence rate to the optimal objective but its implementation requires solving a convex optimization problem at each iteration. This can be computationally costly and may result in large overall convergence times. The decentralized quadratically approximated ADMM algorithm (DQM), which minimizes a quadratic approximation of the objective function that DADMM minimizes at each iteration, is proposed here. The consequent reduction in computational time is shown to have minimal effect on convergence properties. Convergence still proceeds at a linear rate with a guaranteed constant that is asymptotically equivalent to the DADMM linear convergence rate constant. Numerical results demonstrate advantages of DQM relative to DADMM and other alternatives in a logistic regression problem.

  9. The large discretization step method for time-dependent partial differential equations

    NASA Technical Reports Server (NTRS)

    Haras, Zigo; Taasan, Shlomo

    1995-01-01

    A new method for the acceleration of linear and nonlinear time dependent calculations is presented. It is based on the Large Discretization Step (LDS) approximation, defined in this work, which employs an extended system of low accuracy schemes to approximate a high accuracy discrete approximation to a time dependent differential operator. Error bounds on such approximations are derived. These approximations are efficiently implemented in the LDS methods for linear and nonlinear hyperbolic equations, presented here. In these algorithms the high and low accuracy schemes are interpreted as the same discretization of a time dependent operator on fine and coarse grids, respectively. Thus, a system of correction terms and corresponding equations are derived and solved on the coarse grid to yield the fine grid accuracy. These terms are initialized by visiting the fine grid once in many coarse grid time steps. The resulting methods are very general, simple to implement and may be used to accelerate many existing time marching schemes.

  10. Correlation, evaluation, and extension of linearized theories for tire motion and wheel shimmy

    NASA Technical Reports Server (NTRS)

    Smiley, Robert F

    1957-01-01

    An evaluation is made of the existing theories of a linearized tire motion and wheel shimmy. It is demonstrated that most of the previously published theories represent varying degrees of approximation to a summary theory developed in this report which is a minor modification of the basic theory of Von Schlippe and Dietrich. In most cases where strong differences exist between the previously published theories and summary theory, the previously published theories are shown to possess certain deficiencies. A series of systematic approximations to the summary theory is developed for the treatment of problems too simple to merit the use of the complete summary theory, and procedures are discussed for applying the summary theory and its systematic approximations to the shimmy of more complex landing-gear structures than have previously been considered. Comparisons of the existing experimental data with the predictions of the summary theory and the systematic approximations provide a fair substantiation of the more detailed approximate theories.

  11. Nonlinear programming extensions to rational function approximation methods for unsteady aerodynamic forces

    NASA Technical Reports Server (NTRS)

    Tiffany, Sherwood H.; Adams, William M., Jr.

    1988-01-01

    The approximation of unsteady generalized aerodynamic forces in the equations of motion of a flexible aircraft are discussed. Two methods of formulating these approximations are extended to include the same flexibility in constraining the approximations and the same methodology in optimizing nonlinear parameters as another currently used extended least-squares method. Optimal selection of nonlinear parameters is made in each of the three methods by use of the same nonlinear, nongradient optimizer. The objective of the nonlinear optimization is to obtain rational approximations to the unsteady aerodynamics whose state-space realization is lower order than that required when no optimization of the nonlinear terms is performed. The free linear parameters are determined using the least-squares matrix techniques of a Lagrange multiplier formulation of an objective function which incorporates selected linear equality constraints. State-space mathematical models resulting from different approaches are described and results are presented that show comparative evaluations from application of each of the extended methods to a numerical example.

  12. The frequency-dependent response of single aerosol particles to vapour phase oscillations and its application in measuring diffusion coefficients

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

    Preston, Thomas C.; Davies, James F.; Wilson, Kevin R.

    A new method for measuring diffusion in the condensed phase of single aerosol particles is proposed and demonstrated. The technique is based on the frequency-dependent response of a binary particle to oscillations in the vapour phase of one of its chemical components. Here, we discuss how this physical situation allows for what would typically be a non-linear boundary value problem to be approximately reduced to a linear boundary value problem. For the case of aqueous aerosol particles, we investigate the accuracy of the closed-form analytical solution to this linear problem through a comparison with the numerical solution of the fullmore » problem. Then, using experimentally measured whispering gallery modes to track the frequency-dependent response of aqueous particles to relative humidity oscillations, we determine diffusion coefficients as a function of water activity. The measured diffusion coefficients are compared to previously reported values found using the two common experiments: (i) the analysis of the sorption/desorption of water from a particle after a step-wise change to the surrounding relative humidity and (ii) the isotopic exchange of water between a particle and the vapour phase. The technique presented here has two main strengths: first, when compared to the sorption/desorption experiment, it does not require the numerical evaluation of a boundary value problem during the fitting process as a closed-form expression is available. Second, when compared to the isotope exchange experiment, it does not require the use of labeled molecules. Therefore, the frequency-dependent experiment retains the advantages of these two commonly used methods but does not suffer from their drawbacks.« less

  13. Inferring Nonlinear Neuronal Computation Based on Physiologically Plausible Inputs

    PubMed Central

    McFarland, James M.; Cui, Yuwei; Butts, Daniel A.

    2013-01-01

    The computation represented by a sensory neuron's response to stimuli is constructed from an array of physiological processes both belonging to that neuron and inherited from its inputs. Although many of these physiological processes are known to be nonlinear, linear approximations are commonly used to describe the stimulus selectivity of sensory neurons (i.e., linear receptive fields). Here we present an approach for modeling sensory processing, termed the Nonlinear Input Model (NIM), which is based on the hypothesis that the dominant nonlinearities imposed by physiological mechanisms arise from rectification of a neuron's inputs. Incorporating such ‘upstream nonlinearities’ within the standard linear-nonlinear (LN) cascade modeling structure implicitly allows for the identification of multiple stimulus features driving a neuron's response, which become directly interpretable as either excitatory or inhibitory. Because its form is analogous to an integrate-and-fire neuron receiving excitatory and inhibitory inputs, model fitting can be guided by prior knowledge about the inputs to a given neuron, and elements of the resulting model can often result in specific physiological predictions. Furthermore, by providing an explicit probabilistic model with a relatively simple nonlinear structure, its parameters can be efficiently optimized and appropriately regularized. Parameter estimation is robust and efficient even with large numbers of model components and in the context of high-dimensional stimuli with complex statistical structure (e.g. natural stimuli). We describe detailed methods for estimating the model parameters, and illustrate the advantages of the NIM using a range of example sensory neurons in the visual and auditory systems. We thus present a modeling framework that can capture a broad range of nonlinear response functions while providing physiologically interpretable descriptions of neural computation. PMID:23874185

  14. The frequency-dependent response of single aerosol particles to vapour phase oscillations and its application in measuring diffusion coefficients

    DOE PAGES

    Preston, Thomas C.; Davies, James F.; Wilson, Kevin R.

    2017-01-13

    A new method for measuring diffusion in the condensed phase of single aerosol particles is proposed and demonstrated. The technique is based on the frequency-dependent response of a binary particle to oscillations in the vapour phase of one of its chemical components. Here, we discuss how this physical situation allows for what would typically be a non-linear boundary value problem to be approximately reduced to a linear boundary value problem. For the case of aqueous aerosol particles, we investigate the accuracy of the closed-form analytical solution to this linear problem through a comparison with the numerical solution of the fullmore » problem. Then, using experimentally measured whispering gallery modes to track the frequency-dependent response of aqueous particles to relative humidity oscillations, we determine diffusion coefficients as a function of water activity. The measured diffusion coefficients are compared to previously reported values found using the two common experiments: (i) the analysis of the sorption/desorption of water from a particle after a step-wise change to the surrounding relative humidity and (ii) the isotopic exchange of water between a particle and the vapour phase. The technique presented here has two main strengths: first, when compared to the sorption/desorption experiment, it does not require the numerical evaluation of a boundary value problem during the fitting process as a closed-form expression is available. Second, when compared to the isotope exchange experiment, it does not require the use of labeled molecules. Therefore, the frequency-dependent experiment retains the advantages of these two commonly used methods but does not suffer from their drawbacks.« less

  15. Involvement of Linear Plasmids in Aerobic Biodegradation of Vinyl Chloride

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

    BRIGMON, ROBINL.

    2004-06-14

    Pseudomonas putida strain AJ and Ochrobactrum strain TD were isolated from hazardous waste sites based on their ability to use vinyl chloride (VC) as a sole source of carbon and energy under aerobic conditions. Strains AJ and TD also use ethene and ethylene oxide as growth substrates. Strain AJ contained a linear megaplasmid (approximately 260 kb) when grown on VC or ethene, but no circular plasmids. While growing on ethylene oxide, the size of the linear plasmid in strain AJ decreased to approximately 100 kb, although its ability to use VC as a substrate was retained. The linear plasmids inmore » strain AJ were cured and its ability to consume VC, ethene, and ethylene oxide was lost following growth on a rich substrate (Luria-Bertani broth) through at least three transfers. Strain TD contained three linear plasmids, ranging in size from approximately 100 kb to 320 kb, when growing on VC or ethene. As with strain AJ, the linear plasmids in strain TD were cured following growth on Luria -Bertani broth and its ability to consume VC and ethene was lost. Further analysis of these linear plasmids may help reveal the pathway for VC biodegradation in strains AJ and TD and explain why this process occurs at many but not all sites where groundwater is contaminated with chloroethenes. Metabolism of VC and ethene by strains AJ and TD is initiated by an alkene monooxygenase. Their yields during growth on VC (0.15-0.20 mg total suspended solids per mg VC) are similar to the yields reported for other isolates i.e., Mycobacterium sp., Nocardioides sp., and Pseudomonas sp.« less

  16. Non-Condon nonequilibrium Fermi’s golden rule rates from the linearized semiclassical method

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

    Sun, Xiang; Geva, Eitan

    2016-08-14

    The nonequilibrium Fermi’s golden rule describes the transition between a photoexcited bright donor electronic state and a dark acceptor electronic state, when the nuclear degrees of freedom start out in a nonequilibrium state. In a previous paper [X. Sun and E. Geva, J. Chem. Theory Comput. 12, 2926 (2016)], we proposed a new expression for the nonequilibrium Fermi’s golden rule within the framework of the linearized semiclassical approximation and based on the Condon approximation, according to which the electronic coupling between donor and acceptor is assumed constant. In this paper we propose a more general expression, which is applicable tomore » the case of non-Condon electronic coupling. We test the accuracy of the new non-Condon nonequilibrium Fermi’s golden rule linearized semiclassical expression on a model where the donor and acceptor potential energy surfaces are parabolic and identical except for shifts in the equilibrium energy and geometry, and the coupling between them is linear in the nuclear coordinates. Since non-Condon effects may or may not give rise to conical intersections, both possibilities are examined by considering the following: (1) A modified Garg-Onuchic-Ambegaokar model for charge transfer in the condensed phase, where the donor-acceptor coupling is linear in the primary-mode coordinate, and for which non-Condon effects do not give rise to a conical intersection; (2) the linear vibronic coupling model for electronic transitions in gas phase molecules, where non-Condon effects give rise to conical intersections. We also present a comprehensive comparison between the linearized semiclassical expression and a progression of more approximate expressions, in both normal and inverted regions, and over a wide range of initial nonequilibrium states, temperatures, and frictions.« less

  17. Effect of Elastin Digestion on the Quasi-static Tensile Response of Medial Collateral Ligament

    PubMed Central

    Henninger, Heath B.; Underwood, Clayton J.; Romney, Steven J.; Davis, Grant L.; Weiss, Jeffrey A.

