Multivariable control of the Space Shuttle Remote Manipulator System using linearization by state feedback. M.S. Thesis

NASA Technical Reports Server (NTRS)

Gettman, Chang-Ching LO

1993-01-01

This thesis develops and demonstrates an approach to nonlinear control system design using linearization by state feedback. The design provides improved transient response behavior allowing faster maneuvering of payloads by the SRMS. Modeling uncertainty is accounted for by using a second feedback loop designed around the feedback linearized dynamics. A classical feedback loop is developed to provide the easy implementation required for the relatively small on board computers. Feedback linearization also allows the use of higher bandwidth model based compensation in the outer loop, since it helps maintain stability in the presence of the nonlinearities typically neglected in model based designs.

Path integral measure and triangulation independence in discrete gravity

NASA Astrophysics Data System (ADS)

Dittrich, Bianca; Steinhaus, Sebastian

2012-02-01

A path integral measure for gravity should also preserve the fundamental symmetry of general relativity, which is diffeomorphism symmetry. In previous work, we argued that a successful implementation of this symmetry into discrete quantum gravity models would imply discretization independence. We therefore consider the requirement of triangulation independence for the measure in (linearized) Regge calculus, which is a discrete model for quantum gravity, appearing in the semi-classical limit of spin foam models. To this end we develop a technique to evaluate the linearized Regge action associated to Pachner moves in 3D and 4D and show that it has a simple, factorized structure. We succeed in finding a local measure for 3D (linearized) Regge calculus that leads to triangulation independence. This measure factor coincides with the asymptotics of the Ponzano Regge Model, a 3D spin foam model for gravity. We furthermore discuss to which extent one can find a triangulation independent measure for 4D Regge calculus and how such a measure would be related to a quantum model for 4D flat space. To this end, we also determine the dependence of classical Regge calculus on the choice of triangulation in 3D and 4D.

Employment of CB models for non-linear dynamic analysis

NASA Technical Reports Server (NTRS)

Klein, M. R. M.; Deloo, P.; Fournier-Sicre, A.

1990-01-01

The non-linear dynamic analysis of large structures is always very time, effort and CPU consuming. Whenever possible the reduction of the size of the mathematical model involved is of main importance to speed up the computational procedures. Such reduction can be performed for the part of the structure which perform linearly. Most of the time, the classical Guyan reduction process is used. For non-linear dynamic process where the non-linearity is present at interfaces between different structures, Craig-Bampton models can provide a very rich information, and allow easy selection of the relevant modes with respect to the phenomenon driving the non-linearity. The paper presents the employment of Craig-Bampton models combined with Newmark direct integration for solving non-linear friction problems appearing at the interface between the Hubble Space Telescope and its solar arrays during in-orbit maneuvers. Theory, implementation in the FEM code ASKA, and practical results are shown.

An asymptotic Reissner-Mindlin plate model

NASA Astrophysics Data System (ADS)

Licht, Christian; Weller, Thibaut

2018-06-01

A mathematical study via variational convergence of a periodic distribution of classical linearly elastic thin plates softly abutted together shows that it is not necessary to use a different continuum model nor to make constitutive symmetry hypothesis as starting points to deduce the Reissner-Mindlin plate model.

Modeling the free energy surfaces of electron transfer in condensed phases

NASA Astrophysics Data System (ADS)

Matyushov, Dmitry V.; Voth, Gregory A.

2000-10-01

We develop a three-parameter model of electron transfer (ET) in condensed phases based on the Hamiltonian of a two-state solute linearly coupled to a harmonic, classical solvent mode with different force constants in the initial and final states (a classical limit of the quantum Kubo-Toyozawa model). The exact analytical solution for the ET free energy surfaces demonstrates the following features: (i) the range of ET reaction coordinates is limited by a one-sided fluctuation band, (ii) the ET free energies are infinite outside the band, and (iii) the free energy surfaces are parabolic close to their minima and linear far from the minima positions. The model provides an analytical framework to map physical phenomena conflicting with the Marcus-Hush two-parameter model of ET. Nonlinear solvation, ET in polarizable charge-transfer complexes, and configurational flexibility of donor-acceptor complexes are successfully mapped onto the model. The present theory leads to a significant modification of the energy gap law for ET reactions.

Features in visual search combine linearly

PubMed Central

Pramod, R. T.; Arun, S. P.

2014-01-01

Single features such as line orientation and length are known to guide visual search, but relatively little is known about how multiple features combine in search. To address this question, we investigated how search for targets differing in multiple features (intensity, length, orientation) from the distracters is related to searches for targets differing in each of the individual features. We tested race models (based on reaction times) and co-activation models (based on reciprocal of reaction times) for their ability to predict multiple feature searches. Multiple feature searches were best accounted for by a co-activation model in which feature information combined linearly (r = 0.95). This result agrees with the classic finding that these features are separable i.e., subjective dissimilarity ratings sum linearly. We then replicated the classical finding that the length and width of a rectangle are integral features—in other words, they combine nonlinearly in visual search. However, to our surprise, upon including aspect ratio as an additional feature, length and width combined linearly and this model outperformed all other models. Thus, length and width of a rectangle became separable when considered together with aspect ratio. This finding predicts that searches involving shapes with identical aspect ratio should be more difficult than searches where shapes differ in aspect ratio. We confirmed this prediction on a variety of shapes. We conclude that features in visual search co-activate linearly and demonstrate for the first time that aspect ratio is a novel feature that guides visual search. PMID:24715328

Statistical Methodology for the Analysis of Repeated Duration Data in Behavioral Studies

ERIC Educational Resources Information Center

Letué, Frédérique; Martinez, Marie-José; Samson, Adeline; Vilain, Anne; Vilain, Coriandre

2018-01-01

Purpose: Repeated duration data are frequently used in behavioral studies. Classical linear or log-linear mixed models are often inadequate to analyze such data, because they usually consist of nonnegative and skew-distributed variables. Therefore, we recommend use of a statistical methodology specific to duration data. Method: We propose a…

Effective model hierarchies for dynamic and static classical density functional theories

NASA Astrophysics Data System (ADS)

Majaniemi, S.; Provatas, N.; Nonomura, M.

2010-09-01

The origin and methodology of deriving effective model hierarchies are presented with applications to solidification of crystalline solids. In particular, it is discussed how the form of the equations of motion and the effective parameters on larger scales can be obtained from the more microscopic models. It will be shown that tying together the dynamic structure of the projection operator formalism with static classical density functional theories can lead to incomplete (mass) transport properties even though the linearized hydrodynamics on large scales is correctly reproduced. To facilitate a more natural way of binding together the dynamics of the macrovariables and classical density functional theory, a dynamic generalization of density functional theory based on the nonequilibrium generating functional is suggested.

Time Hierarchies and Model Reduction in Canonical Non-linear Models

PubMed Central

Löwe, Hannes; Kremling, Andreas; Marin-Sanguino, Alberto

2016-01-01

The time-scale hierarchies of a very general class of models in differential equations is analyzed. Classical methods for model reduction and time-scale analysis have been adapted to this formalism and a complementary method is proposed. A unified theoretical treatment shows how the structure of the system can be much better understood by inspection of two sets of singular values: one related to the stoichiometric structure of the system and another to its kinetics. The methods are exemplified first through a toy model, then a large synthetic network and finally with numeric simulations of three classical benchmark models of real biological systems. PMID:27708665

Reduced-order model based feedback control of the modified Hasegawa-Wakatani model

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

Goumiri, I. R.; Rowley, C. W.; Ma, Z.

2013-04-15

In this work, the development of model-based feedback control that stabilizes an unstable equilibrium is obtained for the Modified Hasegawa-Wakatani (MHW) equations, a classic model in plasma turbulence. First, a balanced truncation (a model reduction technique that has proven successful in flow control design problems) is applied to obtain a low dimensional model of the linearized MHW equation. Then, a model-based feedback controller is designed for the reduced order model using linear quadratic regulators. Finally, a linear quadratic Gaussian controller which is more resistant to disturbances is deduced. The controller is applied on the non-reduced, nonlinear MHW equations to stabilizemore » the equilibrium and suppress the transition to drift-wave induced turbulence.« less

Planck constant as spectral parameter in integrable systems and KZB equations

NASA Astrophysics Data System (ADS)

Levin, A.; Olshanetsky, M.; Zotov, A.

2014-10-01

We construct special rational gl N Knizhnik-Zamolodchikov-Bernard (KZB) equations with Ñ punctures by deformation of the corresponding quantum gl N rational R-matrix. They have two parameters. The limit of the first one brings the model to the ordinary rational KZ equation. Another one is τ. At the level of classical mechanics the deformation parameter τ allows to extend the previously obtained modified Gaudin models to the modified Schlesinger systems. Next, we notice that the identities underlying generic (elliptic) KZB equations follow from some additional relations for the properly normalized R-matrices. The relations are noncommutative analogues of identities for (scalar) elliptic functions. The simplest one is the unitarity condition. The quadratic (in R matrices) relations are generated by noncommutative Fay identities. In particular, one can derive the quantum Yang-Baxter equations from the Fay identities. The cubic relations provide identities for the KZB equations as well as quadratic relations for the classical r-matrices which can be treated as halves of the classical Yang-Baxter equation. At last we discuss the R-matrix valued linear problems which provide gl Ñ CM models and Painlevé equations via the above mentioned identities. The role of the spectral parameter plays the Planck constant of the quantum R-matrix. When the quantum gl N R-matrix is scalar ( N = 1) the linear problem reproduces the Krichever's ansatz for the Lax matrices with spectral parameter for the gl Ñ CM models. The linear problems for the quantum CM models generalize the KZ equations in the same way as the Lax pairs with spectral parameter generalize those without it.

Reduced-Order Model Based Feedback Control For Modified Hasegawa-Wakatani Model

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

Goumiri, I. R.; Rowley, C. W.; Ma, Z.

2013-01-28

In this work, the development of model-based feedback control that stabilizes an unstable equilibrium is obtained for the Modi ed Hasegawa-Wakatani (MHW) equations, a classic model in plasma turbulence. First, a balanced truncation (a model reduction technique that has proven successful in ow control design problems) is applied to obtain a low dimensional model of the linearized MHW equation. Then a modelbased feedback controller is designed for the reduced order model using linear quadratic regulators (LQR). Finally, a linear quadratic gaussian (LQG) controller, which is more resistant to disturbances is deduced. The controller is applied on the non-reduced, nonlinear MHWmore » equations to stabilize the equilibrium and suppress the transition to drift-wave induced turbulence.« less

Statistical Methodology for the Analysis of Repeated Duration Data in Behavioral Studies.

PubMed

Letué, Frédérique; Martinez, Marie-José; Samson, Adeline; Vilain, Anne; Vilain, Coriandre

2018-03-15

Repeated duration data are frequently used in behavioral studies. Classical linear or log-linear mixed models are often inadequate to analyze such data, because they usually consist of nonnegative and skew-distributed variables. Therefore, we recommend use of a statistical methodology specific to duration data. We propose a methodology based on Cox mixed models and written under the R language. This semiparametric model is indeed flexible enough to fit duration data. To compare log-linear and Cox mixed models in terms of goodness-of-fit on real data sets, we also provide a procedure based on simulations and quantile-quantile plots. We present two examples from a data set of speech and gesture interactions, which illustrate the limitations of linear and log-linear mixed models, as compared to Cox models. The linear models are not validated on our data, whereas Cox models are. Moreover, in the second example, the Cox model exhibits a significant effect that the linear model does not. We provide methods to select the best-fitting models for repeated duration data and to compare statistical methodologies. In this study, we show that Cox models are best suited to the analysis of our data set.

Analytic Methods for Adjusting Subjective Rating Schemes.

ERIC Educational Resources Information Center

Cooper, Richard V. L.; Nelson, Gary R.

Statistical and econometric techniques of correcting for supervisor bias in models of individual performance appraisal were developed, using a variant of the classical linear regression model. Location bias occurs when individual performance is systematically overestimated or underestimated, while scale bias results when raters either exaggerate…

Linear Quantum Systems: Non-Classical States and Robust Stability

DTIC Science & Technology

2016-06-29

quantum linear systems subject to non-classical quantum fields. The major outcomes of this project are (i) derivation of quantum filtering equations for...derivation of quantum filtering equations for systems non-classical input states including single photon states, (ii) determination of how linear...history going back some 50 years, to the birth of modern control theory with Kalman’s foundational work on filtering and LQG optimal control

New Equating Methods and Their Relationships with Levine Observed Score Linear Equating under the Kernel Equating Framework

ERIC Educational Resources Information Center

Chen, Haiwen; Holland, Paul

2010-01-01

In this paper, we develop a new curvilinear equating for the nonequivalent groups with anchor test (NEAT) design under the assumption of the classical test theory model, that we name curvilinear Levine observed score equating. In fact, by applying both the kernel equating framework and the mean preserving linear transformation of…

Regression Methods for Categorical Dependent Variables: Effects on a Model of Student College Choice

ERIC Educational Resources Information Center

Rapp, Kelly E.

2012-01-01

The use of categorical dependent variables with the classical linear regression model (CLRM) violates many of the model's assumptions and may result in biased estimates (Long, 1997; O'Connell, Goldstein, Rogers, & Peng, 2008). Many dependent variables of interest to educational researchers (e.g., professorial rank, educational attainment) are…

Modeling of flexible surfaces: A preliminary study

NASA Technical Reports Server (NTRS)

Banks, H. T.; Majda, G.

1983-01-01

The one-dimensional classical scalar string equation which involves linearization about a horizontal reference or equilibrium position is derived. We then derive a model for small motion about a nonhorizontal reference. The implications of our findings to modeling of flexible antenna surfaces such as that in the Maypole Hoop/Column antenna are discussed.

Onset of fractional-order thermal convection in porous media

NASA Astrophysics Data System (ADS)

Karani, Hamid; Rashtbehesht, Majid; Huber, Christian; Magin, Richard L.

2017-12-01

The macroscopic description of buoyancy-driven thermal convection in porous media is governed by advection-diffusion processes, which in the presence of thermophysical heterogeneities fail to predict the onset of thermal convection and the average rate of heat transfer. This work extends the classical model of heat transfer in porous media by including a fractional-order advective-dispersive term to account for the role of thermophysical heterogeneities in shifting the thermal instability point. The proposed fractional-order model overcomes limitations of the common closure approaches for the thermal dispersion term by replacing the diffusive assumption with a fractional-order model. Through a linear stability analysis and Galerkin procedure, we derive an analytical formula for the critical Rayleigh number as a function of the fractional model parameters. The resulting critical Rayleigh number reduces to the classical value in the absence of thermophysical heterogeneities when solid and fluid phases have similar thermal conductivities. Numerical simulations of the coupled flow equation with the fractional-order energy model near the primary bifurcation point confirm our analytical results. Moreover, data from pore-scale simulations are used to examine the potential of the proposed fractional-order model in predicting the amount of heat transfer across the porous enclosure. The linear stability and numerical results show that, unlike the classical thermal advection-dispersion models, the fractional-order model captures the advance and delay in the onset of convection in porous media and provides correct scalings for the average heat transfer in a thermophysically heterogeneous medium.

Effect Sizes for Growth-Modeling Analysis for Controlled Clinical Trials in the Same Metric as for Classical Analysis

ERIC Educational Resources Information Center

Feingold, Alan

2009-01-01

The use of growth-modeling analysis (GMA)--including hierarchical linear models, latent growth models, and general estimating equations--to evaluate interventions in psychology, psychiatry, and prevention science has grown rapidly over the last decade. However, an effect size associated with the difference between the trajectories of the…

Poster — Thur Eve — 46: Monte Carlo model of the Novalis Classic 6MV stereotactic linear accelerator using the GATE simulation platform

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

Wiebe, J; Department of Physics and Astronomy, University of Calgary, Calgary, AB; Ploquin, N

2014-08-15

Monte Carlo (MC) simulation is accepted as the most accurate method to predict dose deposition when compared to other methods in radiation treatment planning. Current dose calculation algorithms used for treatment planning can become inaccurate when small radiation fields and tissue inhomogeneities are present. At our centre the Novalis Classic linear accelerator (linac) is used for Stereotactic Radiosurgery (SRS). The first MC model to date of the Novalis Classic linac was developed at our centre using the Geant4 Application for Tomographic Emission (GATE) simulation platform. GATE is relatively new, open source MC software built from CERN's Geometry and Tracking 4more » (Geant4) toolkit. The linac geometry was modeled using manufacturer specifications, as well as in-house measurements of the micro MLC's. Among multiple model parameters, the initial electron beam was adjusted so that calculated depth dose curves agreed with measured values. Simulations were run on the European Grid Infrastructure through GateLab. Simulation time is approximately 8 hours on GateLab for a complete head model simulation to acquire a phase space file. Current results have a majority of points within 3% of the measured dose values for square field sizes ranging from 6×6 mm{sup 2} to 98×98 mm{sup 2} (maximum field size on the Novalis Classic linac) at 100 cm SSD. The x-ray spectrum was determined from the MC data as well. The model provides an investigation into GATE'S capabilities and has the potential to be used as a research tool and an independent dose calculation engine for clinical treatment plans.« less

Convergence analysis of the alternating RGLS algorithm for the identification of the reduced complexity Volterra model.

PubMed

Laamiri, Imen; Khouaja, Anis; Messaoud, Hassani

2015-03-01

In this paper we provide a convergence analysis of the alternating RGLS (Recursive Generalized Least Square) algorithm used for the identification of the reduced complexity Volterra model describing stochastic non-linear systems. The reduced Volterra model used is the 3rd order SVD-PARAFC-Volterra model provided using the Singular Value Decomposition (SVD) and the Parallel Factor (PARAFAC) tensor decomposition of the quadratic and the cubic kernels respectively of the classical Volterra model. The Alternating RGLS (ARGLS) algorithm consists on the execution of the classical RGLS algorithm in alternating way. The ARGLS convergence was proved using the Ordinary Differential Equation (ODE) method. It is noted that the algorithm convergence canno׳t be ensured when the disturbance acting on the system to be identified has specific features. The ARGLS algorithm is tested in simulations on a numerical example by satisfying the determined convergence conditions. To raise the elegies of the proposed algorithm, we proceed to its comparison with the classical Alternating Recursive Least Squares (ARLS) presented in the literature. The comparison has been built on a non-linear satellite channel and a benchmark system CSTR (Continuous Stirred Tank Reactor). Moreover the efficiency of the proposed identification approach is proved on an experimental Communicating Two Tank system (CTTS). Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

A new class of ensemble conserving algorithms for approximate quantum dynamics: Theoretical formulation and model problems.

PubMed

Smith, Kyle K G; Poulsen, Jens Aage; Nyman, Gunnar; Rossky, Peter J

2015-06-28

We develop two classes of quasi-classical dynamics that are shown to conserve the initial quantum ensemble when used in combination with the Feynman-Kleinert approximation of the density operator. These dynamics are used to improve the Feynman-Kleinert implementation of the classical Wigner approximation for the evaluation of quantum time correlation functions known as Feynman-Kleinert linearized path-integral. As shown, both classes of dynamics are able to recover the exact classical and high temperature limits of the quantum time correlation function, while a subset is able to recover the exact harmonic limit. A comparison of the approximate quantum time correlation functions obtained from both classes of dynamics is made with the exact results for the challenging model problems of the quartic and double-well potentials. It is found that these dynamics provide a great improvement over the classical Wigner approximation, in which purely classical dynamics are used. In a special case, our first method becomes identical to centroid molecular dynamics.

Bayesian dynamical systems modelling in the social sciences.

PubMed

Ranganathan, Shyam; Spaiser, Viktoria; Mann, Richard P; Sumpter, David J T

2014-01-01

Data arising from social systems is often highly complex, involving non-linear relationships between the macro-level variables that characterize these systems. We present a method for analyzing this type of longitudinal or panel data using differential equations. We identify the best non-linear functions that capture interactions between variables, employing Bayes factor to decide how many interaction terms should be included in the model. This method punishes overly complicated models and identifies models with the most explanatory power. We illustrate our approach on the classic example of relating democracy and economic growth, identifying non-linear relationships between these two variables. We show how multiple variables and variable lags can be accounted for and provide a toolbox in R to implement our approach.

General integrable n-level, many-mode Janes-Cummings-Dicke models and classical r-matrices with spectral parameters

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

Skrypnyk, T., E-mail: taras.skrypnyk@unimib.it, E-mail: tskrypnyk@imath.kiev.ua

Using the technique of classical r-matrices and quantum Lax operators, we construct the most general form of the quantum integrable “n-level, many-mode” spin-boson Jaynes-Cummings-Dicke-type hamiltonians describing an interaction of a molecule of N n-level atoms with many modes of electromagnetic field and containing, in general, additional non-linear interaction terms. We explicitly obtain the corresponding quantum Lax operators and spin-boson analogs of the generalized Gaudin hamiltonians and prove their quantum commutativity. We investigate symmetries of the obtained models that are associated with the geometric symmetries of the classical r-matrices and construct the corresponding algebra of quantum integrals. We consider in detailmore » three classes of non-skew-symmetric classical r-matrices with spectral parameters and explicitly obtain the corresponding quantum Lax operators and Jaynes-Cummings-Dicke-type hamiltonians depending on the considered r-matrix.« less

An accurate nonlinear stochastic model for MEMS-based inertial sensor error with wavelet networks

NASA Astrophysics Data System (ADS)

El-Diasty, Mohammed; El-Rabbany, Ahmed; Pagiatakis, Spiros

2007-12-01

The integration of Global Positioning System (GPS) with Inertial Navigation System (INS) has been widely used in many applications for positioning and orientation purposes. Traditionally, random walk (RW), Gauss-Markov (GM), and autoregressive (AR) processes have been used to develop the stochastic model in classical Kalman filters. The main disadvantage of classical Kalman filter is the potentially unstable linearization of the nonlinear dynamic system. Consequently, a nonlinear stochastic model is not optimal in derivative-based filters due to the expected linearization error. With a derivativeless-based filter such as the unscented Kalman filter or the divided difference filter, the filtering process of a complicated highly nonlinear dynamic system is possible without linearization error. This paper develops a novel nonlinear stochastic model for inertial sensor error using a wavelet network (WN). A wavelet network is a highly nonlinear model, which has recently been introduced as a powerful tool for modelling and prediction. Static and kinematic data sets are collected using a MEMS-based IMU (DQI-100) to develop the stochastic model in the static mode and then implement it in the kinematic mode. The derivativeless-based filtering method using GM, AR, and the proposed WN-based processes are used to validate the new model. It is shown that the first-order WN-based nonlinear stochastic model gives superior positioning results to the first-order GM and AR models with an overall improvement of 30% when 30 and 60 seconds GPS outages are introduced.

Frequency analysis via the method of moment functionals

NASA Technical Reports Server (NTRS)

Pearson, A. E.; Pan, J. Q.

1990-01-01

Several variants are presented of a linear-in-parameters least squares formulation for determining the transfer function of a stable linear system at specified frequencies given a finite set of Fourier series coefficients calculated from transient nonstationary input-output data. The basis of the technique is Shinbrot's classical method of moment functionals using complex Fourier based modulating functions to convert a differential equation model on a finite time interval into an algebraic equation which depends linearly on frequency-related parameters.

Linear regression analysis and its application to multivariate chromatographic calibration for the quantitative analysis of two-component mixtures.

PubMed

Dinç, Erdal; Ozdemir, Abdil

2005-01-01

Multivariate chromatographic calibration technique was developed for the quantitative analysis of binary mixtures enalapril maleate (EA) and hydrochlorothiazide (HCT) in tablets in the presence of losartan potassium (LST). The mathematical algorithm of multivariate chromatographic calibration technique is based on the use of the linear regression equations constructed using relationship between concentration and peak area at the five-wavelength set. The algorithm of this mathematical calibration model having a simple mathematical content was briefly described. This approach is a powerful mathematical tool for an optimum chromatographic multivariate calibration and elimination of fluctuations coming from instrumental and experimental conditions. This multivariate chromatographic calibration contains reduction of multivariate linear regression functions to univariate data set. The validation of model was carried out by analyzing various synthetic binary mixtures and using the standard addition technique. Developed calibration technique was applied to the analysis of the real pharmaceutical tablets containing EA and HCT. The obtained results were compared with those obtained by classical HPLC method. It was observed that the proposed multivariate chromatographic calibration gives better results than classical HPLC.

Stability margin of linear systems with parameters described by fuzzy numbers.

PubMed

Husek, Petr

2011-10-01

This paper deals with the linear systems with uncertain parameters described by fuzzy numbers. The problem of determining the stability margin of those systems with linear affine dependence of the coefficients of a characteristic polynomial on system parameters is studied. Fuzzy numbers describing the system parameters are allowed to be characterized by arbitrary nonsymmetric membership functions. An elegant solution, graphical in nature, based on generalization of the Tsypkin-Polyak plot is presented. The advantage of the presented approach over the classical robust concept is demonstrated on a control of the Fiat Dedra engine model and a control of the quarter car suspension model.

Binary ROCs in Perception and Recognition Memory Are Curved

ERIC Educational Resources Information Center

Dube, Chad; Rotello, Caren M.

2012-01-01

In recognition memory, a classic finding is that receiver operating characteristics (ROCs) are curvilinear. This has been taken to support the fundamental assumptions of signal detection theory (SDT) over discrete-state models such as the double high-threshold model (2HTM), which predicts linear ROCs. Recently, however, Broder and Schutz (2009)…

Does ℏ play a role in multidimensional spectroscopy? Reduced hierarchy equations of motion approach to molecular vibrations.

PubMed

Sakurai, Atsunori; Tanimura, Yoshitaka

2011-04-28

To investigate the role of quantum effects in vibrational spectroscopies, we have carried out numerically exact calculations of linear and nonlinear response functions for an anharmonic potential system nonlinearly coupled to a harmonic oscillator bath. Although one cannot carry out the quantum calculations of the response functions with full molecular dynamics (MD) simulations for a realistic system which consists of many molecules, it is possible to grasp the essence of the quantum effects on the vibrational spectra by employing a model Hamiltonian that describes an intra- or intermolecular vibrational motion in a condensed phase. The present model fully includes vibrational relaxation, while the stochastic model often used to simulate infrared spectra does not. We have employed the reduced quantum hierarchy equations of motion approach in the Wigner space representation to deal with nonperturbative, non-Markovian, and nonsecular system-bath interactions. Taking the classical limit of the hierarchy equations of motion, we have obtained the classical equations of motion that describe the classical dynamics under the same physical conditions as in the quantum case. By comparing the classical and quantum mechanically calculated linear and multidimensional spectra, we found that the profiles of spectra for a fast modulation case were similar, but different for a slow modulation case. In both the classical and quantum cases, we identified the resonant oscillation peak in the spectra, but the quantum peak shifted to the red compared with the classical one if the potential is anharmonic. The prominent quantum effect is the 1-2 transition peak, which appears only in the quantum mechanically calculated spectra as a result of anharmonicity in the potential or nonlinearity of the system-bath coupling. While the contribution of the 1-2 transition is negligible in the fast modulation case, it becomes important in the slow modulation case as long as the amplitude of the frequency fluctuation is small. Thus, we observed a distinct difference between the classical and quantum mechanically calculated multidimensional spectra in the slow modulation case where spectral diffusion plays a role. This fact indicates that one may not reproduce the experimentally obtained multidimensional spectrum for high-frequency vibrational modes based on classical molecular dynamics simulations if the modulation that arises from surrounding molecules is weak and slow. A practical way to overcome the difference between the classical and quantum simulations was discussed.

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.

The Weight of Euro Coins: Its Distribution Might Not Be as Normal as You Would Expect

ERIC Educational Resources Information Center

Shkedy, Ziv; Aerts, Marc; Callaert, Herman

2006-01-01

Classical regression models, ANOVA models and linear mixed models are just three examples (out of many) in which the normal distribution of the response is an essential assumption of the model. In this paper we use a dataset of 2000 euro coins containing information (up to the milligram) about the weight of each coin, to illustrate that the…

Factors associated with parasite dominance in fishes from Brazil.

PubMed

Amarante, Cristina Fernandes do; Tassinari, Wagner de Souza; Luque, Jose Luis; Pereira, Maria Julia Salim

2016-06-14

The present study used regression models to evaluate the existence of factors that may influence the numerical parasite dominance with an epidemiological approximation. A database including 3,746 fish specimens and their respective parasites were used to evaluate the relationship between parasite dominance and biotic characteristics inherent to the studied hosts and the parasite taxa. Multivariate, classical, and mixed effects linear regression models were fitted. The calculations were performed using R software (95% CI). In the fitting of the classical multiple linear regression model, freshwater and planktivorous fish species and body length, as well as the species of the taxa Trematoda, Monogenea, and Hirudinea, were associated with parasite dominance. However, the fitting of the mixed effects model showed that the body length of the host and the species of the taxa Nematoda, Trematoda, Monogenea, Hirudinea, and Crustacea were significantly associated with parasite dominance. Studies that consider specific biological aspects of the hosts and parasites should expand the knowledge regarding factors that influence the numerical dominance of fish in Brazil. The use of a mixed model shows, once again, the importance of the appropriate use of a model correlated with the characteristics of the data to obtain consistent results.

The Biharmonic Oscillator and Asymmetric Linear Potentials: From Classical Trajectories to Momentum-Space Probability Densities in the Extreme Quantum Limit

ERIC Educational Resources Information Center

Ruckle, L. J.; Belloni, M.; Robinett, R. W.

2012-01-01

The biharmonic oscillator and the asymmetric linear well are two confining power-law-type potentials for which complete bound-state solutions are possible in both classical and quantum mechanics. We examine these problems in detail, beginning with studies of their trajectories in position and momentum space, evaluation of the classical probability…

Development of a Linear Stirling Model with Varying Heat Inputs

NASA Technical Reports Server (NTRS)

Regan, Timothy F.; Lewandowski, Edward J.

2007-01-01

The linear model of the Stirling system developed by NASA Glenn Research Center (GRC) has been extended to include a user-specified heat input. Previously developed linear models were limited to the Stirling convertor and electrical load. They represented the thermodynamic cycle with pressure factors that remained constant. The numerical values of the pressure factors were generated by linearizing GRC s non-linear System Dynamic Model (SDM) of the convertor at a chosen operating point. The pressure factors were fixed for that operating point, thus, the model lost accuracy if a transition to a different operating point were simulated. Although the previous linear model was used in developing controllers that manipulated current, voltage, and piston position, it could not be used in the development of control algorithms that regulated hot-end temperature. This basic model was extended to include the thermal dynamics associated with a hot-end temperature that varies over time in response to external changes as well as to changes in the Stirling cycle. The linear model described herein includes not only dynamics of the piston, displacer, gas, and electrical circuit, but also the transient effects of the heater head thermal inertia. The linear version algebraically couples two separate linear dynamic models, one model of the Stirling convertor and one model of the thermal system, through the pressure factors. The thermal system model includes heat flow of heat transfer fluid, insulation loss, and temperature drops from the heat source to the Stirling convertor expansion space. The linear model was compared to a nonlinear model, and performance was very similar. The resulting linear model can be implemented in a variety of computing environments, and is suitable for analysis with classical and state space controls analysis techniques.

Multiple indicators, multiple causes measurement error models

DOE PAGES

Tekwe, Carmen D.; Carter, Randy L.; Cullings, Harry M.; ...

2014-06-25

Multiple indicators, multiple causes (MIMIC) models are often employed by researchers studying the effects of an unobservable latent variable on a set of outcomes, when causes of the latent variable are observed. There are times, however, when the causes of the latent variable are not observed because measurements of the causal variable are contaminated by measurement error. The objectives of this study are as follows: (i) to develop a novel model by extending the classical linear MIMIC model to allow both Berkson and classical measurement errors, defining the MIMIC measurement error (MIMIC ME) model; (ii) to develop likelihood-based estimation methodsmore » for the MIMIC ME model; and (iii) to apply the newly defined MIMIC ME model to atomic bomb survivor data to study the impact of dyslipidemia and radiation dose on the physical manifestations of dyslipidemia. Finally, as a by-product of our work, we also obtain a data-driven estimate of the variance of the classical measurement error associated with an estimate of the amount of radiation dose received by atomic bomb survivors at the time of their exposure.« less

Multiple Indicators, Multiple Causes Measurement Error Models

PubMed Central

Tekwe, Carmen D.; Carter, Randy L.; Cullings, Harry M.; Carroll, Raymond J.

2014-01-01

Multiple Indicators, Multiple Causes Models (MIMIC) are often employed by researchers studying the effects of an unobservable latent variable on a set of outcomes, when causes of the latent variable are observed. There are times however when the causes of the latent variable are not observed because measurements of the causal variable are contaminated by measurement error. The objectives of this paper are: (1) to develop a novel model by extending the classical linear MIMIC model to allow both Berkson and classical measurement errors, defining the MIMIC measurement error (MIMIC ME) model, (2) to develop likelihood based estimation methods for the MIMIC ME model, (3) to apply the newly defined MIMIC ME model to atomic bomb survivor data to study the impact of dyslipidemia and radiation dose on the physical manifestations of dyslipidemia. As a by-product of our work, we also obtain a data-driven estimate of the variance of the classical measurement error associated with an estimate of the amount of radiation dose received by atomic bomb survivors at the time of their exposure. PMID:24962535

Multiple indicators, multiple causes measurement error models

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

Tekwe, Carmen D.; Carter, Randy L.; Cullings, Harry M.