    2014-01-01

    Elastin is a structural protein that provides resilience to biological tissues. We examined the contributions of elastin to the quasi-static tensile response of porcine medial collateral ligament through targeted disruption of the elastin network with pancreatic elastase. Elastase concentration and treatment time were varied to determine a dose response. Whereas elastin content decreased with increasing elastase concentration and treatment time, the change in peak stress after cyclic loading reached a plateau above 1 U/ml elastase and 6 hr treatment. For specimens treated with 2 U/ml elastase for 6 hr, elastin content decreased approximately 35%. Mean peak tissue strain after cyclic loading (4.8%, p≥0.300), modulus (275 MPa, p≥0.114) and hysteresis (20%, p≥0.553) were unaffected by elastase digestion, but stress decreased significantly after treatment (up to 2 MPa, p≤0.049). Elastin degradation had no effect on failure properties, but tissue lengthened under the same pre-stress. Stiffness in the linear region was unaffected by elastase digestion, suggesting that enzyme treatment did not disrupt collagen. These results demonstrate that elastin primarily functions in the toe region of the stress-strain curve, yet contributes load support in the linear region. The increase in length after elastase digestion suggests that elastin may pre-stress and stabilize collagen crimp in ligaments. PMID:23553827

  18. Highly Sensitive and Wide-Dynamic-Range Multichannel Optical-Fiber pH Sensor Based on PWM Technique.

    PubMed

    Khan, Md Rajibur Rahaman; Kang, Shin-Won

    2016-11-09

    In this study, we propose a highly sensitive multichannel pH sensor that is based on an optical-fiber pulse width modulation (PWM) technique. According to the optical-fiber PWM method, the received sensing signal's pulse width changes when the optical-fiber pH sensing-element of the array comes into contact with pH buffer solutions. The proposed optical-fiber PWM pH-sensing system offers a linear sensing response over a wide range of pH values from 2 to 12, with a high pH-sensing ability. The sensitivity of the proposed pH sensor is 0.46 µs/pH, and the correlation coefficient R² is approximately 0.997. Additional advantages of the proposed optical-fiber PWM pH sensor include a short/fast response-time of about 8 s, good reproducibility properties with a relative standard deviation (RSD) of about 0.019, easy fabrication, low cost, small size, reusability of the optical-fiber sensing-element, and the capability of remote sensing. Finally, the performance of the proposed PWM pH sensor was compared with that of potentiometric, optical-fiber modal interferometer, and optical-fiber Fabry-Perot interferometer pH sensors with respect to dynamic range width, linearity as well as response and recovery times. We observed that the proposed sensing systems have better sensing abilities than the above-mentioned pH sensors.

  19. Highly Sensitive and Wide-Dynamic-Range Multichannel Optical-Fiber pH Sensor Based on PWM Technique

    PubMed Central

    Khan, Md. Rajibur Rahaman; Kang, Shin-Won

    2016-01-01

    In this study, we propose a highly sensitive multichannel pH sensor that is based on an optical-fiber pulse width modulation (PWM) technique. According to the optical-fiber PWM method, the received sensing signal’s pulse width changes when the optical-fiber pH sensing-element of the array comes into contact with pH buffer solutions. The proposed optical-fiber PWM pH-sensing system offers a linear sensing response over a wide range of pH values from 2 to 12, with a high pH-sensing ability. The sensitivity of the proposed pH sensor is 0.46 µs/pH, and the correlation coefficient R2 is approximately 0.997. Additional advantages of the proposed optical-fiber PWM pH sensor include a short/fast response-time of about 8 s, good reproducibility properties with a relative standard deviation (RSD) of about 0.019, easy fabrication, low cost, small size, reusability of the optical-fiber sensing-element, and the capability of remote sensing. Finally, the performance of the proposed PWM pH sensor was compared with that of potentiometric, optical-fiber modal interferometer, and optical-fiber Fabry–Perot interferometer pH sensors with respect to dynamic range width, linearity as well as response and recovery times. We observed that the proposed sensing systems have better sensing abilities than the above-mentioned pH sensors. PMID:27834865

  20. Population PK-PD analyses of CD25 occupancy, CD56bright NK cell expansion, and regulatory T cell reduction by daclizumab HYP in subjects with multiple sclerosis.

    PubMed

    Diao, Lei; Hang, Yaming; Othman, Ahmed A; Mehta, Devangi; Amaravadi, Lakshmi; Nestorov, Ivan; Tran, Jonathan Q

    2016-11-01

    Daclizumab high yield process (HYP) is a humanized IgG1 monoclonal antibody that binds to the α-subunit of the interleukin-2 receptor and is being developed for treatment of multiple sclerosis (MS). This manuscript characterized the pharmacokinetic-pharmacodynamic (PK-PD) relationships of daclizumab HYP in subjects with MS. Approximately 1400 subjects and 7000 PD measurements for each of three biomarkers [CD25 occupancy, CD56 bright natural killer (NK) cell count, regulatory T cell (Treg) count] from four clinical trials were analyzed using non-linear mixed effects modelling. Evaluated regimens included 150 or 300 mg subcutaneous (s.c.) every 4 weeks. CD25 occupancy was characterized using a sigmoidal maximum response (E max ) model. Upon daclizumab HYP treatment, CD25 saturation was rapid with complete saturation occurring after approximately 7 h and maintained when daclizumab HYP serum concentration was ≥5 mg l -1 . After the last 150 mg s.c. dose, unoccupied CD25 returned to baseline levels in approximately 24 weeks, with daclizumab HYP serum concentration approximately ≤1 mgl -1 1L. CD56 bright NK cell expansion was characterized using an indirect response model. Following daclizumab HYP 150 mg s.c. every 4 weeks, expansion plateaus approximately at week 36, at which the average maximum expansion ratio is 5.2. After the last dose, CD56 bright NK cells gradually declined to baseline levels within 24 weeks. Treg reduction was characterized by a sigmoidal E max model. Average maximum reduction of 60% occurred approximately 4 days post 150 mg s.c. dose. After the last dose, Tregs were projected to return to baseline levels in approximately 20 weeks. Robust PK-PD models of CD25 occupancy, CD56 bright NK cell expansion and Treg reduction by daclizumab HYP were developed to characterize its key pharmacodynamic effects in the target patient population. © 2016 The British Pharmacological Society.

  1. A Bioluminescent Whole-Cell Reporter for Detection of 2,4-Dichlorophenoxyacetic Acid and 2,4-Dichlorophenol in Soil

    PubMed Central

    Hay, Anthony G.; Rice, James F.; Applegate, Bruce M.; Bright, Nathan G.; Sayler, Gary S.

    2000-01-01

    A bioreporter was made containing a tfdRPDII-luxCDABE fusion in a modified mini-Tn5 construct. When it was introduced into the chromosome of Ralstonia eutropha JMP134, the resulting strain, JMP134-32, produced a sensitive bioluminescent response to 2,4-dichlorophenoxyacetic acid (2,4-D) at concentrations of 2.0 μM to 5.0 mM. This response was linear (R2 = 0.9825) in the range of 2.0 μM to 1.1 × 102 μM. Saturation occurred at higher concentrations, with maximal bioluminescence occurring in the presence of approximately 1.2 mM 2,4-D. A sensitive response was also recorded in the presence of 2,4-dichlorophenol at concentrations below 1.1 × 102 μM; however, only a limited bioluminescent response was recorded in the presence of 3-chlorobenzoic acid at concentrations below 1.0 mM. A significant bioluminescent response was also recorded when strain JMP134-32 was incubated with soils containing aged 2,4-D residues. PMID:11010925

  2. Red and Processed Meat and Colorectal Cancer Incidence: Meta-Analysis of Prospective Studies

    PubMed Central

    Chan, Doris S. M.; Lau, Rosa; Aune, Dagfinn; Vieira, Rui; Greenwood, Darren C.; Kampman, Ellen; Norat, Teresa

    2011-01-01

    Background The evidence that red and processed meat influences colorectal carcinogenesis was judged convincing in the 2007 World Cancer Research Fund/American Institute of Cancer Research report. Since then, ten prospective studies have published new results. Here we update the evidence from prospective studies and explore whether there is a non-linear association of red and processed meats with colorectal cancer risk. Methods and Findings Relevant prospective studies were identified in PubMed until March 2011. For each study, relative risks and 95% confidence intervals (CI) were extracted and pooled with a random-effects model, weighting for the inverse of the variance, in highest versus lowest intake comparison, and dose-response meta-analyses. Red and processed meats intake was associated with increased colorectal cancer risk. The summary relative risk (RR) of colorectal cancer for the highest versus the lowest intake was 1.22 (95% CI  = 1.11−1.34) and the RR for every 100 g/day increase was 1.14 (95% CI  = 1.04−1.24). Non-linear dose-response meta-analyses revealed that colorectal cancer risk increases approximately linearly with increasing intake of red and processed meats up to approximately 140 g/day, where the curve approaches its plateau. The associations were similar for colon and rectal cancer risk. When analyzed separately, colorectal cancer risk was related to intake of fresh red meat (RR for 100 g/day increase  = 1.17, 95% CI  = 1.05−1.31) and processed meat (RR for 50 g/day increase  = 1.18, 95% CI  = 1.10−1.28). Similar results were observed for colon cancer, but for rectal cancer, no significant associations were observed. Conclusions High intake of red and processed meat is associated with significant increased risk of colorectal, colon and rectal cancers. The overall evidence of prospective studies supports limiting red and processed meat consumption as one of the dietary recommendations for the prevention of colorectal cancer. PMID:21674008

  3. Nanoporous TiO2 and WO3 films by anodization of titanium and tungsten substrates: influence of process variables on morphology and photoelectrochemical response.

    PubMed

    de Tacconi, N R; Chenthamarakshan, C R; Yogeeswaran, G; Watcharenwong, A; de Zoysa, R S; Basit, N A; Rajeshwar, K

    2006-12-21

    The photoelectrochemical response of nanoporous films, obtained by anodization of Ti and W substrates in a variety of corrosive media and at preselected voltages in the range from 10 to 60 V, was studied. The as-deposited films were subjected to thermal anneal and characterized by scanning electron microscopy and X-ray diffraction. Along with the anodization media developed by previous authors, the effect of poly(ethylene glycol) (PEG 400) or D-mannitol as a modifier to the NH4F electrolyte and glycerol addition to the oxalic acid electrolyte was studied for TiO2 and WO3, respectively. In general, intermediate anodization voltages and film growth times yielded excellent-quality photoelectrochemical response for both TiO2 and WO3 as assessed by linear-sweep photovoltammetry and photoaction spectra. The photooxidation of water and formate species was used as reaction probes to assess the photoresponse quality of the nanoporous oxide semiconductor films. In the presence of formate as an electron donor, the incident photon to electron conversion efficiency (IPCE) ranged from approximately 130% to approximately 200% for both TiO2 and WO3 depending on the film preparation protocol. The best photoactive films were obtained from poly(ethylene glycol) (PEG 400) containing NH4F for TiO2 and from aqueous NaF for WO3.

  4. Development of wide-band middle ear transmission in the Mongolian gerbil

    NASA Astrophysics Data System (ADS)

    Overstreet, Edward H.; Ruggero, Mario A.

    2002-01-01

    Stapes vibrations were measured in deeply anesthetized adult and neonatal (ages: 14 to 20 days) Mongolian gerbils. In adult gerbils, the velocity magnitude of stapes responses to tones was approximately constant over the entire frequency range of measurements, 1 to 40 kHz. Response phases referred to pressure near the tympanic membrane varied approximately linearly as a function of increasing stimulus frequency, with a slope corresponding to a group delay of 30 μs. In neonatal gerbils, the sensitivity of stapes responses to tones was lower than in adults, especially at mid-frequencies (e.g., by about 15 dB at 10-20 kHz in gerbils aged 14 days). The input impedance of the adult gerbil cochlea, calculated from stapes vibrations and published measurements of pressure in scala vestibuli near the oval window [E. Olson, J. Acoust. Soc. Am. 103, 3445-3463 (1998)], is principally dissipative at frequencies lower than 10 kHz. Conclusions: (a) middle-ear vibrations in adult gerbils do not limit the input to the cochlea up to at least 40 kHz, i.e., within 0.5 oct of the high-frequency cutoff of the behavioral audiogram; and (b) the results in both adult and neonatal gerbils are inconsistent with the hypothesis that mass reactance controls high-frequency ossicular vibrations and support the idea that the middle ear functions as a transmission line.

  5. The convergence rate of approximate solutions for nonlinear scalar conservation laws

    NASA Technical Reports Server (NTRS)

    Nessyahu, Haim; Tadmor, Eitan

    1991-01-01

    The convergence rate is discussed of approximate solutions for the nonlinear scalar conservation law. The linear convergence theory is extended into a weak regime. The extension is based on the usual two ingredients of stability and consistency. On the one hand, the counterexamples show that one must strengthen the linearized L(sup 2)-stability requirement. It is assumed that the approximate solutions are Lip(sup +)-stable in the sense that they satisfy a one-sided Lipschitz condition, in agreement with Oleinik's E-condition for the entropy solution. On the other hand, the lack of smoothness requires to weaken the consistency requirement, which is measured in the Lip'-(semi)norm. It is proved for Lip(sup +)-stable approximate solutions, that their Lip'convergence rate to the entropy solution is of the same order as their Lip'-consistency. The Lip'-convergence rate is then converted into stronger L(sup p) convergence rate estimates.