Multiple indicators, multiple causes (MIMIC) models are often employed by researchers studying the effects of an unobservable latent variable on a set of outcomes, when causes of the latent variable are observed. There are times, however, when the causes of the latent variable are not observed because measurements of the causal variable are contaminated by measurement error. The objectives of this study are as follows: (i) to develop a novel model by extending the classical linear MIMIC model to allow both Berkson and classical measurement errors, defining the MIMIC measurement error (MIMIC ME) model; (ii) to develop likelihood-based estimation methodsmore » for the MIMIC ME model; and (iii) to apply the newly defined MIMIC ME model to atomic bomb survivor data to study the impact of dyslipidemia and radiation dose on the physical manifestations of dyslipidemia. Finally, as a by-product of our work, we also obtain a data-driven estimate of the variance of the classical measurement error associated with an estimate of the amount of radiation dose received by atomic bomb survivors at the time of their exposure.« less

surrosurv: An R package for the evaluation of failure time surrogate endpoints in individual patient data meta-analyses of randomized clinical trials.

PubMed

Rotolo, Federico; Paoletti, Xavier; Michiels, Stefan

2018-03-01

Surrogate endpoints are attractive for use in clinical trials instead of well-established endpoints because of practical convenience. To validate a surrogate endpoint, two important measures can be estimated in a meta-analytic context when individual patient data are available: the R indiv 2 or the Kendall's τ at the individual level, and the R trial 2 at the trial level. We aimed at providing an R implementation of classical and well-established as well as more recent statistical methods for surrogacy assessment with failure time endpoints. We also intended incorporating utilities for model checking and visualization and data generating methods described in the literature to date. In the case of failure time endpoints, the classical approach is based on two steps. First, a Kendall's τ is estimated as measure of individual level surrogacy using a copula model. Then, the R trial 2 is computed via a linear regression of the estimated treatment effects; at this second step, the estimation uncertainty can be accounted for via measurement-error model or via weights. In addition to the classical approach, we recently developed an approach based on bivariate auxiliary Poisson models with individual random effects to measure the Kendall's τ and treatment-by-trial interactions to measure the R trial 2 . The most common data simulation models described in the literature are based on: copula models, mixed proportional hazard models, and mixture of half-normal and exponential random variables. The R package surrosurv implements the classical two-step method with Clayton, Plackett, and Hougaard copulas. It also allows to optionally adjusting the second-step linear regression for measurement-error. The mixed Poisson approach is implemented with different reduced models in addition to the full model. We present the package functions for estimating the surrogacy models, for checking their convergence, for performing leave-one-trial-out cross-validation, and for plotting the results. We illustrate their use in practice on individual patient data from a meta-analysis of 4069 patients with advanced gastric cancer from 20 trials of chemotherapy. The surrosurv package provides an R implementation of classical and recent statistical methods for surrogacy assessment of failure time endpoints. Flexible simulation functions are available to generate data according to the methods described in the literature. Copyright © 2017 Elsevier B.V. All rights reserved.

Experimental quantum computing to solve systems of linear equations.

PubMed

Cai, X-D; Weedbrook, C; Su, Z-E; Chen, M-C; Gu, Mile; Zhu, M-J; Li, Li; Liu, Nai-Le; Lu, Chao-Yang; Pan, Jian-Wei

2013-06-07

Solving linear systems of equations is ubiquitous in all areas of science and engineering. With rapidly growing data sets, such a task can be intractable for classical computers, as the best known classical algorithms require a time proportional to the number of variables N. A recently proposed quantum algorithm shows that quantum computers could solve linear systems in a time scale of order log(N), giving an exponential speedup over classical computers. Here we realize the simplest instance of this algorithm, solving 2×2 linear equations for various input vectors on a quantum computer. We use four quantum bits and four controlled logic gates to implement every subroutine required, demonstrating the working principle of this algorithm.

From integrability to conformal symmetry: Bosonic superconformal Toda theories

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

Bo-Yu Hou; Liu Chao

In this paper the authors study the conformal integrable models obtained from conformal reductions of WZNW theory associated with second order constraints. These models are called bosonic superconformal Toda models due to their conformal spectra and their resemblance to the usual Toda theories. From the reduction procedure they get the equations of motion and the linearized Lax equations in a generic Z gradation of the underlying Lie algebra. Then, in the special case of principal gradation, they derive the classical r matrix, fundamental Poisson relation, exchange algebra of chiral operators and find out the classical vertex operators. The result showsmore » that their model is very similar to the ordinary Toda theories in that one can obtain various conformal properties of the model from its integrability.« less

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.

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.

Development of a Linear Stirling System Model with Varying Heat Inputs

NASA Technical Reports Server (NTRS)

Regan, Timothy F.; Lewandowski, Edward J.

2007-01-01

The linear model of the Stirling system developed by NASA Glenn Research Center (GRC) has been extended to include a user-specified heat input. Previously developed linear models were limited to the Stirling convertor and electrical load. They represented the thermodynamic cycle with pressure factors that remained constant. The numerical values of the pressure factors were generated by linearizing GRC's nonlinear System Dynamic Model (SDM) of the convertor at a chosen operating point. The pressure factors were fixed for that operating point, thus, the model lost accuracy if a transition to a different operating point were simulated. Although the previous linear model was used in developing controllers that manipulated current, voltage, and piston position, it could not be used in the development of control algorithms that regulated hot-end temperature. This basic model was extended to include the thermal dynamics associated with a hot-end temperature that varies over time in response to external changes as well as to changes in the Stirling cycle. The linear model described herein includes not only dynamics of the piston, displacer, gas, and electrical circuit, but also the transient effects of the heater head thermal inertia. The linear version algebraically couples two separate linear dynamic models, one model of the Stirling convertor and one model of the thermal system, through the pressure factors. The thermal system model includes heat flow of heat transfer fluid, insulation loss, and temperature drops from the heat source to the Stirling convertor expansion space. The linear model was compared to a nonlinear model, and performance was very similar. The resulting linear model can be implemented in a variety of computing environments, and is suitable for analysis with classical and state space controls analysis techniques.

Mixtures of Berkson and classical covariate measurement error in the linear mixed model: Bias analysis and application to a study on ultrafine particles.

PubMed

Deffner, Veronika; Küchenhoff, Helmut; Breitner, Susanne; Schneider, Alexandra; Cyrys, Josef; Peters, Annette

2018-05-01

The ultrafine particle measurements in the Augsburger Umweltstudie, a panel study conducted in Augsburg, Germany, exhibit measurement error from various sources. Measurements of mobile devices show classical possibly individual-specific measurement error; Berkson-type error, which may also vary individually, occurs, if measurements of fixed monitoring stations are used. The combination of fixed site and individual exposure measurements results in a mixture of the two error types. We extended existing bias analysis approaches to linear mixed models with a complex error structure including individual-specific error components, autocorrelated errors, and a mixture of classical and Berkson error. Theoretical considerations and simulation results show, that autocorrelation may severely change the attenuation of the effect estimations. Furthermore, unbalanced designs and the inclusion of confounding variables influence the degree of attenuation. Bias correction with the method of moments using data with mixture measurement error partially yielded better results compared to the usage of incomplete data with classical error. Confidence intervals (CIs) based on the delta method achieved better coverage probabilities than those based on Bootstrap samples. Moreover, we present the application of these new methods to heart rate measurements within the Augsburger Umweltstudie: the corrected effect estimates were slightly higher than their naive equivalents. The substantial measurement error of ultrafine particle measurements has little impact on the results. The developed methodology is generally applicable to longitudinal data with measurement error. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Testing a single regression coefficient in high dimensional linear models

PubMed Central

Zhong, Ping-Shou; Li, Runze; Wang, Hansheng; Tsai, Chih-Ling

2017-01-01

In linear regression models with high dimensional data, the classical z-test (or t-test) for testing the significance of each single regression coefficient is no longer applicable. This is mainly because the number of covariates exceeds the sample size. In this paper, we propose a simple and novel alternative by introducing the Correlated Predictors Screening (CPS) method to control for predictors that are highly correlated with the target covariate. Accordingly, the classical ordinary least squares approach can be employed to estimate the regression coefficient associated with the target covariate. In addition, we demonstrate that the resulting estimator is consistent and asymptotically normal even if the random errors are heteroscedastic. This enables us to apply the z-test to assess the significance of each covariate. Based on the p-value obtained from testing the significance of each covariate, we further conduct multiple hypothesis testing by controlling the false discovery rate at the nominal level. Then, we show that the multiple hypothesis testing achieves consistent model selection. Simulation studies and empirical examples are presented to illustrate the finite sample performance and the usefulness of the proposed method, respectively. PMID:28663668

Testing a single regression coefficient in high dimensional linear models.

PubMed

Lan, Wei; Zhong, Ping-Shou; Li, Runze; Wang, Hansheng; Tsai, Chih-Ling

2016-11-01

In linear regression models with high dimensional data, the classical z -test (or t -test) for testing the significance of each single regression coefficient is no longer applicable. This is mainly because the number of covariates exceeds the sample size. In this paper, we propose a simple and novel alternative by introducing the Correlated Predictors Screening (CPS) method to control for predictors that are highly correlated with the target covariate. Accordingly, the classical ordinary least squares approach can be employed to estimate the regression coefficient associated with the target covariate. In addition, we demonstrate that the resulting estimator is consistent and asymptotically normal even if the random errors are heteroscedastic. This enables us to apply the z -test to assess the significance of each covariate. Based on the p -value obtained from testing the significance of each covariate, we further conduct multiple hypothesis testing by controlling the false discovery rate at the nominal level. Then, we show that the multiple hypothesis testing achieves consistent model selection. Simulation studies and empirical examples are presented to illustrate the finite sample performance and the usefulness of the proposed method, respectively.

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

Self-organizing linear output map (SOLO): An artificial neural network suitable for hydrologic modeling and analysis

NASA Astrophysics Data System (ADS)

Hsu, Kuo-Lin; Gupta, Hoshin V.; Gao, Xiaogang; Sorooshian, Soroosh; Imam, Bisher

2002-12-01

Artificial neural networks (ANNs) can be useful in the prediction of hydrologic variables, such as streamflow, particularly when the underlying processes have complex nonlinear interrelationships. However, conventional ANN structures suffer from network training issues that significantly limit their widespread application. This paper presents a multivariate ANN procedure entitled self-organizing linear output map (SOLO), whose structure has been designed for rapid, precise, and inexpensive estimation of network structure/parameters and system outputs. More important, SOLO provides features that facilitate insight into the underlying processes, thereby extending its usefulness beyond forecast applications as a tool for scientific investigations. These characteristics are demonstrated using a classic rainfall-runoff forecasting problem. Various aspects of model performance are evaluated in comparison with other commonly used modeling approaches, including multilayer feedforward ANNs, linear time series modeling, and conceptual rainfall-runoff modeling.

Analysis of stall flutter of a helicopter radar blade

NASA Technical Reports Server (NTRS)

Crimi, P.

1973-01-01

A study of rotor blade aeroelastic stability was carried out, using an analytic model of a two-dimensional airfoil undergoing dynamic stall and an elastomechanical representation including flapping, flapwise bending and torsional degrees of freedom. Results for a hovering rotor demonstrated that the models used are capable of reproducing both classical and stall flutter. The minimum rotor speed for the occurrence of stall flutter in hover, was found to be determined from coupling between torsion and flapping. Instabilities analogous to both classical and stall flutter were found to occur in forward flight. However, the large stall-related torsional oscillations which commonly limit aircraft forward speed appear to be the response to rapid changes in aerodynamic moment which accompany stall and unstall, rather than the result of an aeroelastic instability. The severity of stall-related instabilities and response was found to depend to some extent on linear stability. Increasing linear stability lessens the susceptibility to stall flutter and reduced the magnitude of the torsional response to stall and unstall.

Phylogenetic mixtures and linear invariants for equal input models.

PubMed

Casanellas, Marta; Steel, Mike

2017-04-01

The reconstruction of phylogenetic trees from molecular sequence data relies on modelling site substitutions by a Markov process, or a mixture of such processes. In general, allowing mixed processes can result in different tree topologies becoming indistinguishable from the data, even for infinitely long sequences. However, when the underlying Markov process supports linear phylogenetic invariants, then provided these are sufficiently informative, the identifiability of the tree topology can be restored. In this paper, we investigate a class of processes that support linear invariants once the stationary distribution is fixed, the 'equal input model'. This model generalizes the 'Felsenstein 1981' model (and thereby the Jukes-Cantor model) from four states to an arbitrary number of states (finite or infinite), and it can also be described by a 'random cluster' process. We describe the structure and dimension of the vector spaces of phylogenetic mixtures and of linear invariants for any fixed phylogenetic tree (and for all trees-the so called 'model invariants'), on any number n of leaves. We also provide a precise description of the space of mixtures and linear invariants for the special case of [Formula: see text] leaves. By combining techniques from discrete random processes and (multi-) linear algebra, our results build on a classic result that was first established by James Lake (Mol Biol Evol 4:167-191, 1987).

OPLS statistical model versus linear regression to assess sonographic predictors of stroke prognosis.

PubMed

Vajargah, Kianoush Fathi; Sadeghi-Bazargani, Homayoun; Mehdizadeh-Esfanjani, Robab; Savadi-Oskouei, Daryoush; Farhoudi, Mehdi

2012-01-01

The objective of the present study was to assess the comparable applicability of orthogonal projections to latent structures (OPLS) statistical model vs traditional linear regression in order to investigate the role of trans cranial doppler (TCD) sonography in predicting ischemic stroke prognosis. The study was conducted on 116 ischemic stroke patients admitted to a specialty neurology ward. The Unified Neurological Stroke Scale was used once for clinical evaluation on the first week of admission and again six months later. All data was primarily analyzed using simple linear regression and later considered for multivariate analysis using PLS/OPLS models through the SIMCA P+12 statistical software package. The linear regression analysis results used for the identification of TCD predictors of stroke prognosis were confirmed through the OPLS modeling technique. Moreover, in comparison to linear regression, the OPLS model appeared to have higher sensitivity in detecting the predictors of ischemic stroke prognosis and detected several more predictors. Applying the OPLS model made it possible to use both single TCD measures/indicators and arbitrarily dichotomized measures of TCD single vessel involvement as well as the overall TCD result. In conclusion, the authors recommend PLS/OPLS methods as complementary rather than alternative to the available classical regression models such as linear regression.

Estimating and testing interactions when explanatory variables are subject to non-classical measurement error.

PubMed

Murad, Havi; Kipnis, Victor; Freedman, Laurence S

2016-10-01

Assessing interactions in linear regression models when covariates have measurement error (ME) is complex.We previously described regression calibration (RC) methods that yield consistent estimators and standard errors for interaction coefficients of normally distributed covariates having classical ME. Here we extend normal based RC (NBRC) and linear RC (LRC) methods to a non-classical ME model, and describe more efficient versions that combine estimates from the main study and internal sub-study. We apply these methods to data from the Observing Protein and Energy Nutrition (OPEN) study. Using simulations we show that (i) for normally distributed covariates efficient NBRC and LRC were nearly unbiased and performed well with sub-study size ≥200; (ii) efficient NBRC had lower MSE than efficient LRC; (iii) the naïve test for a single interaction had type I error probability close to the nominal significance level, whereas efficient NBRC and LRC were slightly anti-conservative but more powerful; (iv) for markedly non-normal covariates, efficient LRC yielded less biased estimators with smaller variance than efficient NBRC. Our simulations suggest that it is preferable to use: (i) efficient NBRC for estimating and testing interaction effects of normally distributed covariates and (ii) efficient LRC for estimating and testing interactions for markedly non-normal covariates. © The Author(s) 2013.

Tutorial: Asteroseismic Stellar Modelling with AIMS

NASA Astrophysics Data System (ADS)

Lund, Mikkel N.; Reese, Daniel R.

The goal of aims (Asteroseismic Inference on a Massive Scale) is to estimate stellar parameters and credible intervals/error bars in a Bayesian manner from a set of asteroseismic frequency data and so-called classical constraints. To achieve reliable parameter estimates and computational efficiency, it searches through a grid of pre-computed models using an MCMC algorithm—interpolation within the grid of models is performed by first tessellating the grid using a Delaunay triangulation and then doing a linear barycentric interpolation on matching simplexes. Inputs for the modelling consist of individual frequencies from peak-bagging, which can be complemented with classical spectroscopic constraints. aims is mostly written in Python with a modular structure to facilitate contributions from the community. Only a few computationally intensive parts have been rewritten in Fortran in order to speed up calculations.

The Fisher-KPP problem with doubly nonlinear diffusion

NASA Astrophysics Data System (ADS)

Audrito, Alessandro; Vázquez, Juan Luis

2017-12-01

The famous Fisher-KPP reaction-diffusion model combines linear diffusion with the typical KPP reaction term, and appears in a number of relevant applications in biology and chemistry. It is remarkable as a mathematical model since it possesses a family of travelling waves that describe the asymptotic behaviour of a large class solutions 0 ≤ u (x , t) ≤ 1 of the problem posed in the real line. The existence of propagation waves with finite speed has been confirmed in some related models and disproved in others. We investigate here the corresponding theory when the linear diffusion is replaced by the "slow" doubly nonlinear diffusion and we find travelling waves that represent the wave propagation of more general solutions even when we extend the study to several space dimensions. A similar study is performed in the critical case that we call "pseudo-linear", i.e., when the operator is still nonlinear but has homogeneity one. With respect to the classical model and the "pseudo-linear" case, the "slow" travelling waves exhibit free boundaries.

Dielectric response in Bloch’s hydrodynamic model of an electron-ion plasma

NASA Astrophysics Data System (ADS)

Ishikawa, K.; Felderhof, B. U.

The linear response of an electron-ion plasma to an applied oscillating electric field is studied within the framework of Bloch’s classical hydrodynamic model. The ions are assumed to be fixed in space and distributed according to a known probability distribution. The linearized equations of motion for electron density and flow velocity are studied with the aid of a multiple scattering analysis and cluster expansion. This allows systematic reduction of the many-ion problem to a composition of few-ion problems, and shows how the longitudinal dielectric response function can in principle be calculated.

Principal Curves on Riemannian Manifolds.

PubMed

Hauberg, Soren

2016-09-01

Euclidean statistics are often generalized to Riemannian manifolds by replacing straight-line interpolations with geodesic ones. While these Riemannian models are familiar-looking, they are restricted by the inflexibility of geodesics, and they rely on constructions which are optimal only in Euclidean domains. We consider extensions of Principal Component Analysis (PCA) to Riemannian manifolds. Classic Riemannian approaches seek a geodesic curve passing through the mean that optimizes a criteria of interest. The requirements that the solution both is geodesic and must pass through the mean tend to imply that the methods only work well when the manifold is mostly flat within the support of the generating distribution. We argue that instead of generalizing linear Euclidean models, it is more fruitful to generalize non-linear Euclidean models. Specifically, we extend the classic Principal Curves from Hastie & Stuetzle to data residing on a complete Riemannian manifold. We show that for elliptical distributions in the tangent of spaces of constant curvature, the standard principal geodesic is a principal curve. The proposed model is simple to compute and avoids many of the pitfalls of traditional geodesic approaches. We empirically demonstrate the effectiveness of the Riemannian principal curves on several manifolds and datasets.

A generalization of the Becker model in linear viscoelasticity: creep, relaxation and internal friction

NASA Astrophysics Data System (ADS)

Mainardi, Francesco; Masina, Enrico; Spada, Giorgio

2018-02-01

We present a new rheological model depending on a real parameter ν \\in [0,1], which reduces to the Maxwell body for ν =0 and to the Becker body for ν =1. The corresponding creep law is expressed in an integral form in which the exponential function of the Becker model is replaced and generalized by a Mittag-Leffler function of order ν . Then the corresponding non-dimensional creep function and its rate are studied as functions of time for different values of ν in order to visualize the transition from the classical Maxwell body to the Becker body. Based on the hereditary theory of linear viscoelasticity, we also approximate the relaxation function by solving numerically a Volterra integral equation of the second kind. In turn, the relaxation function is shown versus time for different values of ν to visualize again the transition from the classical Maxwell body to the Becker body. Furthermore, we provide a full characterization of the new model by computing, in addition to the creep and relaxation functions, the so-called specific dissipation Q^{-1} as a function of frequency, which is of particular relevance for geophysical applications.

Simulation of Blast Loading on an Ultrastructurally-based Computational Model of the Ocular Lens

DTIC Science & Technology

2016-12-01

organelles. Additionally, the cell membranes demonstrated the classic ball-and-socket loops . For the SEM images, they were placed in two fixatives and mounted...considered (fibrous network and matrix), both components are modelled using a hyper - elastic framework, and the resulting constitutive model is embedded in a...within the framework of hyper - elasticity). Full details on the linearization procedures that were adopted in these previous models or the convergence

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.

Classical Michaelis-Menten and system theory approach to modeling metabolite formation kinetics.

PubMed

Popović, Jovan

2004-01-01

When single doses of drug are administered and kinetics are linear, techniques, which are based on the compartment approach and the linear system theory approach, in modeling the formation of the metabolite from the parent drug are proposed. Unlike the purpose-specific compartment approach, the methodical, conceptual and computational uniformity in modeling various linear biomedical systems is the dominant characteristic of the linear system approach technology. Saturation of the metabolic reaction results in nonlinear kinetics according to the Michaelis-Menten equation. The two compartment open model with Michaelis-Menten elimination kinetics is theorethicaly basic when single doses of drug are administered. To simulate data or to fit real data using this model, one must resort to numerical integration. A biomathematical model for multiple dosage regimen calculations of nonlinear metabolic systems in steady-state and a working example with phenytoin are presented. High correlation between phenytoin steady-state serum levels calculated from individual Km and Vmax values in the 15 adult epileptic outpatients and the observed levels at the third adjustment of phenytoin daily dose (r=0.961, p<0.01) were found.

Reductions in finite-dimensional integrable systems and special points of classical r-matrices

NASA Astrophysics Data System (ADS)

Skrypnyk, T.

2016-12-01

For a given 𝔤 ⊗ 𝔤-valued non-skew-symmetric non-dynamical classical r-matrices r(u, v) with spectral parameters, we construct the general form of 𝔤-valued Lax matrices of finite-dimensional integrable systems satisfying linear r-matrix algebra. We show that the reduction in the corresponding finite-dimensional integrable systems is connected with "the special points" of the classical r-matrices in which they become degenerated. We also propose a systematic way of the construction of additional integrals of the Lax-integrable systems associated with the symmetries of the corresponding r-matrices. We consider examples of the Lax matrices and integrable systems that are obtained in the framework of the general scheme. Among them there are such physically important systems as generalized Gaudin systems in an external magnetic field, ultimate integrable generalization of Toda-type chains (including "modified" or "deformed" Toda chains), generalized integrable Jaynes-Cummings-Dicke models, integrable boson models generalizing Bose-Hubbard dimer models, etc.

Time Domain Stability Margin Assessment Method

NASA Technical Reports Server (NTRS)

Clements, Keith

2017-01-01

The baseline stability margins for NASA's Space Launch System (SLS) launch vehicle were generated via the classical approach of linearizing the system equations of motion and determining the gain and phase margins from the resulting frequency domain model. To improve the fidelity of the classical methods, the linear frequency domain approach can be extended by replacing static, memoryless nonlinearities with describing functions. This technique, however, does not address the time varying nature of the dynamics of a launch vehicle in flight. An alternative technique for the evaluation of the stability of the nonlinear launch vehicle dynamics along its trajectory is to incrementally adjust the gain and/or time delay in the time domain simulation until the system exhibits unstable behavior. This technique has the added benefit of providing a direct comparison between the time domain and frequency domain tools in support of simulation validation.

Time-Domain Stability Margin Assessment

NASA Technical Reports Server (NTRS)

Clements, Keith

2016-01-01

The baseline stability margins for NASA's Space Launch System (SLS) launch vehicle were generated via the classical approach of linearizing the system equations of motion and determining the gain and phase margins from the resulting frequency domain model. To improve the fidelity of the classical methods, the linear frequency domain approach can be extended by replacing static, memoryless nonlinearities with describing functions. This technique, however, does not address the time varying nature of the dynamics of a launch vehicle in flight. An alternative technique for the evaluation of the stability of the nonlinear launch vehicle dynamics along its trajectory is to incrementally adjust the gain and/or time delay in the time domain simulation until the system exhibits unstable behavior. This technique has the added benefit of providing a direct comparison between the time domain and frequency domain tools in support of simulation validation.

Development and application of a local linearization algorithm for the integration of quaternion rate equations in real-time flight simulation problems

NASA Technical Reports Server (NTRS)

Barker, L. E., Jr.; Bowles, R. L.; Williams, L. H.

1973-01-01

High angular rates encountered in real-time flight simulation problems may require a more stable and accurate integration method than the classical methods normally used. A study was made to develop a general local linearization procedure of integrating dynamic system equations when using a digital computer in real-time. The procedure is specifically applied to the integration of the quaternion rate equations. For this application, results are compared to a classical second-order method. The local linearization approach is shown to have desirable stability characteristics and gives significant improvement in accuracy over the classical second-order integration methods.

An algebraic method for constructing stable and consistent autoregressive filters

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

Harlim, John, E-mail: jharlim@psu.edu; Department of Meteorology, the Pennsylvania State University, University Park, PA 16802; Hong, Hoon, E-mail: hong@ncsu.edu

2015-02-15

In this paper, we introduce an algebraic method to construct stable and consistent univariate autoregressive (AR) models of low order for filtering and predicting nonlinear turbulent signals with memory depth. By stable, we refer to the classical stability condition for the AR model. By consistent, we refer to the classical consistency constraints of Adams–Bashforth methods of order-two. One attractive feature of this algebraic method is that the model parameters can be obtained without directly knowing any training data set as opposed to many standard, regression-based parameterization methods. It takes only long-time average statistics as inputs. The proposed method provides amore » discretization time step interval which guarantees the existence of stable and consistent AR model and simultaneously produces the parameters for the AR models. In our numerical examples with two chaotic time series with different characteristics of decaying time scales, we find that the proposed AR models produce significantly more accurate short-term predictive skill and comparable filtering skill relative to the linear regression-based AR models. These encouraging results are robust across wide ranges of discretization times, observation times, and observation noise variances. Finally, we also find that the proposed model produces an improved short-time prediction relative to the linear regression-based AR-models in forecasting a data set that characterizes the variability of the Madden–Julian Oscillation, a dominant tropical atmospheric wave pattern.« less

Linearization of digital derived rate algorithm for use in linear stability analysis

NASA Technical Reports Server (NTRS)

Graham, R. E.; Porada, T. W.

1985-01-01

The digital derived rate (DDR) algorithm is used to calculate the rate of rotation of the Centaur upper-stage rocket. The DDR is highly nonlinear algorithm, and classical linear stability analysis of the spacecraft cannot be performed without linearization. The performance of this rate algorithm is characterized by a gain and phase curve that drop off at the same frequency. This characteristic is desirable for many applications. A linearization technique for the DDR algorithm is investigated. The linearization method is described. Examples of the results of the linearization technique are illustrated, and the effects of linearization are described. A linear digital filter may be used as a substitute for performing classical linear stability analyses, while the DDR itself may be used in time response analysis.

A theoretical framework for constructing elastic/plastic constitutive models of triaxial tests

NASA Astrophysics Data System (ADS)

Collins, Ian F.; Hilder, Tamsyn

2002-11-01

Modern ideas of thermomechanics are used to develop families of models describing the elastic/plastic behaviour of cohesionless soils deforming under triaxial conditions. Once the form of the free energy and dissipation potential functions have been specified, the corresponding yield loci, flow rules, isotropic and kinematic hardening rules as well as the elasticity law are deduced in a systematic manner. The families contain the classical linear frictional (Coulomb type) models and the classical critical state models as special cases. The generalized models discussed here include non-associated flow rules, shear as well as volumetric hardening, anisotropic responses and rotational yield loci. The various parameters needed to describe the models can be interpreted in terms of ratio of the plastic work, which is dissipated, to that which is stored. Non-associated behaviour is found to occur whenever this division between dissipated and stored work is not equal. Micro-level interpretations of stored plastic work are discussed. The models automatically satisfy the laws of thermodynamics, and there is no need to invoke any stability postulates. Some classical forms of the peak-strength/dilatancy relationship are established theoretically. Some representative drained and undrained paths are computed.

Neuroimaging Research: from Null-Hypothesis Falsification to Out-Of-Sample Generalization

ERIC Educational Resources Information Center

Bzdok, Danilo; Varoquaux, Gaël; Thirion, Bertrand

2017-01-01

Brain-imaging technology has boosted the quantification of neurobiological phenomena underlying human mental operations and their disturbances. Since its inception, drawing inference on neurophysiological effects hinged on classical statistical methods, especially, the general linear model. The tens of thousands of variables per brain scan were…

Integrability and correspondence of classical and quantum non-linear three-mode systems

NASA Astrophysics Data System (ADS)

Odzijewicz, A.; Wawreniuk, E.

2018-04-01

The relationship between classical and quantum three one-mode systems interacting in a non-linear way is described. We investigate the integrability of these systems by using the reduction procedure. The reduced coherent states for the quantum system are constructed. We find the explicit formulas for the reproducing measure for these states. Examples of some applications of the obtained results in non-linear quantum optics are presented.

Limiting Surface Density Method Adapted to Large Arrays of Heterogeneous Shipping Packages with Nonlinear Responses

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

Stover, Tracy E.; Baker, James S.; Ratliff, Michael D.

The classic Limiting Surface Density (LSD) method is an empirical calculation technique for analyzing and setting mass limits for fissile items in storage arrays. LSD is a desirable method because it can reduce or eliminate the need for lengthy detailed Monte Carlo models of storage arrays. The original (or classic) method was developed based on idealized arrays of bare spherical metal items in air-spaced cubic units in a water-reflected cubic array. In this case, the geometric and material-based surface densities were acceptably correlated by linear functions. Later updates to the method were made to allow for concrete reflection rather thanmore » water, cylindrical masses rather than spheres, different material forms, and noncubic arrays. However, in the intervening four decades since those updates, little work has been done to update the method, especially for use with contemporary highly heterogeneous shipping packages that are noncubic and stored in noncubic arrays. In this work, the LSD method is reevaluated for application to highly heterogeneous shipping packages for fissile material. The package modeled is the 9975 shipping package, currently the primary package used to store fissile material at Savannah River Site’s K-Area Complex. The package is neither cubic nor rectangular but resembles nested cylinders of stainless steel, lead, aluminum, and Celotex. The fissile content is assumed to be a cylinder of plutonium metal. The packages may be arranged in arrays with both an equal number of packages per side (package cubic) and an unequal number of packages per side (noncubic). The cubic arrangements are used to derive the 9975-specific material and geometry constants for the classic linear form LSD method. The linear form of the LSD, with noncubic array adjustment, is applied and evaluated against computational models for these packages to determine the critical unit fissile mass. Sensitivity equations are derived from the classic method, and these are also used to make projections of the critical unit fissile mass. It was discovered that the heterogeneous packages have a nonlinear surface density versus critical mass relationship compared to the acceptably linear response of bare spherical fissile masses. Methodology is developed to address the nonlinear response. In so doing, the solution to the nonlinear LSD method becomes decoupled from the critical mass of a single unit, adding to its flexibility. The ability of the method to predict changes in neutron multiplication due to perturbations in a parameter is examined to provide a basis for analyzing upset conditions. In conclusion, a full rederivation of the classic LSD method from diffusion theory is also included as this was found to be lacking in the available literature.« less

Limiting Surface Density Method Adapted to Large Arrays of Heterogeneous Shipping Packages with Nonlinear Responses

DOE PAGES

Stover, Tracy E.; Baker, James S.; Ratliff, Michael D.; ...

2018-03-02

The classic Limiting Surface Density (LSD) method is an empirical calculation technique for analyzing and setting mass limits for fissile items in storage arrays. LSD is a desirable method because it can reduce or eliminate the need for lengthy detailed Monte Carlo models of storage arrays. The original (or classic) method was developed based on idealized arrays of bare spherical metal items in air-spaced cubic units in a water-reflected cubic array. In this case, the geometric and material-based surface densities were acceptably correlated by linear functions. Later updates to the method were made to allow for concrete reflection rather thanmore » water, cylindrical masses rather than spheres, different material forms, and noncubic arrays. However, in the intervening four decades since those updates, little work has been done to update the method, especially for use with contemporary highly heterogeneous shipping packages that are noncubic and stored in noncubic arrays. In this work, the LSD method is reevaluated for application to highly heterogeneous shipping packages for fissile material. The package modeled is the 9975 shipping package, currently the primary package used to store fissile material at Savannah River Site’s K-Area Complex. The package is neither cubic nor rectangular but resembles nested cylinders of stainless steel, lead, aluminum, and Celotex. The fissile content is assumed to be a cylinder of plutonium metal. The packages may be arranged in arrays with both an equal number of packages per side (package cubic) and an unequal number of packages per side (noncubic). The cubic arrangements are used to derive the 9975-specific material and geometry constants for the classic linear form LSD method. The linear form of the LSD, with noncubic array adjustment, is applied and evaluated against computational models for these packages to determine the critical unit fissile mass. Sensitivity equations are derived from the classic method, and these are also used to make projections of the critical unit fissile mass. It was discovered that the heterogeneous packages have a nonlinear surface density versus critical mass relationship compared to the acceptably linear response of bare spherical fissile masses. Methodology is developed to address the nonlinear response. In so doing, the solution to the nonlinear LSD method becomes decoupled from the critical mass of a single unit, adding to its flexibility. The ability of the method to predict changes in neutron multiplication due to perturbations in a parameter is examined to provide a basis for analyzing upset conditions. In conclusion, a full rederivation of the classic LSD method from diffusion theory is also included as this was found to be lacking in the available literature.« less

The formal de Rham complex

NASA Astrophysics Data System (ADS)

Zharinov, V. V.