  6. Harmonic-phase path-integral approximation of thermal quantum correlation functions

    NASA Astrophysics Data System (ADS)

    Robertson, Christopher; Habershon, Scott

    2018-03-01

    We present an approximation to the thermal symmetric form of the quantum time-correlation function in the standard position path-integral representation. By transforming to a sum-and-difference position representation and then Taylor-expanding the potential energy surface of the system to second order, the resulting expression provides a harmonic weighting function that approximately recovers the contribution of the phase to the time-correlation function. This method is readily implemented in a Monte Carlo sampling scheme and provides exact results for harmonic potentials (for both linear and non-linear operators) and near-quantitative results for anharmonic systems for low temperatures and times that are likely to be relevant to condensed phase experiments. This article focuses on one-dimensional examples to provide insights into convergence and sampling properties, and we also discuss how this approximation method may be extended to many-dimensional systems.

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

    NASA Technical Reports Server (NTRS)

    Banks, H. T.; Kunisch, K.

    1982-01-01

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

  8. A problem in non-linear Diophantine approximation

    NASA Astrophysics Data System (ADS)

    Harrap, Stephen; Hussain, Mumtaz; Kristensen, Simon

    2018-05-01

    In this paper we obtain the Lebesgue and Hausdorff measure results for the set of vectors satisfying infinitely many fully non-linear Diophantine inequalities. The set is associated with a class of linear inhomogeneous partial differential equations whose solubility depends on a certain Diophantine condition. The failure of the Diophantine condition guarantees the existence of a smooth solution.

  9. Blending Velocities In Task Space In Computing Robot Motions

    NASA Technical Reports Server (NTRS)

    Volpe, Richard A.

    1995-01-01

    Blending of linear and angular velocities between sequential specified points in task space constitutes theoretical basis of improved method of computing trajectories followed by robotic manipulators. In method, generalized velocity-vector-blending technique provides relatively simple, common conceptual framework for blending linear, angular, and other parametric velocities. Velocity vectors originate from straight-line segments connecting specified task-space points, called "via frames" and represent specified robot poses. Linear-velocity-blending functions chosen from among first-order, third-order-polynomial, and cycloidal options. Angular velocities blended by use of first-order approximation of previous orientation-matrix-blending formulation. Angular-velocity approximation yields small residual error, quantified and corrected. Method offers both relative simplicity and speed needed for generation of robot-manipulator trajectories in real time.

  10. Krylov subspace methods - Theory, algorithms, and applications

    NASA Technical Reports Server (NTRS)

    Sad, Youcef

    1990-01-01

    Projection methods based on Krylov subspaces for solving various types of scientific problems are reviewed. The main idea of this class of methods when applied to a linear system Ax = b, is to generate in some manner an approximate solution to the original problem from the so-called Krylov subspace span. Thus, the original problem of size N is approximated by one of dimension m, typically much smaller than N. Krylov subspace methods have been very successful in solving linear systems and eigenvalue problems and are now becoming popular for solving nonlinear equations. The main ideas in Krylov subspace methods are shown and their use in solving linear systems, eigenvalue problems, parabolic partial differential equations, Liapunov matrix equations, and nonlinear system of equations are discussed.

  11. Effects of source shape on the numerical aperture factor with a geometrical-optics model.

    PubMed

    Wan, Der-Shen; Schmit, Joanna; Novak, Erik

    2004-04-01

    We study the effects of an extended light source on the calibration of an interference microscope, also referred to as an optical profiler. Theoretical and experimental numerical aperture (NA) factors for circular and linear light sources along with collimated laser illumination demonstrate that the shape of the light source or effective aperture cone is critical for a correct NA factor calculation. In practice, more-accurate results for the NA factor are obtained when a linear approximation to the filament light source shape is used in a geometric model. We show that previously measured and derived NA factors show some discrepancies because a circular rather than linear approximation to the filament source was used in the modeling.

  12. Single-qubit decoherence under a separable coupling to a random matrix environment

    NASA Astrophysics Data System (ADS)

    Carrera, M.; Gorin, T.; Seligman, T. H.

    2014-08-01

    This paper describes the dynamics of a quantum two-level system (qubit) under the influence of an environment modeled by an ensemble of random matrices. In distinction to earlier work, we consider here separable couplings and focus on a regime where the decoherence time is of the same order of magnitude as the environmental Heisenberg time. We derive an analytical expression in the linear response approximation, and study its accuracy by comparison with numerical simulations. We discuss a series of unusual properties, such as purity oscillations, strong signatures of spectral correlations (in the environment Hamiltonian), memory effects, and symmetry-breaking equilibrium states.

  13. ISAC: A tool for aeroservoelastic modeling and analysis

    NASA Technical Reports Server (NTRS)

    Adams, William M., Jr.; Hoadley, Sherwood Tiffany

    1993-01-01

    The capabilities of the Interaction of Structures, Aerodynamics, and Controls (ISAC) system of program modules is discussed. The major modeling, analysis, and data management components of ISAC are identified. Equations of motion are displayed for a Laplace-domain representation of the unsteady aerodynamic forces. Options for approximating a frequency-domain representation of unsteady aerodynamic forces with rational functions of the Laplace variable are shown. Linear time invariant state-space equations of motion that result are discussed. Model generation and analyses of stability and dynamic response characteristics are shown for an aeroelastic vehicle which illustrates some of the capabilities of ISAC as a modeling and analysis tool for aeroelastic applications.

  14. Photoionization cross section by Stieltjes imaging applied to coupled cluster Lanczos pseudo-spectra

    NASA Astrophysics Data System (ADS)

    Cukras, Janusz; Coriani, Sonia; Decleva, Piero; Christiansen, Ove; Norman, Patrick

    2013-09-01

    A recently implemented asymmetric Lanczos algorithm for computing (complex) linear response functions within the coupled cluster singles (CCS), coupled cluster singles and iterative approximate doubles (CC2), and coupled cluster singles and doubles (CCSD) is coupled to a Stieltjes imaging technique in order to describe the photoionization cross section of atoms and molecules, in the spirit of a similar procedure recently proposed by Averbukh and co-workers within the Algebraic Diagrammatic Construction approach. Pilot results are reported for the atoms He, Ne, and Ar and for the molecules H2, H2O, NH3, HF, CO, and CO2.

  15. Photoionization cross section by Stieltjes imaging applied to coupled cluster Lanczos pseudo-spectra.

    PubMed

    Cukras, Janusz; Coriani, Sonia; Decleva, Piero; Christiansen, Ove; Norman, Patrick

    2013-09-07

    A recently implemented asymmetric Lanczos algorithm for computing (complex) linear response functions within the coupled cluster singles (CCS), coupled cluster singles and iterative approximate doubles (CC2), and coupled cluster singles and doubles (CCSD) is coupled to a Stieltjes imaging technique in order to describe the photoionization cross section of atoms and molecules, in the spirit of a similar procedure recently proposed by Averbukh and co-workers within the Algebraic Diagrammatic Construction approach. Pilot results are reported for the atoms He, Ne, and Ar and for the molecules H2, H2O, NH3, HF, CO, and CO2.

  16. Solution of non-steady-state substrate concentration in the action of biosensor response at mixed enzyme kinetics

    NASA Astrophysics Data System (ADS)

    Senthamarai, R.; Jana Ranjani, R.

    2018-04-01

    In this paper, a mathematical model of an amperometric biosensor at mixed enzyme kinetics and diffusion limitation in the case of substrate inhibition has been developed. The model is based on time dependent reaction diffusion equation containing a non -linear term related to non -Michaelis - Menten kinetics of the enzymatic reaction. Solution for the concentration of the substrate has been derived for all values of parameters using the homotopy perturbation method. All the approximate analytic expressions of substrate concentration are compared with simulation results using Scilab/Matlab program. Finally, we have given a satisfactory agreement between them.

  17. Nonlinear vibrations of thin arbitrarily laminated composite plates subjected to harmonic excitations using DKT elements

    NASA Astrophysics Data System (ADS)

    Chiang, C. K.; Xue, David Y.; Mei, Chuh

    1993-04-01

    A finite element formulation is presented for determining the large-amplitude free and steady-state forced vibration response of arbitrarily laminated anisotropic composite thin plates using the Discrete Kirchhoff Theory (DKT) triangular elements. The nonlinear stiffness and harmonic force matrices of an arbitrarily laminated composite triangular plate element are developed for nonlinear free and forced vibration analyses. The linearized updated-mode method with nonlinear time function approximation is employed for the solution of the system nonlinear eigenvalue equations. The amplitude-frequency relations for convergence with gridwork refinement, triangular plates, different boundary conditions, lamination angles, number of plies, and uniform versus concentrated loads are presented.

  18. Nonlinear vibrations of thin arbitrarily laminated composite plates subjected to harmonic excitations using DKT elements

    NASA Technical Reports Server (NTRS)

    Chiang, C. K.; Xue, David Y.; Mei, Chuh

    1993-01-01

    A finite element formulation is presented for determining the large-amplitude free and steady-state forced vibration response of arbitrarily laminated anisotropic composite thin plates using the Discrete Kirchhoff Theory (DKT) triangular elements. The nonlinear stiffness and harmonic force matrices of an arbitrarily laminated composite triangular plate element are developed for nonlinear free and forced vibration analyses. The linearized updated-mode method with nonlinear time function approximation is employed for the solution of the system nonlinear eigenvalue equations. The amplitude-frequency relations for convergence with gridwork refinement, triangular plates, different boundary conditions, lamination angles, number of plies, and uniform versus concentrated loads are presented.

  19. Linear analysis of time dependent properties of Child-Langmuir flow

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

    Rokhlenko, A.

    We continue our analysis of the time dependent behavior of the electron flow in the Child-Langmuir system, removing an approximation used earlier. We find a modified set of oscillatory decaying modes with frequencies of the same order as the inverse of the electron transient time. This range (typically MHz) allows simple experimental detection and maybe exploitation. We then study the time evolution of the current in response to a slow change of the anode voltage where the same modes of oscillations appear too. The cathode current in this case is systematically advanced or retarded depending on the direction of themore » voltage change.« less

  20. Coupled electrostatic and material surface stresses yield anomalous particle interactions and deformation

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

    Kemp, B. A., E-mail: bkemp@astate.edu; Nikolayev, I.; Sheppard, C. J.

    2016-04-14

    Like-charges repel, and opposite charges attract. This fundamental tenet is a result of Coulomb's law. However, the electrostatic interactions between dielectric particles remain topical due to observations of like-charged particle attraction and the self-assembly of colloidal systems. Here, we show, using both an approximate description and an exact solution of Maxwell's equations, that nonlinear charged particle forces result even for linear material systems and can be responsible for anomalous electrostatic interactions such as like-charged particle attraction and oppositely charged particle repulsion. Furthermore, these electrostatic interactions and the deformation of such particles have fundamental implications for our understanding of macroscopic electrodynamics.

  1. Readout models for BaFBr0.85I0.15:Eu image plates

    NASA Astrophysics Data System (ADS)

    Stoeckl, M.; Solodov, A. A.

    2018-06-01

    The linearity of the photostimulated luminescence process makes repeated image-plate scanning a viable technique to extract a more dynamic range. In order to obtain a response estimate, two semi-empirical models for the readout fading of an image plate are introduced; they relate the depth distribution of activated photostimulated luminescence centers within an image plate to the recorded signal. Model parameters are estimated from image-plate scan series with BAS-MS image plates and the Typhoon FLA 7000 scanner for the hard x-ray image-plate diagnostic over a collection of experiments providing x-ray energy spectra whose approximate shape is a double exponential.

  2. Influence of the electron intrinsic magnetic moment on the transverse dielectric permittivity of degenerate electron gas

    NASA Astrophysics Data System (ADS)

    Maslov, S. A.; Bobrov, V. B.; Kirillin, A. V.; Trigger, S. A.

    2018-01-01

    Using the linear response theory, the transverse dielectric permittivity of a homogeneous and isotropic system of charged particles is considered. In the ideal gas approximation for the polarization function, an explicit analytical expression for the transverse permittivity of a degenerate electron plasma, which takes into account electron spin, is found. This result describes both the Landau diamagnetism and Pauli paramagnetism in electron plasma. The influence of the electron intrinsic magnetic moment on the spatial and frequency dispersion of the transverse dielectric permittivity of degenerate electron plasma is numerically studied, that is crucial for determining the optical characteristics of plasma.

  3. Linear analysis of time dependent properties of Child-Langmuir flow

    NASA Astrophysics Data System (ADS)

    Rokhlenko, A.

    2013-01-01

    We continue our analysis of the time dependent behavior of the electron flow in the Child-Langmuir system, removing an approximation used earlier. We find a modified set of oscillatory decaying modes with frequencies of the same order as the inverse of the electron transient time. This range (typically MHz) allows simple experimental detection and maybe exploitation. We then study the time evolution of the current in response to a slow change of the anode voltage where the same modes of oscillations appear too. The cathode current in this case is systematically advanced or retarded depending on the direction of the voltage change.

  4. Optical generation of millimeter-wave pulses using a fiber Bragg grating in a fiber-optics system.

    PubMed

    Ye, Qing; Qu, Ronghui; Fang, Zujie

    2007-04-10

    A scheme is proposed to transform an optical pulse into a millimeter-wave frequency modulation pulse by using a weak fiber Bragg grating (FBG) in a fiber-optics system. The Fourier transformation method is used to obtain the required spectrum response function of the FBG for the Gaussian pulse, soliton pulse, and Lorenz shape pulse. On the condition of the first-order Born approximation of the weak fiber grating, the relation of the refractive index distribution and the spectrum response function of the FBG satisfies the Fourier transformation, and the corresponding refractive index distribution forms are obtained for single-frequency modulation and linear-frequency modulation millimeter-wave pulse generation. The performances of the designed fiber gratings are also studied by a numerical simulation method for a supershort pulse transmission.

  5. Dynamic analysis of a magnetic bearing system with flux control

    NASA Technical Reports Server (NTRS)

    Knight, Josiah; Walsh, Thomas; Virgin, Lawrence

    1994-01-01

    Using measured values of two-dimensional forces in a magnetic actuator, equations of motion for an active magnetic bearing are presented. The presence of geometric coupling between coordinate directions causes the equations of motion to be nonlinear. Two methods are used to examine the unbalance response of the system: simulation by direct integration in time; and determination of approximate steady state solutions by harmonic balance. For relatively large values of the derivative control coefficient, the system behaves in an essentially linear manner, but for lower values of this parameter, or for higher values of the coupling coefficient, the response shows a split of amplitudes in the two principal directions. This bifurcation is sensitive to initial conditions. The harmonic balance solution shows that the separation of amplitudes actually corresponds to a change in stability of multiple coexisting solutions.

  6. On foundations of discrete element analysis of contact in diarthrodial joints.

    PubMed

    Volokh, K Y; Chao, E Y S; Armand, M

    2007-06-01

    Information about the stress distribution on contact surfaces of adjacent bones is indispensable for analysis of arthritis, bone fracture and remodeling. Numerical solution of the contact problem based on the classical approaches of solid mechanics is sophisticated and time-consuming. However, the solution can be essentially simplified on the following physical grounds. The bone contact surfaces are covered with a layer of articular cartilage, which is a soft tissue as compared to the hard bone. The latter allows ignoring the bone compliance in analysis of the contact problem, i.e. rigid bones are considered to interact through a compliant cartilage. Moreover, cartilage shear stresses and strains can be ignored because of the negligible friction between contacting cartilage layers. Thus, the cartilage can be approximated by a set of unilateral compressive springs normal to the bone surface. The forces in the springs can be computed from the equilibrium equations iteratively accounting for the changing contact area. This is the essence of the discrete element analysis (DEA). Despite the success in applications of DEA to various bone contact problems, its classical formulation required experimental validation because the springs approximating the cartilage were assumed linear while the real articular cartilage exhibited non-linear mechanical response in reported tests. Recent experimental results of Ateshian and his co-workers allow for revisiting the classical DEA formulation and establishing the limits of its applicability. In the present work, it is shown that the linear spring model is remarkably valid within a wide range of large deformations of the cartilage. It is also shown how to extend the classical DEA to the case of strong nonlinearity if necessary.

  7. Correcting Borehole Temperture Profiles for the Effects of Postglacial Warming

    NASA Astrophysics Data System (ADS)

    Rath, V.; Gonzalez-Rouco, J. F.

    2010-09-01

    Though the investigation of observed borehole temperatures has proved to be a valuable tool for the reconstruction of ground surface temperature histories, there are many open questions concerning the signifcance and accuracy of the reconstructions from these data. In particular, the temperature signal of the warming after the Last glacial Maximum (LGM) is still present in borehole temperature proiles. It also influences the relatively shallow boreholes used in current paleoclimate inversions to estimate temperature changes in the last centuries. This is shown using Monte Carlo experiments on past surface temperature change, using plausible distributions for the most important parameters, i.e.,amplitude and timing of the glacial-interglacial transition, the prior average temperature, and petrophysical properties. It has been argued that the signature of the last glacial-interglacial transition could be responsible for the high amplitudes of millennial temperature reconstructions. However, in shallow boreholes the additional effect of past climate can reasonably approximated by a linear variation of temperature with depth, and thus be accommodated by a "biased" background heat flow. This is good news for borehole climatology. A simple correction based on subtracting an appropriate prior surface temperature history shows promising results reducing these errors considerably, in particular with deeper boreholes, where the warming signal in heat flow can no longer be approximated linearly. We will show examples from North America and Eurasia, comparing temperatures reduced the proposed algoritm with AOGCM modeling results.

  8. The Dropout Learning Algorithm

    PubMed Central

    Baldi, Pierre; Sadowski, Peter

    2014-01-01

    Dropout is a recently introduced algorithm for training neural network by randomly dropping units during training to prevent their co-adaptation. A mathematical analysis of some of the static and dynamic properties of dropout is provided using Bernoulli gating variables, general enough to accommodate dropout on units or connections, and with variable rates. The framework allows a complete analysis of the ensemble averaging properties of dropout in linear networks, which is useful to understand the non-linear case. The ensemble averaging properties of dropout in non-linear logistic networks result from three fundamental equations: (1) the approximation of the expectations of logistic functions by normalized geometric means, for which bounds and estimates are derived; (2) the algebraic equality between normalized geometric means of logistic functions with the logistic of the means, which mathematically characterizes logistic functions; and (3) the linearity of the means with respect to sums, as well as products of independent variables. The results are also extended to other classes of transfer functions, including rectified linear functions. Approximation errors tend to cancel each other and do not accumulate. Dropout can also be connected to stochastic neurons and used to predict firing rates, and to backpropagation by viewing the backward propagation as ensemble averaging in a dropout linear network. Moreover, the convergence properties of dropout can be understood in terms of stochastic gradient descent. Finally, for the regularization properties of dropout, the expectation of the dropout gradient is the gradient of the corresponding approximation ensemble, regularized by an adaptive weight decay term with a propensity for self-consistent variance minimization and sparse representations. PMID:24771879

  9. Relaxation approximations to second-order traffic flow models by high-resolution schemes

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

    Nikolos, I.K.; Delis, A.I.; Papageorgiou, M.

    2015-03-10

    A relaxation-type approximation of second-order non-equilibrium traffic models, written in conservation or balance law form, is considered. Using the relaxation approximation, the nonlinear equations are transformed to a semi-linear diagonilizable problem with linear characteristic variables and stiff source terms with the attractive feature that neither Riemann solvers nor characteristic decompositions are in need. In particular, it is only necessary to provide the flux and source term functions and an estimate of the characteristic speeds. To discretize the resulting relaxation system, high-resolution reconstructions in space are considered. Emphasis is given on a fifth-order WENO scheme and its performance. The computations reportedmore » demonstrate the simplicity and versatility of relaxation schemes as numerical solvers.« less

  10. Gaseous Viscous Peeling of Linearly Elastic Substrates

    NASA Astrophysics Data System (ADS)

    Elbaz, Shai; Jacob, Hila; Gat, Amir

    2017-11-01

    We study pressure-driven propagation of gas into a micron-scale gap between two linearly elastic substrates. Applying the lubrication approximation, the governing nonlinear evolution equation describes the interaction between elasticity and viscosity, as well as weak rarefaction and low-Mach-number compressibility, characteristic to gaseous microflows. Several physical limits allow simplification of the evolution equation and enable solution by self-similarity. During the peeling process the flow-field transitions between the different limits and the respective approximate solutions. The sequence of limits occurring during the propagation dynamics can be related to the thickness of the prewetting layer of the configuration at rest, yielding an approximate description of the entire peeling dynamics. The results are validated by numerical solutions of the evolution equation. Israel Science Foundation 818/13.

  11. Venus - Volcanic features in Atla Region

    NASA Technical Reports Server (NTRS)

    1991-01-01

    This Magellan image from the Atla region of Venus shows several types of volcanic features and superimposed surface fractures. The area in the image is approximately 350 kilometers (217 miles) across, centered at 9 degrees south latitude, 199 degrees east longitude. Lava flows emanating from circular pits or linear fissures form flower-shaped patterns in several areas. A collapse depression approximately 20 kilometers by 10 kilometers (12 by 6 miles) near the center of the image is drained by a lava channel approximately 40 kilometers (25 miles) long. Numerous surface fractures and graben (linear valleys) criss-cross the volcanic deposits in north to northeast trends. The fractures are not buried by the lavas, indicating that the tectonic activity post-dates most of the volcanic activity.

  12. Boxing headguard performance in punch machine tests.

    PubMed

    McIntosh, Andrew S; Patton, Declan A

    2015-09-01

    The paper presents a novel laboratory method for assessing boxing headguard impact performance. The method is applied to examine the effects of headguards on head impact dynamics and injury risk. A linear impactor was developed, and a range of impacts was delivered to an instrumented Hybrid III head and neck system both with and without an AIBA (Association Internationale de Boxe Amateur)-approved headguard. Impacts at selected speeds between 4.1 and 8.3 m/s were undertaken. The impactor mass was approximately 4 kg and an interface comprising a semirigid 'fist' with a glove was used. The peak contact forces were in the range 1.9-5.9 kN. Differences in head impact responses between the Top Ten AIBA-approved headguard and bare headform in the lateral and forehead tests were large and/or significant. In the 8.3 m/s fist-glove impacts, the mean peak resultant headform accelerations for bare headform tests was approximately 130 g compared with approximately 85 g in the forehead impacts. In the 6.85 m/s bare headform impacts, mean peak resultant angular head accelerations were in the range of 5200-5600 rad/s(2) and almost halved by the headguard. Linear and angular accelerations in 45° forehead and 60° jaw impacts were reduced by the headguard. The data support the opinion that current AIBA headguards can play an important role in reducing the risk of concussion and superficial injury in boxing competition and training. Published by the BMJ Publishing Group Limited. For permission to use (where not already granted under a licence) please go to http://group.bmj.com/group/rights-licensing/permissions.

  13. Progress in linear optics, non-linear optics and surface alignment of liquid crystals

    NASA Astrophysics Data System (ADS)

    Ong, H. L.; Meyer, R. B.; Hurd, A. J.; Karn, A. J.; Arakelian, S. M.; Shen, Y. R.; Sanda, P. N.; Dove, D. B.; Jansen, S. A.; Hoffmann, R.

    We first discuss the progress in linear optics, in particular, the formulation and application of geometrical-optics approximation and its generalization. We then discuss the progress in non-linear optics, in particular, the enhancement of a first-order Freedericksz transition and intrinsic optical bistability in homeotropic and parallel oriented nematic liquid crystal cells. Finally, we discuss the liquid crystal alignment and surface effects on field-induced Freedericksz transition.

  14. Testing the Linearity of the Cosmic Origins Spectrograph FUV Channel Thermal Correction

    NASA Astrophysics Data System (ADS)

    Fix, Mees B.; De Rosa, Gisella; Sahnow, David

    2018-05-01

    The Far Ultraviolet Cross Delay Line (FUV XDL) detector on the Cosmic Origins Spectrograph (COS) is subject to temperature-dependent distortions. The correction performed by the COS calibration pipeline (CalCOS) assumes that these changes are linear across the detector. In this report we evaluate the accuracy of the linear approximations using data obtained on orbit. Our results show that the thermal distortions are consistent with our current linear model.