2013-02-01

We propose a formal construction generalizing the classic de Rham complex to a wide class of models in mathematical physics and analysis. The presentation is divided into a sequence of definitions and elementary, easily verified statements; proofs are therefore given only in the key case. Linear operations are everywhere performed over a fixed number field {F} = {R},{C}. All linear spaces, algebras, and modules, although not stipulated explicitly, are by definition or by construction endowed with natural locally convex topologies, and their morphisms are continuous.

Global stability and periodic solution of the viral dynamics

NASA Astrophysics Data System (ADS)

Song, Xinyu; Neumann, Avidan U.

2007-05-01

It is well known that the mathematical models provide very important information for the research of human immunodeficiency virus-type 1 and hepatitis C virus (HCV). However, the infection rate of almost all mathematical models is linear. The linearity shows the simple interaction between the T cells and the viral particles. In this paper, we consider the classical mathematical model with saturation response of the infection rate. By stability analysis we obtain sufficient conditions on the parameters for the global stability of the infected steady state and the infection-free steady state. We also obtain the conditions for the existence of an orbitally asymptotically stable periodic solution. Numerical simulations are presented to illustrate the results.

A Flight Dynamics Model for a Multi-Actuated Flexible Rocket Vehicle

NASA Technical Reports Server (NTRS)

Orr, Jeb S.

2011-01-01

A comprehensive set of motion equations for a multi-actuated flight vehicle is presented. The dynamics are derived from a vector approach that generalizes the classical linear perturbation equations for flexible launch vehicles into a coupled three-dimensional model. The effects of nozzle and aerosurface inertial coupling, sloshing propellant, and elasticity are incorporated without restrictions on the position, orientation, or number of model elements. The present formulation is well suited to matrix implementation for large-scale linear stability and sensitivity analysis and is also shown to be extensible to nonlinear time-domain simulation through the application of a special form of Lagrange s equations in quasi-coordinates. The model is validated through frequency-domain response comparison with a high-fidelity planar implementation.

Predicting musically induced emotions from physiological inputs: linear and neural network models.

PubMed

Russo, Frank A; Vempala, Naresh N; Sandstrom, Gillian M

2013-01-01

Listening to music often leads to physiological responses. Do these physiological responses contain sufficient information to infer emotion induced in the listener? The current study explores this question by attempting to predict judgments of "felt" emotion from physiological responses alone using linear and neural network models. We measured five channels of peripheral physiology from 20 participants-heart rate (HR), respiration, galvanic skin response, and activity in corrugator supercilii and zygomaticus major facial muscles. Using valence and arousal (VA) dimensions, participants rated their felt emotion after listening to each of 12 classical music excerpts. After extracting features from the five channels, we examined their correlation with VA ratings, and then performed multiple linear regression to see if a linear relationship between the physiological responses could account for the ratings. Although linear models predicted a significant amount of variance in arousal ratings, they were unable to do so with valence ratings. We then used a neural network to provide a non-linear account of the ratings. The network was trained on the mean ratings of eight of the 12 excerpts and tested on the remainder. Performance of the neural network confirms that physiological responses alone can be used to predict musically induced emotion. The non-linear model derived from the neural network was more accurate than linear models derived from multiple linear regression, particularly along the valence dimension. A secondary analysis allowed us to quantify the relative contributions of inputs to the non-linear model. The study represents a novel approach to understanding the complex relationship between physiological responses and musically induced emotion.

Vortex unbinding in 2D classical JJ arrays

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

Minnhagen, Petter

1998-05-15

Vortices for 2D superfluids are introduced and are described in terms of a 2D Coulomb gas. The 2D classical JJ array is modeled by a 2D XY-model and a mapping between the XY-model and the Coulomb gas is given. The physical properties of a JJ array are then given in terms of the corresponding Coulomb gas properties. First aspects of the Kosterlitz-Thouless vortex unbinding transitions are reviewed. Consequences for the resistance as well as the frequency dependent conductivity are described. Next the vortex unbinding induced by an external current is considered with Consequencies for the non-linear IV-characteristics. Finally some somemore » effects of a perpendicular magnetic field are discussed in terms of an interplay between free vortices and bound vortex pairs.« less

Order Selection for General Expression of Nonlinear Autoregressive Model Based on Multivariate Stepwise Regression

NASA Astrophysics Data System (ADS)

Shi, Jinfei; Zhu, Songqing; Chen, Ruwen

2017-12-01

An order selection method based on multiple stepwise regressions is proposed for General Expression of Nonlinear Autoregressive model which converts the model order problem into the variable selection of multiple linear regression equation. The partial autocorrelation function is adopted to define the linear term in GNAR model. The result is set as the initial model, and then the nonlinear terms are introduced gradually. Statistics are chosen to study the improvements of both the new introduced and originally existed variables for the model characteristics, which are adopted to determine the model variables to retain or eliminate. So the optimal model is obtained through data fitting effect measurement or significance test. The simulation and classic time-series data experiment results show that the method proposed is simple, reliable and can be applied to practical engineering.

Fluid overpressures and strength of the sedimentary upper crust

NASA Astrophysics Data System (ADS)

Suppe, John

2014-12-01

The classic crustal strength-depth profile based on rock mechanics predicts a brittle strength σ1 -σ3 = κ(ρbar gz -Pf) that increases linearly with depth as a consequence of [1] the intrinsic brittle pressure dependence κ plus [2] an assumption of hydrostatic pore-fluid pressure, Pf = ρwgz. Many deep borehole stress data agree with a critical state of failure of this form. In contrast, fluid pressures greater than hydrostatic ρbar gz >Pf >ρw gz are normally observed in clastic continental margins and shale-rich mountain belts. Therefore we explore the predicted shapes of strength-depth profiles using data from overpressured regions, especially those dominated by the widespread disequilibrium-compaction mechanism, in which fluid pressures are hydrostatic above the fluid-retention depth zFRD and overpressured below, increasing parallel to the lithostatic gradient ρbar gz . Both brittle crustal strength and frictional fault strength below the zFRD must be constant with depth because effective stress (ρbar gz -Pf) is constant, in contrast with the classic linearly increasing profile. Borehole stress and fluid-pressure measurements in several overpressured deforming continental margins agree with this constant-strength prediction, with the same pressure-dependence κ as the overlying hydrostatic strata. The role of zFRD in critical-taper wedge mechanics and jointing is illustrated. The constant-strength approximation is more appropriate for overpressured crust than classic linearly increasing models.

Information transport in classical statistical systems

NASA Astrophysics Data System (ADS)

Wetterich, C.

2018-02-01

For "static memory materials" the bulk properties depend on boundary conditions. Such materials can be realized by classical statistical systems which admit no unique equilibrium state. We describe the propagation of information from the boundary to the bulk by classical wave functions. The dependence of wave functions on the location of hypersurfaces in the bulk is governed by a linear evolution equation that can be viewed as a generalized Schrödinger equation. Classical wave functions obey the superposition principle, with local probabilities realized as bilinears of wave functions. For static memory materials the evolution within a subsector is unitary, as characteristic for the time evolution in quantum mechanics. The space-dependence in static memory materials can be used as an analogue representation of the time evolution in quantum mechanics - such materials are "quantum simulators". For example, an asymmetric Ising model on a Euclidean two-dimensional lattice represents the time evolution of free relativistic fermions in two-dimensional Minkowski space.

Population decoding of motor cortical activity using a generalized linear model with hidden states.

PubMed

Lawhern, Vernon; Wu, Wei; Hatsopoulos, Nicholas; Paninski, Liam

2010-06-15

Generalized linear models (GLMs) have been developed for modeling and decoding population neuronal spiking activity in the motor cortex. These models provide reasonable characterizations between neural activity and motor behavior. However, they lack a description of movement-related terms which are not observed directly in these experiments, such as muscular activation, the subject's level of attention, and other internal or external states. Here we propose to include a multi-dimensional hidden state to address these states in a GLM framework where the spike count at each time is described as a function of the hand state (position, velocity, and acceleration), truncated spike history, and the hidden state. The model can be identified by an Expectation-Maximization algorithm. We tested this new method in two datasets where spikes were simultaneously recorded using a multi-electrode array in the primary motor cortex of two monkeys. It was found that this method significantly improves the model-fitting over the classical GLM, for hidden dimensions varying from 1 to 4. This method also provides more accurate decoding of hand state (reducing the mean square error by up to 29% in some cases), while retaining real-time computational efficiency. These improvements on representation and decoding over the classical GLM model suggest that this new approach could contribute as a useful tool to motor cortical decoding and prosthetic applications. Copyright (c) 2010 Elsevier B.V. All rights reserved.

Population Decoding of Motor Cortical Activity using a Generalized Linear Model with Hidden States

PubMed Central

Lawhern, Vernon; Wu, Wei; Hatsopoulos, Nicholas G.; Paninski, Liam

2010-01-01

Generalized linear models (GLMs) have been developed for modeling and decoding population neuronal spiking activity in the motor cortex. These models provide reasonable characterizations between neural activity and motor behavior. However, they lack a description of movement-related terms which are not observed directly in these experiments, such as muscular activation, the subject's level of attention, and other internal or external states. Here we propose to include a multi-dimensional hidden state to address these states in a GLM framework where the spike count at each time is described as a function of the hand state (position, velocity, and acceleration), truncated spike history, and the hidden state. The model can be identified by an Expectation-Maximization algorithm. We tested this new method in two datasets where spikes were simultaneously recorded using a multi-electrode array in the primary motor cortex of two monkeys. It was found that this method significantly improves the model-fitting over the classical GLM, for hidden dimensions varying from 1 to 4. This method also provides more accurate decoding of hand state (lowering the Mean Square Error by up to 29% in some cases), while retaining real-time computational efficiency. These improvements on representation and decoding over the classical GLM model suggest that this new approach could contribute as a useful tool to motor cortical decoding and prosthetic applications. PMID:20359500

On the consistency between nearest-neighbor peridynamic discretizations and discretized classical elasticity models

DOE PAGES

Seleson, Pablo; Du, Qiang; Parks, Michael L.

2016-08-16

The peridynamic theory of solid mechanics is a nonlocal reformulation of the classical continuum mechanics theory. At the continuum level, it has been demonstrated that classical (local) elasticity is a special case of peridynamics. Such a connection between these theories has not been extensively explored at the discrete level. This paper investigates the consistency between nearest-neighbor discretizations of linear elastic peridynamic models and finite difference discretizations of the Navier–Cauchy equation of classical elasticity. While nearest-neighbor discretizations in peridynamics have been numerically observed to present grid-dependent crack paths or spurious microcracks, this paper focuses on a different, analytical aspect of suchmore » discretizations. We demonstrate that, even in the absence of cracks, such discretizations may be problematic unless a proper selection of weights is used. Specifically, we demonstrate that using the standard meshfree approach in peridynamics, nearest-neighbor discretizations do not reduce, in general, to discretizations of corresponding classical models. We study nodal-based quadratures for the discretization of peridynamic models, and we derive quadrature weights that result in consistency between nearest-neighbor discretizations of peridynamic models and discretized classical models. The quadrature weights that lead to such consistency are, however, model-/discretization-dependent. We motivate the choice of those quadrature weights through a quadratic approximation of displacement fields. The stability of nearest-neighbor peridynamic schemes is demonstrated through a Fourier mode analysis. Finally, an approach based on a normalization of peridynamic constitutive constants at the discrete level is explored. This approach results in the desired consistency for one-dimensional models, but does not work in higher dimensions. The results of the work presented in this paper suggest that even though nearest-neighbor discretizations should be avoided in peridynamic simulations involving cracks, such discretizations are viable, for example for verification or validation purposes, in problems characterized by smooth deformations. Furthermore, we demonstrate that better quadrature rules in peridynamics can be obtained based on the functional form of solutions.« less

Time Domain Stability Margin Assessment of the NASA Space Launch System GN&C Design for Exploration Mission One

NASA Technical Reports Server (NTRS)

Clements, Keith; Wall, John

2017-01-01

The baseline stability margins for NASA's Space Launch System (SLS) launch vehicle were generated via the classical approach of linearizing the system equations of motion and determining the gain and phase margins from the resulting frequency domain model. To improve the fidelity of the classical methods, the linear frequency domain approach can be extended by replacing static, memoryless nonlinearities with describing functions. This technique, however, does not address the time varying nature of the dynamics of a launch vehicle in flight. An alternative technique for the evaluation of the stability of the nonlinear launch vehicle dynamics along its trajectory is to incrementally adjust the gain and/or time delay in the time domain simulation until the system exhibits unstable behavior. This technique has the added benefit of providing a direct comparison between the time domain and frequency domain tools in support of simulation validation.

Time Domain Stability Margin Assessment of the NS Space Launch System GN&C Design for Exploration Mission One

NASA Technical Reports Server (NTRS)

Clements, Keith; Wall, John

2017-01-01

The baseline stability margins for NASA's Space Launch System (SLS) launch vehicle were generated via the classical approach of linearizing the system equations of motion and determining the gain and phase margins from the resulting frequency domain model. To improve the fidelity of the classical methods, the linear frequency domain approach can be extended by replacing static, memoryless nonlinearities with describing functions. This technique, however, does not address the time varying nature of the dynamics of a launch vehicle in flight. An alternative technique for the evaluation of the stability of the nonlinear launch vehicle dynamics along its trajectory is to incrementally adjust the gain and/or time delay in the time domain simulation until the system exhibits unstable behavior. This technique has the added benefit of providing a direct comparison between the time domain and frequency domain tools in support of simulation validation.

Real time correlation function in a single phase space integral beyond the linearized semiclassical initial value representation.

PubMed

Liu, Jian; Miller, William H

2007-06-21

It is shown how quantum mechanical time correlation functions [defined, e.g., in Eq. (1.1)] can be expressed, without approximation, in the same form as the linearized approximation of the semiclassical initial value representation (LSC-IVR), or classical Wigner model, for the correlation function [cf. Eq. (2.1)], i.e., as a phase space average (over initial conditions for trajectories) of the Wigner functions corresponding to the two operators. The difference is that the trajectories involved in the LSC-IVR evolve classically, i.e., according to the classical equations of motion, while in the exact theory they evolve according to generalized equations of motion that are derived here. Approximations to the exact equations of motion are then introduced to achieve practical methods that are applicable to complex (i.e., large) molecular systems. Four such methods are proposed in the paper--the full Wigner dynamics (full WD) and the second order WD based on "Wigner trajectories" [H. W. Lee and M. D. Scully, J. Chem. Phys. 77, 4604 (1982)] and the full Donoso-Martens dynamics (full DMD) and the second order DMD based on "Donoso-Martens trajectories" [A. Donoso and C. C. Martens, Phys. Rev. Lett. 8722, 223202 (2001)]--all of which can be viewed as generalizations of the original LSC-IVR method. Numerical tests of the four versions of this new approach are made for two anharmonic model problems, and for each the momentum autocorrelation function (i.e., operators linear in coordinate or momentum operators) and the force autocorrelation function (nonlinear operators) have been calculated. These four new approximate treatments are indeed seen to be significant improvements to the original LSC-IVR approximation.

Sampling schemes and parameter estimation for nonlinear Bernoulli-Gaussian sparse models

NASA Astrophysics Data System (ADS)

Boudineau, Mégane; Carfantan, Hervé; Bourguignon, Sébastien; Bazot, Michael

2016-06-01

We address the sparse approximation problem in the case where the data are approximated by the linear combination of a small number of elementary signals, each of these signals depending non-linearly on additional parameters. Sparsity is explicitly expressed through a Bernoulli-Gaussian hierarchical model in a Bayesian framework. Posterior mean estimates are computed using Markov Chain Monte-Carlo algorithms. We generalize the partially marginalized Gibbs sampler proposed in the linear case in [1], and build an hybrid Hastings-within-Gibbs algorithm in order to account for the nonlinear parameters. All model parameters are then estimated in an unsupervised procedure. The resulting method is evaluated on a sparse spectral analysis problem. It is shown to converge more efficiently than the classical joint estimation procedure, with only a slight increase of the computational cost per iteration, consequently reducing the global cost of the estimation procedure.

Fuzzy branching temporal logic.

PubMed

Moon, Seong-ick; Lee, Kwang H; Lee, Doheon

2004-04-01

Intelligent systems require a systematic way to represent and handle temporal information containing uncertainty. In particular, a logical framework is needed that can represent uncertain temporal information and its relationships with logical formulae. Fuzzy linear temporal logic (FLTL), a generalization of propositional linear temporal logic (PLTL) with fuzzy temporal events and fuzzy temporal states defined on a linear time model, was previously proposed for this purpose. However, many systems are best represented by branching time models in which each state can have more than one possible future path. In this paper, fuzzy branching temporal logic (FBTL) is proposed to address this problem. FBTL adopts and generalizes concurrent tree logic (CTL*), which is a classical branching temporal logic. The temporal model of FBTL is capable of representing fuzzy temporal events and fuzzy temporal states, and the order relation among them is represented as a directed graph. The utility of FBTL is demonstrated using a fuzzy job shop scheduling problem as an example.

Oligopolies with contingent workforce and unemployment insurance systems

NASA Astrophysics Data System (ADS)

Matsumoto, Akio; Merlone, Ugo; Szidarovszky, Ferenc

2015-10-01

In the recent literature the introduction of modified cost functions has added reality into the classical oligopoly analysis. Furthermore, the market evolution requires much more flexibility to firms, and in several countries contingent workforce plays an important role in the production choices by the firms. Therefore, an analysis of dynamic adjustment costs is in order to understand oligopoly dynamics. In this paper, dynamic single-product oligopolies without product differentiation are first examined with the additional consideration of production adjustment costs. Linear inverse demand and cost functions are considered and it is assumed that the firms adjust their outputs partially toward best response. The set of the steady states is characterized by a system of linear inequalities and there are usually infinitely many steady states. The asymptotic behavior of the output trajectories is examined by using computer simulation. The numerical results indicate that the resulting dynamics is richer than in the case of the classical Cournot model. This model and results are then compared to oligopolies with unemployment insurance systems when the additional cost is considered if firms do not use their maximum capacities.

A new state space model for the NASA/JPL 70-meter antenna servo controls

NASA Technical Reports Server (NTRS)

Hill, R. E.

1987-01-01

A control axis referenced model of the NASA/JPL 70-m antenna structure is combined with the dynamic equations of servo components to produce a comprehansive state variable (matrix) model of the coupled system. An interactive Fortran program for generating the linear system model and computing its salient parameters is described. Results are produced in a state variable, block diagram, and in factored transfer function forms to facilitate design and analysis by classical as well as modern control methods.

Q-balls in flat potentials

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

Copeland, Edmund J.; Tsumagari, Mitsuo I.

2009-07-15

We study the classical and absolute stability of Q-balls in scalar field theories with flat potentials arising in both gravity-mediated and gauge-mediated models. We show that the associated Q-matter formed in gravity-mediated potentials can be stable against decay into their own free particles as long as the coupling constant of the nonrenormalizable term is small, and that all of the possible three-dimensional Q-ball configurations are classically stable against linear fluctuations. Three-dimensional gauge-mediated Q-balls can be absolutely stable in the thin-wall limit, but are completely unstable in the thick-wall limit.

Lattice Boltzmann methods for global linear instability analysis

NASA Astrophysics Data System (ADS)

Pérez, José Miguel; Aguilar, Alfonso; Theofilis, Vassilis

2017-12-01

Modal global linear instability analysis is performed using, for the first time ever, the lattice Boltzmann method (LBM) to analyze incompressible flows with two and three inhomogeneous spatial directions. Four linearization models have been implemented in order to recover the linearized Navier-Stokes equations in the incompressible limit. Two of those models employ the single relaxation time and have been proposed previously in the literature as linearization of the collision operator of the lattice Boltzmann equation. Two additional models are derived herein for the first time by linearizing the local equilibrium probability distribution function. Instability analysis results are obtained in three benchmark problems, two in closed geometries and one in open flow, namely the square and cubic lid-driven cavity flow and flow in the wake of the circular cylinder. Comparisons with results delivered by classic spectral element methods verify the accuracy of the proposed new methodologies and point potential limitations particular to the LBM approach. The known issue of appearance of numerical instabilities when the SRT model is used in direct numerical simulations employing the LBM is shown to be reflected in a spurious global eigenmode when the SRT model is used in the instability analysis. Although this mode is absent in the multiple relaxation times model, other spurious instabilities can also arise and are documented herein. Areas of potential improvements in order to make the proposed methodology competitive with established approaches for global instability analysis are discussed.

The Fundamental Solution of the Linearized Navier Stokes Equations for Spinning Bodies in Three Spatial Dimensions Time Dependent Case

NASA Astrophysics Data System (ADS)

Thomann, Enrique A.; Guenther, Ronald B.

2006-02-01

Explicit formulae for the fundamental solution of the linearized time dependent Navier Stokes equations in three spatial dimensions are obtained. The linear equations considered in this paper include those used to model rigid bodies that are translating and rotating at a constant velocity. Estimates extending those obtained by Solonnikov in [23] for the fundamental solution of the time dependent Stokes equations, corresponding to zero translational and angular velocity, are established. Existence and uniqueness of solutions of these linearized problems is obtained for a class of functions that includes the classical Lebesgue spaces L p (R 3), 1 < p < ∞. Finally, the asymptotic behavior and semigroup properties of the fundamental solution are established.

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.

On the classification of the spectrally stable standing waves of the Hartree problem

NASA Astrophysics Data System (ADS)

Georgiev, Vladimir; Stefanov, Atanas

2018-05-01

We consider the fractional Hartree model, with general power non-linearity and arbitrary spatial dimension. We construct variationally the "normalized" solutions for the corresponding Choquard-Pekar model-in particular a number of key properties, like smoothness and bell-shapedness are established. As a consequence of the construction, we show that these solitons are spectrally stable as solutions to the time-dependent Hartree model. In addition, we analyze the spectral stability of the Moroz-Van Schaftingen solitons of the classical Hartree problem, in any dimensions and power non-linearity. A full classification is obtained, the main conclusion of which is that only and exactly the "normalized" solutions (which exist only in a portion of the range) are spectrally stable.

Note: Wide-operating-range control for thermoelectric coolers.

PubMed

Peronio, P; Labanca, I; Ghioni, M; Rech, I

2017-11-01

A new algorithm for controlling the temperature of a thermoelectric cooler is proposed. Unlike a classic proportional-integral-derivative (PID) control, which computes the bias voltage from the temperature error, the proposed algorithm exploits the linear relation that exists between the cold side's temperature and the amount of heat that is removed per unit time. Since this control is based on an existing linear relation, it is insensitive to changes in the operating point that are instead crucial in classic PID control of a non-linear system.

Note: Wide-operating-range control for thermoelectric coolers

NASA Astrophysics Data System (ADS)

Peronio, P.; Labanca, I.; Ghioni, M.; Rech, I.

2017-11-01

A new algorithm for controlling the temperature of a thermoelectric cooler is proposed. Unlike a classic proportional-integral-derivative (PID) control, which computes the bias voltage from the temperature error, the proposed algorithm exploits the linear relation that exists between the cold side's temperature and the amount of heat that is removed per unit time. Since this control is based on an existing linear relation, it is insensitive to changes in the operating point that are instead crucial in classic PID control of a non-linear system.

Tomographic PIV: particles versus blobs

NASA Astrophysics Data System (ADS)

Champagnat, Frédéric; Cornic, Philippe; Cheminet, Adam; Leclaire, Benjamin; Le Besnerais, Guy; Plyer, Aurélien

2014-08-01

We present an alternative approach to tomographic particle image velocimetry (tomo-PIV) that seeks to recover nearly single voxel particles rather than blobs of extended size. The baseline of our approach is a particle-based representation of image data. An appropriate discretization of this representation yields an original linear forward model with a weight matrix built with specific samples of the system’s point spread function (PSF). Such an approach requires only a few voxels to explain the image appearance, therefore it favors much more sparsely reconstructed volumes than classic tomo-PIV. The proposed forward model is general and flexible and can be embedded in a classical multiplicative algebraic reconstruction technique (MART) or a simultaneous multiplicative algebraic reconstruction technique (SMART) inversion procedure. We show, using synthetic PIV images and by way of a large exploration of the generating conditions and a variety of performance metrics, that the model leads to better results than the classical tomo-PIV approach, in particular in the case of seeding densities greater than 0.06 particles per pixel and of PSFs characterized by a standard deviation larger than 0.8 pixels.

Nonextensive Thomas-Fermi model

NASA Astrophysics Data System (ADS)

Shivamoggi, Bhimsen; Martinenko, Evgeny

2007-11-01

Nonextensive Thomas-Fermi model was father investigated in the following directions: Heavy atom in strong magnetic field. following Shivamoggi work on the extension of Kadomtsev equation we applied nonextensive formalism to father generalize TF model for the very strong magnetic fields (of order 10e12 G). The generalized TF equation and the binding energy of atom were calculated which contain a new nonextensive term dominating the classical one. The binding energy of a heavy atom was also evaluated. Thomas-Fermi equations in N dimensions which is technically the same as in Shivamoggi (1998) ,but behavior is different and in interesting 2 D case nonextesivity prevents from becoming linear ODE as in classical case. Effect of nonextensivity on dielectrical screening reveals itself in the reduction of the envelope radius. It was shown that nonextesivity in each case is responsible for new term dominating classical thermal correction term by order of magnitude, which is vanishing in a limit q->1. Therefore it appears that nonextensive term is ubiquitous for a wide range of systems and father work is needed to understand the origin of it.

Conceptual Foundations of Soliton Versus Particle Dualities Toward a Topological Model for Matter

NASA Astrophysics Data System (ADS)

Kouneiher, Joseph

2016-06-01

The idea that fermions could be solitons was actually confirmed in theoretical models in 1975 in the case when the space-time is two-dimensional and with the sine-Gordon model. More precisely S. Coleman showed that two different classical models end up describing the same fermions particle, when the quantum theory is constructed. But in one model the fermion is a quantum excitation of the field and in the other model the particle is a soliton. Hence both points of view can be reconciliated.The principal aim in this paper is to exhibit a solutions of topological type for the fermions in the wave zone, where the equations of motion are non-linear field equations, i.e. using a model generalizing sine- Gordon model to four dimensions, and describe the solutions for linear and circular polarized waves. In other words, the paper treat fermions as topological excitations of a bosonic field.

Comprehensive study of the dynamics of a classical Kitaev Spin Liquid

NASA Astrophysics Data System (ADS)

Samarakoon, Anjana; Banerjee, Arnab; Batista, Cristian; Kamiya, Yoshitomo; Tennant, Alan; Nagler, Stephen

Quantum spin liquids (QSLs) have achieved great interest in both theoretical and experimental condensed matter physics due to their remarkable topological properties. Among many different candidates, the Kitaev model on the honeycomb lattice is a 2D prototypical QSL which can be experimentally studied in materials based on iridium or ruthenium.Here we study the spin-1/2 Kitaev model using classical Monte-Carlo and semiclassical spin dynamics of classical spins on a honeycomb lattice. Both real and reciprocal space pictures highlighting the differences and similarities of the results to the linear spin wave theory will be discussed in terms dispersion relations of the pure-Kitaev limit and beyond. Interestingly, this technique could capture some of the salient features of the exact quantum solution of the Kitaev model, such as features resembling the Majorana-like mode comparable to the Kitaev energy, which is spectrally narrowed compared to the quantum result, can be explained by magnon excitations on fluctuating onedimensional manifolds (loops). Hence the difference from the classical limit to the quantum limit can be understood by the fractionalization of a magnon to Majorana fermions. The calculations will be directly compared with our neutron scattering data on α-RuCl3 which is a prime candidate for experimental realization of Kitaev physics.

On a q-extension of the linear harmonic oscillator with the continuous orthogonality property on ℝ

NASA Astrophysics Data System (ADS)

Alvarez-Nodarse, R.; Atakishiyeva, M. K.; Atakishiyev, N. M.

2005-11-01

We discuss a q-analogue of the linear harmonic oscillator in quantum mechanics based on a q-extension of the classical Hermite polynomials H n ( x) recently introduced by us in R. Alvarez-Nodarse et al.: Boletin de la Sociedad Matematica Mexicana (3) 8 (2002) 127. The wave functions in this q-model of the quantum harmonic oscillator possess the continuous orthogonality property on the whole real line ℝ with respect to a positive weight function. A detailed description of the corresponding q-system is carried out.

Evaluation of Wall Interference Effects in a Two-Dimensional Transonic Wind Tunnel by Subsonic Linear Theory,

DTIC Science & Technology

1979-02-01

tests were conducted on two geometrica lly similar models of each of two aerofoil sections -—t he NA CA 00/ 2 and the BGK- 1 sections -and covered a...and slotted-wall tes t sections are corrected for wind tunnel wall interference efJ~cts by the application of classical linearized theory. For the...solid wall results , these corrections appear to produce data which are very close to being free of the effects of interference. In the case of

Mathematical Modeling of Intestinal Iron Absorption Using Genetic Programming

PubMed Central

Colins, Andrea; Gerdtzen, Ziomara P.; Nuñez, Marco T.; Salgado, J. Cristian

2017-01-01

Iron is a trace metal, key for the development of living organisms. Its absorption process is complex and highly regulated at the transcriptional, translational and systemic levels. Recently, the internalization of the DMT1 transporter has been proposed as an additional regulatory mechanism at the intestinal level, associated to the mucosal block phenomenon. The short-term effect of iron exposure in apical uptake and initial absorption rates was studied in Caco-2 cells at different apical iron concentrations, using both an experimental approach and a mathematical modeling framework. This is the first report of short-term studies for this system. A non-linear behavior in the apical uptake dynamics was observed, which does not follow the classic saturation dynamics of traditional biochemical models. We propose a method for developing mathematical models for complex systems, based on a genetic programming algorithm. The algorithm is aimed at obtaining models with a high predictive capacity, and considers an additional parameter fitting stage and an additional Jackknife stage for estimating the generalization error. We developed a model for the iron uptake system with a higher predictive capacity than classic biochemical models. This was observed both with the apical uptake dataset used for generating the model and with an independent initial rates dataset used to test the predictive capacity of the model. The model obtained is a function of time and the initial apical iron concentration, with a linear component that captures the global tendency of the system, and a non-linear component that can be associated to the movement of DMT1 transporters. The model presented in this paper allows the detailed analysis, interpretation of experimental data, and identification of key relevant components for this complex biological process. This general method holds great potential for application to the elucidation of biological mechanisms and their key components in other complex systems. PMID:28072870

Scalar field quantum cosmology: A Schrödinger picture

NASA Astrophysics Data System (ADS)

Vakili, Babak

2012-11-01

We study the classical and quantum models of a scalar field Friedmann-Robertson-Walker (FRW) cosmology with an eye to the issue of time problem in quantum cosmology. We introduce a canonical transformation on the scalar field sector of the action such that the momentum conjugate to the new canonical variable appears linearly in the transformed Hamiltonian. Using this canonical transformation, we show that, it may lead to the identification of a time parameter for the corresponding dynamical system. In the cases of flat, closed and open FRW universes the classical cosmological solutions are obtained in terms of the introduced time parameter. Moreover, this formalism gives rise to a Schrödinger-Wheeler-DeWitt equation for the quantum-mechanical description of the model under consideration, the eigenfunctions of which can be used to construct the wave function of the universe. We use the resulting wave functions in order to investigate the possible corrections to the classical cosmologies due to quantum effects by means of the many-worlds and ontological interpretation of quantum cosmology.

Causal implications of viscous damping in compressible fluid flows

PubMed

Jordan; Meyer; Puri

2000-12-01

Classically, a compressible, isothermal, viscous fluid is regarded as a mathematical continuum and its motion is governed by the linearized continuity, Navier-Stokes, and state equations. Unfortunately, solutions of this system are of a diffusive nature and hence do not satisfy causality. However, in the case of a half-space of fluid set to motion by a harmonically vibrating plate the classical equation of motion can, under suitable conditions, be approximated by the damped wave equation. Since this equation is hyperbolic, the resulting solutions satisfy causal requirements. In this work the Laplace transform and other analytical and numerical tools are used to investigate this apparent contradiction. To this end the exact solutions, as well as their special and limiting cases, are found and compared for the two models. The effects of the physical parameters on the solutions and associated quantities are also studied. It is shown that propagating wave fronts are only possible under the hyperbolic model and that the concept of phase speed has different meanings in the two formulations. In addition, discontinuities and shock waves are noted and a physical system is modeled under both formulations. Overall, it is shown that the hyperbolic form gives a more realistic description of the physical problem than does the classical theory. Lastly, a simple mechanical analog is given and connections to viscoelastic fluids are noted. In particular, the research presented here supports the notion that linear compressible, isothermal, viscous fluids can, at least in terms of causality, be better characterized as a type of viscoelastic fluid.

Real-time Adaptive Control Using Neural Generalized Predictive Control

NASA Technical Reports Server (NTRS)

Haley, Pam; Soloway, Don; Gold, Brian

1999-01-01

The objective of this paper is to demonstrate the feasibility of a Nonlinear Generalized Predictive Control algorithm by showing real-time adaptive control on a plant with relatively fast time-constants. Generalized Predictive Control has classically been used in process control where linear control laws were formulated for plants with relatively slow time-constants. The plant of interest for this paper is a magnetic levitation device that is nonlinear and open-loop unstable. In this application, the reference model of the plant is a neural network that has an embedded nominal linear model in the network weights. The control based on the linear model provides initial stability at the beginning of network training. In using a neural network the control laws are nonlinear and online adaptation of the model is possible to capture unmodeled or time-varying dynamics. Newton-Raphson is the minimization algorithm. Newton-Raphson requires the calculation of the Hessian, but even with this computational expense the low iteration rate make this a viable algorithm for real-time control.

Mixed effect Poisson log-linear models for clinical and epidemiological sleep hypnogram data

PubMed Central

Swihart, Bruce J.; Caffo, Brian S.; Crainiceanu, Ciprian; Punjabi, Naresh M.

2013-01-01

Bayesian Poisson log-linear multilevel models scalable to epidemiological studies are proposed to investigate population variability in sleep state transition rates. Hierarchical random effects are used to account for pairings of subjects and repeated measures within those subjects, as comparing diseased to non-diseased subjects while minimizing bias is of importance. Essentially, non-parametric piecewise constant hazards are estimated and smoothed, allowing for time-varying covariates and segment of the night comparisons. The Bayesian Poisson regression is justified through a re-derivation of a classical algebraic likelihood equivalence of Poisson regression with a log(time) offset and survival regression assuming exponentially distributed survival times. Such re-derivation allows synthesis of two methods currently used to analyze sleep transition phenomena: stratified multi-state proportional hazards models and log-linear models with GEE for transition counts. An example data set from the Sleep Heart Health Study is analyzed. Supplementary material includes the analyzed data set as well as the code for a reproducible analysis. PMID:22241689

Deformed coset models from gauged WZW actions

NASA Astrophysics Data System (ADS)

Park, Q.-Han

1994-06-01

A general Lagrangian formulation of integrably deformed G/H-coset models is given. We consider the G/H-coset model in terms of the gauged Wess-Zumino-Witten action and obtain an integrable deformation by adding a potential energy term Tr(gTg -1overlineT) , where algebra elements T, overlineT belong to the center of the algebra h associated with the subgroup H. We show that the classical equation of motion of the deformed coset model can be identified with the integrability condition of certain linear equations which makes the use of the inverse scattering method possible. Using the linear equation, we give a systematic way to construct infinitely many conserved currents as well as soliton solutions. In the case of the parafermionic SU(2)/U(1)-coset model, we derive n-solitons and conserved currents explicitly.

Quantum Theories of Self-Localization

NASA Astrophysics Data System (ADS)

Bernstein, Lisa Joan

In the classical dynamics of coupled oscillator systems, nonlinearity leads to the existence of stable solutions in which energy remains localized for all time. Here the quantum-mechanical counterpart of classical self-localization is investigated in the context of two model systems. For these quantum models, the terms corresponding to classical nonlinearities modify a subset of the stationary quantum states to be particularly suited to the creation of nonstationary wavepackets that localize energy for long times. The first model considered here is the Quantized Discrete Self-Trapping model (QDST), a system of anharmonic oscillators with linear dispersive coupling used to model local modes of vibration in polyatomic molecules. A simple formula is derived for a particular symmetry class of QDST systems which gives an analytic connection between quantum self-localization and classical local modes. This formula is also shown to be useful in the interpretation of the vibrational spectra of some molecules. The second model studied is the Frohlich/Einstein Dimer (FED), a two-site system of anharmonically coupled oscillators based on the Frohlich Hamiltonian and motivated by the theory of Davydov solitons in biological protein. The Born-Oppenheimer perturbation method is used to obtain approximate stationary state wavefunctions with error estimates for the FED at the first excited level. A second approach is used to reduce the first excited level FED eigenvalue problem to a system of ordinary differential equations. A simple theory of low-energy self-localization in the FED is discussed. The quantum theories of self-localization in the intrinsic QDST model and the extrinsic FED model are compared.

Reliability of Total Test Scores When Considered as Ordinal Measurements

ERIC Educational Resources Information Center

Biswas, Ajoy Kumar

2006-01-01

This article studies the ordinal reliability of (total) test scores. This study is based on a classical-type linear model of observed score (X), true score (T), and random error (E). Based on the idea of Kendall's tau-a coefficient, a measure of ordinal reliability for small-examinee populations is developed. This measure is extended to large…

Power loss of an oscillating electric dipole in a quantum plasma

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

Ghaderipoor, L.; Mehramiz, A.

2012-12-15

A system of linearized quantum plasma equations (quantum hydrodynamic model) has been used for investigating the dispersion equation for electrostatic waves in the plasma. Furthermore, dispersion relations and their modifications due to quantum effects are used for calculating the power loss of an oscillating electric dipole. Finally, the results are compared in quantum and classical regimes.

Stability analysis of spacecraft power systems

NASA Technical Reports Server (NTRS)

Halpin, S. M.; Grigsby, L. L.; Sheble, G. B.; Nelms, R. M.

1990-01-01

The problems in applying standard electric utility models, analyses, and algorithms to the study of the stability of spacecraft power conditioning and distribution systems are discussed. Both single-phase and three-phase systems are considered. Of particular concern are the load and generator models that are used in terrestrial power system studies, as well as the standard assumptions of load and topological balance that lead to the use of the positive sequence network. The standard assumptions regarding relative speeds of subsystem dynamic responses that are made in the classical transient stability algorithm, which forms the backbone of utility-based studies, are examined. The applicability of these assumptions to a spacecraft power system stability study is discussed in detail. In addition to the classical indirect method, the applicability of Liapunov's direct methods to the stability determination of spacecraft power systems is discussed. It is pointed out that while the proposed method uses a solution process similar to the classical algorithm, the models used for the sources, loads, and networks are, in general, more accurate. Some preliminary results are given for a linear-graph, state-variable-based modeling approach to the study of the stability of space-based power distribution networks.

A novel approach for inventory problem in the pharmaceutical supply chain.

PubMed

Candan, Gökçe; Yazgan, Harun Reşit

2016-02-24

In pharmaceutical enterprises, keeping up with global market conditions is possible with properly selected supply chain management policies. Generally; demand-driven classical supply chain model is used in the pharmaceutical industry. In this study, a new mathematical model is developed to solve an inventory problem in the pharmaceutical supply chain. Unlike the studies in literature, the "shelf life and product transition times" constraints are considered, simultaneously, first time in the pharmaceutical production inventory problem. The problem is formulated as a mixed-integer linear programming (MILP) model with a hybrid time representation. The objective is to maximize total net profit. Effectiveness of the proposed model is illustrated considering a classical and a vendor managed inventory (VMI) supply chain on an experimental study. To show the effectiveness of the model, an experimental study is performed; which contains 2 different supply chain policy (Classical and VMI), 24 and 30 months planning horizon, 10 and 15 different cephalosporin products. Finally the mathematical model is compared to another model in literature and the results show that proposed model is superior. This study suggest a novel approach for solving pharmaceutical inventory problem. The developed model is maximizing total net profit while determining optimal production plan under shelf life and product transition constraints in the pharmaceutical industry. And we believe that the proposed model is much more closed to real life unlike the other studies in literature.

Rhombic micro-displacement amplifier for piezoelectric actuator and its linear and hybrid model

NASA Astrophysics Data System (ADS)

Chen, Jinglong; Zhang, Chunlin; Xu, Minglong; Zi, Yanyang; Zhang, Xinong

2015-01-01

This paper proposes rhombic micro-displacement amplifier (RMDA) for piezoelectric actuator (PA). First, the geometric amplification relations are analyzed and linear model is built to analyze the mechanical and electrical properties of this amplifier. Next, the accurate modeling method of amplifier is studied for important application of precise servo control. The classical Preisach model (CPM) is generally implemented using a numerical technique based on the first-order reversal curves (FORCs). The accuracy of CPM mainly depends on the number of FORCs. However, it is generally difficult to achieve enough number of FORCs in practice. So, Support Vector Machine (SVM) is employed in the work to circumvent the deficiency of the CPM. Then the hybrid model, which is based on discrete CPM and SVM is developed to account for hysteresis and dynamic effects. Finally, experimental validation is carried out. The analyzed result shows that this amplifier with the hybrid model is suitable for control application.

Thermal and viscous effects on sound waves: revised classical theory.

PubMed

Davis, Anthony M J; Brenner, Howard

2012-11-01

In this paper the recently developed, bi-velocity model of fluid mechanics based on the principles of linear irreversible thermodynamics (LIT) is applied to sound propagation in gases taking account of first-order thermal and viscous dissipation effects. The results are compared and contrasted with the classical Navier-Stokes-Fourier results of Pierce for this same situation cited in his textbook. Comparisons are also made with the recent analyses of Dadzie and Reese, whose molecularly based sound propagation calculations furnish results virtually identical with the purely macroscopic LIT-based bi-velocity results below, as well as being well-supported by experimental data. Illustrative dissipative sound propagation examples involving application of the bi-velocity model to several elementary situations are also provided, showing the disjoint entropy mode and the additional, evanescent viscous mode.

Computational approach to Thornley's problem by bivariate operational calculus

NASA Astrophysics Data System (ADS)

Bazhlekova, E.; Dimovski, I.

2012-10-01

Thornley's problem is an initial-boundary value problem with a nonlocal boundary condition for linear onedimensional reaction-diffusion equation, used as a mathematical model of spiral phyllotaxis in botany. Applying a bivariate operational calculus we find explicit representation of the solution, containing two convolution products of special solutions and the arbitrary initial and boundary functions. We use a non-classical convolution with respect to the space variable, extending in this way the classical Duhamel principle. The special solutions involved are represented in the form of fast convergent series. Numerical examples are considered to show the application of the present technique and to analyze the character of the solution.

Discriminative components of data.

PubMed

Peltonen, Jaakko; Kaski, Samuel

2005-01-01

A simple probabilistic model is introduced to generalize classical linear discriminant analysis (LDA) in finding components that are informative of or relevant for data classes. The components maximize the predictability of the class distribution which is asymptotically equivalent to 1) maximizing mutual information with the classes, and 2) finding principal components in the so-called learning or Fisher metrics. The Fisher metric measures only distances that are relevant to the classes, that is, distances that cause changes in the class distribution. The components have applications in data exploration, visualization, and dimensionality reduction. In empirical experiments, the method outperformed, in addition to more classical methods, a Renyi entropy-based alternative while having essentially equivalent computational cost.

Quasi-Static Analysis of Round LaRC THUNDER Actuators

NASA Technical Reports Server (NTRS)

Campbell, Joel F.

2007-01-01

An analytic approach is developed to predict the shape and displacement with voltage in the quasi-static limit of round LaRC Thunder Actuators. The problem is treated with classical lamination theory and Von Karman non-linear analysis. In the case of classical lamination theory exact analytic solutions are found. It is shown that classical lamination theory is insufficient to describe the physical situation for large actuators but is sufficient for very small actuators. Numerical results are presented for the non-linear analysis and compared with experimental measurements. Snap-through behavior, bifurcation, and stability are presented and discussed.

Quasi-Static Analysis of LaRC THUNDER Actuators

NASA Technical Reports Server (NTRS)

Campbell, Joel F.

2007-01-01

An analytic approach is developed to predict the shape and displacement with voltage in the quasi-static limit of LaRC Thunder Actuators. The problem is treated with classical lamination theory and Von Karman non-linear analysis. In the case of classical lamination theory exact analytic solutions are found. It is shown that classical lamination theory is insufficient to describe the physical situation for large actuators but is sufficient for very small actuators. Numerical results are presented for the non-linear analysis and compared with experimental measurements. Snap-through behavior, bifurcation, and stability are presented and discussed.

DBI potential, DBI inflation action and general Lagrangian relative to phantom, K-essence and quintessence

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

Zhang, Qing; Huang, Yong-Chang, E-mail: ychuang@bjut.edu.cn

We derive a Dirac-Born-Infeld (DBI) potential and DBI inflation action by rescaling the metric. The determinant of the induced metric naturally includes the kinetic energy and the potential energy. In particular, the potential energy and kinetic energy can convert into each other in any order, which is in agreement with the limit of classical physics. This is quite different from the usual DBI action. We show that the Taylor expansion of the DBI action can be reduced into the form in the non-linear classical physics. These investigations are the support for the statement that the results of string theory aremore » consistent with quantum mechanics and classical physics. We deduce the Phantom, K-essence, Quintessence and Generalized Klein-Gordon Equation from the DBI model.« less

Amicus Plato, sed magis amica veritas: plots must obey the laws they refer to and models shall describe biophysical reality!

PubMed

Katkov, Igor I

2011-06-01

In the companion paper, we discussed in details proper linearization, calculation of the inactive osmotic volume, and analysis of the results on the Boyle-vant' Hoff plots. In this Letter, we briefly address some common errors and misconceptions in osmotic modeling and propose some approaches, namely: (1) inapplicability of the Kedem-Katchalsky formalism model in regards to the cryobiophysical reality, (2) calculation of the membrane hydraulic conductivity L(p) in the presence of permeable solutes, (3) proper linearization of the Arrhenius plots for the solute membrane permeability, (4) erroneous use of the term "toxicity" for the cryoprotective agents, and (5) advantages of the relativistic permeability approach (RP) developed by us vs. traditional ("classic") 2-parameter model. Copyright © 2011 Elsevier Inc. All rights reserved.

Coherent-state constellations and polar codes for thermal Gaussian channels

NASA Astrophysics Data System (ADS)

Lacerda, Felipe; Renes, Joseph M.; Scholz, Volkher B.

2017-06-01

Optical communication channels are ultimately quantum mechanical in nature, and we must therefore look beyond classical information theory to determine their communication capacity as well as to find efficient encoding and decoding schemes of the highest rates. Thermal channels, which arise from linear coupling of the field to a thermal environment, are of particular practical relevance; their classical capacity has been recently established, but their quantum capacity remains unknown. While the capacity sets the ultimate limit on reliable communication rates, it does not promise that such rates are achievable by practical means. Here we construct efficiently encodable codes for thermal channels which achieve the classical capacity and the so-called Gaussian coherent information for transmission of classical and quantum information, respectively. Our codes are based on combining polar codes with a discretization of the channel input into a finite "constellation" of coherent states. Encoding of classical information can be done using linear optics.

Energy diffusion controlled reaction rate of reacting particle driven by broad-band noise

NASA Astrophysics Data System (ADS)

Deng, M. L.; Zhu, W. Q.

2007-10-01

The energy diffusion controlled reaction rate of a reacting particle with linear weak damping and broad-band noise excitation is studied by using the stochastic averaging method. First, the stochastic averaging method for strongly nonlinear oscillators under broad-band noise excitation using generalized harmonic functions is briefly introduced. Then, the reaction rate of the classical Kramers' reacting model with linear weak damping and broad-band noise excitation is investigated by using the stochastic averaging method. The averaged Itô stochastic differential equation describing the energy diffusion and the Pontryagin equation governing the mean first-passage time (MFPT) are established. The energy diffusion controlled reaction rate is obtained as the inverse of the MFPT by solving the Pontryagin equation. The results of two special cases of broad-band noises, i.e. the harmonic noise and the exponentially corrected noise, are discussed in details. It is demonstrated that the general expression of reaction rate derived by the authors can be reduced to the classical ones via linear approximation and high potential barrier approximation. The good agreement with the results of the Monte Carlo simulation verifies that the reaction rate can be well predicted using the stochastic averaging method.

Conditional random slope: A new approach for estimating individual child growth velocity in epidemiological research.

PubMed

Leung, Michael; Bassani, Diego G; Racine-Poon, Amy; Goldenberg, Anna; Ali, Syed Asad; Kang, Gagandeep; Premkumar, Prasanna S; Roth, Daniel E

2017-09-10

Conditioning child growth measures on baseline accounts for regression to the mean (RTM). Here, we present the "conditional random slope" (CRS) model, based on a linear-mixed effects model that incorporates a baseline-time interaction term that can accommodate multiple data points for a child while also directly accounting for RTM. In two birth cohorts, we applied five approaches to estimate child growth velocities from 0 to 12 months to assess the effect of increasing data density (number of measures per child) on the magnitude of RTM of unconditional estimates, and the correlation and concordance between the CRS and four alternative metrics. Further, we demonstrated the differential effect of the choice of velocity metric on the magnitude of the association between infant growth and stunting at 2 years. RTM was minimally attenuated by increasing data density for unconditional growth modeling approaches. CRS and classical conditional models gave nearly identical estimates with two measures per child. Compared to the CRS estimates, unconditional metrics had moderate correlation (r = 0.65-0.91), but poor agreement in the classification of infants with relatively slow growth (kappa = 0.38-0.78). Estimates of the velocity-stunting association were the same for CRS and classical conditional models but differed substantially between conditional versus unconditional metrics. The CRS can leverage the flexibility of linear mixed models while addressing RTM in longitudinal analyses. © 2017 The Authors American Journal of Human Biology Published by Wiley Periodicals, Inc.

Parametric models to compute tryptophan fluorescence wavelengths from classical protein simulations.

PubMed

Lopez, Alvaro J; Martínez, Leandro

2018-02-26

Fluorescence spectroscopy is an important method to study protein conformational dynamics and solvation structures. Tryptophan (Trp) residues are the most important and practical intrinsic probes for protein fluorescence due to the variability of their fluorescence wavelengths: Trp residues emit in wavelengths ranging from 308 to 360 nm depending on the local molecular environment. Fluorescence involves electronic transitions, thus its computational modeling is a challenging task. We show that it is possible to predict the wavelength of emission of a Trp residue from classical molecular dynamics simulations by computing the solvent-accessible surface area or the electrostatic interaction between the indole group and the rest of the system. Linear parametric models are obtained to predict the maximum emission wavelengths with standard errors of the order 5 nm. In a set of 19 proteins with emission wavelengths ranging from 308 to 352 nm, the best model predicts the maximum wavelength of emission with a standard error of 4.89 nm and a quadratic Pearson correlation coefficient of 0.81. These models can be used for the interpretation of fluorescence spectra of proteins with multiple Trp residues, or for which local Trp environmental variability exists and can be probed by classical molecular dynamics simulations. © 2018 Wiley Periodicals, Inc. © 2018 Wiley Periodicals, Inc.

Element enrichment factor calculation using grain-size distribution and functional data regression.

PubMed

Sierra, C; Ordóñez, C; Saavedra, A; Gallego, J R

2015-01-01

In environmental geochemistry studies it is common practice to normalize element concentrations in order to remove the effect of grain size. Linear regression with respect to a particular grain size or conservative element is a widely used method of normalization. In this paper, the utility of functional linear regression, in which the grain-size curve is the independent variable and the concentration of pollutant the dependent variable, is analyzed and applied to detrital sediment. After implementing functional linear regression and classical linear regression models to normalize and calculate enrichment factors, we concluded that the former regression technique has some advantages over the latter. First, functional linear regression directly considers the grain-size distribution of the samples as the explanatory variable. Second, as the regression coefficients are not constant values but functions depending on the grain size, it is easier to comprehend the relationship between grain size and pollutant concentration. Third, regularization can be introduced into the model in order to establish equilibrium between reliability of the data and smoothness of the solutions. Copyright © 2014 Elsevier Ltd. All rights reserved.

Can a minimalist model of wind forced baroclinic Rossby waves produce reasonable results?

NASA Astrophysics Data System (ADS)

Watanabe, Wandrey B.; Polito, Paulo S.; da Silveira, Ilson C. A.

2016-04-01

The linear theory predicts that Rossby waves are the large scale mechanism of adjustment to perturbations of the geophysical fluid. Satellite measurements of sea level anomaly (SLA) provided sturdy evidence of the existence of these waves. Recent studies suggest that the variability in the altimeter records is mostly due to mesoscale nonlinear eddies and challenges the original interpretation of westward propagating features as Rossby waves. The objective of this work is to test whether a classic linear dynamic model is a reasonable explanation for the observed SLA. A linear-reduced gravity non-dispersive Rossby wave model is used to estimate the SLA forced by direct and remote wind stress. Correlations between model results and observations are up to 0.88. The best agreement is in the tropical region of all ocean basins. These correlations decrease towards insignificance in mid-latitudes. The relative contributions of eastern boundary (remote) forcing and local wind forcing in the generation of Rossby waves are also estimated and suggest that the main wave forming mechanism is the remote forcing. Results suggest that linear long baroclinic Rossby wave dynamics explain a significant part of the SLA annual variability at least in the tropical oceans.

Modeling and simulation of protein elution in linear pH and salt gradients on weak, strong and mixed cation exchange resins applying an extended Donnan ion exchange model.

PubMed

Wittkopp, Felix; Peeck, Lars; Hafner, Mathias; Frech, Christian

2018-04-13

Process development and characterization based on mathematic modeling provides several advantages and has been applied more frequently over the last few years. In this work, a Donnan equilibrium ion exchange (DIX) model is applied for modelling and simulation of ion exchange chromatography of a monoclonal antibody in linear chromatography. Four different cation exchange resin prototypes consisting of weak, strong and mixed ligands are characterized using pH and salt gradient elution experiments applying the extended DIX model. The modelling results are compared with the results using a classic stoichiometric displacement model. The Donnan equilibrium model is able to describe all four prototype resins while the stoichiometric displacement model fails for the weak and mixed weak/strong ligands. Finally, in silico chromatogram simulations of pH and pH/salt dual gradients are performed to verify the results and to show the consistency of the developed model. Copyright © 2018 Elsevier B.V. All rights reserved.

Dynamic optimization and its relation to classical and quantum constrained systems

NASA Astrophysics Data System (ADS)

Contreras, Mauricio; Pellicer, Rely; Villena, Marcelo

2017-08-01

We study the structure of a simple dynamic optimization problem consisting of one state and one control variable, from a physicist's point of view. By using an analogy to a physical model, we study this system in the classical and quantum frameworks. Classically, the dynamic optimization problem is equivalent to a classical mechanics constrained system, so we must use the Dirac method to analyze it in a correct way. We find that there are two second-class constraints in the model: one fix the momenta associated with the control variables, and the other is a reminder of the optimal control law. The dynamic evolution of this constrained system is given by the Dirac's bracket of the canonical variables with the Hamiltonian. This dynamic results to be identical to the unconstrained one given by the Pontryagin equations, which are the correct classical equations of motion for our physical optimization problem. In the same Pontryagin scheme, by imposing a closed-loop λ-strategy, the optimality condition for the action gives a consistency relation, which is associated to the Hamilton-Jacobi-Bellman equation of the dynamic programming method. A similar result is achieved by quantizing the classical model. By setting the wave function Ψ(x , t) =e iS(x , t) in the quantum Schrödinger equation, a non-linear partial equation is obtained for the S function. For the right-hand side quantization, this is the Hamilton-Jacobi-Bellman equation, when S(x , t) is identified with the optimal value function. Thus, the Hamilton-Jacobi-Bellman equation in Bellman's maximum principle, can be interpreted as the quantum approach of the optimization problem.

Modeling and comparative study of linear and nonlinear controllers for rotary inverted pendulum

NASA Astrophysics Data System (ADS)

Lima, Byron; Cajo, Ricardo; Huilcapi, Víctor; Agila, Wilton

2017-01-01

The rotary inverted pendulum (RIP) is a problem difficult to control, several studies have been conducted where different control techniques have been applied. Literature reports that, although problem is nonlinear, classical PID controllers presents appropriate performances when applied to the system. In this paper, a comparative study of the performances of linear and nonlinear PID structures is carried out. The control algorithms are evaluated in the RIP system, using indices of performance and power consumption, which allow the categorization of control strategies according to their performance. This article also presents the modeling system, which has been estimated some of the parameters involved in the RIP system, using computer-aided design tools (CAD) and experimental methods or techniques proposed by several authors attended. The results indicate a better performance of the nonlinear controller with an increase in the robustness and faster response than the linear controller.

Origin of nonsaturating linear magnetoresistivity

NASA Astrophysics Data System (ADS)

Kisslinger, Ferdinand; Ott, Christian; Weber, Heiko B.

2017-01-01

The observation of nonsaturating classical linear magnetoresistivity has been an enigmatic phenomenon in solid-state physics. We present a study of a two-dimensional ohmic conductor, including local Hall effect and a self-consistent consideration of the environment. An equivalent-circuit scheme delivers a simple and convincing argument why the magnetoresistivity is linear in strong magnetic field, provided that current and biasing electric field are misaligned by a nonlocal mechanism. A finite-element model of a two-dimensional conductor is suited to display the situations that create such deviating currents. Besides edge effects next to electrodes, charge carrier density fluctuations are efficiently generating this effect. However, mobility fluctuations that have frequently been related to linear magnetoresistivity are barely relevant. Despite its rare observation, linear magnetoresitivity is rather the rule than the exception in a regime of low charge carrier densities, misaligned current pathways and strong magnetic field.

Quantum Kramers model: Corrections to the linear response theory for continuous bath spectrum

NASA Astrophysics Data System (ADS)

Rips, Ilya

2017-01-01

Decay of the metastable state is analyzed within the quantum Kramers model in the weak-to-intermediate dissipation regime. The decay kinetics in this regime is determined by energy exchange between the unstable mode and the stable modes of thermal bath. In our previous paper [Phys. Rev. A 42, 4427 (1990), 10.1103/PhysRevA.42.4427], Grabert's perturbative approach to well dynamics in the case of the discrete bath [Phys. Rev. Lett. 61, 1683 (1988), 10.1103/PhysRevLett.61.1683] has been extended to account for the second order terms in the classical equations of motion (EOM) for the stable modes. Account of the secular terms reduces EOM for the stable modes to those of the forced oscillator with the time-dependent frequency (TDF oscillator). Analytic expression for the characteristic function of energy loss of the unstable mode has been derived in terms of the generating function of the transition probabilities for the quantum forced TDF oscillator. In this paper, the approach is further developed and applied to the case of the continuous frequency spectrum of the bath. The spectral density functions of the bath of stable modes are expressed in terms of the dissipative properties (the friction function) of the original bath. They simplify considerably for the one-dimensional systems, when the density of phonon states is constant. Explicit expressions for the fourth order corrections to the linear response theory result for the characteristic function of the energy loss and its cumulants are obtained for the particular case of the cubic potential with Ohmic (Markovian) dissipation. The range of validity of the perturbative approach in this case is determined (γ /ωb<0.26 ), which includes the turnover region. The dominant correction to the linear response theory result is associated with the "work function" and leads to reduction of the average energy loss and its dispersion. This reduction increases with the increasing dissipation strength (up to ˜10 % ) within the range of validity of the approach. We have also calculated corrections to the depopulation factor and the escape rate for the quantum and for the classical Kramers models. Results for the classical escape rate are in very good agreement with the numerical simulations for high barriers. The results can serve as an additional proof of the robustness and accuracy of the linear response theory.

Quantum Kramers model: Corrections to the linear response theory for continuous bath spectrum.

PubMed

Rips, Ilya

2017-01-01

Decay of the metastable state is analyzed within the quantum Kramers model in the weak-to-intermediate dissipation regime. The decay kinetics in this regime is determined by energy exchange between the unstable mode and the stable modes of thermal bath. In our previous paper [Phys. Rev. A 42, 4427 (1990)PLRAAN1050-294710.1103/PhysRevA.42.4427], Grabert's perturbative approach to well dynamics in the case of the discrete bath [Phys. Rev. Lett. 61, 1683 (1988)PRLTAO0031-900710.1103/PhysRevLett.61.1683] has been extended to account for the second order terms in the classical equations of motion (EOM) for the stable modes. Account of the secular terms reduces EOM for the stable modes to those of the forced oscillator with the time-dependent frequency (TDF oscillator). Analytic expression for the characteristic function of energy loss of the unstable mode has been derived in terms of the generating function of the transition probabilities for the quantum forced TDF oscillator. In this paper, the approach is further developed and applied to the case of the continuous frequency spectrum of the bath. The spectral density functions of the bath of stable modes are expressed in terms of the dissipative properties (the friction function) of the original bath. They simplify considerably for the one-dimensional systems, when the density of phonon states is constant. Explicit expressions for the fourth order corrections to the linear response theory result for the characteristic function of the energy loss and its cumulants are obtained for the particular case of the cubic potential with Ohmic (Markovian) dissipation. The range of validity of the perturbative approach in this case is determined (γ/ω_{b}<0.26), which includes the turnover region. The dominant correction to the linear response theory result is associated with the "work function" and leads to reduction of the average energy loss and its dispersion. This reduction increases with the increasing dissipation strength (up to ∼10%) within the range of validity of the approach. We have also calculated corrections to the depopulation factor and the escape rate for the quantum and for the classical Kramers models. Results for the classical escape rate are in very good agreement with the numerical simulations for high barriers. The results can serve as an additional proof of the robustness and accuracy of the linear response theory.

Stable long-time semiclassical description of zero-point energy in high-dimensional molecular systems.

PubMed

Garashchuk, Sophya; Rassolov, Vitaly A

2008-07-14

Semiclassical implementation of the quantum trajectory formalism [J. Chem. Phys. 120, 1181 (2004)] is further developed to give a stable long-time description of zero-point energy in anharmonic systems of high dimensionality. The method is based on a numerically cheap linearized quantum force approach; stabilizing terms compensating for the linearization errors are added into the time-evolution equations for the classical and nonclassical components of the momentum operator. The wave function normalization and energy are rigorously conserved. Numerical tests are performed for model systems of up to 40 degrees of freedom.

Central Limit Theorems for Linear Statistics of Heavy Tailed Random Matrices

NASA Astrophysics Data System (ADS)

Benaych-Georges, Florent; Guionnet, Alice; Male, Camille

2014-07-01

We show central limit theorems (CLT) for the linear statistics of symmetric matrices with independent heavy tailed entries, including entries in the domain of attraction of α-stable laws and entries with moments exploding with the dimension, as in the adjacency matrices of Erdös-Rényi graphs. For the second model, we also prove a central limit theorem of the moments of its empirical eigenvalues distribution. The limit laws are Gaussian, but unlike the case of standard Wigner matrices, the normalization is the one of the classical CLT for independent random variables.

Extracting surface diffusion coefficients from batch adsorption measurement data: application of the classic Langmuir kinetics model.

PubMed

Chu, Khim Hoong

2017-11-09

Surface diffusion coefficients may be estimated by fitting solutions of a diffusion model to batch kinetic data. For non-linear systems, a numerical solution of the diffusion model's governing equations is generally required. We report here the application of the classic Langmuir kinetics model to extract surface diffusion coefficients from batch kinetic data. The use of the Langmuir kinetics model in lieu of the conventional surface diffusion model allows derivation of an analytical expression. The parameter estimation procedure requires determining the Langmuir rate coefficient from which the pertinent surface diffusion coefficient is calculated. Surface diffusion coefficients within the 10 -9 to 10 -6  cm 2 /s range obtained by fitting the Langmuir kinetics model to experimental kinetic data taken from the literature are found to be consistent with the corresponding values obtained from the traditional surface diffusion model. The virtue of this simplified parameter estimation method is that it reduces the computational complexity as the analytical expression involves only an algebraic equation in closed form which is easily evaluated by spreadsheet computation.

Survey of non-linear hydrodynamic models of type-II Cepheids

NASA Astrophysics Data System (ADS)

Smolec, R.

2016-03-01

We present a grid of non-linear convective type-II Cepheid models. The dense model grids are computed for 0.6 M⊙ and a range of metallicities ([Fe/H] = -2.0, -1.5, -1.0), and for 0.8 M⊙ ([Fe/H] = -1.5). Two sets of convective parameters are considered. The models cover the full temperature extent of the classical instability strip, but are limited in luminosity; for the most luminous models, violent pulsation leads to the decoupling of the outermost model shell. Hence, our survey reaches only the shortest period RV Tau domain. In the Hertzsprung-Russell diagram, we detect two domains in which period-doubled pulsation is possible. The first extends through the BL Her domain and low-luminosity W Vir domain (pulsation periods ˜2-6.5 d). The second domain extends at higher luminosities (W Vir domain; periods >9.5 d). Some models within these domains display period-4 pulsation. We also detect very narrow domains (˜10 K wide) in which modulation of pulsation is possible. Another interesting phenomenon we detect is double-mode pulsation in the fundamental mode and in the fourth radial overtone. Fourth overtone is a surface mode, trapped in the outer model layers. Single-mode pulsation in the fourth overtone is also possible on the hot side of the classical instability strip. The origin of the above phenomena is discussed. In particular, the role of resonances in driving different pulsation dynamics as well as in shaping the morphology of the radius variation curves is analysed.