  15. Discrete Applied Mathematics

    DTIC Science & Technology

    1993-05-31

    program. In paper [28], we give a brief and elementary proof of a result of Hoffman [1952) about approximate solutions to systems, of linear inequalities...UCLA, Vestvood, CA, February 1993. " Linear Problems: Formulation and Solution," International Linear Algebra Society, Pensacola, FL, May 1993. Denise S...thresAold If there is a number h and a linear k-separator w assigning a real number to each vertex so that for any subset S of vertices, the sum of w

  16. Microwave imaging by three-dimensional Born linearization of electromagnetic scattering

    NASA Astrophysics Data System (ADS)

    Caorsi, S.; Gragnani, G. L.; Pastorino, M.

    1990-11-01

    An approach to microwave imaging is proposed that uses a three-dimensional vectorial form of the Born approximation to linearize the equation of electromagnetic scattering. The inverse scattering problem is numerically solved for three-dimensional geometries by means of the moment method. A pseudoinversion algorithm is adopted to overcome ill conditioning. Results show that the method is well suited for qualitative imaging purposes, while its capability for exactly reconstructing the complex dielectric permittivity is affected by the limitations inherent in the Born approximation and in ill conditioning.

  17. Convergence of a sequence of dual variables at the solution of a completely degenerate problem of linear programming

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

    Dikin, I.

    1994-12-31

    We survey results about the convergence of the primal affine scaling method at solutions of a completely degenerate problem of linear programming. Moreover we are studying the case when a next approximation is on the boundary of the affine scaling ellipsoid. Convergence of successive approximation to an interior point u of the solution for the dual problem is proved. Coordinates of the vector u are determined only by the input data of the problem; they do not depend of the choice of the starting point.

  18. Dense grid sibling frames with linear phase filters

    NASA Astrophysics Data System (ADS)

    Abdelnour, Farras

    2013-09-01

    We introduce new 5-band dyadic sibling frames with dense time-frequency grid. Given a lowpass filter satisfying certain conditions, the remaining filters are obtained using spectral factorization. The analysis and synthesis filterbanks share the same lowpass and bandpass filters but have different and oversampled highpass filters. This leads to wavelets approximating shift-invariance. The filters are FIR, have linear phase, and the resulting wavelets have vanishing moments. The filters are designed using spectral factorization method. The proposed method leads to smooth limit functions with higher approximation order, and computationally stable filterbanks.

  19. Exact Doppler broadening of tabulated cross sections. [SIGMA 1 kernel broadening method

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

    Cullen, D.E.; Weisbin, C.R.

    1976-07-01

    The SIGMA1 kernel broadening method is presented to Doppler broaden to any required accuracy a cross section that is described by a table of values and linear-linear interpolation in energy-cross section between tabulated values. The method is demonstrated to have no temperature or energy limitations and to be equally applicable to neutron or charged-particle cross sections. The method is qualitatively and quantitatively compared to contemporary approximate methods of Doppler broadening with particular emphasis on the effect of each approximation introduced.

  20. Electrostatic solvation free energies of charged hard spheres using molecular dynamics with density functional theory interactions

    DOE PAGES

    Duignan, Timothy T.; Baer, Marcel D.; Schenter, Gregory K.; ...

    2017-07-26

    Determining the solvation free energies of single ions in water is one of the most fundamental problems in physical chemistry and yet many unresolved questions remain. In particular, the ability to decompose the solvation free energy into simple and intuitive contributions will have important implications for models of electrolyte solution. In this paper, we provide definitions of the various types of single ion solvation free energies based on different simulation protocols. We calculate solvation free energies of charged hard spheres using density functional theory interaction potentials with molecular dynamics simulation and isolate the effects of charge and cavitation, comparing tomore » the Born (linear response) model. We show that using uncorrected Ewald summation leads to unphysical values for the single ion solvation free energy and that charging free energies for cations are approximately linear as a function of charge but that there is a small non-linearity for small anions. The charge hydration asymmetry for hard spheres, determined with quantum mechanics, is much larger than for the analogous real ions. Finally, this suggests that real ions, particularly anions, are significantly more complex than simple charged hard spheres, a commonly employed representation.« less

  1. Limits of linearity and detection for some drugs of abuse.

    PubMed

    Needleman, S B; Romberg, R W

    1990-01-01

    The limits of linearity (LOL) and detection (LOD) are important factors in establishing the reliability of an analytical procedure for accurately assaying drug concentrations in urine specimens. Multiple analyses of analyte over an extended range of concentrations provide a measure of the ability of the analytical procedure to correctly identify known quantities of drug in a biofluid matrix. Each of the seven drugs of abuse gives linear analytical responses from concentrations at or near their LOD to concentrations several-fold higher than those generally encountered in the drug screening laboratory. The upper LOL exceeds the Department of Navy (DON) cutoff values by factors of approximately 2 to 160. The LOD varies from 0.4 to 5.0% of the DON cutoff value for each drug. The limit of quantitation (LOQ) is calculated as the LOD + 7 SD. The range for LOL is greater for drugs analyzed with deuterated internal standards compared with those using conventional internal standards. For THC acid, cocaine, PCP, and morphine, LOLs are 8 to 160-fold greater than the defined cutoff concentrations. For the other drugs, the LOL's are only 2 to 4-fold greater than the defined cutoff concentrations.

  2. Electrostatic solvation free energies of charged hard spheres using molecular dynamics with density functional theory interactions

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

    Duignan, Timothy T.; Baer, Marcel D.; Schenter, Gregory K.

    Determining the solvation free energies of single ions in water is one of the most fundamental problems in physical chemistry and yet many unresolved questions remain. In particular, the ability to decompose the solvation free energy into simple and intuitive contributions will have important implications for models of electrolyte solution. In this paper, we provide definitions of the various types of single ion solvation free energies based on different simulation protocols. We calculate solvation free energies of charged hard spheres using density functional theory interaction potentials with molecular dynamics simulation and isolate the effects of charge and cavitation, comparing tomore » the Born (linear response) model. We show that using uncorrected Ewald summation leads to unphysical values for the single ion solvation free energy and that charging free energies for cations are approximately linear as a function of charge but that there is a small non-linearity for small anions. The charge hydration asymmetry for hard spheres, determined with quantum mechanics, is much larger than for the analogous real ions. Finally, this suggests that real ions, particularly anions, are significantly more complex than simple charged hard spheres, a commonly employed representation.« less

  3. Electrostatic solvation free energies of charged hard spheres using molecular dynamics with density functional theory interactions

    NASA Astrophysics Data System (ADS)

    Duignan, Timothy T.; Baer, Marcel D.; Schenter, Gregory K.; Mundy, Chistopher J.

    2017-10-01

    Determining the solvation free energies of single ions in water is one of the most fundamental problems in physical chemistry and yet many unresolved questions remain. In particular, the ability to decompose the solvation free energy into simple and intuitive contributions will have important implications for models of electrolyte solution. Here, we provide definitions of the various types of single ion solvation free energies based on different simulation protocols. We calculate solvation free energies of charged hard spheres using density functional theory interaction potentials with molecular dynamics simulation and isolate the effects of charge and cavitation, comparing to the Born (linear response) model. We show that using uncorrected Ewald summation leads to unphysical values for the single ion solvation free energy and that charging free energies for cations are approximately linear as a function of charge but that there is a small non-linearity for small anions. The charge hydration asymmetry for hard spheres, determined with quantum mechanics, is much larger than for the analogous real ions. This suggests that real ions, particularly anions, are significantly more complex than simple charged hard spheres, a commonly employed representation.

  4. Quantitative imaging features of pretreatment CT predict volumetric response to chemotherapy in patients with colorectal liver metastases.

    PubMed

    Creasy, John M; Midya, Abhishek; Chakraborty, Jayasree; Adams, Lauryn B; Gomes, Camilla; Gonen, Mithat; Seastedt, Kenneth P; Sutton, Elizabeth J; Cercek, Andrea; Kemeny, Nancy E; Shia, Jinru; Balachandran, Vinod P; Kingham, T Peter; Allen, Peter J; DeMatteo, Ronald P; Jarnagin, William R; D'Angelica, Michael I; Do, Richard K G; Simpson, Amber L

    2018-06-19

    This study investigates whether quantitative image analysis of pretreatment CT scans can predict volumetric response to chemotherapy for patients with colorectal liver metastases (CRLM). Patients treated with chemotherapy for CRLM (hepatic artery infusion (HAI) combined with systemic or systemic alone) were included in the study. Patients were imaged at baseline and approximately 8 weeks after treatment. Response was measured as the percentage change in tumour volume from baseline. Quantitative imaging features were derived from the index hepatic tumour on pretreatment CT, and features statistically significant on univariate analysis were included in a linear regression model to predict volumetric response. The regression model was constructed from 70% of data, while 30% were reserved for testing. Test data were input into the trained model. Model performance was evaluated with mean absolute prediction error (MAPE) and R 2 . Clinicopatholologic factors were assessed for correlation with response. 157 patients were included, split into training (n = 110) and validation (n = 47) sets. MAPE from the multivariate linear regression model was 16.5% (R 2 = 0.774) and 21.5% in the training and validation sets, respectively. Stratified by HAI utilisation, MAPE in the validation set was 19.6% for HAI and 25.1% for systemic chemotherapy alone. Clinical factors associated with differences in median tumour response were treatment strategy, systemic chemotherapy regimen, age and KRAS mutation status (p < 0.05). Quantitative imaging features extracted from pretreatment CT are promising predictors of volumetric response to chemotherapy in patients with CRLM. Pretreatment predictors of response have the potential to better select patients for specific therapies. • Colorectal liver metastases (CRLM) are downsized with chemotherapy but predicting the patients that will respond to chemotherapy is currently not possible. • Heterogeneity and enhancement patterns of CRLM can be measured with quantitative imaging. • Prediction model constructed that predicts volumetric response with 20% error suggesting that quantitative imaging holds promise to better select patients for specific treatments.

  5. Nonpolar Solvation Free Energy from Proximal Distribution Functions

    PubMed Central

    Ou, Shu-Ching; Drake, Justin A.; Pettitt, B. Montgomery

    2017-01-01

    Using precomputed near neighbor or proximal distribution functions (pDFs) that approximate solvent density about atoms in a chemically bonded context one can estimate the solvation structures around complex solutes and the corresponding solute–solvent energetics. In this contribution, we extend this technique to calculate the solvation free energies (ΔG) of a variety of solutes. In particular we use pDFs computed for small peptide molecules to estimate ΔG for larger peptide systems. We separately compute the non polar (ΔGvdW) and electrostatic (ΔGelec) components of the underlying potential model. Here we show how the former can be estimated by thermodynamic integration using pDF-reconstructed solute–solvent interaction energy. The electrostatic component can be approximated with Linear Response theory as half of the electrostatic solute–solvent interaction energy. We test the method by calculating the solvation free energies of butane, propanol, polyalanine, and polyglycine and by comparing with traditional free energy simulations. Results indicate that the pDF-reconstruction algorithm approximately reproduces ΔGvdW calculated by benchmark free energy simulations to within ~ kcal/mol accuracy. The use of transferable pDFs for each solute atom allows for a rapid estimation of ΔG for arbitrary molecular systems. PMID:27992228

  6. The most likely voltage path and large deviations approximations for integrate-and-fire neurons.

    PubMed

    Paninski, Liam

    2006-08-01

    We develop theory and numerical methods for computing the most likely subthreshold voltage path of a noisy integrate-and-fire (IF) neuron, given observations of the neuron's superthreshold spiking activity. This optimal voltage path satisfies a second-order ordinary differential (Euler-Lagrange) equation which may be solved analytically in a number of special cases, and which may be solved numerically in general via a simple "shooting" algorithm. Our results are applicable for both linear and nonlinear subthreshold dynamics, and in certain cases may be extended to correlated subthreshold noise sources. We also show how this optimal voltage may be used to obtain approximations to (1) the likelihood that an IF cell with a given set of parameters was responsible for the observed spike train; and (2) the instantaneous firing rate and interspike interval distribution of a given noisy IF cell. The latter probability approximations are based on the classical Freidlin-Wentzell theory of large deviations principles for stochastic differential equations. We close by comparing this most likely voltage path to the true observed subthreshold voltage trace in a case when intracellular voltage recordings are available in vitro.

  7. Iterative methods for 3D implicit finite-difference migration using the complex Padé approximation

    NASA Astrophysics Data System (ADS)

    Costa, Carlos A. N.; Campos, Itamara S.; Costa, Jessé C.; Neto, Francisco A.; Schleicher, Jörg; Novais, Amélia

    2013-08-01

    Conventional implementations of 3D finite-difference (FD) migration use splitting techniques to accelerate performance and save computational cost. However, such techniques are plagued with numerical anisotropy that jeopardises the correct positioning of dipping reflectors in the directions not used for the operator splitting. We implement 3D downward continuation FD migration without splitting using a complex Padé approximation. In this way, the numerical anisotropy is eliminated at the expense of a computationally more intensive solution of a large-band linear system. We compare the performance of the iterative stabilized biconjugate gradient (BICGSTAB) and that of the multifrontal massively parallel direct solver (MUMPS). It turns out that the use of the complex Padé approximation not only stabilizes the solution, but also acts as an effective preconditioner for the BICGSTAB algorithm, reducing the number of iterations as compared to the implementation using the real Padé expansion. As a consequence, the iterative BICGSTAB method is more efficient than the direct MUMPS method when solving a single term in the Padé expansion. The results of both algorithms, here evaluated by computing the migration impulse response in the SEG/EAGE salt model, are of comparable quality.

  8. Application of ab initio many-body perturbation theory with Gaussian basis sets to the singlet and triplet excitations of organic molecules

    NASA Astrophysics Data System (ADS)

    Hamed, Samia; Rangel, Tonatiuh; Bruneval, Fabien; Neaton, Jeffrey B.

    Quantitative understanding of charged and neutral excitations of organic molecules is critical in diverse areas of study that include astrophysics and the development of energy technologies that are clean and efficient. The recent use of local basis sets with ab initio many-body perturbation theory in the GW approximation and the Bethe-Saltpeter equation approach (BSE), methods traditionally applied to periodic condensed phases with a plane-wave basis, has opened the door to detailed study of such excitations for molecules, as well as accurate numerical benchmarks. Here, through a series of systematic benchmarks with a Gaussian basis, we report on the extent to which the predictive power and utility of this approach depend critically on interdependent underlying approximations and choices for molecules, including the mean-field starting point (eg optimally-tuned range separated hybrids, pure DFT functionals, and untuned hybrids), the GW scheme, and the Tamm Dancoff approximation. We demonstrate the effects of these choices in the context of Thiels' set while drawing analogies to linear-response time-dependent DFT and making comparisons to best theoretical estimates from higher-order wavefunction-based theories.

  9. Energy dependence corrections to MOSFET dosimetric sensitivity.

    PubMed

    Cheung, T; Butson, M J; Yu, P K N

    2009-03-01

    Metal Oxide Semiconductor Field Effect Transistors (MOSFET's) are dosimeters which are now frequently utilized in radiotherapy treatment applications. An improved MOSFET, clinical semiconductor dosimetry system (CSDS) which utilizes improved packaging for the MOSFET device has been studied for energy dependence of sensitivity to x-ray radiation measurement. Energy dependence from 50 kVp to 10 MV x-rays has been studied and found to vary by up to a factor of 3.2 with 75 kVp producing the highest sensitivity response. The detectors average life span in high sensitivity mode is energy related and ranges from approximately 100 Gy for 75 kVp x-rays to approximately 300 Gy at 6 MV x-ray energy. The MOSFET detector has also been studied for sensitivity variations with integrated dose history. It was found to become less sensitive to radiation with age and the magnitude of this effect is dependant on radiation energy with lower energies producing a larger sensitivity reduction with integrated dose. The reduction in sensitivity is however approximated reproducibly by a slightly non linear, second order polynomial function allowing corrections to be made to readings to account for this effect to provide more accurate dose assessments both in phantom and in-vivo.

  10. Deformed Palmprint Matching Based on Stable Regions.

    PubMed

    Wu, Xiangqian; Zhao, Qiushi

    2015-12-01

    Palmprint recognition (PR) is an effective technology for personal recognition. A main problem, which deteriorates the performance of PR, is the deformations of palmprint images. This problem becomes more severe on contactless occasions, in which images are acquired without any guiding mechanisms, and hence critically limits the applications of PR. To solve the deformation problems, in this paper, a model for non-linearly deformed palmprint matching is derived by approximating non-linear deformed palmprint images with piecewise-linear deformed stable regions. Based on this model, a novel approach for deformed palmprint matching, named key point-based block growing (KPBG), is proposed. In KPBG, an iterative M-estimator sample consensus algorithm based on scale invariant feature transform features is devised to compute piecewise-linear transformations to approximate the non-linear deformations of palmprints, and then, the stable regions complying with the linear transformations are decided using a block growing algorithm. Palmprint feature extraction and matching are performed over these stable regions to compute matching scores for decision. Experiments on several public palmprint databases show that the proposed models and the KPBG approach can effectively solve the deformation problem in palmprint verification and outperform the state-of-the-art methods.

  11. Chaos as an intermittently forced linear system.

    PubMed

    Brunton, Steven L; Brunton, Bingni W; Proctor, Joshua L; Kaiser, Eurika; Kutz, J Nathan

    2017-05-30

    Understanding the interplay of order and disorder in chaos is a central challenge in modern quantitative science. Approximate linear representations of nonlinear dynamics have long been sought, driving considerable interest in Koopman theory. We present a universal, data-driven decomposition of chaos as an intermittently forced linear system. This work combines delay embedding and Koopman theory to decompose chaotic dynamics into a linear model in the leading delay coordinates with forcing by low-energy delay coordinates; this is called the Hankel alternative view of Koopman (HAVOK) analysis. This analysis is applied to the Lorenz system and real-world examples including Earth's magnetic field reversal and measles outbreaks. In each case, forcing statistics are non-Gaussian, with long tails corresponding to rare intermittent forcing that precedes switching and bursting phenomena. The forcing activity demarcates coherent phase space regions where the dynamics are approximately linear from those that are strongly nonlinear.The huge amount of data generated in fields like neuroscience or finance calls for effective strategies that mine data to reveal underlying dynamics. Here Brunton et al.develop a data-driven technique to analyze chaotic systems and predict their dynamics in terms of a forced linear model.

  12. Nonlinear programming extensions to rational function approximations of unsteady aerodynamics

    NASA Technical Reports Server (NTRS)

    Tiffany, Sherwood H.; Adams, William M., Jr.

    1987-01-01

    This paper deals with approximating unsteady generalized aerodynamic forces in the equations of motion of a flexible aircraft. Two methods of formulating these approximations are extended to include both the same flexibility in constraining them and the same methodology in optimizing nonlinear parameters as another currently used 'extended least-squares' method. Optimal selection of 'nonlinear' parameters is made in each of the three methods by use of the same nonlinear (nongradient) optimizer. The objective of the nonlinear optimization is to obtain rational approximations to the unsteady aerodynamics whose state-space realization is of lower order than that required when no optimization of the nonlinear terms is performed. The free 'linear' parameters are determined using least-squares matrix techniques on a Lagrange multiplier formulation of an objective function which incorporates selected linear equality constraints. State-space mathematical models resulting from the different approaches are described, and results are presented which show comparative evaluations from application of each of the extended methods to a numerical example. The results obtained for the example problem show a significant (up to 63 percent) reduction in the number of differential equations used to represent the unsteady aerodynamic forces in linear time-invariant equations of motion as compared to a conventional method in which nonlinear terms are not optimized.

  13. Difference equation state approximations for nonlinear hereditary control problems

    NASA Technical Reports Server (NTRS)

    Rosen, I. G.

    1982-01-01

    Discrete approximation schemes for the solution of nonlinear hereditary control problems are constructed. The methods involve approximation by a sequence of optimal control problems in which the original infinite dimensional state equation has been approximated by a finite dimensional discrete difference equation. Convergence of the state approximations is argued using linear semigroup theory and is then used to demonstrate that solutions to the approximating optimal control problems in some sense approximate solutions to the original control problem. Two schemes, one based upon piecewise constant approximation, and the other involving spline functions are discussed. Numerical results are presented, analyzed and used to compare the schemes to other available approximation methods for the solution of hereditary control problems.

  14. A research on Performance Efficiency of Rubber Metal Support Structures

    NASA Astrophysics Data System (ADS)

    Mkrtychev, Oleg V.; Bunov, Artem A.

    2017-11-01

    The paper scrutinizes structural behavior of lead rubber bearings by a Chinese manufacturer subjected to a single-component seismic action. Several problems were solved using specialized software complexes, which conducted forth integration of motion equations through the explicit method or response spectrum method. Depending on the calculation method, the diagram of the bearing performance was assumed to be either an actual diagram approximated by an idealized non-linear diagram or an idealized linear diagram with a specific stiffness. The computational model was assumed to be a single-mass oscillator with a lumped mass. The effort undertaken facilitated the investigation of the patterns of horizontal displacement of the bearing top relative to bottom caused by earthquakes modeled as accelerograms with different spectral compositions. The behavior of the support structure was benchmarked against similar supports by another manufacturer. The paper presents the outcomes of the research effort and draws conclusions about the efficiency of using the bearings of this particular type and model.

  15. Interior Temperature Measurement Using Curved Mercury Capillary Sensor Based on X-ray Radiography

    NASA Astrophysics Data System (ADS)

    Chen, Shuyue; Jiang, Xing; Lu, Guirong

    2017-07-01

    A method was presented for measuring the interior temperature of objects using a curved mercury capillary sensor based on X-ray radiography. The sensor is composed of a mercury bubble, a capillary and a fixed support. X-ray digital radiography was employed to capture image of the mercury column in the capillary, and a temperature control system was designed for the sensor calibration. We adopted livewire algorithms and mathematical morphology to calculate the mercury length. A measurement model relating mercury length to temperature was established, and the measurement uncertainty associated with the mercury column length and the linear model fitted by least-square method were analyzed. To verify the system, the interior temperature measurement of an autoclave, which is totally closed, was taken from 29.53°C to 67.34°C. The experiment results show that the response of the system is approximately linear with an uncertainty of maximum 0.79°C. This technique provides a new approach to measure interior temperature of objects.

  16. How quantitative measures unravel design principles in multi-stage phosphorylation cascades.

    PubMed

    Frey, Simone; Millat, Thomas; Hohmann, Stefan; Wolkenhauer, Olaf

    2008-09-07

    We investigate design principles of linear multi-stage phosphorylation cascades by using quantitative measures for signaling time, signal duration and signal amplitude. We compare alternative pathway structures by varying the number of phosphorylations and the length of the cascade. We show that a model for a weakly activated pathway does not reflect the biological context well, unless it is restricted to certain parameter combinations. Focusing therefore on a more general model, we compare alternative structures with respect to a multivariate optimization criterion. We test the hypothesis that the structure of a linear multi-stage phosphorylation cascade is the result of an optimization process aiming for a fast response, defined by the minimum of the product of signaling time and signal duration. It is then shown that certain pathway structures minimize this criterion. Several popular models of MAPK cascades form the basis of our study. These models represent different levels of approximation, which we compare and discuss with respect to the quantitative measures.

  17. Efficiency in nonequilibrium molecular dynamics Monte Carlo simulations

    DOE PAGES

    Radak, Brian K.; Roux, Benoît

    2016-10-07

    Hybrid algorithms combining nonequilibrium molecular dynamics and Monte Carlo (neMD/MC) offer a powerful avenue for improving the sampling efficiency of computer simulations of complex systems. These neMD/MC algorithms are also increasingly finding use in applications where conventional approaches are impractical, such as constant-pH simulations with explicit solvent. However, selecting an optimal nonequilibrium protocol for maximum efficiency often represents a non-trivial challenge. This work evaluates the efficiency of a broad class of neMD/MC algorithms and protocols within the theoretical framework of linear response theory. The approximations are validated against constant pH-MD simulations and shown to provide accurate predictions of neMD/MC performance.more » An assessment of a large set of protocols confirms (both theoretically and empirically) that a linear work protocol gives the best neMD/MC performance. Lastly, a well-defined criterion for optimizing the time parameters of the protocol is proposed and demonstrated with an adaptive algorithm that improves the performance on-the-fly with minimal cost.« less

  18. Magnetic specific heat and structural phase transitions in (CH3)4NMnCl3 (TMMC) and TMMC:Cu2+ studied by crystal optics

    NASA Astrophysics Data System (ADS)

    Levola, T.; Kleemann, W.