Lattice model of linear telechelic polymer melts. II. Influence of chain stiffness on basic thermodynamic properties

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

Xu, Wen-Sheng, E-mail: wsxu@uchicago.edu; Freed, Karl F., E-mail: freed@uchicago.edu; Department of Chemistry, The University of Chicago, Chicago, Illinois 60637

2015-07-14

The lattice cluster theory (LCT) for semiflexible linear telechelic melts, developed in Paper I, is applied to examine the influence of chain stiffness on the average degree of self-assembly and the basic thermodynamic properties of linear telechelic polymer melts. Our calculations imply that chain stiffness promotes self-assembly of linear telechelic polymer melts that assemble on cooling when either polymer volume fraction ϕ or temperature T is high, but opposes self-assembly when both ϕ and T are sufficiently low. This allows us to identify a boundary line in the ϕ-T plane that separates two regions of qualitatively different influence of chainmore » stiffness on self-assembly. The enthalpy and entropy of self-assembly are usually treated as adjustable parameters in classical Flory-Huggins type theories for the equilibrium self-assembly of polymers, but they are demonstrated here to strongly depend on chain stiffness. Moreover, illustrative calculations for the dependence of the entropy density of linear telechelic polymer melts on chain stiffness demonstrate the importance of including semiflexibility within the LCT when exploring the nature of glass formation in models of linear telechelic polymer melts.« less

Simple analytical model of a thermal diode

NASA Astrophysics Data System (ADS)

Kaushik, Saurabh; Kaushik, Sachin; Marathe, Rahul

2018-05-01

Recently there is a lot of attention given to manipulation of heat by constructing thermal devices such as thermal diodes, transistors and logic gates. Many of the models proposed have an asymmetry which leads to the desired effect. Presence of non-linear interactions among the particles is also essential. But, such models lack analytical understanding. Here we propose a simple, analytically solvable model of a thermal diode. Our model consists of classical spins in contact with multiple heat baths and constant external magnetic fields. Interestingly the magnetic field is the only parameter required to get the effect of heat rectification.

Spectral likelihood expansions for Bayesian inference

NASA Astrophysics Data System (ADS)

Nagel, Joseph B.; Sudret, Bruno

2016-03-01

A spectral approach to Bayesian inference is presented. It pursues the emulation of the posterior probability density. The starting point is a series expansion of the likelihood function in terms of orthogonal polynomials. From this spectral likelihood expansion all statistical quantities of interest can be calculated semi-analytically. The posterior is formally represented as the product of a reference density and a linear combination of polynomial basis functions. Both the model evidence and the posterior moments are related to the expansion coefficients. This formulation avoids Markov chain Monte Carlo simulation and allows one to make use of linear least squares instead. The pros and cons of spectral Bayesian inference are discussed and demonstrated on the basis of simple applications from classical statistics and inverse modeling.

Kinetics of the chiral phase transition in a linear σ model

NASA Astrophysics Data System (ADS)

Wesp, Christian; van Hees, Hendrik; Meistrenko, Alex; Greiner, Carsten

2018-02-01

We study the dynamics of the chiral phase transition in a linear quark-meson σ model using a novel approach based on semiclassical wave-particle duality. The quarks are treated as test particles in a Monte Carlo simulation of elastic collisions and the coupling to the σ meson, which is treated as a classical field, via a kinetic approach motivated by wave-particle duality. The exchange of energy and momentum between particles and fields is described in terms of appropriate Gaussian wave packets. It has been demonstrated that energy-momentum conservation and the principle of detailed balance are fulfilled, and that the dynamics leads to the correct equilibrium limit. First schematic studies of the dynamics of matter produced in heavy-ion collisions are presented.

Response statistics of rotating shaft with non-linear elastic restoring forces by path integration

NASA Astrophysics Data System (ADS)

Gaidai, Oleg; Naess, Arvid; Dimentberg, Michael

2017-07-01

Extreme statistics of random vibrations is studied for a Jeffcott rotor under uniaxial white noise excitation. Restoring force is modelled as elastic non-linear; comparison is done with linearized restoring force to see the force non-linearity effect on the response statistics. While for the linear model analytical solutions and stability conditions are available, it is not generally the case for non-linear system except for some special cases. The statistics of non-linear case is studied by applying path integration (PI) method, which is based on the Markov property of the coupled dynamic system. The Jeffcott rotor response statistics can be obtained by solving the Fokker-Planck (FP) equation of the 4D dynamic system. An efficient implementation of PI algorithm is applied, namely fast Fourier transform (FFT) is used to simulate dynamic system additive noise. The latter allows significantly reduce computational time, compared to the classical PI. Excitation is modelled as Gaussian white noise, however any kind distributed white noise can be implemented with the same PI technique. Also multidirectional Markov noise can be modelled with PI in the same way as unidirectional. PI is accelerated by using Monte Carlo (MC) estimated joint probability density function (PDF) as initial input. Symmetry of dynamic system was utilized to afford higher mesh resolution. Both internal (rotating) and external damping are included in mechanical model of the rotor. The main advantage of using PI rather than MC is that PI offers high accuracy in the probability distribution tail. The latter is of critical importance for e.g. extreme value statistics, system reliability, and first passage probability.

Application of linear logic to simulation

NASA Astrophysics Data System (ADS)

Clarke, Thomas L.

1998-08-01

Linear logic, since its introduction by Girard in 1987 has proven expressive and powerful. Linear logic has provided natural encodings of Turing machines, Petri nets and other computational models. Linear logic is also capable of naturally modeling resource dependent aspects of reasoning. The distinguishing characteristic of linear logic is that it accounts for resources; two instances of the same variable are considered differently from a single instance. Linear logic thus must obey a form of the linear superposition principle. A proportion can be reasoned with only once, unless a special operator is applied. Informally, linear logic distinguishes two kinds of conjunction, two kinds of disjunction, and also introduces a modal storage operator that explicitly indicates propositions that can be reused. This paper discuses the application of linear logic to simulation. A wide variety of logics have been developed; in addition to classical logic, there are fuzzy logics, affine logics, quantum logics, etc. All of these have found application in simulations of one sort or another. The special characteristics of linear logic and its benefits for simulation will be discussed. Of particular interest is a connection that can be made between linear logic and simulated dynamics by using the concept of Lie algebras and Lie groups. Lie groups provide the connection between the exponential modal storage operators of linear logic and the eigen functions of dynamic differential operators. Particularly suggestive are possible relations between complexity result for linear logic and non-computability results for dynamical systems.

Heat capacities and volumetric changes in the glass transition range: a constitutive approach based on the standard linear solid

NASA Astrophysics Data System (ADS)

Lion, Alexander; Mittermeier, Christoph; Johlitz, Michael

2017-09-01

A novel approach to represent the glass transition is proposed. It is based on a physically motivated extension of the linear viscoelastic Poynting-Thomson model. In addition to a temperature-dependent damping element and two linear springs, two thermal strain elements are introduced. In order to take the process dependence of the specific heat into account and to model its characteristic behaviour below and above the glass transition, the Helmholtz free energy contains an additional contribution which depends on the temperature history and on the current temperature. The model describes the process-dependent volumetric and caloric behaviour of glass-forming materials, and defines a functional relationship between pressure, volumetric strain, and temperature. If a model for the isochoric part of the material behaviour is already available, for example a model of finite viscoelasticity, the caloric and volumetric behaviour can be represented with the current approach. The proposed model allows computing the isobaric and isochoric heat capacities in closed form. The difference c_p -c_v is process-dependent and tends towards the classical expression in the glassy and equilibrium ranges. Simulations and theoretical studies demonstrate the physical significance of the model.

Exotic states of matter with polariton chains

NASA Astrophysics Data System (ADS)

Kalinin, Kirill P.; Lagoudakis, Pavlos G.; Berloff, Natalia G.

2018-04-01

We consider linear periodic chains of exciton-polariton condensates formed by pumping polaritons nonresonantly into a linear network. To the leading order such a sequence of condensates establishes relative phases as to minimize a classical one-dimensional X Y Hamiltonian with nearest and next-to-nearest neighbors. We show that the low-energy states of polaritonic linear chains demonstrate various classical regimes: ferromagnetic, antiferromagnetic, and frustrated spiral phases where quantum or thermal fluctuations are expected to give rise to a spin-liquid state. At the same time nonlinear interactions at higher pumping intensities bring about phase chaos and novel exotic phases.

Coupling machine learning with mechanistic models to study runoff production and river flow at the hillslope scale

NASA Astrophysics Data System (ADS)

Marçais, J.; Gupta, H. V.; De Dreuzy, J. R.; Troch, P. A. A.

2016-12-01

Geomorphological structure and geological heterogeneity of hillslopes are major controls on runoff responses. The diversity of hillslopes (morphological shapes and geological structures) on one hand, and the highly non linear runoff mechanism response on the other hand, make it difficult to transpose what has been learnt at one specific hillslope to another. Therefore, making reliable predictions on runoff appearance or river flow for a given hillslope is a challenge. Applying a classic model calibration (based on inverse problems technique) requires doing it for each specific hillslope and having some data available for calibration. When applied to thousands of cases it cannot always be promoted. Here we propose a novel modeling framework based on coupling process based models with data based approach. First we develop a mechanistic model, based on hillslope storage Boussinesq equations (Troch et al. 2003), able to model non linear runoff responses to rainfall at the hillslope scale. Second we set up a model database, representing thousands of non calibrated simulations. These simulations investigate different hillslope shapes (real ones obtained by analyzing 5m digital elevation model of Brittany and synthetic ones), different hillslope geological structures (i.e. different parametrizations) and different hydrologic forcing terms (i.e. different infiltration chronicles). Then, we use this model library to train a machine learning model on this physically based database. Machine learning model performance is then assessed by a classic validating phase (testing it on new hillslopes and comparing machine learning with mechanistic outputs). Finally we use this machine learning model to learn what are the hillslope properties controlling runoffs. This methodology will be further tested combining synthetic datasets with real ones.

3D inelastic analysis methods for hot section components

NASA Technical Reports Server (NTRS)

Dame, L. T.; Chen, P. C.; Hartle, M. S.; Huang, H. T.

1985-01-01

The objective is to develop analytical tools capable of economically evaluating the cyclic time dependent plasticity which occurs in hot section engine components in areas of strain concentration resulting from the combination of both mechanical and thermal stresses. Three models were developed. A simple model performs time dependent inelastic analysis using the power law creep equation. The second model is the classical model of Professors Walter Haisler and David Allen of Texas A and M University. The third model is the unified model of Bodner, Partom, et al. All models were customized for linear variation of loads and temperatures with all material properties and constitutive models being temperature dependent.

Data dependent systems approach to modal analysis Part 1: Theory

NASA Astrophysics Data System (ADS)

Pandit, S. M.; Mehta, N. P.

1988-05-01

The concept of Data Dependent Systems (DDS) and its applicability in the context of modal vibration analysis is presented. The ability of the DDS difference equation models to provide a complete representation of a linear dynamic system from its sampled response data forms the basis of the approach. The models are decomposed into deterministic and stochastic components so that system characteristics are isolated from noise effects. The modelling strategy is outlined, and the method of analysis associated with modal parameter identification is described in detail. Advantages and special features of the DDS methodology are discussed. Since the correlated noise is appropriately and automatically modelled by the DDS, the modal parameters are shown to be estimated very accurately and hence no preprocessing of the data is needed. Complex mode shapes and non-classical damping are as easily analyzed as the classical normal mode analysis. These features are illustrated by using simulated data in this Part I and real data on a disc-brake rotor in Part II.

Study of the slope of the linear relationship between retention and mobile phase composition (Snyder-Soczewiñski model) in normal phase liquid chromatography with bonded and charge-transfer phases.

PubMed

Wu, Di; Lucy, Charles A

2016-12-02

The Snyder model and the Soczewiñski model are compared on classic NPLC bonded phases using literature data, and on the charge transfer 2, 4-dinitroanilinopropyl (DNAP) column using experimentally collected data. Overall, the Snyder model slightly better predicts the n-slope than the Soczewiñski model. However, both models give comparable uncertainty in predicting n-slope for a given compound. The number of aromatic double bonds was the most suitable descriptor for estimating the relative n-slope of PAHs, as it correlated with behavior better than the number of aromatic rings and is simpler to calculate than the solute adsorption area. On the DNAP phase, a modified Soczewiñski model is suggested to allow for the significant contribution of the aromatic rings to the n-slope. For classic NPLC bonded phases and DNAP columns, the contribution of polar group to the n-slope parallels the adsorption energy of each polar group. Copyright © 2016 Elsevier B.V. All rights reserved.

A new model-free index of dynamic cerebral blood flow autoregulation.

PubMed

Chacón, Max; Jara, José Luis; Panerai, Ronney B

2014-01-01

The classic dynamic autoregulatory index (ARI), proposed by Aaslid and Tiecks, is one of the most widely used methods to assess the efficiency of dynamic cerebral autoregulation. Although this index is often used in clinical research and is also included in some commercial equipment, it exhibits considerable intra-subject variability, and has the tendency to produce false positive results in clinical applications. An alternative index of dynamic cerebral autoregulation is proposed, which overcomes most of the limitations of the classic method and also has the advantage of being model-free. This new index uses two parameters that are obtained directly from the response signal of the cerebral blood flow velocity to a transient decrease in arterial blood pressure provoked by the sudden release of bilateral thigh cuffs, and a third parameter measuring the difference in slope of this response and the change in arterial blood pressure achieved. With the values of these parameters, a corresponding classic autoregulatory index value could be calculated by using a linear regression model built from theoretical curves generated with the Aaslid-Tiecks model. In 16 healthy subjects who underwent repeated thigh-cuff manoeuvres, the model-free approach exhibited significantly lower intra-subject variability, as measured by the unbiased coefficient of variation, than the classic autoregulatory index (p = 0.032) and the Rate of Return (p<0.001), another measure of cerebral autoregulation used for this type of systemic pressure stimulus, from 39.23%±41.91% and 55.31%±31.27%, respectively, to 15.98%±7.75%.

A New Model-Free Index of Dynamic Cerebral Blood Flow Autoregulation

PubMed Central

Chacón, Max; Jara, José Luis; Panerai, Ronney B.

2014-01-01

The classic dynamic autoregulatory index (ARI), proposed by Aaslid and Tiecks, is one of the most widely used methods to assess the efficiency of dynamic cerebral autoregulation. Although this index is often used in clinical research and is also included in some commercial equipment, it exhibits considerable intra-subject variability, and has the tendency to produce false positive results in clinical applications. An alternative index of dynamic cerebral autoregulation is proposed, which overcomes most of the limitations of the classic method and also has the advantage of being model-free. This new index uses two parameters that are obtained directly from the response signal of the cerebral blood flow velocity to a transient decrease in arterial blood pressure provoked by the sudden release of bilateral thigh cuffs, and a third parameter measuring the difference in slope of this response and the change in arterial blood pressure achieved. With the values of these parameters, a corresponding classic autoregulatory index value could be calculated by using a linear regression model built from theoretical curves generated with the Aaslid-Tiecks model. In 16 healthy subjects who underwent repeated thigh-cuff manoeuvres, the model-free approach exhibited significantly lower intra-subject variability, as measured by the unbiased coefficient of variation, than the classic autoregulatory index (p = 0.032) and the Rate of Return (p<0.001), another measure of cerebral autoregulation used for this type of systemic pressure stimulus, from 39.23%±41.91% and 55.31%±31.27%, respectively, to 15.98%±7.75%. PMID:25313519

Cocaine Dependence Treatment Data: Methods for Measurement Error Problems With Predictors Derived From Stationary Stochastic Processes

PubMed Central

Guan, Yongtao; Li, Yehua; Sinha, Rajita

2011-01-01

In a cocaine dependence treatment study, we use linear and nonlinear regression models to model posttreatment cocaine craving scores and first cocaine relapse time. A subset of the covariates are summary statistics derived from baseline daily cocaine use trajectories, such as baseline cocaine use frequency and average daily use amount. These summary statistics are subject to estimation error and can therefore cause biased estimators for the regression coefficients. Unlike classical measurement error problems, the error we encounter here is heteroscedastic with an unknown distribution, and there are no replicates for the error-prone variables or instrumental variables. We propose two robust methods to correct for the bias: a computationally efficient method-of-moments-based method for linear regression models and a subsampling extrapolation method that is generally applicable to both linear and nonlinear regression models. Simulations and an application to the cocaine dependence treatment data are used to illustrate the efficacy of the proposed methods. Asymptotic theory and variance estimation for the proposed subsampling extrapolation method and some additional simulation results are described in the online supplementary material. PMID:21984854

From localization to anomalous diffusion in the dynamics of coupled kicked rotors

NASA Astrophysics Data System (ADS)

Notarnicola, Simone; Iemini, Fernando; Rossini, Davide; Fazio, Rosario; Silva, Alessandro; Russomanno, Angelo

2018-02-01

We study the effect of many-body quantum interference on the dynamics of coupled periodically kicked systems whose classical dynamics is chaotic and shows an unbounded energy increase. We specifically focus on an N -coupled kicked rotors model: We find that the interplay of quantumness and interactions dramatically modifies the system dynamics, inducing a transition between energy saturation and unbounded energy increase. We discuss this phenomenon both numerically and analytically through a mapping onto an N -dimensional Anderson model. The thermodynamic limit N →∞ , in particular, always shows unbounded energy growth. This dynamical delocalization is genuinely quantum and very different from the classical one: Using a mean-field approximation, we see that the system self-organizes so that the energy per site increases in time as a power law with exponent smaller than 1. This wealth of phenomena is a genuine effect of quantum interference: The classical system for N ≥2 always behaves ergodically with an energy per site linearly increasing in time. Our results show that quantum mechanics can deeply alter the regularity or ergodicity properties of a many-body-driven system.

Comparison of a Classical and Quantum Based Restricted Boltzmann Machine (RBM) for Application to Non-linear Multivariate Regression.

NASA Astrophysics Data System (ADS)

Dorband, J. E.; Tilak, N.; Radov, A.

2016-12-01

In this paper, a classical computer implementation of RBM is compared to a quantum annealing based RBM running on a D-Wave 2X (an adiabatic quantum computer). The codes for both are essentially identical. Only a flag is set to change the activation function from a classically computed logistic function to the D-Wave. To obtain greater understanding of the behavior of the D-Wave, a study of the stochastic properties of a virtual qubit (a 12 qubit chain) and a cell of qubits (an 8 qubit cell) was performed. We will present the results of comparing the D-Wave implementation with a theoretically errorless adiabatic quantum computer. The main purpose of this study is to develop a generic RBM regression tool in order to infer CO2 fluxes from the NASA satellite OCO-2 observed CO2 concentrations and predicted atmospheric states using regression models. The carbon fluxes will then be assimilated into a land surface model to predict the Net Ecosystem Exchange at globally distributed regional sites.

Transverse instability of periodic and generalized solitary waves for a fifth-order KP model

NASA Astrophysics Data System (ADS)

Haragus, Mariana; Wahlén, Erik

2017-02-01

We consider a fifth-order Kadomtsev-Petviashvili equation which arises as a two-dimensional model in the classical water-wave problem. This equation possesses a family of generalized line solitary waves which decay exponentially to periodic waves at infinity. We prove that these solitary waves are transversely spectrally unstable and that this instability is induced by the transverse instability of the periodic tails. We rely upon a detailed spectral analysis of some suitably chosen linear operators.

Stability Assessment and Tuning of an Adaptively Augmented Classical Controller for Launch Vehicle Flight Control

NASA Technical Reports Server (NTRS)

VanZwieten, Tannen; Zhu, J. Jim; Adami, Tony; Berry, Kyle; Grammar, Alex; Orr, Jeb S.; Best, Eric A.

2014-01-01

Recently, a robust and practical adaptive control scheme for launch vehicles [ [1] has been introduced. It augments a classical controller with a real-time loop-gain adaptation, and it is therefore called Adaptive Augmentation Control (AAC). The loop-gain will be increased from the nominal design when the tracking error between the (filtered) output and the (filtered) command trajectory is large; whereas it will be decreased when excitation of flex or sloshing modes are detected. There is a need to determine the range and rate of the loop-gain adaptation in order to retain (exponential) stability, which is critical in vehicle operation, and to develop some theoretically based heuristic tuning methods for the adaptive law gain parameters. The classical launch vehicle flight controller design technics are based on gain-scheduling, whereby the launch vehicle dynamics model is linearized at selected operating points along the nominal tracking command trajectory, and Linear Time-Invariant (LTI) controller design techniques are employed to ensure asymptotic stability of the tracking error dynamics, typically by meeting some prescribed Gain Margin (GM) and Phase Margin (PM) specifications. The controller gains at the design points are then scheduled, tuned and sometimes interpolated to achieve good performance and stability robustness under external disturbances (e.g. winds) and structural perturbations (e.g. vehicle modeling errors). While the GM does give a bound for loop-gain variation without losing stability, it is for constant dispersions of the loop-gain because the GM is based on frequency-domain analysis, which is applicable only for LTI systems. The real-time adaptive loop-gain variation of the AAC effectively renders the closed-loop system a time-varying system, for which it is well-known that the LTI system stability criterion is neither necessary nor sufficient when applying to a Linear Time-Varying (LTV) system in a frozen-time fashion. Therefore, a generalized stability metric for time-varying loop=gain perturbations is needed for the AAC.

Research on transient thermal process of a friction brake during repetitive cycles of operation

NASA Astrophysics Data System (ADS)

Slavchev, Yanko; Dimitrov, Lubomir; Dimitrov, Yavor

2017-12-01

Simplified models are used in the classical engineering analyses of the friction brake heating temperature during repetitive cycles of operation to determine basically the maximum and minimum brake temperatures. The objective of the present work is to broaden and complement the possibilities for research through a model that is based on the classical scheme of the Newton's law of cooling and improves the studies by adding a disturbance function for a corresponding braking process. A general case of braking in non-periodic repetitive mode is considered, for which a piecewise function is defined to apply pulse thermal loads to the system. Cases with rectangular and triangular waveforms are presented. Periodic repetitive braking process is also studied using a periodic rectangular waveform until a steady thermal state is achieved. Different numerical methods such as the Euler's method, the classical fourth order Runge-Kutta (RK4) and the Runge-Kutta-Fehlberg 4-5 (RKF45) are used to solve the non-linear differential equation of the model. The constructed model allows during pre-engineering calculations to be determined effectively the time for reaching the steady thermal state of the brake, to be simulated actual braking modes in vehicles and material handling machines, and to be accounted for the thermal impact when performing fatigue calculations.

Electrical fatigue behaviour in lead zirconate titanate: an experimental and theoretical study

NASA Astrophysics Data System (ADS)

Bhattacharyya, Mainak; Arockiarajan, A.

2013-08-01

A systematic investigation on electrical fatigue in lead zirconate titanate (PZT) is carried out for different loading frequencies. Experiments are conducted up to 106 cycles to measure the electrical displacement and longitudinal strain on bulk ceramics in the bipolar mode with large electrical loading conditions. A simplified macroscopic model based on physical mechanisms of domain switching is developed to predict the non-linear behaviour. In this model, the volume fraction of a domain is used as the internal variable by considering the mechanisms of domain nucleation and propagation (domain wall movement). The measured material properties at different fatigue cycles are incorporated into the switching model as damage parameters and the classical strain versus electric field and electric displacement versus electric field curves are simulated. Comparison between the experiments and simulations shows that the proposed model can reproduce the characteristics of non-linear as well as fatigue responses.

Glomerular structural-functional relationship models of diabetic nephropathy are robust in type 1 diabetic patients.

PubMed

Mauer, Michael; Caramori, Maria Luiza; Fioretto, Paola; Najafian, Behzad

2015-06-01

Studies of structural-functional relationships have improved understanding of the natural history of diabetic nephropathy (DN). However, in order to consider structural end points for clinical trials, the robustness of the resultant models needs to be verified. This study examined whether structural-functional relationship models derived from a large cohort of type 1 diabetic (T1D) patients with a wide range of renal function are robust. The predictability of models derived from multiple regression analysis and piecewise linear regression analysis was also compared. T1D patients (n = 161) with research renal biopsies were divided into two equal groups matched for albumin excretion rate (AER). Models to explain AER and glomerular filtration rate (GFR) by classical DN lesions in one group (T1D-model, or T1D-M) were applied to the other group (T1D-test, or T1D-T) and regression analyses were performed. T1D-M-derived models explained 70 and 63% of AER variance and 32 and 21% of GFR variance in T1D-M and T1D-T, respectively, supporting the substantial robustness of the models. Piecewise linear regression analyses substantially improved predictability of the models with 83% of AER variance and 66% of GFR variance explained by classical DN glomerular lesions alone. These studies demonstrate that DN structural-functional relationship models are robust, and if appropriate models are used, glomerular lesions alone explain a major proportion of AER and GFR variance in T1D patients. © The Author 2014. Published by Oxford University Press on behalf of ERA-EDTA. All rights reserved.

Application of singular value decomposition to structural dynamics systems with constraints

NASA Technical Reports Server (NTRS)

Juang, J.-N.; Pinson, L. D.

1985-01-01

Singular value decomposition is used to construct a coordinate transformation for a linear dynamic system subject to linear, homogeneous constraint equations. The method is compared with two commonly used methods, namely classical Gaussian elimination and Walton-Steeves approach. Although the classical method requires fewer numerical operations, the singular value decomposition method is more accurate and convenient in eliminating the dependent coordinates. Numerical examples are presented to demonstrate the application of the method.

Classical and quantum communication without a shared reference frame.

PubMed

Bartlett, Stephen D; Rudolph, Terry; Spekkens, Robert W

2003-07-11

We show that communication without a shared reference frame is possible using entangled states. Both classical and quantum information can be communicated with perfect fidelity without a shared reference frame at a rate that asymptotically approaches one classical bit or one encoded qubit per transmitted qubit. We present an optical scheme to communicate classical bits without a shared reference frame using entangled photon pairs and linear optical Bell state measurements.

Modeling pinchoff and reconnection in a Hele-Shaw cell. I. The models and their calibration

NASA Astrophysics Data System (ADS)

Lee, Hyeong-Gi; Lowengrub, J. S.; Goodman, J.

2002-02-01

This is the first paper in a two-part series in which we analyze two model systems to study pinchoff and reconnection in binary fluid flow in a Hele-Shaw cell with arbitrary density and viscosity contrast between the components. The systems stem from a simplification of a general system of equations governing the motion of a binary fluid (NSCH model [Lowengrub and Truskinovsky, Proc. R. Soc. London, Ser. A 454, 2617 (1998)]) to flow in a Hele-Shaw cell. The system takes into account the chemical diffusivity between different components of a fluid mixture and the reactive stresses induced by inhomogeneity. In one of the systems we consider (HSCH), the binary fluid may be compressible due to diffusion. In the other system (BHSCH), a Boussinesq approximation is used and the fluid is incompressible. In this paper, we motivate, present and calibrate the HSCH/BHSCH equations so as to yield the classical sharp interface model as a limiting case. We then analyze their equilibria, one dimensional evolution and linear stability. In the second paper [paper II, Phys. Fluids 14, 514 (2002)], we analyze the behavior of the models in the fully nonlinear regime. In the BHSCH system, the equilibrium concentration profile is obtained using the classical Maxwell construction [Rowlinson and Widom, Molecular Theory of Capillarity (Clarendon, Oxford, 1979)] and does not depend on the orientation of the gravitational field. We find that the equilibria in the HSCH model are somewhat surprising as the gravitational field actually affects the internal structure of an isolated interface by driving additional stratification of light and heavy fluids over that predicted in the Boussinesq case. A comparison of the linear growth rates indicates that the HSCH system is slightly more diffusive than the BHSCH system. In both, linear convergence to the sharp interface growth rates is observed in a parameter controlling the interface thickness. In addition, we identify the effect that each of the parameters, in the HSCH/BHSCH models, has on the linear growth rates. We then show how this analysis may be used to suggest a set of modified parameters which, when used in the HSCH/BHSCH systems, yield improved agreement with the sharp interface model at a finite interface thickness. Evidence of this improved agreement may be found in paper II.

Classical and quantum simulations of warm dense carbon

NASA Astrophysics Data System (ADS)

Whitley, Heather; Sanchez, David; Hamel, Sebastien; Correa, Alfredo; Benedict, Lorin

We have applied classical and DFT-based molecular dynamics (MD) simulations to study the equation of state of carbon in the warm dense matter regime (ρ = 3.7 g/cc, 0.86 eV

Public and Private School Distinction, Regional Development Differences, and Other Factors Influencing the Success of Primary School Students in Turkey

ERIC Educational Resources Information Center

Sulku, Seher Nur; Abdioglu, Zehra

2015-01-01

This study investigates the factors influencing the success of students in primary schools in Turkey. TIMSS 2011 data for Turkey, measuring the success of eighth-grade students in the field of mathematics, were used in an econometric analysis, performed using classical linear regression models. Two hundred thirty-nine schools participated in the…

Cumulants, free cumulants and half-shuffles

PubMed Central

Ebrahimi-Fard, Kurusch; Patras, Frédéric

2015-01-01

Free cumulants were introduced as the proper analogue of classical cumulants in the theory of free probability. There is a mix of similarities and differences, when one considers the two families of cumulants. Whereas the combinatorics of classical cumulants is well expressed in terms of set partitions, that of free cumulants is described and often introduced in terms of non-crossing set partitions. The formal series approach to classical and free cumulants also largely differs. The purpose of this study is to put forward a different approach to these phenomena. Namely, we show that cumulants, whether classical or free, can be understood in terms of the algebra and combinatorics underlying commutative as well as non-commutative (half-)shuffles and (half-) unshuffles. As a corollary, cumulants and free cumulants can be characterized through linear fixed point equations. We study the exponential solutions of these linear fixed point equations, which display well the commutative, respectively non-commutative, character of classical and free cumulants. PMID:27547078

Precise measurement of coupling strength and high temperature quantum effect in a nonlinearly coupled qubit-oscillator system

NASA Astrophysics Data System (ADS)

Ge, Li; Zhao, Nan

2018-04-01

We study the coherence dynamics of a qubit coupled to a harmonic oscillator with both linear and quadratic interactions. As long as the linear coupling strength is much smaller than the oscillator frequency, the long time behavior of the coherence is dominated by the quadratic coupling strength g 2. The coherence decays and revives at a period , with the width of coherence peak decreasing as the temperature increases, hence providing a way to measure g 2 precisely without cooling. Unlike the case of linear coupling, here the coherence dynamics never reduces to the classical limit in which the oscillator is classical. Finally, the validity of linear coupling approximation is discussed and the coherence under Hahn-echo is evaluated.

FAST TRACK PAPER: Non-iterative multiple-attenuation methods: linear inverse solutions to non-linear inverse problems - II. BMG approximation

NASA Astrophysics Data System (ADS)

Ikelle, Luc T.; Osen, Are; Amundsen, Lasse; Shen, Yunqing

2004-12-01

The classical linear solutions to the problem of multiple attenuation, like predictive deconvolution, τ-p filtering, or F-K filtering, are generally fast, stable, and robust compared to non-linear solutions, which are generally either iterative or in the form of a series with an infinite number of terms. These qualities have made the linear solutions more attractive to seismic data-processing practitioners. However, most linear solutions, including predictive deconvolution or F-K filtering, contain severe assumptions about the model of the subsurface and the class of free-surface multiples they can attenuate. These assumptions limit their usefulness. In a recent paper, we described an exception to this assertion for OBS data. We showed in that paper that a linear and non-iterative solution to the problem of attenuating free-surface multiples which is as accurate as iterative non-linear solutions can be constructed for OBS data. We here present a similar linear and non-iterative solution for attenuating free-surface multiples in towed-streamer data. For most practical purposes, this linear solution is as accurate as the non-linear ones.

Robust linear discriminant analysis with distance based estimators

NASA Astrophysics Data System (ADS)

Lim, Yai-Fung; Yahaya, Sharipah Soaad Syed; Ali, Hazlina

2017-11-01

Linear discriminant analysis (LDA) is one of the supervised classification techniques concerning relationship between a categorical variable and a set of continuous variables. The main objective of LDA is to create a function to distinguish between populations and allocating future observations to previously defined populations. Under the assumptions of normality and homoscedasticity, the LDA yields optimal linear discriminant rule (LDR) between two or more groups. However, the optimality of LDA highly relies on the sample mean and pooled sample covariance matrix which are known to be sensitive to outliers. To alleviate these conflicts, a new robust LDA using distance based estimators known as minimum variance vector (MVV) has been proposed in this study. The MVV estimators were used to substitute the classical sample mean and classical sample covariance to form a robust linear discriminant rule (RLDR). Simulation and real data study were conducted to examine on the performance of the proposed RLDR measured in terms of misclassification error rates. The computational result showed that the proposed RLDR is better than the classical LDR and was comparable with the existing robust LDR.

A Discrete Velocity Kinetic Model with Food Metric: Chemotaxis Traveling Waves.

PubMed

Choi, Sun-Ho; Kim, Yong-Jung

2017-02-01

We introduce a mesoscopic scale chemotaxis model for traveling wave phenomena which is induced by food metric. The organisms of this simplified kinetic model have two discrete velocity modes, [Formula: see text] and a constant tumbling rate. The main feature of the model is that the speed of organisms is constant [Formula: see text] with respect to the food metric, not the Euclidean metric. The uniqueness and the existence of the traveling wave solution of the model are obtained. Unlike the classical logarithmic model case there exist traveling waves under super-linear consumption rates and infinite population pulse-type traveling waves are obtained. Numerical simulations are also provided.

Linear Quantum Systems: Non-Classical States and Robust Stability

DTIC Science & Technology

2016-06-29

has a history going back some 50 years, to the birth of modern control theory with Kalman’s foundational work on filtering and LQG optimal control ...information   if it does not display a currently valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ORGANIZATION. 1. REPORT DATE (DD...analysis and control of quantum linear systems and their interactions with non-classical quantum fields by developing control theoretic concepts exploiting

Large-scale geomorphology: Classical concepts reconciled and integrated with contemporary ideas via a surface processes model

NASA Astrophysics Data System (ADS)

Kooi, Henk; Beaumont, Christopher

1996-02-01

Linear systems analysis is used to investigate the response of a surface processes model (SPM) to tectonic forcing. The SPM calculates subcontinental scale denudational landscape evolution on geological timescales (1 to hundreds of million years) as the result of simultaneous hillslope transport, modeled by diffusion, and fluvial transport, modeled by advection and reaction. The tectonically forced SPM accommodates the large-scale behavior envisaged in classical and contemporary conceptual geomorphic models and provides a framework for their integration and unification. The following three model scales are considered: micro-, meso-, and macroscale. The concepts of dynamic equilibrium and grade are quantified at the microscale for segments of uniform gradient subject to tectonic uplift. At the larger meso- and macroscales (which represent individual interfluves and landscapes including a number of drainage basins, respectively) the system response to tectonic forcing is linear for uplift geometries that are symmetric with respect to baselevel and which impose a fully integrated drainage to baselevel. For these linear models the response time and the transfer function as a function of scale characterize the model behavior. Numerical experiments show that the styles of landscape evolution depend critically on the timescales of the tectonic processes in relation to the response time of the landscape. When tectonic timescales are much longer than the landscape response time, the resulting dynamic equilibrium landscapes correspond to those envisaged by Hack (1960). When tectonic timescales are of the same order as the landscape response time and when tectonic variations take the form of pulses (much shorter than the response time), evolving landscapes conform to the Penck type (1972) and to the Davis (1889, 1899) and King (1953, 1962) type frameworks, respectively. The behavior of the SPM highlights the importance of phase shifts or delays of the landform response and sediment yield in relation to the tectonic forcing. Finally, nonlinear behavior resulting from more general uplift geometries is discussed. A number of model experiments illustrate the importance of "fundamental form," which is an expression of the conformity of antecedent topography with the current tectonic regime. Lack of conformity leads to models that exhibit internal thresholds and a complex response.

Novel windowing technique realized in FPGA for radar system

NASA Astrophysics Data System (ADS)

Escamilla-Hernandez, E.; Kravchenko, V. F.; Ponomaryov, V. I.; Ikuo, Arai

2006-02-01

To improve the weak target detection ability in radar applications a pulse compression is usually used that in the case linear FM modulation can improve the SNR. One drawback in here is that it can add the range side-lobes in reflectivity measurements. Using weighting window processing in time domain it is possible to decrease significantly the side-lobe level (SLL) and resolve small or low power targets those are masked by powerful ones. There are usually used classical windows such as Hamming, Hanning, etc. in window processing. Additionally to classical ones in this paper we also use a novel class of windows based on atomic functions (AF) theory. For comparison of simulation and experimental results we applied the standard parameters, such as coefficient of amplification, maximum level of side-lobe, width of main lobe, etc. To implement the compression-windowing model on hardware level it has been employed FPGA. This work aims at demonstrating a reasonably flexible implementation of FM-linear signal, pulse compression and windowing employing FPGA's. Classical and novel AF window technique has been investigated to reduce the SLL taking into account the noise influence and increasing the detection ability of the small or weak targets in the imaging radar. Paper presents the experimental hardware results of windowing in pulse compression radar resolving several targets for rectangular, Hamming, Kaiser-Bessel, (see manuscript for formula) functions windows. The windows created by use the atomic functions offer sufficiently better decreasing of the SLL in case of noise presence and when we move away of the main lobe in comparison with classical windows.

Event-based hydrological modeling for detecting dominant hydrological process and suitable model strategy for semi-arid catchments

NASA Astrophysics Data System (ADS)

Huang, Pengnian; Li, Zhijia; Chen, Ji; Li, Qiaoling; Yao, Cheng

2016-11-01

To simulate the hydrological processes in semi-arid areas properly is still challenging. This study assesses the impact of different modeling strategies on simulating flood processes in semi-arid catchments. Four classic hydrological models, TOPMODEL, XINANJIANG (XAJ), SAC-SMA and TANK, were selected and applied to three semi-arid catchments in North China. Based on analysis and comparison of the simulation results of these classic models, four new flexible models were constructed and used to further investigate the suitability of various modeling strategies for semi-arid environments. Numerical experiments were also designed to examine the performances of the models. The results show that in semi-arid catchments a suitable model needs to include at least one nonlinear component to simulate the main process of surface runoff generation. If there are more than two nonlinear components in the hydrological model, they should be arranged in parallel, rather than in series. In addition, the results show that the parallel nonlinear components should be combined by multiplication rather than addition. Moreover, this study reveals that the key hydrological process over semi-arid catchments is the infiltration excess surface runoff, a non-linear component.

Extensions of the Ferry shear wave model for active linear and nonlinear microrheology

PubMed Central

Mitran, Sorin M.; Forest, M. Gregory; Yao, Lingxing; Lindley, Brandon; Hill, David B.

2009-01-01

The classical oscillatory shear wave model of Ferry et al. [J. Polym. Sci. 2:593-611, (1947)] is extended for active linear and nonlinear microrheology. In the Ferry protocol, oscillation and attenuation lengths of the shear wave measured from strobe photographs determine storage and loss moduli at each frequency of plate oscillation. The microliter volumes typical in biology require modifications of experimental method and theory. Microbead tracking replaces strobe photographs. Reflection from the top boundary yields counterpropagating modes which are modeled here for linear and nonlinear viscoelastic constitutive laws. Furthermore, bulk imposed strain is easily controlled, and we explore the onset of normal stress generation and shear thinning using nonlinear viscoelastic models. For this paper, we present the theory, exact linear and nonlinear solutions where possible, and simulation tools more generally. We then illustrate errors in inverse characterization by application of the Ferry formulas, due to both suppression of wave reflection and nonlinearity, even if there were no experimental error. This shear wave method presents an active and nonlinear analog of the two-point microrheology of Crocker et al. [Phys. Rev. Lett. 85: 888 - 891 (2000)]. Nonlocal (spatially extended) deformations and stresses are propagated through a small volume sample, on wavelengths long relative to bead size. The setup is ideal for exploration of nonlinear threshold behavior. PMID:20011614

A methodology for design of a linear referencing system for surface transportation

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

Vonderohe, A.; Hepworth, T.

1997-06-01

The transportation community has recently placed significant emphasis on development of data models, procedural standards, and policies for management of linearly-referenced data. There is an Intelligent Transportation Systems initiative underway to create a spatial datum for location referencing in one, two, and three dimensions. Most recently, a call was made for development of a unified linear reference system to support public, private, and military surface transportation needs. A methodology for design of the linear referencing system was developed from geodetic engineering principles and techniques used for designing geodetic control networks. The method is founded upon the law of propagation ofmore » random error and the statistical analysis of systems of redundant measurements, used to produce best estimates for unknown parameters. A complete mathematical development is provided. Example adjustments of linear distance measurement systems are included. The classical orders of design are discussed with regard to the linear referencing system. A simple design example is provided. A linear referencing system designed and analyzed with this method will not only be assured of meeting the accuracy requirements of users, it will have the potential for supporting delivery of error estimates along with the results of spatial analytical queries. Modeling considerations, alternative measurement methods, implementation strategies, maintenance issues, and further research needs are discussed. Recommendations are made for further advancement of the unified linear referencing system concept.« less

Nonlinear multivariate and time series analysis by neural network methods

NASA Astrophysics Data System (ADS)

Hsieh, William W.

2004-03-01

Methods in multivariate statistical analysis are essential for working with large amounts of geophysical data, data from observational arrays, from satellites, or from numerical model output. In classical multivariate statistical analysis, there is a hierarchy of methods, starting with linear regression at the base, followed by principal component analysis (PCA) and finally canonical correlation analysis (CCA). A multivariate time series method, the singular spectrum analysis (SSA), has been a fruitful extension of the PCA technique. The common drawback of these classical methods is that only linear structures can be correctly extracted from the data. Since the late 1980s, neural network methods have become popular for performing nonlinear regression and classification. More recently, neural network methods have been extended to perform nonlinear PCA (NLPCA), nonlinear CCA (NLCCA), and nonlinear SSA (NLSSA). This paper presents a unified view of the NLPCA, NLCCA, and NLSSA techniques and their applications to various data sets of the atmosphere and the ocean (especially for the El Niño-Southern Oscillation and the stratospheric quasi-biennial oscillation). These data sets reveal that the linear methods are often too simplistic to describe real-world systems, with a tendency to scatter a single oscillatory phenomenon into numerous unphysical modes or higher harmonics, which can be largely alleviated in the new nonlinear paradigm.

Structured functional additive regression in reproducing kernel Hilbert spaces.

PubMed

Zhu, Hongxiao; Yao, Fang; Zhang, Hao Helen

2014-06-01

Functional additive models (FAMs) provide a flexible yet simple framework for regressions involving functional predictors. The utilization of data-driven basis in an additive rather than linear structure naturally extends the classical functional linear model. However, the critical issue of selecting nonlinear additive components has been less studied. In this work, we propose a new regularization framework for the structure estimation in the context of Reproducing Kernel Hilbert Spaces. The proposed approach takes advantage of the functional principal components which greatly facilitates the implementation and the theoretical analysis. The selection and estimation are achieved by penalized least squares using a penalty which encourages the sparse structure of the additive components. Theoretical properties such as the rate of convergence are investigated. The empirical performance is demonstrated through simulation studies and a real data application.

Weak Galerkin method for the Biot’s consolidation model

DOE PAGES

Hu, Xiaozhe; Mu, Lin; Ye, Xiu

2017-08-23

In this study, we develop a weak Galerkin (WG) finite element method for the Biot’s consolidation model in the classical displacement–pressure two-field formulation. Weak Galerkin linear finite elements are used for both displacement and pressure approximations in spatial discretizations. Backward Euler scheme is used for temporal discretization in order to obtain an implicit fully discretized scheme. We study the well-posedness of the linear system at each time step and also derive the overall optimal-order convergence of the WG formulation. Such WG scheme is designed on general shape regular polytopal meshes and provides stable and oscillation-free approximation for the pressure withoutmore » special treatment. Lastlyl, numerical experiments are presented to demonstrate the efficiency and accuracy of the proposed weak Galerkin finite element method.« less

Weak Galerkin method for the Biot’s consolidation model

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

Hu, Xiaozhe; Mu, Lin; Ye, Xiu

In this study, we develop a weak Galerkin (WG) finite element method for the Biot’s consolidation model in the classical displacement–pressure two-field formulation. Weak Galerkin linear finite elements are used for both displacement and pressure approximations in spatial discretizations. Backward Euler scheme is used for temporal discretization in order to obtain an implicit fully discretized scheme. We study the well-posedness of the linear system at each time step and also derive the overall optimal-order convergence of the WG formulation. Such WG scheme is designed on general shape regular polytopal meshes and provides stable and oscillation-free approximation for the pressure withoutmore » special treatment. Lastlyl, numerical experiments are presented to demonstrate the efficiency and accuracy of the proposed weak Galerkin finite element method.« less

Linear and Nonlinear Analysis of Magnetic Bearing Bandwidth Due to Eddy Current Limitations

NASA Technical Reports Server (NTRS)

Kenny, Andrew; Palazzolo, Alan

2000-01-01

Finite element analysis was used to study the bandwidth of alloy hyperco50a and silicon iron laminated rotors and stators in magnetic bearings. A three dimensional model was made of a heteropolar bearing in which all the flux circulated in the plane of the rotor and stator laminate. A three dimensional model of a plate similar to the region of a pole near the gap was also studied with a very fine mesh. Nonlinear time transient solutions for the net flux carried by the plate were compared to steady state time harmonic solutions. Both linear and quasi-nonlinear steady state time harmonic solutions were calculated and compared. The finite element solutions for power loss and flux bandwidth were compared to those determined from classical analytical solutions to Maxwell's equations.

A Nonlocal Peridynamic Plasticity Model for the Dynamic Flow and Fracture of Concrete.

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

Vogler, Tracy; Lammi, Christopher James

A nonlocal, ordinary peridynamic constitutive model is formulated to numerically simulate the pressure-dependent flow and fracture of heterogeneous, quasi-brittle ma- terials, such as concrete. Classical mechanics and traditional computational modeling methods do not accurately model the distributed fracture observed within this family of materials. The peridynamic horizon, or range of influence, provides a characteristic length to the continuum and limits localization of fracture. Scaling laws are derived to relate the parameters of peridynamic constitutive model to the parameters of the classical Drucker-Prager plasticity model. Thermodynamic analysis of associated and non-associated plastic flow is performed. An implicit integration algorithm is formu-more » lated to calculate the accumulated plastic bond extension and force state. The gov- erning equations are linearized and the simulation of the quasi-static compression of a cylinder is compared to the classical theory. A dissipation-based peridynamic bond failure criteria is implemented to model fracture and the splitting of a concrete cylinder is numerically simulated. Finally, calculation of the impact and spallation of a con- crete structure is performed to assess the suitability of the material and failure models for simulating concrete during dynamic loadings. The peridynamic model is found to accurately simulate the inelastic deformation and fracture behavior of concrete during compression, splitting, and dynamically induced spall. The work expands the types of materials that can be modeled using peridynamics. A multi-scale methodology for simulating concrete to be used in conjunction with the plasticity model is presented. The work was funded by LDRD 158806.« less

Dynamical localization of coupled relativistic kicked rotors

NASA Astrophysics Data System (ADS)

Rozenbaum, Efim B.; Galitski, Victor

2017-02-01

A periodically driven rotor is a prototypical model that exhibits a transition to chaos in the classical regime and dynamical localization (related to Anderson localization) in the quantum regime. In a recent work [Phys. Rev. B 94, 085120 (2016), 10.1103/PhysRevB.94.085120], A. C. Keser et al. considered a many-body generalization of coupled quantum kicked rotors, and showed that in the special integrable linear case, dynamical localization survives interactions. By analogy with many-body localization, the phenomenon was dubbed dynamical many-body localization. In the present work, we study nonintegrable models of single and coupled quantum relativistic kicked rotors (QRKRs) that bridge the gap between the conventional quadratic rotors and the integrable linear models. For a single QRKR, we supplement the recent analysis of the angular-momentum-space dynamics with a study of the spin dynamics. Our analysis of two and three coupled QRKRs along with the proved localization in the many-body linear model indicate that dynamical localization exists in few-body systems. Moreover, the relation between QRKR and linear rotor models implies that dynamical many-body localization can exist in generic, nonintegrable many-body systems. And localization can generally result from a complicated interplay between Anderson mechanism and limiting integrability, since the many-body linear model is a high-angular-momentum limit of many-body QRKRs. We also analyze the dynamics of two coupled QRKRs in the highly unusual superballistic regime and find that the resonance conditions are relaxed due to interactions. Finally, we propose experimental realizations of the QRKR model in cold atoms in optical lattices.

Preparing Greenberger-Horne-Zeilinger and W states on a long-range Ising spin model by global controls

NASA Astrophysics Data System (ADS)

Chen, Jiahui; Zhou, Hui; Duan, Changkui; Peng, Xinhua

2017-03-01

Entanglement, a unique quantum resource with no classical counterpart, remains at the heart of quantum information. The Greenberger-Horne-Zeilinger (GHZ) and W states are two inequivalent classes of multipartite entangled states which cannot be transformed into each other by means of local operations and classic communication. In this paper, we present the methods to prepare the GHZ and W states via global controls on a long-range Ising spin model. For the GHZ state, general solutions are analytically obtained for an arbitrary-size spin system, while for the W state, we find a standard way to prepare the W state that is analytically illustrated in three- and four-spin systems and numerically demonstrated for larger-size systems. The number of parameters required in the numerical search increases only linearly with the size of the system.

Analytic Methods for Adjusting Subjective Rating Schemes

DTIC Science & Technology

1976-06-01

individual performance. The approach developed here is a variant of the classical linear regression model. Specifically, it la proposed that...values of y and X. Moreover, this difference la gener- ally independent of sample size, so that LS estimates are different from ML estimates at...baervationa. H^ever, aa T. -. - ,„ aU . th(. Hit (4.10) la aatlafled, and EKV and ML eatlnatea are equlvalent A practical proble, in applying

Drive mechanisms to the inner and outer hair cell stereocilia

NASA Astrophysics Data System (ADS)

Maftoon, Nima; Motallebzadeh, Hamid; Guinan, John J.; Puria, Sunil

2018-05-01

It has been long believed that inner hair cell (IHC) stimulation can be gleaned from the classic ter-Kuile shear motion between the reticular lamina (RL) and tectorial membrane (TM). The present study explores this and other IHC stimulation mechanisms using a finite-element-model representation of an organ of Corti (OoC) cross section with fluid-structure interaction. A 3-D model of a cross section of the OoC including soft tissue and the fluid in the sub-tectorial space, tunnel of Corti and above the TM was formulated based on anatomical measurements from the gerbil apical turn. The outer hair cells (OHCs), Deiter's cells and their phalangeal processes are represented as Y-shaped building-block elements. Each of the IHC and OHC bundles is represented by a single sterocilium. Linearized Navier-Stokes equations coupled with linear-elastic equations discretized with tetrahedral elements are solved in the frequency domain. We evaluated the dynamic changes in the OoC motion including sub-tectorial gap dimensions for 0.1 to 10 kHz input frequencies. Calculations show the classic ter-Kuile motion but more importantly they show that the gap-height changes which produce oscillatory radial flow in the subtectorial space. Phase changes in the stereocilia across OHC rows and the IHC are also observed.

Projective limits of state spaces III. Toy-models

NASA Astrophysics Data System (ADS)

Lanéry, Suzanne; Thiemann, Thomas

2018-01-01

In this series of papers, we investigate the projective framework initiated by Kijowski (1977) and Okołów (2009, 2014, 2013) [1,2], which describes the states of a quantum theory as projective families of density matrices. A short reading guide to the series can be found in Lanéry (2016). A strategy to implement the dynamics in this formalism was presented in our first paper Lanéry and Thiemann (2017) (see also Lanéry, 2016, section 4), which we now test in two simple toy-models. The first one is a very basic linear model, meant as an illustration of the general procedure, and we will only discuss it at the classical level. In the second one, we reformulate the Schrödinger equation, treated as a classical field theory, within this projective framework, and proceed to its (non-relativistic) second quantization. We are then able to reproduce the physical content of the usual Fock quantization.

Is 3D true non linear traveltime tomography reasonable ?

NASA Astrophysics Data System (ADS)

Herrero, A.; Virieux, J.

2003-04-01

The data sets requiring 3D analysis tools in the context of seismic exploration (both onshore and offshore experiments) or natural seismicity (micro seismicity surveys or post event measurements) are more and more numerous. Classical linearized tomographies and also earthquake localisation codes need an accurate 3D background velocity model. However, if the medium is complex and a priori information not available, a 1D analysis is not able to provide an adequate background velocity image. Moreover, the design of the acquisition layouts is often intrinsically 3D and renders difficult even 2D approaches, especially in natural seismicity cases. Thus, the solution relies on the use of a 3D true non linear approach, which allows to explore the model space and to identify an optimal velocity image. The problem becomes then practical and its feasibility depends on the available computing resources (memory and time). In this presentation, we show that facing a 3D traveltime tomography problem with an extensive non-linear approach combining fast travel time estimators based on level set methods and optimisation techniques such as multiscale strategy is feasible. Moreover, because management of inhomogeneous inversion parameters is more friendly in a non linear approach, we describe how to perform a jointly non-linear inversion for the seismic velocities and the sources locations.

Computational simulations of hydrogen circular migration in protonated acetylene induced by circularly polarized light

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

Shi, Xuetao; Li, Wen; Schlegel, H. Bernhard, E-mail: hbs@chem.wayne.edu

2016-08-28

The hydrogens in protonated acetylene are very mobile and can easily migrate around the C{sub 2} core by moving between classical and non-classical structures of the cation. The lowest energy structure is the T-shaped, non-classical cation with a hydrogen bridging the two carbons. Conversion to the classical H{sub 2}CCH{sup +} ion requires only 4 kcal/mol. The effect of circularly polarized light on the migration of hydrogens in oriented C{sub 2}H{sub 3}{sup +} has been simulated by Born-Oppenheimer molecular dynamics. Classical trajectory calculations were carried out with the M062X/6-311+G(3df,2pd) level of theory using linearly and circularly polarized 32 cycle 7 μmmore » cosine squared pulses with peak intensity of 5.6 × 10{sup 13} W/cm{sup 2} and 3.15 × 10{sup 13} W/cm{sup 2}, respectively. These linearly and circularly polarized pulses transfer similar amounts of energy and total angular momentum to C{sub 2}H{sub 3}{sup +}. The average angular momentum vectors of the three hydrogens show opposite directions of rotation for right and left circularly polarized light, but no directional preference for linearly polarized light. This difference results in an appreciable amount of angular displacement of the three hydrogens relative to the C{sub 2} core for circularly polarized light, but only an insignificant amount for linearly polarized light. Over the course of the simulation with circularly polarized light, this corresponds to a propeller-like motion of the three hydrogens around the C{sub 2} core of protonated acetylene.« less

The Madden-Julian Oscillation and the Indo-Pacific Warm Pool

NASA Astrophysics Data System (ADS)

Raymond, David J.; Fuchs, Željka

2018-04-01

A minimal model of the interaction of the Madden-Julian oscillation (MJO) with the Indo-Pacific warm pool is presented. This model is based on the linear superposition of the flow associated with a highly simplified treatment of the MJO plus the flow induced by the warm pool itself. Both of these components parameterize rainfall as proportional to the column water vapor, which in turn is governed by a linearized moisture equation in which WISHE (wind induced surface heat exchange) plays a governing role. The MJO component has maximum growth rate for planetary wavenumber 1 and is equatorially trapped with purely zonal winds. The warm pool component exhibits a complex flow pattern, differing significantly from the classical Gill model as a result of the mean easterly flow. The combination of the two produce a flow that reproduces many aspects of the observed global flow associated with the MJO.

Scaling properties of ballistic nano-transistors

PubMed Central

2011-01-01

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

CLASSICAL AREAS OF PHENOMENOLOGY: Study on the design and Zernike aberrations of a segmented mirror telescope

NASA Astrophysics Data System (ADS)

Jiang, Zhen-Yu; Li, Lin; Huang, Yi-Fan

2009-07-01

The segmented mirror telescope is widely used. The aberrations of segmented mirror systems are different from single mirror systems. This paper uses the Fourier optics theory to analyse the Zernike aberrations of segmented mirror systems. It concludes that the Zernike aberrations of segmented mirror systems obey the linearity theorem. The design of a segmented space telescope and segmented schemes are discussed, and its optical model is constructed. The computer simulation experiment is performed with this optical model to verify the suppositions. The experimental results confirm the correctness of the model.

Asymptotic theory of neutral stability of the Couette flow of a vibrationally excited gas

NASA Astrophysics Data System (ADS)

Grigor'ev, Yu. N.; Ershov, I. V.

2017-01-01

An asymptotic theory of the neutral stability curve for a supersonic plane Couette flow of a vibrationally excited gas is developed. The initial mathematical model consists of equations of two-temperature viscous gas dynamics, which are used to derive a spectral problem for a linear system of eighth-order ordinary differential equations within the framework of the classical linear stability theory. Unified transformations of the system for all shear flows are performed in accordance with the classical Lin scheme. The problem is reduced to an algebraic secular equation with separation into the "inviscid" and "viscous" parts, which is solved numerically. It is shown that the thus-calculated neutral stability curves agree well with the previously obtained results of the direct numerical solution of the original spectral problem. In particular, the critical Reynolds number increases with excitation enhancement, and the neutral stability curve is shifted toward the domain of higher wave numbers. This is also confirmed by means of solving an asymptotic equation for the critical Reynolds number at the Mach number M ≤ 4.

Generalized Onsager's reciprocal relations for the master and Fokker-Planck equations

NASA Astrophysics Data System (ADS)

Peng, Liangrong; Zhu, Yi; Hong, Liu

2018-06-01

The Onsager's reciprocal relation plays a fundamental role in the nonequilibrium thermodynamics. However, unfortunately, its classical version is valid only within a narrow region near equilibrium due to the linear regression hypothesis, which largely restricts its usage. In this paper, based on the conservation-dissipation formalism, a generalized version of Onsager's relations for the master equations and Fokker-Planck equations was derived. Nonlinear constitutive relations with nonsymmetric and positively stable operators, which become symmetric under the detailed balance condition, constitute key features of this new generalization. Similar conclusions also hold for many other classical models in physics and chemistry, which in turn make the current study as a benchmark for the application of generalized Onsager's relations in nonequilibrium thermodynamics.

Experimental demonstration of entanglement-enhanced classical communication over a quantum channel with correlated noise.

PubMed

Banaszek, Konrad; Dragan, Andrzej; Wasilewski, Wojciech; Radzewicz, Czesław

2004-06-25

We present an experiment demonstrating the entanglement enhanced capacity of a quantum channel with correlated noise, modeled by a fiber optic link exhibiting fluctuating birefringence. In this setting, introducing entanglement between two photons is required to maximize the amount of information that can be encoded into their joint polarization degree of freedom. We demonstrated this effect using a fiber-coupled source of entangled photon pairs based on spontaneous parametric down-conversion, and a linear-optics Bell state measurement. The obtained experimental classical capacity with entangled states is equal to 0.82+/-0.04 per a photon pair, and it exceeds approximately 2.5 times the theoretical upper limit when no quantum correlations are allowed.

Experimental and numerical analysis of pre-compressed masonry walls in two-way-bending with second order effects

NASA Astrophysics Data System (ADS)

Milani, Gabriele; Olivito, Renato S.; Tralli, Antonio

2014-10-01

The buckling behavior of slender unreinforced masonry (URM) walls subjected to axial compression and out-of-plane lateral loads is investigated through a combined experimental and numerical homogenizedapproach. After a preliminary analysis performed on a unit cell meshed by means of elastic FEs and non-linear interfaces, macroscopic moment-curvature diagrams so obtained are implemented at a structural level, discretizing masonry by means of rigid triangular elements and non-linear interfaces. The non-linear incremental response of the structure is accounted for a specific quadratic programming routine. In parallel, a wide experimental campaign is conducted on walls in two way bending, with the double aim of both validating the numerical model and investigating the behavior of walls that may not be reduced to simple cantilevers or simply supported beams. Panels investigated are dry-joint in scale square walls simply supported at the base and on a vertical edge, exhibiting the classical Rondelet's mechanism. The results obtained are compared with those provided by the numerical model.

Generalized cable equation model for myelinated nerve fiber.

PubMed

Einziger, Pinchas D; Livshitz, Leonid M; Mizrahi, Joseph

2005-10-01

Herein, the well-known cable equation for nonmyelinated axon model is extended analytically for myelinated axon formulation. The myelinated membrane conductivity is represented via the Fourier series expansion. The classical cable equation is thereby modified into a linear second order ordinary differential equation with periodic coefficients, known as Hill's equation. The general internal source response, expressed via repeated convolutions, uniformly converges provided that the entire periodic membrane is passive. The solution can be interpreted as an extended source response in an equivalent nonmyelinated axon (i.e., the response is governed by the classical cable equation). The extended source consists of the original source and a novel activation function, replacing the periodic membrane in the myelinated axon model. Hill's equation is explicitly integrated for the specific choice of piecewise constant membrane conductivity profile, thereby resulting in an explicit closed form expression for the transmembrane potential in terms of trigonometric functions. The Floquet's modes are recognized as the nerve fiber activation modes, which are conventionally associated with the nonlinear Hodgkin-Huxley formulation. They can also be incorporated in our linear model, provided that the periodic membrane point-wise passivity constraint is properly modified. Indeed, the modified condition, enforcing the periodic membrane passivity constraint on the average conductivity only leads, for the first time, to the inclusion of the nerve fiber activation modes in our novel model. The validity of the generalized transmission-line and cable equation models for a myelinated nerve fiber, is verified herein through a rigorous Green's function formulation and numerical simulations for transmembrane potential induced in three-dimensional myelinated cylindrical cell. It is shown that the dominant pole contribution of the exact modal expansion is the transmembrane potential solution of our generalized model.

Closed-Loop System Identification Experience for Flight Control Law and Flying Qualities Evaluation of a High Performance Fighter Aircraft

NASA Technical Reports Server (NTRS)

Murphy, Patrick C.

1996-01-01

This paper highlights some of the results and issues associated with estimating models to evaluate control law design methods and design criteria for advanced high performance aircraft. Experimental fighter aircraft such as the NASA-High Alpha Research Vehicle (HARV) have the capability to maneuver at very high angles of attack where nonlinear aerodynamics often predominate. HARV is an experimental F/A-18, configured with thrust vectoring and conformal actuated nose strakes. Identifying closed-loop models for this type of aircraft can be made difficult by nonlinearities and high order characteristics of the system. In this paper, only lateral-directional axes are considered since the lateral-directional control law was specifically designed to produce classical airplane responses normally expected with low-order, rigid-body systems. Evaluation of the control design methodology was made using low-order equivalent systems determined from flight and simulation. This allowed comparison of the closed-loop rigid-body dynamics achieved in flight with that designed in simulation. In flight, the On Board Excitation System was used to apply optimal inputs to lateral stick and pedals at five angles at attack : 5, 20, 30, 45, and 60 degrees. Data analysis and closed-loop model identification were done using frequency domain maximum likelihood. The structure of identified models was a linear state-space model reflecting classical 4th-order airplane dynamics. Input time delays associated with the high-order controller and aircraft system were accounted for in data preprocessing. A comparison of flight estimated models with small perturbation linear design models highlighted nonlinearities in the system and indicated that the closed-loop rigid-body dynamics were sensitive to input amplitudes at 20 and 30 degrees angle of attack.

Sex determination from the femur in Portuguese populations with classical and machine-learning classifiers.

PubMed

Curate, F; Umbelino, C; Perinha, A; Nogueira, C; Silva, A M; Cunha, E

2017-11-01

The assessment of sex is of paramount importance in the establishment of the biological profile of a skeletal individual. Femoral relevance for sex estimation is indisputable, particularly when other exceedingly dimorphic skeletal regions are missing. As such, this study intended to generate population-specific osteometric models for the estimation of sex with the femur and to compare the accuracy of the models obtained through classical and machine-learning classifiers. A set of 15 standard femoral measurements was acquired in a training sample (100 females; 100 males) from the Coimbra Identified Skeletal Collection (University of Coimbra, Portugal) and models for sex classification were produced with logistic regression (LR), linear discriminant analysis (LDA), support vector machines (SVM), and reduce error pruning trees (REPTree). Under cross-validation, univariable sectioning points generated with REPTree correctly estimated sex in 60.0-87.5% of cases (systematic error ranging from 0.0 to 37.0%), while multivariable models correctly classified sex in 84.0-92.5% of cases (bias from 0.0 to 7.0%). All models were assessed in a holdout sample (24 females; 34 males) from the 21st Century Identified Skeletal Collection (University of Coimbra, Portugal), with an allocation accuracy ranging from 56.9 to 86.2% (bias from 4.4 to 67.0%) in the univariable models, and from 84.5 to 89.7% (bias from 3.7 to 23.3%) in the multivariable models. This study makes available a detailed description of sexual dimorphism in femoral linear dimensions in two Portuguese identified skeletal samples, emphasizing the relevance of the femur for the estimation of sex in skeletal remains in diverse conditions of completeness and preservation. Copyright © 2017 Elsevier Ltd and Faculty of Forensic and Legal Medicine. All rights reserved.

Closed-Loop System Identification Experience for Flight Control Law and Flying Qualities Evaluation of a High Performance Fighter Aircraft

NASA Technical Reports Server (NTRS)

Murphy, Patrick C.

1999-01-01

This paper highlights some of the results and issues associated with estimating models to evaluate control law design methods and design criteria for advanced high performance aircraft. Experimental fighter aircraft such as the NASA High Alpha Research Vehicle (HARV) have the capability to maneuver at very high angles of attack where nonlinear aerodynamics often predominate. HARV is an experimental F/A-18, configured with thrust vectoring and conformal actuated nose strakes. Identifying closed-loop models for this type of aircraft can be made difficult by nonlinearities and high-order characteristics of the system. In this paper only lateral-directional axes are considered since the lateral-directional control law was specifically designed to produce classical airplane responses normally expected with low-order, rigid-body systems. Evaluation of the control design methodology was made using low-order equivalent systems determined from flight and simulation. This allowed comparison of the closed-loop rigid-body dynamics achieved in flight with that designed in simulation. In flight, the On Board Excitation System was used to apply optimal inputs to lateral stick and pedals at five angles of attack: 5, 20, 30, 45, and 60 degrees. Data analysis and closed-loop model identification were done using frequency domain maximum likelihood. The structure of the identified models was a linear state-space model reflecting classical 4th-order airplane dynamics. Input time delays associated with the high-order controller and aircraft system were accounted for in data preprocessing. A comparison of flight estimated models with small perturbation linear design models highlighted nonlinearities in the system and indicated that the estimated closed-loop rigid-body dynamics were sensitive to input amplitudes at 20 and 30 degrees angle of attack.

Symplectic evolution of Wigner functions in Markovian open systems.

PubMed

Brodier, O; Almeida, A M Ozorio de

2004-01-01

The Wigner function is known to evolve classically under the exclusive action of a quadratic Hamiltonian. If the system also interacts with the environment through Lindblad operators that are complex linear functions of position and momentum, then the general evolution is the convolution of a non-Hamiltonian classical propagation of the Wigner function with a phase space Gaussian that broadens in time. We analyze the consequences of this in the three generic cases of elliptic, hyperbolic, and parabolic Hamiltonians. The Wigner function always becomes positive in a definite time, which does not depend on the initial pure state. We observe the influence of classical dynamics and dissipation upon this threshold. We also derive an exact formula for the evolving linear entropy as the average of a narrowing Gaussian taken over a probability distribution that depends only on the initial state. This leads to a long time asymptotic formula for the growth of linear entropy. We finally discuss the possibility of recovering the initial state.