    1985-10-01

    High-resolution refractive index (RI) and linear birefringence (LB) measurements are performed on the one-dimensional antiferromagnet tetramethyl ammonium manganese trichloride (TMMC) in order to reveal the temperature dependence of the magnetic short-range order. In agreement with values obtained by other methods an exchange constant J/kB=-7.3 K is reliably extracted. Anomalies of the in-plane LB and of the ordinary RI at the hexagonal-to-monoclinic structural phase transition (Tc=126 K) are successfully described with the use of linear elasto-optic response theory and the Landau approximation, which accounts for symmetry-adapted coupling between the components of the order parameter and of the spontaneous strain. Cu2+ ions, substituting Mn2+ ions of TMMC at a rate exceeding x=1.5%, are shown to stabilize an intermediate, possibly incommensurate phase. Its stability range is marked by very drastic decreases &=145 K and &=55 K for x=4.5%, respectively.

  19. Physical aging effects on the compressive linear viscoelastic creep of IM7/K3B composite

    NASA Technical Reports Server (NTRS)

    Veazie, David R.; Gates, Thomas S.

    1995-01-01

    An experimental study was undertaken to establish the viscoelastic behavior of 1M7/K3B composite in compression at elevated temperature. Creep compliance, strain recovery and the effects of physical aging on the time dependent response was measured for uniaxial loading at several isothermal conditions below the glass transition temperature (T(g)). The IM7/K3B composite is a graphite reinforced thermoplastic polyimide with a T(g) of approximately 240 C. In a composite, the two matrix dominated compliance terms associated with time dependent behavior occur in the transverse and shear directions. Linear viscoelasticity was used to characterize the creep/recovery behavior and superposition techniques were used to establish the physical aging related material constants. Creep strain was converted to compliance and measured as a function of test time and aging time. Results included creep compliance master curves, physical aging shift factors and shift rates. The description of the unique experimental techniques required for compressive testing is also given.

  20. Enhanced Sensitivity of Wireless Chemical Sensor Based on Love Wave Mode

    NASA Astrophysics Data System (ADS)

    Wang, Wen; Oh, Haekwan; Lee, Keekeun; Yang, Sangsik

    2008-09-01

    A 440 MHz wireless and passive Love-wave-based chemical sensor was developed for CO2 detection. The developed device was composed of a reflective delay line patterned on 41° YX LiNbO3 piezoelectric substrate, a poly(methyl methacrylate) (PMMA) waveguide layer, and Teflon AF 2400 sensitive film. A theoretical model is presented to describe wave propagation in Love wave devices with large piezoelectricity and to allow the design of an optimized structure. In wireless device testing using a network analyzer, infusion of CO2 into the testing chamber induced large phase shifts of the reflection peaks owing to the interaction between the sensing film and the test gas (CO2). Good linearity and repeatability were observed at CO2 concentrations of 0-350 ppm. The obtained sensitivity from the Love wave device was approximately 7.07° ppm-1. The gas response properties of the fabricated Love-wave sensor in terms of linearity and sensitivity were provided, and a comparison to surface acoustic wave devices was also discussed.

  1. Band-gap tuning and optical response of two-dimensional Si x C 1 - x : A first-principles real-space study of disordered two-dimensional materials

    DOE PAGES

    Sadhukhan, Banasree; Singh, Prashant; Nayak, Arabinda; ...

    2017-08-09

    We present a real-space formulation for calculating the electronic structure and optical conductivity of random alloys based on Kubo-Greenwood formalism interfaced with augmented space recursion technique formulated with the tight-binding linear muffin-tin orbital basis with the van Leeuwen–Baerends corrected exchange potential. This approach has been used to quantitatively analyze the effect of chemical disorder on the configuration averaged electronic properties and optical response of two-dimensional honeycomb siliphene Si xC 1–x beyond the usual Dirac-cone approximation. We predicted the quantitative effect of disorder on both the electronic structure and optical response over a wide energy range, and the results are discussedmore » in the light of the available experimental and other theoretical data. As a result, our proposed formalism may open up a facile way for planned band-gap engineering in optoelectronic applications.« less

  2. Analysis of nystagmus response to a pseudorandom velocity input

    NASA Technical Reports Server (NTRS)

    Lessard, C. S.

    1986-01-01

    Space motion sickness was not reported during the first Apollo missions; however, since Apollo 8 through the current Shuttle and Skylab missions, approximately 50% of the crewmembers have experienced instances of space motion sickness. Space motion sickness, renamed space adaptation syndrome, occurs primarily during the initial period of a mission until habilation takes place. One of NASA's efforts to resolve the space adaptation syndrome is to model the individual's vestibular response for basis knowledge and as a possible predictor of an individual's susceptibility to the disorder. This report describes a method to analyse the vestibular system when subjected to a pseudorandom angular velocity input. A sum of sinusoids (pseudorandom) input lends itself to analysis by linear frequency methods. Resultant horizontal ocular movements were digitized, filtered and transformed into the frequency domain. Programs were developed and evaluated to obtain the (1) auto spectra of input stimulus and resultant ocular resonse, (2) cross spectra, (3) the estimated vestibular-ocular system transfer function gain and phase, and (4) coherence function between stimulus and response functions.

  3. Inertia-Controlled Twinning in Ni-Mn-Ga Actuators: A Discrete Twin-Boundary Dynamics Study

    NASA Astrophysics Data System (ADS)

    Faran, Eilon; Riccardi, Leonardo; Shilo, Doron

    2017-09-01

    A discrete twin-boundary modeling approach is applied for simulating the dynamic magnetomechanical response of a Ni-Mn-Ga actuator over a wide frequency range. The model is based on experimentally measured kinetic relation of individual twin boundaries and takes into account inertial forces due to acceleration of the actuator's mass. The calculated results show good agreement with experimental measurements performed on a specially designed Ni-Mn-Ga linear spring-mass actuator. In addition, the simulation reveals several new effects that have not been considered before and can be applied to the design of improved actuators. It is identified that the demagnetization effect plays a role of an "effective spring" and results in a resonance-type response. The effects of the actuator's mass and the twin-boundary density on the resonance response and the actuator performance are explored numerically. In particular, it is shown that mass-inertia poses an inherent upper limit over the actuator's bandwidth, which is approximately constant and equals to about 200 Hz.

  4. Band-gap tuning and optical response of two-dimensional Si x C 1 - x : A first-principles real-space study of disordered two-dimensional materials

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

    Sadhukhan, Banasree; Singh, Prashant; Nayak, Arabinda

    We present a real-space formulation for calculating the electronic structure and optical conductivity of random alloys based on Kubo-Greenwood formalism interfaced with augmented space recursion technique formulated with the tight-binding linear muffin-tin orbital basis with the van Leeuwen–Baerends corrected exchange potential. This approach has been used to quantitatively analyze the effect of chemical disorder on the configuration averaged electronic properties and optical response of two-dimensional honeycomb siliphene Si xC 1–x beyond the usual Dirac-cone approximation. We predicted the quantitative effect of disorder on both the electronic structure and optical response over a wide energy range, and the results are discussedmore » in the light of the available experimental and other theoretical data. As a result, our proposed formalism may open up a facile way for planned band-gap engineering in optoelectronic applications.« less

  5. The Linear Mixing Approximation for Planetary Ices

    NASA Astrophysics Data System (ADS)

    Bethkenhagen, M.; Meyer, E. R.; Hamel, S.; Nettelmann, N.; French, M.; Scheibe, L.; Ticknor, C.; Collins, L. A.; Kress, J. D.; Fortney, J. J.; Redmer, R.

    2017-12-01

    We investigate the validity of the widely used linear mixing approximation for the equations of state (EOS) of planetary ices, which are thought to dominate the interior of the ice giant planets Uranus and Neptune. For that purpose we perform density functional theory molecular dynamics simulations using the VASP code.[1] In particular, we compute 1:1 binary mixtures of water, ammonia, and methane, as well as their 2:1:4 ternary mixture at pressure-temperature conditions typical for the interior of Uranus and Neptune.[2,3] In addition, a new ab initio EOS for methane is presented. The linear mixing approximation is verified for the conditions present inside Uranus ranging up to 10 Mbar based on the comprehensive EOS data set. We also calculate the diffusion coefficients for the ternary mixture along different Uranus interior profiles and compare them to the values of the pure compounds. We find that deviations of the linear mixing approximation from the real mixture are generally small; for the EOS they fall within about 4% uncertainty while the diffusion coefficients deviate up to 20% . The EOS of planetary ices are applied to adiabatic models of Uranus. It turns out that a deep interior of almost pure ices is consistent with the gravity field data, in which case the planet becomes rather cold (T core ˜ 4000 K). [1] G. Kresse and J. Hafner, Physical Review B 47, 558 (1993). [2] R. Redmer, T.R. Mattsson, N. Nettelmann and M. French, Icarus 211, 798 (2011). [3] N. Nettelmann, K. Wang, J. J. Fortney, S. Hamel, S. Yellamilli, M. Bethkenhagen and R. Redmer, Icarus 275, 107 (2016).

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

    NASA Technical Reports Server (NTRS)

    Tal-Ezer, Hillel

    1987-01-01

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

  7. Low-Rank Correction Methods for Algebraic Domain Decomposition Preconditioners

    DOE PAGES

    Li, Ruipeng; Saad, Yousef

    2017-08-01

    This study presents a parallel preconditioning method for distributed sparse linear systems, based on an approximate inverse of the original matrix, that adopts a general framework of distributed sparse matrices and exploits domain decomposition (DD) and low-rank corrections. The DD approach decouples the matrix and, once inverted, a low-rank approximation is applied by exploiting the Sherman--Morrison--Woodbury formula, which yields two variants of the preconditioning methods. The low-rank expansion is computed by the Lanczos procedure with reorthogonalizations. Numerical experiments indicate that, when combined with Krylov subspace accelerators, this preconditioner can be efficient and robust for solving symmetric sparse linear systems. Comparisonsmore » with pARMS, a DD-based parallel incomplete LU (ILU) preconditioning method, are presented for solving Poisson's equation and linear elasticity problems.« less

  8. Low-Rank Correction Methods for Algebraic Domain Decomposition Preconditioners

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

    Li, Ruipeng; Saad, Yousef

    This study presents a parallel preconditioning method for distributed sparse linear systems, based on an approximate inverse of the original matrix, that adopts a general framework of distributed sparse matrices and exploits domain decomposition (DD) and low-rank corrections. The DD approach decouples the matrix and, once inverted, a low-rank approximation is applied by exploiting the Sherman--Morrison--Woodbury formula, which yields two variants of the preconditioning methods. The low-rank expansion is computed by the Lanczos procedure with reorthogonalizations. Numerical experiments indicate that, when combined with Krylov subspace accelerators, this preconditioner can be efficient and robust for solving symmetric sparse linear systems. Comparisonsmore » with pARMS, a DD-based parallel incomplete LU (ILU) preconditioning method, are presented for solving Poisson's equation and linear elasticity problems.« less

  9. Simultaneous voltammetric determination of prednisone and prednisolone in human body fluids.

    PubMed

    Goyal, Rajendra N; Bishnoi, Sunita

    2009-08-15

    A sensitive, rapid and reliable electrochemical method based on voltammetry at single wall carbon nanotube (SWNT) modified edge plane pyrolytic graphite electrode (EPPGE) is proposed for the simultaneous determination of prednisolone and prednisone in human body fluids and pharmaceutical preparations. The electrochemical response of both the drugs was evaluated by osteryoung square wave voltammetry (OSWV) in phosphate buffer medium of pH 7.2. The modified electrode exhibited good electrocatalytic properties towards prednisone and prednisolone reduction with a peak potential of approximately -1230 and approximately -1332 mV respectively. The concentration versus peak current plots were linear for both the analytes in the range 0.01-100 microM and the detection limit (3 sigma/slope) observed for prednisone and prednisolone were 0.45 x 10(-8), 0.90 x 10(-8)M, respectively. The results of the quantitative estimation of prednisone and prednisolone in biological fluids were also compared with HPLC and the results were in good agreement.