Energy density and energy flow of surface waves in a strongly magnetized graphene

NASA Astrophysics Data System (ADS)

Moradi, Afshin

2018-01-01

General expressions for the energy density and energy flow of plasmonic waves in a two-dimensional massless electron gas (as a simple model of graphene) are obtained by means of the linearized magneto-hydrodynamic model and classical electromagnetic theory when a strong external magnetic field perpendicular to the system is present. Also, analytical expressions for the energy velocity, wave polarization, wave impedance, transverse and longitudinal field strength functions, and attenuation length of surface magneto-plasmon-polariton waves are derived, and numerical results are prepared.

On the use of fractional order PK-PD models

NASA Astrophysics Data System (ADS)

Ionescu, Clara; Copot, Dana

2017-01-01

Quantifying and controlling depth of anesthesia is a challenging process due to lack of measurement technology for direct effects of drug supply into the body. Efforts are being made to develop new sensor techniques and new horizons are explored for modeling this intricate process. This paper introduces emerging tools available on the ‘engineering market’ imported from the area of fractional calculus. A novel interpretation of the classical drug-effect curve is given, enabling linear control. This enables broadening the horizon of signal processing and control techniques and suggests future research lines.

Canards in a minimal piecewise-linear square-wave burster

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

Desroches, M.; Krupa, M.; Fernández-García, S., E-mail: soledad@us.es

We construct a piecewise-linear (PWL) approximation of the Hindmarsh-Rose (HR) neuron model that is minimal, in the sense that the vector field has the least number of linearity zones, in order to reproduce all the dynamics present in the original HR model with classical parameter values. This includes square-wave bursting and also special trajectories called canards, which possess long repelling segments and organise the transitions between stable bursting patterns with n and n + 1 spikes, also referred to as spike-adding canard explosions. We propose a first approximation of the smooth HR model, using a continuous PWL system, and show that itsmore » fast subsystem cannot possess a homoclinic bifurcation, which is necessary to obtain proper square-wave bursting. We then relax the assumption of continuity of the vector field across all zones, and we show that we can obtain a homoclinic bifurcation in the fast subsystem. We use the recently developed canard theory for PWL systems in order to reproduce the spike-adding canard explosion feature of the HR model as studied, e.g., in Desroches et al., Chaos 23(4), 046106 (2013).« less

Loop Shaping Control Design for a Supersonic Propulsion System Model Using Quantitative Feedback Theory (QFT) Specifications and Bounds

NASA Technical Reports Server (NTRS)

Connolly, Joseph W.; Kopasakis, George

2010-01-01

This paper covers the propulsion system component modeling and controls development of an integrated mixed compression inlet and turbojet engine that will be used for an overall vehicle Aero-Propulso-Servo-Elastic (APSE) model. Using previously created nonlinear component-level propulsion system models, a linear integrated propulsion system model and loop shaping control design have been developed. The design includes both inlet normal shock position control and jet engine rotor speed control for a potential supersonic commercial transport. A preliminary investigation of the impacts of the aero-elastic effects on the incoming flow field to the propulsion system are discussed, however, the focus here is on developing a methodology for the propulsion controls design that prevents unstart in the inlet and minimizes the thrust oscillation experienced by the vehicle. Quantitative Feedback Theory (QFT) specifications and bounds, and aspects of classical loop shaping are used in the control design process. Model uncertainty is incorporated in the design to address possible error in the system identification mapping of the nonlinear component models into the integrated linear model.

Bidirectional Classical Stochastic Processes with Measurements and Feedback

NASA Technical Reports Server (NTRS)

Hahne, G. E.

2005-01-01

A measurement on a quantum system is said to cause the "collapse" of the quantum state vector or density matrix. An analogous collapse occurs with measurements on a classical stochastic process. This paper addresses the question of describing the response of a classical stochastic process when there is feedback from the output of a measurement to the input, and is intended to give a model for quantum-mechanical processes that occur along a space-like reaction coordinate. The classical system can be thought of in physical terms as two counterflowing probability streams, which stochastically exchange probability currents in a way that the net probability current, and hence the overall probability, suitably interpreted, is conserved. The proposed formalism extends the . mathematics of those stochastic processes describable with linear, single-step, unidirectional transition probabilities, known as Markov chains and stochastic matrices. It is shown that a certain rearrangement and combination of the input and output of two stochastic matrices of the same order yields another matrix of the same type. Each measurement causes the partial collapse of the probability current distribution in the midst of such a process, giving rise to calculable, but non-Markov, values for the ensuing modification of the system's output probability distribution. The paper concludes with an analysis of a classical probabilistic version of the so-called grandfather paradox.

Nonlinear Wave Propagation

DTIC Science & Technology

1984-09-01

Asymptotic Results for a Model Equation for Low Reynolds Number Flow, SIAM J. Appi. Math., 35, July 1978. 3. A. S. Yokes : Group Theoretical Aspects of...Quadratic and Cubic Invariants in’ Classical Mechanics, J. Math. Anal. Appl.,’ 74, 342, (1980). 5. A. S. Pokas , P. A. Lagerstrom: On the Use of Lie...Mathematical Methods in Hydrodynamics and %Integrability in Dynamical System, pp. 237-241. 24. 14. J. Ablovitz and A. S. Pokas : A Direct Linearization

Classical Mathematical Models for Description and Prediction of Experimental Tumor Growth

PubMed Central

Benzekry, Sébastien; Lamont, Clare; Beheshti, Afshin; Tracz, Amanda; Ebos, John M. L.; Hlatky, Lynn; Hahnfeldt, Philip

2014-01-01

Despite internal complexity, tumor growth kinetics follow relatively simple laws that can be expressed as mathematical models. To explore this further, quantitative analysis of the most classical of these were performed. The models were assessed against data from two in vivo experimental systems: an ectopic syngeneic tumor (Lewis lung carcinoma) and an orthotopically xenografted human breast carcinoma. The goals were threefold: 1) to determine a statistical model for description of the measurement error, 2) to establish the descriptive power of each model, using several goodness-of-fit metrics and a study of parametric identifiability, and 3) to assess the models' ability to forecast future tumor growth. The models included in the study comprised the exponential, exponential-linear, power law, Gompertz, logistic, generalized logistic, von Bertalanffy and a model with dynamic carrying capacity. For the breast data, the dynamics were best captured by the Gompertz and exponential-linear models. The latter also exhibited the highest predictive power, with excellent prediction scores (≥80%) extending out as far as 12 days in the future. For the lung data, the Gompertz and power law models provided the most parsimonious and parametrically identifiable description. However, not one of the models was able to achieve a substantial prediction rate (≥70%) beyond the next day data point. In this context, adjunction of a priori information on the parameter distribution led to considerable improvement. For instance, forecast success rates went from 14.9% to 62.7% when using the power law model to predict the full future tumor growth curves, using just three data points. These results not only have important implications for biological theories of tumor growth and the use of mathematical modeling in preclinical anti-cancer drug investigations, but also may assist in defining how mathematical models could serve as potential prognostic tools in the clinic. PMID:25167199

Classical mathematical models for description and prediction of experimental tumor growth.

PubMed

Benzekry, Sébastien; Lamont, Clare; Beheshti, Afshin; Tracz, Amanda; Ebos, John M L; Hlatky, Lynn; Hahnfeldt, Philip

2014-08-01

Despite internal complexity, tumor growth kinetics follow relatively simple laws that can be expressed as mathematical models. To explore this further, quantitative analysis of the most classical of these were performed. The models were assessed against data from two in vivo experimental systems: an ectopic syngeneic tumor (Lewis lung carcinoma) and an orthotopically xenografted human breast carcinoma. The goals were threefold: 1) to determine a statistical model for description of the measurement error, 2) to establish the descriptive power of each model, using several goodness-of-fit metrics and a study of parametric identifiability, and 3) to assess the models' ability to forecast future tumor growth. The models included in the study comprised the exponential, exponential-linear, power law, Gompertz, logistic, generalized logistic, von Bertalanffy and a model with dynamic carrying capacity. For the breast data, the dynamics were best captured by the Gompertz and exponential-linear models. The latter also exhibited the highest predictive power, with excellent prediction scores (≥80%) extending out as far as 12 days in the future. For the lung data, the Gompertz and power law models provided the most parsimonious and parametrically identifiable description. However, not one of the models was able to achieve a substantial prediction rate (≥70%) beyond the next day data point. In this context, adjunction of a priori information on the parameter distribution led to considerable improvement. For instance, forecast success rates went from 14.9% to 62.7% when using the power law model to predict the full future tumor growth curves, using just three data points. These results not only have important implications for biological theories of tumor growth and the use of mathematical modeling in preclinical anti-cancer drug investigations, but also may assist in defining how mathematical models could serve as potential prognostic tools in the clinic.

Least Squares Procedures.

ERIC Educational Resources Information Center

Hester, Yvette

Least squares methods are sophisticated mathematical curve fitting procedures used in all classical parametric methods. The linear least squares approximation is most often associated with finding the "line of best fit" or the regression line. Since all statistical analyses are correlational and all classical parametric methods are least…

Structured functional additive regression in reproducing kernel Hilbert spaces

PubMed Central

Zhu, Hongxiao; Yao, Fang; Zhang, Hao Helen

2013-01-01

Summary Functional additive models (FAMs) provide a flexible yet simple framework for regressions involving functional predictors. The utilization of data-driven basis in an additive rather than linear structure naturally extends the classical functional linear model. However, the critical issue of selecting nonlinear additive components has been less studied. In this work, we propose a new regularization framework for the structure estimation in the context of Reproducing Kernel Hilbert Spaces. The proposed approach takes advantage of the functional principal components which greatly facilitates the implementation and the theoretical analysis. The selection and estimation are achieved by penalized least squares using a penalty which encourages the sparse structure of the additive components. Theoretical properties such as the rate of convergence are investigated. The empirical performance is demonstrated through simulation studies and a real data application. PMID:25013362

Large power factor and anomalous Hall effect and their correlation with observed linear magneto resistance in Co-doped Bi2Se3 3D topological insulator

NASA Astrophysics Data System (ADS)

Singh, Rahul; Shukla, K. K.; Kumar, A.; Okram, G. S.; Singh, D.; Ganeshan, V.; Lakhani, Archana; Ghosh, A. K.; Chatterjee, Sandip

2016-09-01

Magnetoresistance (MR), thermo power, magnetization and Hall effect measurements have been performed on Co-doped Bi2Se3 topological insulators. The undoped sample shows that the maximum MR as a destructive interference due to a π-Berry phase leads to a decrease of MR. As the Co is doped, the linearity in MR is increased. The observed MR of Bi2Se3 can be explained with the classical model. The low temperature MR behavior of Co doped samples cannot be explained with the same model, but can be explained with the quantum linear MR model. Magnetization behavior indicates the establishment of ferromagnetic ordering with Co doping. Hall effect data also supports the establishment of ferromagnetic ordering in Co-doped Bi2Se3 samples by showing the anomalous Hall effect. Furthermore, when spectral weight suppression is insignificant, Bi2Se3 behaves as a dilute magnetic semiconductor. Moreover, the maximum power factor is observed when time reversal symmetry (TRS) is maintained. As the TRS is broken the power factor value is decreased, which indicates that with the rise of Dirac cone above the Fermi level the anomalous Hall effect and linearity in MR increase and the power factor decreases.

Analysis of linear measurements on 3D surface models using CBCT data segmentation obtained by automatic standard pre-set thresholds in two segmentation software programs: an in vitro study.

PubMed

Poleti, Marcelo Lupion; Fernandes, Thais Maria Freire; Pagin, Otávio; Moretti, Marcela Rodrigues; Rubira-Bullen, Izabel Regina Fischer

2016-01-01

The aim of this in vitro study was to evaluate the reliability and accuracy of linear measurements on three-dimensional (3D) surface models obtained by standard pre-set thresholds in two segmentation software programs. Ten mandibles with 17 silica markers were scanned for 0.3-mm voxels in the i-CAT Classic (Imaging Sciences International, Hatfield, PA, USA). Twenty linear measurements were carried out by two observers two times on the 3D surface models: the Dolphin Imaging 11.5 (Dolphin Imaging & Management Solutions, Chatsworth, CA, USA), using two filters(Translucent and Solid-1), and in the InVesalius 3.0.0 (Centre for Information Technology Renato Archer, Campinas, SP, Brazil). The physical measurements were made by another observer two times using a digital caliper on the dry mandibles. Excellent intra- and inter-observer reliability for the markers, physical measurements, and 3D surface models were found (intra-class correlation coefficient (ICC) and Pearson's r ≥ 0.91). The linear measurements on 3D surface models by Dolphin and InVesalius software programs were accurate (Dolphin Solid-1 > InVesalius > Dolphin Translucent). The highest absolute and percentage errors were obtained for the variable R1-R1 (1.37 mm) and MF-AC (2.53 %) in the Dolphin Translucent and InVesalius software, respectively. Linear measurements on 3D surface models obtained by standard pre-set thresholds in the Dolphin and InVesalius software programs are reliable and accurate compared with physical measurements. Studies that evaluate the reliability and accuracy of the 3D models are necessary to ensure error predictability and to establish diagnosis, treatment plan, and prognosis in a more realistic way.

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

NASA Astrophysics Data System (ADS)

Malpetti, Daniele; Roscilde, Tommaso

2017-02-01

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

A Binomial Modeling Approach for Upscaling Colloid Transport Under Unfavorable Attachment Conditions: Emergent Prediction of Nonmonotonic Retention Profiles

NASA Astrophysics Data System (ADS)

Hilpert, Markus; Johnson, William P.

2018-01-01

We used a recently developed simple mathematical network model to upscale pore-scale colloid transport information determined under unfavorable attachment conditions. Classical log-linear and nonmonotonic retention profiles, both well-reported under favorable and unfavorable attachment conditions, respectively, emerged from our upscaling. The primary attribute of the network is colloid transfer between bulk pore fluid, the near-surface fluid domain (NSFD), and attachment (treated as irreversible). The network model accounts for colloid transfer to the NSFD of downgradient grains and for reentrainment to bulk pore fluid via diffusion or via expulsion at rear flow stagnation zones (RFSZs). The model describes colloid transport by a sequence of random trials in a one-dimensional (1-D) network of Happel cells, which contain a grain and a pore. Using combinatorial analysis that capitalizes on the binomial coefficient, we derived from the pore-scale information the theoretical residence time distribution of colloids in the network. The transition from log-linear to nonmonotonic retention profiles occurs when the conditions underlying classical filtration theory are not fulfilled, i.e., when an NSFD colloid population is maintained. Then, nonmonotonic retention profiles result potentially both for attached and NSFD colloids. The concentration maxima shift downgradient depending on specific parameter choice. The concentration maxima were also shown to shift downgradient temporally (with continued elution) under conditions where attachment is negligible, explaining experimentally observed downgradient transport of retained concentration maxima of adhesion-deficient bacteria. For the case of zero reentrainment, we develop closed-form, analytical expressions for the shape, and the maximum of the colloid retention profile.

Application of third molar development and eruption models in estimating dental age in Malay sub-adults.

PubMed

Mohd Yusof, Mohd Yusmiaidil Putera; Cauwels, Rita; Deschepper, Ellen; Martens, Luc

2015-08-01

The third molar development (TMD) has been widely utilized as one of the radiographic method for dental age estimation. By using the same radiograph of the same individual, third molar eruption (TME) information can be incorporated to the TMD regression model. This study aims to evaluate the performance of dental age estimation in individual method models and the combined model (TMD and TME) based on the classic regressions of multiple linear and principal component analysis. A sample of 705 digital panoramic radiographs of Malay sub-adults aged between 14.1 and 23.8 years was collected. The techniques described by Gleiser and Hunt (modified by Kohler) and Olze were employed to stage the TMD and TME, respectively. The data was divided to develop three respective models based on the two regressions of multiple linear and principal component analysis. The trained models were then validated on the test sample and the accuracy of age prediction was compared between each model. The coefficient of determination (R²) and root mean square error (RMSE) were calculated. In both genders, adjusted R² yielded an increment in the linear regressions of combined model as compared to the individual models. The overall decrease in RMSE was detected in combined model as compared to TMD (0.03-0.06) and TME (0.2-0.8). In principal component regression, low value of adjusted R(2) and high RMSE except in male were exhibited in combined model. Dental age estimation is better predicted using combined model in multiple linear regression models. Copyright © 2015 Elsevier Ltd and Faculty of Forensic and Legal Medicine. All rights reserved.

Classical and sequential limit analysis revisited

NASA Astrophysics Data System (ADS)

Leblond, Jean-Baptiste; Kondo, Djimédo; Morin, Léo; Remmal, Almahdi

2018-04-01

Classical limit analysis applies to ideal plastic materials, and within a linearized geometrical framework implying small displacements and strains. Sequential limit analysis was proposed as a heuristic extension to materials exhibiting strain hardening, and within a fully general geometrical framework involving large displacements and strains. The purpose of this paper is to study and clearly state the precise conditions permitting such an extension. This is done by comparing the evolution equations of the full elastic-plastic problem, the equations of classical limit analysis, and those of sequential limit analysis. The main conclusion is that, whereas classical limit analysis applies to materials exhibiting elasticity - in the absence of hardening and within a linearized geometrical framework -, sequential limit analysis, to be applicable, strictly prohibits the presence of elasticity - although it tolerates strain hardening and large displacements and strains. For a given mechanical situation, the relevance of sequential limit analysis therefore essentially depends upon the importance of the elastic-plastic coupling in the specific case considered.

Bivariate least squares linear regression: Towards a unified analytic formalism. I. Functional models

NASA Astrophysics Data System (ADS)

Caimmi, R.

2011-08-01

Concerning bivariate least squares linear regression, the classical approach pursued for functional models in earlier attempts ( York, 1966, 1969) is reviewed using a new formalism in terms of deviation (matrix) traces which, for unweighted data, reduce to usual quantities leaving aside an unessential (but dimensional) multiplicative factor. Within the framework of classical error models, the dependent variable relates to the independent variable according to the usual additive model. The classes of linear models considered are regression lines in the general case of correlated errors in X and in Y for weighted data, and in the opposite limiting situations of (i) uncorrelated errors in X and in Y, and (ii) completely correlated errors in X and in Y. The special case of (C) generalized orthogonal regression is considered in detail together with well known subcases, namely: (Y) errors in X negligible (ideally null) with respect to errors in Y; (X) errors in Y negligible (ideally null) with respect to errors in X; (O) genuine orthogonal regression; (R) reduced major-axis regression. In the limit of unweighted data, the results determined for functional models are compared with their counterparts related to extreme structural models i.e. the instrumental scatter is negligible (ideally null) with respect to the intrinsic scatter ( Isobe et al., 1990; Feigelson and Babu, 1992). While regression line slope and intercept estimators for functional and structural models necessarily coincide, the contrary holds for related variance estimators even if the residuals obey a Gaussian distribution, with the exception of Y models. An example of astronomical application is considered, concerning the [O/H]-[Fe/H] empirical relations deduced from five samples related to different stars and/or different methods of oxygen abundance determination. For selected samples and assigned methods, different regression models yield consistent results within the errors (∓ σ) for both heteroscedastic and homoscedastic data. Conversely, samples related to different methods produce discrepant results, due to the presence of (still undetected) systematic errors, which implies no definitive statement can be made at present. A comparison is also made between different expressions of regression line slope and intercept variance estimators, where fractional discrepancies are found to be not exceeding a few percent, which grows up to about 20% in the presence of large dispersion data. An extension of the formalism to structural models is left to a forthcoming paper.

Application of classical thermodynamics to the conductivity in non-polar media

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

Gourdin-Bertin, S.; Chassagne, C.

Electrical conductivity in non-polar media is a subject which recently regained interest. If most of experiments and theoretical developments were done more than 50 years ago, new experiments and theories have been recently published. As the electrical conductivity describes, at low field, the equilibrium state of a system, it is natural to apply theories based on equilibrium thermodynamics. In this article, well-established classical thermodynamics and solvations models are applied to recently published data. This enables to get a new insight in intriguing phenomena, such as the linear dependence of the conductivity on the concentration of ionic surfactant and the evaluationmore » of conductivity for the mixture of two miscible fluids, such as alcohol and alcane, which have very different conductivities.« less

Physical interpretation and application of principles of ultrasonic nondestructive evaluation of high-performance materials

NASA Technical Reports Server (NTRS)

Miller, James G.

1990-01-01

An ultrasonic measurement system employed in the experimental interrogation of the anisotropic properties (through the measurement of the elastic stiffness constants) of the uniaxial graphite-epoxy composites is presented. The continuing effort for the development of improved visualization techniques for physical parameters is discussed. The background is set for the understanding and visualization of the relationship between the phase and energy/group velocity for propagation in high-performance anisotropic materials by investigating the general requirements imposed by the classical wave equation. The consequences are considered when the physical parameters of the anisotropic material are inserted into the classical wave equation by a linear elastic model. The relationship is described between the phase velocity and the energy/group velocity three dimensional surfaces through graphical techniques.

Rotational dynamics of a diatomic molecular ion in a Paul trap

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

Hashemloo, A.; Dion, C. M., E-mail: claude.dion@umu.se

We present models for a heteronuclear diatomic molecular ion in a linear Paul trap in a rigid-rotor approximation, one purely classical and the other where the center-of-mass motion is treated classically, while rotational motion is quantized. We study the rotational dynamics and their influence on the motion of the center-of-mass, in the presence of the coupling between the permanent dipole moment of the ion and the trapping electric field. We show that the presence of the permanent dipole moment affects the trajectory of the ion and that it departs from the Mathieu equation solution found for atomic ions. For themore » case of quantum rotations, we also evidence the effect of the above-mentioned coupling on the rotational states of the ion.« less

Quantum Sheaf Cohomology on Grassmannians

NASA Astrophysics Data System (ADS)

Guo, Jirui; Lu, Zhentao; Sharpe, Eric

2017-05-01

In this paper we study the quantum sheaf cohomology of Grassmannians with deformations of the tangent bundle. Quantum sheaf cohomology is a (0,2) deformation of the ordinary quantum cohomology ring, realized as the OPE ring in A/2-twisted theories. Quantum sheaf cohomology has previously been computed for abelian gauged linear sigma models (GLSMs); here, we study (0,2) deformations of nonabelian GLSMs, for which previous methods have been intractable. Combined with the classical result, the quantum ring structure is derived from the one-loop effective potential. We also utilize recent advances in supersymmetric localization to compute A/2 correlation functions and check the general result in examples. In this paper we focus on physics derivations and examples; in a companion paper, we will provide a mathematically rigorous derivation of the classical sheaf cohomology ring.

A comparison of mixed-integer linear programming models for workforce scheduling with position-dependent processing times

NASA Astrophysics Data System (ADS)

Moreno-Camacho, Carlos A.; Montoya-Torres, Jairo R.; Vélez-Gallego, Mario C.

2018-06-01

Only a few studies in the available scientific literature address the problem of having a group of workers that do not share identical levels of productivity during the planning horizon. This study considers a workforce scheduling problem in which the actual processing time is a function of the scheduling sequence to represent the decline in workers' performance, evaluating two classical performance measures separately: makespan and maximum tardiness. Several mathematical models are compared with each other to highlight the advantages of each approach. The mathematical models are tested with randomly generated instances available from a public e-library.

Application of principal component regression and artificial neural network in FT-NIR soluble solids content determination of intact pear fruit

NASA Astrophysics Data System (ADS)

Ying, Yibin; Liu, Yande; Fu, Xiaping; Lu, Huishan

2005-11-01

The artificial neural networks (ANNs) have been used successfully in applications such as pattern recognition, image processing, automation and control. However, majority of today's applications of ANNs is back-propagate feed-forward ANN (BP-ANN). In this paper, back-propagation artificial neural networks (BP-ANN) were applied for modeling soluble solid content (SSC) of intact pear from their Fourier transform near infrared (FT-NIR) spectra. One hundred and sixty-four pear samples were used to build the calibration models and evaluate the models predictive ability. The results are compared to the classical calibration approaches, i.e. principal component regression (PCR), partial least squares (PLS) and non-linear PLS (NPLS). The effects of the optimal methods of training parameters on the prediction model were also investigated. BP-ANN combine with principle component regression (PCR) resulted always better than the classical PCR, PLS and Weight-PLS methods, from the point of view of the predictive ability. Based on the results, it can be concluded that FT-NIR spectroscopy and BP-ANN models can be properly employed for rapid and nondestructive determination of fruit internal quality.

Classical boson sampling algorithms with superior performance to near-term experiments

NASA Astrophysics Data System (ADS)

Neville, Alex; Sparrow, Chris; Clifford, Raphaël; Johnston, Eric; Birchall, Patrick M.; Montanaro, Ashley; Laing, Anthony

2017-12-01

It is predicted that quantum computers will dramatically outperform their conventional counterparts. However, large-scale universal quantum computers are yet to be built. Boson sampling is a rudimentary quantum algorithm tailored to the platform of linear optics, which has sparked interest as a rapid way to demonstrate such quantum supremacy. Photon statistics are governed by intractable matrix functions, which suggests that sampling from the distribution obtained by injecting photons into a linear optical network could be solved more quickly by a photonic experiment than by a classical computer. The apparently low resource requirements for large boson sampling experiments have raised expectations of a near-term demonstration of quantum supremacy by boson sampling. Here we present classical boson sampling algorithms and theoretical analyses of prospects for scaling boson sampling experiments, showing that near-term quantum supremacy via boson sampling is unlikely. Our classical algorithm, based on Metropolised independence sampling, allowed the boson sampling problem to be solved for 30 photons with standard computing hardware. Compared to current experiments, a demonstration of quantum supremacy over a successful implementation of these classical methods on a supercomputer would require the number of photons and experimental components to increase by orders of magnitude, while tackling exponentially scaling photon loss.

Linear, multivariable robust control with a mu perspective

NASA Technical Reports Server (NTRS)

Packard, Andy; Doyle, John; Balas, Gary

1993-01-01

The structured singular value is a linear algebra tool developed to study a particular class of matrix perturbation problems arising in robust feedback control of multivariable systems. These perturbations are called linear fractional, and are a natural way to model many types of uncertainty in linear systems, including state-space parameter uncertainty, multiplicative and additive unmodeled dynamics uncertainty, and coprime factor and gap metric uncertainty. The structured singular value theory provides a natural extension of classical SISO robustness measures and concepts to MIMO systems. The structured singular value analysis, coupled with approximate synthesis methods, make it possible to study the tradeoff between performance and uncertainty that occurs in all feedback systems. In MIMO systems, the complexity of the spatial interactions in the loop gains make it difficult to heuristically quantify the tradeoffs that must occur. This paper examines the role played by the structured singular value (and its computable bounds) in answering these questions, as well as its role in the general robust, multivariable control analysis and design problem.

Numerical analysis of behaviour of cross laminated timber (CLT) in blast loading

NASA Astrophysics Data System (ADS)

Šliseris, J.; Gaile, L.; Pakrastiņš, L.

2017-10-01

A non-linear computation model for CLT wall element that includes explicit dynamics and composite damage constitutive model was developed. The numerical model was compared with classical beam theory and it turned out that shear wood layer has significant shear deformations that must be taken into account when designing CLT. It turned out that impulse duration time has a major effect on the strength of CLT. Special attention must be payed when designing CLT wall, window and door architectural system in order to guarantee the robustness of structure. The proposed numerical modelling framework can be used when designing CLT buildings that can be affected by blast loading, whilst structural robustness must be guaranteed.

Fractal attractors in economic growth models with random pollution externalities

NASA Astrophysics Data System (ADS)

La Torre, Davide; Marsiglio, Simone; Privileggi, Fabio

2018-05-01

We analyze a discrete time two-sector economic growth model where the production technologies in the final and human capital sectors are affected by random shocks both directly (via productivity and factor shares) and indirectly (via a pollution externality). We determine the optimal dynamics in the decentralized economy and show how these dynamics can be described in terms of a two-dimensional affine iterated function system with probability. This allows us to identify a suitable parameter configuration capable of generating exactly the classical Barnsley's fern as the attractor of the log-linearized optimal dynamical system.

On integrable boundaries in the 2 dimensional O(N) σ-models

NASA Astrophysics Data System (ADS)

Aniceto, Inês; Bajnok, Zoltán; Gombor, Tamás; Kim, Minkyoo; Palla, László

2017-09-01

We make an attempt to map the integrable boundary conditions for 2 dimensional non-linear O(N) σ-models. We do it at various levels: classically, by demanding the existence of infinitely many conserved local charges and also by constructing the double row transfer matrix from the Lax connection, which leads to the spectral curve formulation of the problem; at the quantum level, we describe the solutions of the boundary Yang-Baxter equation and derive the Bethe-Yang equations. We then show how to connect the thermodynamic limit of the boundary Bethe-Yang equations to the spectral curve.

Fermi problem in disordered systems

NASA Astrophysics Data System (ADS)

Menezes, G.; Svaiter, N. F.; de Mello, H. R.; Zarro, C. A. D.

2017-10-01

We revisit the Fermi two-atom problem in the framework of disordered systems. In our model, we consider a two-qubit system linearly coupled with a quantum massless scalar field. We analyze the energy transfer between the qubits under different experimental perspectives. In addition, we assume that the coefficients of the Klein-Gordon equation are random functions of the spatial coordinates. The disordered medium is modeled by a centered, stationary, and Gaussian process. We demonstrate that the classical notion of causality emerges only in the wave zone in the presence of random fluctuations of the light cone. Possible repercussions are discussed.

Quantum algorithm for linear regression

NASA Astrophysics Data System (ADS)

Wang, Guoming

2017-07-01

We present a quantum algorithm for fitting a linear regression model to a given data set using the least-squares approach. Differently from previous algorithms which yield a quantum state encoding the optimal parameters, our algorithm outputs these numbers in the classical form. So by running it once, one completely determines the fitted model and then can use it to make predictions on new data at little cost. Moreover, our algorithm works in the standard oracle model, and can handle data sets with nonsparse design matrices. It runs in time poly( log2(N ) ,d ,κ ,1 /ɛ ) , where N is the size of the data set, d is the number of adjustable parameters, κ is the condition number of the design matrix, and ɛ is the desired precision in the output. We also show that the polynomial dependence on d and κ is necessary. Thus, our algorithm cannot be significantly improved. Furthermore, we also give a quantum algorithm that estimates the quality of the least-squares fit (without computing its parameters explicitly). This algorithm runs faster than the one for finding this fit, and can be used to check whether the given data set qualifies for linear regression in the first place.

Computing the Evans function via solving a linear boundary value ODE

NASA Astrophysics Data System (ADS)

Wahl, Colin; Nguyen, Rose; Ventura, Nathaniel; Barker, Blake; Sandstede, Bjorn

2015-11-01

Determining the stability of traveling wave solutions to partial differential equations can oftentimes be computationally intensive but of great importance to understanding the effects of perturbations on the physical systems (chemical reactions, hydrodynamics, etc.) they model. For waves in one spatial dimension, one may linearize around the wave and form an Evans function - an analytic Wronskian-like function which has zeros that correspond in multiplicity to the eigenvalues of the linearized system. If eigenvalues with a positive real part do not exist, the traveling wave will be stable. Two methods exist for calculating the Evans function numerically: the exterior-product method and the method of continuous orthogonalization. The first is numerically expensive, and the second reformulates the originally linear system as a nonlinear system. We develop a new algorithm for computing the Evans function through appropriate linear boundary-value problems. This algorithm is cheaper than the previous methods, and we prove that it preserves analyticity of the Evans function. We also provide error estimates and implement it on some classical one- and two-dimensional systems, one being the Swift-Hohenberg equation in a channel, to show the advantages.

Linearized-moment analysis of the temperature jump and temperature defect in the Knudsen layer of a rarefied gas.

PubMed

Gu, Xiao-Jun; Emerson, David R

2014-06-01

Understanding the thermal behavior of a rarefied gas remains a fundamental problem. In the present study, we investigate the predictive capabilities of the regularized 13 and 26 moment equations. In this paper, we consider low-speed problems with small gradients, and to simplify the analysis, a linearized set of moment equations is derived to explore a classic temperature problem. Analytical solutions obtained for the linearized 26 moment equations are compared with available kinetic models and can reliably capture all qualitative trends for the temperature-jump coefficient and the associated temperature defect in the thermal Knudsen layer. In contrast, the linearized 13 moment equations lack the necessary physics to capture these effects and consistently underpredict kinetic theory. The deviation from kinetic theory for the 13 moment equations increases significantly for specular reflection of gas molecules, whereas the 26 moment equations compare well with results from kinetic theory. To improve engineering analyses, expressions for the effective thermal conductivity and Prandtl number in the Knudsen layer are derived with the linearized 26 moment equations.

A fictitious domain approach for the simulation of dense suspensions

NASA Astrophysics Data System (ADS)

Gallier, Stany; Lemaire, Elisabeth; Lobry, Laurent; Peters, François

2014-01-01

Low Reynolds number concentrated suspensions do exhibit an intricate physics which can be partly unraveled by the use of numerical simulation. To this end, a Lagrange multiplier-free fictitious domain approach is described in this work. Unlike some methods recently proposed, the present approach is fully Eulerian and therefore does not need any transfer between the Eulerian background grid and some Lagrangian nodes attached to particles. Lubrication forces between particles play an important role in the suspension rheology and have been properly accounted for in the model. A robust and effective lubrication scheme is outlined which consists in transposing the classical approach used in Stokesian Dynamics to our present direct numerical simulation. This lubrication model has also been adapted to account for solid boundaries such as walls. Contact forces between particles are modeled using a classical Discrete Element Method (DEM), a widely used method in granular matter physics. Comprehensive validations are presented on various one-particle, two-particle or three-particle configurations in a linear shear flow as well as some O(103) and O(104) particle simulations.