  10. Dynamic perturbation effects upon the circular dichroism intensity induced in an aggregate of dye chromophores bound to biopolymers

    NASA Astrophysics Data System (ADS)

    Kamiya, Mamoru

    1980-11-01

    The dynamic perturbation effects of polarizable monomer perturbers upon the circular dichroism intensity arising from absorption transitions of an arbitrary aggregate of dye chromophores bound to a large host polymer are formulated using the linear response theory in the decorrelation approximation, where the interchromophoric retardation phase factors are eliminated by a first-order Taylor expansion which is compatible with the use of the retarded helix selection rules in the long-wavelength approximation. A space-averaged and closed-form formulation of the non-conservative circular dichroism intensity which is perturbed by intensity with the outside perturber transitions is derived in the limit of the weak dynamic perturbation where perturber—perturber interactions are negligible. The relevant formulation is applied in order to investigate the intercalation model dependence of the non-conservative circular dichroism intensity induced at the visible absorption band of proflavine molecules intercalated in either poly(A—T) or poly(G—C).

  11. Additive-Multiplicative Approximation of Genotype-Environment Interaction

    PubMed Central

    Gimelfarb, A.

    1994-01-01

    A model of genotype-environment interaction in quantitative traits is considered. The model represents an expansion of the traditional additive (first degree polynomial) approximation of genotypic and environmental effects to a second degree polynomial incorporating a multiplicative term besides the additive terms. An experimental evaluation of the model is suggested and applied to a trait in Drosophila melanogaster. The environmental variance of a genotype in the model is shown to be a function of the genotypic value: it is a convex parabola. The broad sense heritability in a population depends not only on the genotypic and environmental variances, but also on the position of the genotypic mean in the population relative to the minimum of the parabola. It is demonstrated, using the model, that GXE interaction rectional may cause a substantial non-linearity in offspring-parent regression and a reversed response to directional selection. It is also shown that directional selection may be accompanied by an increase in the heritability. PMID:7896113

  12. Solving Laplace equation to investigate the volcanic ground deformation pattern

    NASA Astrophysics Data System (ADS)

    Brahmi, Mouna; Castaldo, Raffaele; Barone, Andrea; Fedi, Maurizio; Tizzani, Pietro

    2017-04-01

    Volcanic eruptions are generally preceded by unrest phenomena, which are characterized by variations in the geophysical and geochemical state of the system. The most evident unrest parameters are the spatial and temporal topographic changes, which typically result in uplift or subsidence of the volcano edifice, usually caused by magma accumulation or hot fluid concentration in shallow reservoirs (Denasoquo et al., 2009). If the observed ground deformation phenomenon is very quick and the time evolution of the process shows a linear tendency, we can approximate the problem by using an elastic rheology model of the crust beneath the volcano. In this scenario, by considering the elastic field theory under the Boussinesq (1885) and Love (1892) approximations, we can evaluate the displacement field induced by a generic source in a homogeneous, elastic, half-space at an arbitrary point. To this purpose, we use the depth to extreme points (DEXP) method. By using this approach, we are able to estimate the depth and the geometry of the active source, responsible of the observed ground deformation.

  13. Ab Initio Studies of Fluorine and Chlorine Oxide and Nitrogen Oxide Species of Interest in Stratospheric Chemistry

    NASA Technical Reports Server (NTRS)

    Lee, Timothy J.; Langhoff, Stephen R. (Technical Monitor)

    1995-01-01

    The quality of fundamental vibrational frequencies determined using the CCSD(T) method (singles and doubles coupled-cluster theory plus a perturbational estimate of the effects of connected triple excitations) is shown to be very good, usually predicting band centers to within plus or minus 8 per centimeter. This approach is applied to several molecules of interest in atmospheric chemistry, such as HNO, cis-FONO, cis-ClONO, and ClOOH. The HNO molecule displays a large and unusual anharmonicity in the H-N stretch. For the calculation of ultraviolet (UV) spectra, the linear response CCSD (LRCCSD) approach (which is equivalent to EOM-CCSD) has been shown to yield vertical excitation energies that are accurate to approximately equal to 0.1 eV for singly excited electronic states. This method together with more approximate methods is used to examine the UV spectra of several molecules important in stratospheric chemistry, including HOCl, Cl2O, ClONO2, HONO2, ClOOCl, ClOOH, and HOOH.

  14. Strain effects on the optical conductivity of gapped graphene in the presence of Holstein phonons beyond the Dirac cone approximation

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

    Yarmohammadi, Mohsen, E-mail: m.yarmohammadi69@gmail.com

    2016-08-15

    In this paper we study the optical conductivity and density of states (DOS) of doped gapped graphene beyond the Dirac cone approximation in the presence of electron-phonon (e-ph) interaction under strain, i.e., within the framework of a full π-band Holstein model, by using the Kubo linear response formalism that is established upon the retarded self-energy. A new peak in the optical conductivity for a large enough e-ph interaction strength is found which is associated to transitions between the midgap states and the Van Hove singularities of the main π-band. Optical conductivity decreases with strain and at large strains, the systemmore » has a zero optical conductivity at low energies due to optically inter-band excitations through the limit of zero doping. As a result, the Drude weight changes with e-ph interaction, temperature and strain. Consequently, DOS and optical conductivity remains stable with temperature at low e-ph coupling strengths.« less

  15. Conic Sector Analysis of Hybrid Control Systems. Ph.D. Thesis

    NASA Technical Reports Server (NTRS)

    Thompson, P. M.

    1982-01-01

    A hybrid control system contains an analog plant and a hybrid (or sampled-data) compensator. In this thesis a new conic sector is determined which is constructive and can be used to: (1) determine closed loop stability, (2) analyze robustness with respect to modelling uncertainties, (3) analyze steady state response to commands, and (4) select the sample rate. The use of conic sectors allows the designer to treat hybrid control systems as though they were analog control systems. The center of the conic sector can be used as a rigorous linear time invariant approximation of the hybrid control system, and the radius places a bound on the errors of this approximation. The hybrid feedback system can be multivariable, and the sampler is assumed to be synchronous. Algorithms to compute the conic sector are presented. Several examples demonstrate how the conic sector analysis techniques are applied. Extensions to single loop multirate hybrid feedback systems are presented. Further extensions are proposed for multiloop multirate hybrid feedback system and for single rate systems with asynchronous sampling.

  16. Evaluation of alternative snow plow cutting edges.

    DOT National Transportation Integrated Search

    2009-05-01

    With approximately 450 snow plow trucks, the Maine Department of Transportation (MaineDOT) uses in : excess of 10,000 linear feet of plow cutting edges each winter season. Using the 2008-2009 cost per linear : foot of $48.32, the Departments total co...

  17. Earthquake site response in Santa Cruz, California

    USGS Publications Warehouse

    Carver, D.; Hartzell, S.H.

    1996-01-01

    Aftershocks of the 1989 Loma Prieta, California, earthquake are used to estimate site response in a 12-km2 area centered on downtown Santa Cruz. A total of 258 S-wave records from 36 aftershocks recorded at 33 sites are used in a linear inversion for site-response spectra. The inversion scheme takes advantage of the redundancy of the large data set for which several aftershocks are recorded at each site. The scheme decomposes the observed spectra into source, path, and site terms. The path term is specified before the inversion. The undetermined degree of freedom in the decomposition into source and site spectra is removed by specifying the site-response factor to be approximately 1.0 at two sites on crystalline bedrock. The S-wave site responses correlate well with the surficial geology and observed damage pattern of the mainshock. The site-response spectra of the floodplain sites, which include the heavily damaged downtown area, exhibit significant peaks. The largest peaks are between 1 and 4 Hz. Five floodplain sites have amplification factors of 10 or greater. Most of the floodplain site-response spectra also have a smaller secondary peak between 6 and 8 Hz. Residential areas built on marine terraces above the flood-plain experienced much less severe damage. Site-response spectra for these areas also have their largest peaks between 1 and 4 Hz, but the amplification is generally below 6. Several of these sites also have a secondary peak between 6 and 8 Hz. The response peaks seen at nearly all sites between 1 and 4 Hz are probably caused by the natural resonance of the sedimentary rock column. The higher amplifications at floodplain sites may be caused by surface waves generated at the basin margins. The secondary peak between 6 and 8 Hz at many sites may be a harmonic of the 1- to 4-Hz peaks. We used waveforms from a seven-station approximately linear array located on the floodplain to calculate the apparent velocity and azimuth of propagation of coherent arrivals within moving windows of the S-wave codas. The initial windows give results that are consistent with direct S-wave arrivals. The apparent velocities are high (greater than 4.0 km/sec), and azimuths are from the source. Waves arriving later than 2 sec after the direct S waves have apparent velocities of less than 1 km/ sec, indicating that they are surface waves, and arrive from divergent azimuths. This analysis indicates that after the direct S-wave arrival, long-duration shaking comes from surface waves that are generated at the basin margin and reverberate in the floodplain sediments.

  18. Reduced linear noise approximation for biochemical reaction networks with time-scale separation: The stochastic tQSSA+

    NASA Astrophysics Data System (ADS)

    Herath, Narmada; Del Vecchio, Domitilla

    2018-03-01

    Biochemical reaction networks often involve reactions that take place on different time scales, giving rise to "slow" and "fast" system variables. This property is widely used in the analysis of systems to obtain dynamical models with reduced dimensions. In this paper, we consider stochastic dynamics of biochemical reaction networks modeled using the Linear Noise Approximation (LNA). Under time-scale separation conditions, we obtain a reduced-order LNA that approximates both the slow and fast variables in the system. We mathematically prove that the first and second moments of this reduced-order model converge to those of the full system as the time-scale separation becomes large. These mathematical results, in particular, provide a rigorous justification to the accuracy of LNA models derived using the stochastic total quasi-steady state approximation (tQSSA). Since, in contrast to the stochastic tQSSA, our reduced-order model also provides approximations for the fast variable stochastic properties, we term our method the "stochastic tQSSA+". Finally, we demonstrate the application of our approach on two biochemical network motifs found in gene-regulatory and signal transduction networks.

  19. Flexible polyurethane foam modelling and identification of viscoelastic parameters for automotive seating applications

    NASA Astrophysics Data System (ADS)

    Deng, R.; Davies, P.; Bajaj, A. K.

    2003-05-01

    A hereditary model and a fractional derivative model for the dynamic properties of flexible polyurethane foams used in automotive seat cushions are presented. Non-linear elastic and linear viscoelastic properties are incorporated into these two models. A polynomial function of compression is used to represent the non-linear elastic behavior. The viscoelastic property is modelled by a hereditary integral with a relaxation kernel consisting of two exponential terms in the hereditary model and by a fractional derivative term in the fractional derivative model. The foam is used as the only viscoelastic component in a foam-mass system undergoing uniaxial compression. One-term harmonic balance solutions are developed to approximate the steady state response of the foam-mass system to the harmonic base excitation. System identification procedures based on the direct non-linear optimization and a sub-optimal method are formulated to estimate the material parameters. The effects of the choice of the cost function, frequency resolution of data and imperfections in experiments are discussed. The system identification procedures are also applied to experimental data from a foam-mass system. The performances of the two models for data at different compression and input excitation levels are compared, and modifications to the structure of the fractional derivative model are briefly explored. The role of the viscous damping term in both types of model is discussed.

  20. Nonlinear and threshold of the association between meteorological factors and bacillary dysentery in Beijing, China.

    PubMed

    Li, Z J; Zhang, X J; Hou, X X; Xu, S; Zhang, J S; Song, H B; Lin, H L

    2015-12-01

    Previous studies examining the weather-bacillary dysentery association were of a large time scale (monthly or weekly) and examined the linear relationship without checking the linearity assumption. We examined this association in Beijing at a daily scale based on the exposure-response curves using generalized additive models. Our analyses suggested that there were thresholds for effects of temperature and relative humidity, with an approximately linear effect for temperature >12·5 °C [excess risk (ER) for 1 °C increase: 1·06%, 95% confidence interval (CI) 0·63-1·49 on lag day 3] and for relative humidity >40% (ER for 1% increase: 0·18%, 95% CI 0·12-0·24 at lag day 4); and there were linear effects of rainfall (ER for 1-mm increase: 0·22%, 95% CI 0·12-0·32), negative effects for wind speed (ER: -2·91%, 95% CI -4·28 to -1·52 at lag day 3) and sunshine duration (ER: -0·25% 95% CI -0·43 to -0·07 at lag day 4). This study suggests that there are thresholds for the effects of temperature and relative humidity on bacillary dysentery, and these findings should be considered in its prevention and control programmes.

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