Dipolar order by disorder in the classical Heisenberg antiferromagnet on the kagome lattice

NASA Astrophysics Data System (ADS)

Chern, Gia-Wei

2014-03-01

The first experiments on the ``kagome bilayer'' SCGO triggered a wave of interest in kagome antiferromagnets in particular, and frustrated systems in general. A cluster of early seminal theoretical papers established kagome magnets as model systems for novel ordering phenomena, discussing in particular spin liquidity, partial order, disorder-free glassiness and order by disorder. Despite significant recent progress in understanding the ground state for the quantum S = 1 / 2 model, the nature of the low-temperature phase for the classical kagome Heisenberg antiferromagnet has remained a mystery: the non-linear nature of the fluctuations around the exponentially numerous harmonically degenerate ground states has not permitted a controlled theory, while its complex energy landscape has precluded numerical simulations at low temperature. Here we present an efficient Monte Carlo algorithm which removes the latter obstacle. Our simulations detect a low-temperature regime in which correlations saturate at a remarkably small value. Feeding these results into an effective model and analyzing the results in the framework of an appropriate field theory implies the presence of long-range dipolar spin order with a tripled unit cell.

Classical dimer model with anisotropic interactions on the square lattice

NASA Astrophysics Data System (ADS)

Otsuka, Hiromi

2009-07-01

We discuss phase transitions and the phase diagram of a classical dimer model with anisotropic interactions defined on a square lattice. For the attractive region, the perturbation of the orientational order parameter introduced by the anisotropy causes the Berezinskii-Kosterlitz-Thouless transitions from a dimer-liquid to columnar phases. According to the discussion by Nomura and Okamoto for a quantum-spin chain system [J. Phys. A 27, 5773 (1994)], we proffer criteria to determine transition points and also universal level-splitting conditions. Subsequently, we perform numerical diagonalization calculations of the nonsymmetric real transfer matrices up to linear dimension specified by L=20 and determine the global phase diagram. For the repulsive region, we find the boundary between the dimer-liquid and the strong repulsion phases. Based on the dispersion relation of the one-string motion, which exhibits a twofold “zero-energy flat band” in the strong repulsion limit, we give an intuitive account for the property of the strong repulsion phase.

Structural health monitoring based on sensitivity vector fields and attractor morphing.

PubMed

Yin, Shih-Hsun; Epureanu, Bogdan I

2006-09-15

The dynamic responses of a thermo-shielding panel forced by unsteady aerodynamic loads and a classical Duffing oscillator are investigated to detect structural damage. A nonlinear aeroelastic model is obtained for the panel by using third-order piston theory to model the unsteady supersonic flow, which interacts with the panel. To identify damage, we analyse the morphology (deformation and movement) of the attractor of the dynamics of the aeroelastic system and the Duffing oscillator. Damages of various locations, extents and levels are shown to be revealed by the attractor-based analysis. For the panel, the type of damage considered is a local reduction in the bending stiffness. For the Duffing oscillator, variations in the linear and nonlinear stiffnesses and damping are considered as damage. Present studies of such problems are based on linear theories. In contrast, the presented approach using nonlinear dynamics has the potential of enhancing accuracy and sensitivity of detection.

Local tuning of the order parameter in superconducting weak links: A zero-inductance nanodevice

NASA Astrophysics Data System (ADS)

Winik, Roni; Holzman, Itamar; Dalla Torre, Emanuele G.; Buks, Eyal; Ivry, Yachin

2018-03-01

Controlling both the amplitude and the phase of the superconducting quantum order parameter (" separators="|ψ ) in nanostructures is important for next-generation information and communication technologies. The lack of electric resistance in superconductors, which may be advantageous for some technologies, hinders convenient voltage-bias tuning and hence limits the tunability of ψ at the microscopic scale. Here, we demonstrate the local tunability of the phase and amplitude of ψ, obtained by patterning with a single lithography step a Nb nano-superconducting quantum interference device (nano-SQUID) that is biased at its nanobridges. We accompany our experimental results by a semi-classical linearized model that is valid for generic nano-SQUIDs with multiple ports and helps simplify the modelling of non-linear couplings among the Josephson junctions. Our design helped us reveal unusual electric characteristics with effective zero inductance, which is promising for nanoscale magnetic sensing and quantum technologies.

Validation of Blockage Interference Corrections in the National Transonic Facility

NASA Technical Reports Server (NTRS)

Walker, Eric L.

2007-01-01

A validation test has recently been constructed for wall interference methods as applied to the National Transonic Facility (NTF). The goal of this study was to begin to address the uncertainty of wall-induced-blockage interference corrections, which will make it possible to address the overall quality of data generated by the facility. The validation test itself is not specific to any particular modeling. For this present effort, the Transonic Wall Interference Correction System (TWICS) as implemented at the NTF is the mathematical model being tested. TWICS uses linear, potential boundary conditions that must first be calibrated. These boundary conditions include three different classical, linear. homogeneous forms that have been historically used to approximate the physical behavior of longitudinally slotted test section walls. Results of the application of the calibrated wall boundary conditions are discussed in the context of the validation test.

On the form of ROCs constructed from confidence ratings.

PubMed

Malmberg, Kenneth J

2002-03-01

A classical question for memory researchers is whether memories vary in an all-or-nothing, discrete manner (e.g., stored vs. not stored, recalled vs. not recalled), or whether they vary along a continuous dimension (e.g., strength, similarity, or familiarity). For yes-no classification tasks, continuous- and discrete-state models predict nonlinear and linear receiver operating characteristics (ROCs), respectively (D. M. Green & J. A. Swets, 1966; N. A. Macmillan & C. D. Creelman, 1991). Recently, several authors have assumed that these predictions are generalizable to confidence ratings tasks (J. Qin, C. L. Raye, M. K. Johnson, & K. J. Mitchell, 2001; S. D. Slotnick, S. A. Klein, C. S. Dodson, & A. P. Shimamura, 2000, and A. P. Yonelinas, 1999). This assumption is shown to be unwarranted by showing that discrete-state ratings models predict both linear and nonlinear ROCs. The critical factor determining the form of the discrete-state ROC is the response strategy adopted by the classifier.

A Linear Bicharacteristic FDTD Method

NASA Technical Reports Server (NTRS)

Beggs, John H.

2001-01-01

The linear bicharacteristic scheme (LBS) was originally developed to improve unsteady solutions in computational acoustics and aeroacoustics [1]-[7]. It is a classical leapfrog algorithm, but is combined with upwind bias in the spatial derivatives. This approach preserves the time-reversibility of the leapfrog algorithm, which results in no dissipation, and it permits more flexibility by the ability to adopt a characteristic based method. The use of characteristic variables allows the LBS to treat the outer computational boundaries naturally using the exact compatibility equations. The LBS offers a central storage approach with lower dispersion than the Yee algorithm, plus it generalizes much easier to nonuniform grids. It has previously been applied to two and three-dimensional freespace electromagnetic propagation and scattering problems [3], [6], [7]. This paper extends the LBS to model lossy dielectric and magnetic materials. Results are presented for several one-dimensional model problems, and the FDTD algorithm is chosen as a convenient reference for comparison.

Linear and Non-linear Information Flows In Rainfall Field

NASA Astrophysics Data System (ADS)

Molini, A.; La Barbera, P.; Lanza, L. G.

The rainfall process is the result of a complex framework of non-linear dynamical in- teractions between the different components of the atmosphere. It preserves the com- plexity and the intermittent features of the generating system in space and time as well as the strong dependence of these properties on the scale of observations. The understanding and quantification of how the non-linearity of the generating process comes to influence the single rain events constitute relevant research issues in the field of hydro-meteorology, especially in those applications where a timely and effective forecasting of heavy rain events is able to reduce the risk of failure. This work focuses on the characterization of the non-linear properties of the observed rain process and on the influence of these features on hydrological models. Among the goals of such a survey is the research of regular structures of the rainfall phenomenon and the study of the information flows within the rain field. The research focuses on three basic evo- lution directions for the system: in time, in space and between the different scales. In fact, the information flows that force the system to evolve represent in general a connection between the different locations in space, the different instants in time and, unless assuming the hypothesis of scale invariance is verified "a priori", the different characteristic scales. A first phase of the analysis is carried out by means of classic statistical methods, then a survey of the information flows within the field is devel- oped by means of techniques borrowed from the Information Theory, and finally an analysis of the rain signal in the time and frequency domains is performed, with par- ticular reference to its intermittent structure. The methods adopted in this last part of the work are both the classic techniques of statistical inference and a few procedures for the detection of non-linear and non-stationary features within the process starting from measured data.

Non-Linear Analysis of Mode II Fracture in the end Notched Flexure Beam

NASA Astrophysics Data System (ADS)

Rizov, V.

2016-03-01

Analysis is carried-out of fracture in the End Notched Flex- ure (ENF) beam configuration, taking into account the material nonlin- earity. For this purpose, the J-integral approach is applied. A non-linear model, based on the Classical beam theory is used. The mechanical be- haviour of the ENF configuration is described by the Ramberg-Osgood stress-strain curve. It is assumed that the material possesses the same properties in tension and compression. The influence is evaluated of the material constants in the Ramberg-Osgood stress-strain equation on the fracture behaviour. The effect of the crack length on the J-integral value is investigated, too. The analytical approach, developed in the present paper, is very useful for parametric analyses, since the simple formulae obtained capture the essentials of the non-linear fracture in the ENF con- figuration.

Computation of the bluff-body sound generation by a self-consistent mean flow formulation

NASA Astrophysics Data System (ADS)

Fani, A.; Citro, V.; Giannetti, F.; Auteri, F.

2018-03-01

The sound generated by the flow around a circular cylinder is numerically investigated by using a finite-element method. In particular, we study the acoustic emissions generated by the flow past the bluff body at low Mach and Reynolds numbers. We perform a global stability analysis by using the compressible linearized Navier-Stokes equations. The resulting direct global mode provides detailed information related to the underlying hydrodynamic instability and data on the acoustic field generated. In order to recover the intensity of the produced sound, we apply the self-consistent model for non-linear saturation proposed by Mantič-Lugo, Arratia, and Gallaire ["Self-consistent mean flow description of the nonlinear saturation of the vortex shedding in the cylinder wake," Phys. Rev. Lett. 113, 084501 (2014)]. The application of this model allows us to compute the amplitude of the resulting linear mode and the effects of saturation on the mode structure and acoustic field. Our results show excellent agreement with those obtained by a full compressible simulation direct numerical simulation and those derived by the application of classical acoustic analogy formulations.

Experimental and numerical analysis of pre-compressed masonry walls in two-way-bending with second order effects

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

Milani, Gabriele, E-mail: milani@stru.polimi.it; Olivito, Renato S.; Tralli, Antonio

2014-10-06

The buckling behavior of slender unreinforced masonry (URM) walls subjected to axial compression and out-of-plane lateral loads is investigated through a combined experimental and numerical homogenizedapproach. After a preliminary analysis performed on a unit cell meshed by means of elastic FEs and non-linear interfaces, macroscopic moment-curvature diagrams so obtained are implemented at a structural level, discretizing masonry by means of rigid triangular elements and non-linear interfaces. The non-linear incremental response of the structure is accounted for a specific quadratic programming routine. In parallel, a wide experimental campaign is conducted on walls in two way bending, with the double aim ofmore » both validating the numerical model and investigating the behavior of walls that may not be reduced to simple cantilevers or simply supported beams. Panels investigated are dry-joint in scale square walls simply supported at the base and on a vertical edge, exhibiting the classical Rondelet’s mechanism. The results obtained are compared with those provided by the numerical model.« less

Classical-trajectory simulation of accelerating neutral atoms with polarized intense laser pulses

NASA Astrophysics Data System (ADS)

Xia, Q. Z.; Fu, L. B.; Liu, J.

2013-03-01

In the present paper, we perform the classical trajectory Monte Carlo simulation of the complex dynamics of accelerating neutral atoms with linearly or circularly polarized intense laser pulses. Our simulations involve the ion motion as well as the tunneling ionization and the scattering dynamics of valence electron in the combined Coulomb and electromagnetic fields, for both helium (He) and magnesium (Mg). We show that for He atoms, only linearly polarized lasers can effectively accelerate the atoms, while for Mg atoms, we find that both linearly and circularly polarized lasers can successively accelerate the atoms. The underlying mechanism is discussed and the subcycle dynamics of accelerating trajectories is investigated. We have compared our theoretical results with a recent experiment [Eichmann Nature (London)NATUAS0028-083610.1038/nature08481 461, 1261 (2009)].

Allele Age Under Non-Classical Assumptions is Clarified by an Exact Computational Markov Chain Approach.

PubMed

De Sanctis, Bianca; Krukov, Ivan; de Koning, A P Jason

2017-09-19

Determination of the age of an allele based on its population frequency is a well-studied problem in population genetics, for which a variety of approximations have been proposed. We present a new result that, surprisingly, allows the expectation and variance of allele age to be computed exactly (within machine precision) for any finite absorbing Markov chain model in a matter of seconds. This approach makes none of the classical assumptions (e.g., weak selection, reversibility, infinite sites), exploits modern sparse linear algebra techniques, integrates over all sample paths, and is rapidly computable for Wright-Fisher populations up to N e  = 100,000. With this approach, we study the joint effect of recurrent mutation, dominance, and selection, and demonstrate new examples of "selective strolls" where the classical symmetry of allele age with respect to selection is violated by weakly selected alleles that are older than neutral alleles at the same frequency. We also show evidence for a strong age imbalance, where rare deleterious alleles are expected to be substantially older than advantageous alleles observed at the same frequency when population-scaled mutation rates are large. These results highlight the under-appreciated utility of computational methods for the direct analysis of Markov chain models in population genetics.

Non-stationary pre-envelope covariances of non-classically damped systems

NASA Astrophysics Data System (ADS)

Muscolino, G.

1991-08-01

A new formulation is given to evaluate the stationary and non-stationary response of linear non-classically damped systems subjected to multi-correlated non-separable Gaussian input processes. This formulation is based on a new and more suitable definition of the impulse response function matrix for such systems. It is shown that, when using this definition, the stochastic response of non-classically damped systems involves the evaluation of quantities similar to those of classically damped ones. Furthermore, considerations about non-stationary cross-covariances, spectral moments and pre-envelope cross-covariances are presented for a monocorrelated input process.

Lenard-Balescu calculations and classical molecular dynamics simulations of electrical and thermal conductivities of hydrogen plasmas

DOE PAGES

Whitley, Heather D.; Scullard, Christian R.; Benedict, Lorin X.; ...

2014-12-04

Here, we present a discussion of kinetic theory treatments of linear electrical and thermal transport in hydrogen plasmas, for a regime of interest to inertial confinement fusion applications. In order to assess the accuracy of one of the more involved of these approaches, classical Lenard-Balescu theory, we perform classical molecular dynamics simulations of hydrogen plasmas using 2-body quantum statistical potentials and compute both electrical and thermal conductivity from out particle trajectories using the Kubo approach. Our classical Lenard-Balescu results employing the identical statistical potentials agree well with the simulations.

Boosting multi-state models.

PubMed

Reulen, Holger; Kneib, Thomas

2016-04-01

One important goal in multi-state modelling is to explore information about conditional transition-type-specific hazard rate functions by estimating influencing effects of explanatory variables. This may be performed using single transition-type-specific models if these covariate effects are assumed to be different across transition-types. To investigate whether this assumption holds or whether one of the effects is equal across several transition-types (cross-transition-type effect), a combined model has to be applied, for instance with the use of a stratified partial likelihood formulation. Here, prior knowledge about the underlying covariate effect mechanisms is often sparse, especially about ineffectivenesses of transition-type-specific or cross-transition-type effects. As a consequence, data-driven variable selection is an important task: a large number of estimable effects has to be taken into account if joint modelling of all transition-types is performed. A related but subsequent task is model choice: is an effect satisfactory estimated assuming linearity, or is the true underlying nature strongly deviating from linearity? This article introduces component-wise Functional Gradient Descent Boosting (short boosting) for multi-state models, an approach performing unsupervised variable selection and model choice simultaneously within a single estimation run. We demonstrate that features and advantages in the application of boosting introduced and illustrated in classical regression scenarios remain present in the transfer to multi-state models. As a consequence, boosting provides an effective means to answer questions about ineffectiveness and non-linearity of single transition-type-specific or cross-transition-type effects.

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

Jing Yanfei, E-mail: yanfeijing@uestc.edu.c; Huang Tingzhu, E-mail: tzhuang@uestc.edu.c; Duan Yong, E-mail: duanyong@yahoo.c

This study is mainly focused on iterative solutions with simple diagonal preconditioning to two complex-valued nonsymmetric systems of linear equations arising from a computational chemistry model problem proposed by Sherry Li of NERSC. Numerical experiments show the feasibility of iterative methods to some extent when applied to the problems and reveal the competitiveness of our recently proposed Lanczos biconjugate A-orthonormalization methods to other classic and popular iterative methods. By the way, experiment results also indicate that application specific preconditioners may be mandatory and required for accelerating convergence.

Research in Computational Aeroscience Applications Implemented on Advanced Parallel Computing Systems

NASA Technical Reports Server (NTRS)

Wigton, Larry

1996-01-01

Improving the numerical linear algebra routines for use in new Navier-Stokes codes, specifically Tim Barth's unstructured grid code, with spin-offs to TRANAIR is reported. A fast distance calculation routine for Navier-Stokes codes using the new one-equation turbulence models is written. The primary focus of this work was devoted to improving matrix-iterative methods. New algorithms have been developed which activate the full potential of classical Cray-class computers as well as distributed-memory parallel computers.

Simulation and measurement of nonlinear behavior in a high-power test cell.

PubMed

Harvey, Gerald; Gachagan, Anthony

2011-04-01

High-power ultrasound has many diverse uses in process applications in industries ranging from food to pharmaceutical. Because cavitation is frequently a desirable effect within many high-power, low-frequency systems, these systems are commonly expected to feature highly nonlinear acoustic propagation because of the high input levels employed. This generation of harmonics significantly alters the field profile compared with that of a linear system, making accurate field modeling difficult. However, when the short propagation distances involved are considered, it is not unreasonable to assume that these systems may remain largely linear until the onset of cavitation, in terms of classical acoustic propagation. The purpose of this paper is to investigate the possible nonlinear effects within such systems before the onset of cavitation. A theoretical description of nonlinear propagation will be presented and the merits of common analytical models will be discussed. Following this, a numerical model of nonlinearity will be outlined and the advantages it presents for representing nonlinear effects in bounded fields will be discussed. Next, the driving equipment and transducers will be evaluated for linearity to disengage any effects from those formed in the transmission load. Finally, the linearity of the system will be measured using an acoustic hydrophone and compared with finite element analysis to confirm that nonlinear effects are not prevalent in such systems at the onset of cavitation. © 2011 IEEE

Phototransduction early steps model based on Beer-Lambert optical law.

PubMed

Salido, Ezequiel M; Servalli, Leonardo N; Gomez, Juan Carlos; Verrastro, Claudio

2017-02-01

The amount of available rhodopsin on the photoreceptor outer segment and its change over time is not considered in classic models of phototransduction. Thus, those models do not take into account the absorptance variation of the outer segment under different brightness conditions. The relationship between the light absorbed by a medium and its absorptance is well described by the Beer-Lambert law. This newly proposed model implements the absorptance variation phenomenon in a set of equations that admit photons per second as input and results in active rhodopsins per second as output. This study compares the classic model of phototransduction developed by Forti et al. (1989) to this new model by using different light stimuli to measure active rhodopsin and photocurrent. The results show a linear relationship between light stimulus and active rhodopsin in the Forti model and an exponential saturation in the new model. Further, photocurrent values have shown that the new model behaves equivalently to the experimental and theoretical data as published by Forti in dark-adapted rods, but fits significantly better under light-adapted conditions. The new model successfully introduced a physics optical law to the standard model of phototransduction adding a new processing layer that had not been mathematically implemented before. In addition, it describes the physiological concept of saturation and delivers outputs in concordance to input magnitudes. Copyright © 2017 Elsevier Ltd. All rights reserved.

Effect Sizes for Growth-Modeling Analysis for Controlled Clinical Trials in the Same Metric as for Classical Analysis

PubMed Central

Feingold, Alan

2009-01-01

The use of growth-modeling analysis (GMA)--including Hierarchical Linear Models, Latent Growth Models, and General Estimating Equations--to evaluate interventions in psychology, psychiatry, and prevention science has grown rapidly over the last decade. However, an effect size associated with the difference between the trajectories of the intervention and control groups that captures the treatment effect is rarely reported. This article first reviews two classes of formulas for effect sizes associated with classical repeated-measures designs that use the standard deviation of either change scores or raw scores for the denominator. It then broadens the scope to subsume GMA, and demonstrates that the independent groups, within-subjects, pretest-posttest control-group, and GMA designs all estimate the same effect size when the standard deviation of raw scores is uniformly used. Finally, it is shown that the correct effect size for treatment efficacy in GMA--the difference between the estimated means of the two groups at end of study (determined from the coefficient for the slope difference and length of study) divided by the baseline standard deviation--is not reported in clinical trials. PMID:19271847

A Fluid Structure Algorithm with Lagrange Multipliers to Model Free Swimming

NASA Astrophysics Data System (ADS)

Sahin, Mehmet; Dilek, Ezgi

2017-11-01

A new monolithic approach is prosed to solve the fluid-structure interaction (FSI) problem with Lagrange multipliers in order to model free swimming/flying. In the present approach, the fluid domain is modeled by the incompressible Navier-Stokes equations and discretized using an Arbitrary Lagrangian-Eulerian (ALE) formulation based on the stable side-centered unstructured finite volume method. The solid domain is modeled by the constitutive laws for the nonlinear Saint Venant-Kirchhoff material and the classical Galerkin finite element method is used to discretize the governing equations in a Lagrangian frame. In order to impose the body motion/deformation, the distance between the constraint pair nodes is imposed using the Lagrange multipliers, which is independent from the frame of reference. The resulting algebraic linear equations are solved in a fully coupled manner using a dual approach (null space method). The present numerical algorithm is initially validated for the classical FSI benchmark problems and then applied to the free swimming of three linked ellipses. The authors are grateful for the use of the computing resources provided by the National Center for High Performance Computing (UYBHM) under Grant Number 10752009 and the computing facilities at TUBITAK-ULAKBIM, High Performance and Grid Computing Center.

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

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

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

2016-07-14

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

Classical theory of atom-surface scattering: The rainbow effect

NASA Astrophysics Data System (ADS)

Miret-Artés, Salvador; Pollak, Eli

The scattering of heavy atoms and molecules from surfaces is oftentimes dominated by classical mechanics. A large body of experiments have gathered data on the angular distributions of the scattered species, their energy loss distribution, sticking probability, dependence on surface temperature and more. For many years these phenomena have been considered theoretically in the framework of the "washboard model" in which the interaction of the incident particle with the surface is described in terms of hard wall potentials. Although this class of models has helped in elucidating some of the features it left open many questions such as: true potentials are clearly not hard wall potentials, it does not provide a realistic framework for phonon scattering, and it cannot explain the incident angle and incident energy dependence of rainbow scattering, nor can it provide a consistent theory for sticking. In recent years we have been developing a classical perturbation theory approach which has provided new insight into the dynamics of atom-surface scattering. The theory includes both surface corrugation as well as interaction with surface phonons in terms of harmonic baths which are linearly coupled to the system coordinates. This model has been successful in elucidating many new features of rainbow scattering in terms of frictions and bath fluctuations or noise. It has also given new insight into the origins of asymmetry in atomic scattering from surfaces. New phenomena deduced from the theory include friction induced rainbows, energy loss rainbows, a theory of super-rainbows, and more. In this review we present the classical theory of atom-surface scattering as well as extensions and implications for semiclassical scattering and the further development of a quantum theory of surface scattering. Special emphasis is given to the inversion of scattering data into information on the particle-surface interactions.

Computing the Polarimetric and Photometric Variability of Be Stars

NASA Astrophysics Data System (ADS)

Marr, K. C.; Jones, C. E.; Halonen, R. J.

2018-01-01

We investigate variations in the linear polarization as well as in the V-band and B-band color–magnitudes for classical Be star disks. We present two models: disks with enhanced disk density and disks that are tilted or warped from the stellar equatorial plane. In both cases, we predict variation in observable properties of the system as the disk rotates. We use a non-LTE radiative transfer code BEDISK (Sigut & Jones) in combination with a Monte Carlo routine that includes multiple scattering (Halonen et al.) to model classical Be star systems. We find that a disk with an enhanced density region that is one order of magnitude denser than the disk’s base density shows as much as ∼ 0.2 % variability in the polarization while the polarization position angle varies by ∼ 8^\\circ . The ΔV magnitude for the same system shows variations of up to ∼ 0.4 mag while the Δ(B–V) color varies by at most ∼ 0.01 mag. We find that disks tilted from the equatorial plane at small angles of ∼ 30^\\circ more strongly reflect the values of polarization and color–magnitudes reported in the literature than disks tilted at larger angles. For this model, the linear polarization varies by ∼ 0.3 % , the polarization position angle varies by ∼ 60^\\circ , the ΔV magnitude varies up to 0.35 mag, and the Δ(B–V) color varies by up to 0.1 mag. We find that the enhanced disk density models show ranges of polarization and color–magnitudes that are commensurate with what is reported in the literature for all sizes of the density-enhanced regions. From this, we cannot determine any preference for small or large density-enhanced regions.

Acoustic and Seismic Dispersion in Complex Fluids and Solids

NASA Astrophysics Data System (ADS)

Goddard, Joe

2017-04-01

The first part of the present paper is the continuation of a previous work [3] on the effects of higher spatial gradients and temporal relaxation on stress and heat flux in complex fluids. In particular, the general linear theory is applied to acoustic dispersion, extending a simpler model proposed by Davis and Brenner [2]. The theory is applied to a linearized version of the Chapman-Enskog fluid [1] valid to terms of Burnett order and including Maxwell-Cataneo relaxation of stress and heat flux on relaxation time scales τ. For this model, the dispersion relation k(ω) giving spatial wave number k as function of temporal frequency ω is a cubic in k2, in contrast to the quadratic in k2 given by the classical model and the recently proposed modification [2]. The cubic terms are shown to be important only for ωτ = O(1) where Maxwell-Cataneo relaxation is also important. As a second part of the present work, it is shown how the above model can also be applied to isotropic solids, where both shear and pressure waves are important. Finally, consideration is given to hyperstress in micro- polar continua, including both graded and micro-morphic varieties. [1]S. Chapman and T. Cowling. The mathematical theory of non-uniform gases. Cambridge University Press, [Cambridge, UK], 1960. [2]A. M.J. Davis and H. Brenner. Thermal and viscous effects on sound waves: revised classical theory. J. Acoust. Soc. Am., 132(5):2963-9, 2012. [3] J.D. Goddard. On material velocities and non-locality in the thermo-mechanics of continua. Int. J. Eng. Sci., 48(11):1279-88, 2010.

Dynamics of Transformation from Segregation to Mixed Wealth Cities

PubMed Central

Sahasranaman, Anand; Jensen, Henrik Jeldtoft

2016-01-01

We model the dynamics of a variation of the Schelling model for agents described simply by a continuously distributed variable—wealth. Agent movement is not dictated by agent choice as in the classic Schelling model, but by their wealth status. Agents move to neighborhoods where their wealth is not lesser than that of some proportion of their neighbors, the threshold level. As in the case of the classic Schelling model, we find here that wealth-based segregation occurs and persists. However, introducing uncertainty into the decision to move—that is, with some probability, if agents are allowed to move even though the threshold condition is contravened—we find that even for small proportions of such disallowed moves, the dynamics no longer yield segregation but instead sharply transition into a persistent mixed wealth distribution, consistent with empirical findings of Benenson, Hatna, and Or. We investigate the nature of this sharp transformation, and find that it is because of a non-linear relationship between allowed moves (moves where threshold condition is satisfied) and disallowed moves (moves where it is not). For small increases in disallowed moves, there is a rapid corresponding increase in allowed moves (before the rate of increase tapers off and tends to zero), and it is the effect of this non-linearity on the dynamics of the system that causes the rapid transition from a segregated to a mixed wealth state. The contravention of the tolerance condition, sanctioning disallowed moves, could be interpreted as public policy interventions to drive de-segregation. Our finding therefore suggests that it might require limited, but continually implemented, public intervention—just sufficient to enable a small, persistently sustained fraction of disallowed moves so as to trigger the dynamics that drive the transformation from a segregated to mixed equilibrium. PMID:27861578

Multiple spatially localized dynamical states in friction-excited oscillator chains

NASA Astrophysics Data System (ADS)

Papangelo, A.; Hoffmann, N.; Grolet, A.; Stender, M.; Ciavarella, M.

2018-03-01

Friction-induced vibrations are known to affect many engineering applications. Here, we study a chain of friction-excited oscillators with nearest neighbor elastic coupling. The excitation is provided by a moving belt which moves at a certain velocity vd while friction is modelled with an exponentially decaying friction law. It is shown that in a certain range of driving velocities, multiple stable spatially localized solutions exist whose dynamical behavior (i.e. regular or irregular) depends on the number of oscillators involved in the vibration. The classical non-repeatability of friction-induced vibration problems can be interpreted in light of those multiple stable dynamical states. These states are found within a "snaking-like" bifurcation pattern. Contrary to the classical Anderson localization phenomenon, here the underlying linear system is perfectly homogeneous and localization is solely triggered by the friction nonlinearity.

Symbolic Solution of Linear Differential Equations

NASA Technical Reports Server (NTRS)

Feinberg, R. B.; Grooms, R. G.

1981-01-01

An algorithm for solving linear constant-coefficient ordinary differential equations is presented. The computational complexity of the algorithm is discussed and its implementation in the FORMAC system is described. A comparison is made between the algorithm and some classical algorithms for solving differential equations.

Non-linear vibrations of sandwich viscoelastic shells

NASA Astrophysics Data System (ADS)

Benchouaf, Lahcen; Boutyour, El Hassan; Daya, El Mostafa; Potier-Ferry, Michel

2018-04-01

This paper deals with the non-linear vibration of sandwich viscoelastic shell structures. Coupling a harmonic balance method with the Galerkin's procedure, one obtains an amplitude equation depending on two complex coefficients. The latter are determined by solving a classical eigenvalue problem and two linear ones. This permits to get the non-linear frequency and the non-linear loss factor as functions of the displacement amplitude. To validate our approach, these relationships are illustrated in the case of a circular sandwich ring.

The generalized Hill model: A kinematic approach towards active muscle contraction

NASA Astrophysics Data System (ADS)

Göktepe, Serdar; Menzel, Andreas; Kuhl, Ellen

2014-12-01

Excitation-contraction coupling is the physiological process of converting an electrical stimulus into a mechanical response. In muscle, the electrical stimulus is an action potential and the mechanical response is active contraction. The classical Hill model characterizes muscle contraction though one contractile element, activated by electrical excitation, and two non-linear springs, one in series and one in parallel. This rheology translates into an additive decomposition of the total stress into a passive and an active part. Here we supplement this additive decomposition of the stress by a multiplicative decomposition of the deformation gradient into a passive and an active part. We generalize the one-dimensional Hill model to the three-dimensional setting and constitutively define the passive stress as a function of the total deformation gradient and the active stress as a function of both the total deformation gradient and its active part. We show that this novel approach combines the features of both the classical stress-based Hill model and the recent active-strain models. While the notion of active stress is rather phenomenological in nature, active strain is micro-structurally motivated, physically measurable, and straightforward to calibrate. We demonstrate that our model is capable of simulating excitation-contraction coupling in cardiac muscle with its characteristic features of wall thickening, apical lift, and ventricular torsion.

Growth models of Rhizophora mangle L. seedlings in tropical southwestern Atlantic

NASA Astrophysics Data System (ADS)

Lima, Karen Otoni de Oliveira; Tognella, Mônica Maria Pereira; Cunha, Simone Rabelo; Andrade, Humber Agrelli de

2018-07-01

The present study selected and compared regression models that best describe the growth curves of Rhizophora mangle seedlings based on the height (cm) and time (days) variables. The Linear, Exponential, Power Law, Monomolecular, Logistic, and Gompertz models were adjusted with non-linear formulations and minimization of the sum of the squares of the residues. The Akaike Information Criterion was used to select the best model for each seedling. After this selection, the determination coefficient, which evaluates how well a model describes height variation as a time function, was inspected. Differing from the classic population ecology studies, the Monomolecular, Three-parameter Logistic, and Gompertz models presented the best performance in describing growth, suggesting they are the most adequate options for long-term studies. The different growth curves reflect the complexity of stem growth at the seedling stage for R. mangle. The analysis of the joint distribution of the parameters initial height, growth rate, and, asymptotic size allowed the study of the species ecological attributes and to observe its intraspecific variability in each model. Our results provide a basis for interpretation of the dynamics of seedlings growth during their establishment in a mature forest, as well as its regeneration processes.

Comparing Models of Spontaneous Variations, Maneuvers and Indexes to Assess Dynamic Cerebral Autoregulation.

PubMed

Chacón, Max; Noh, Sun-Ho; Landerretche, Jean; Jara, José L

2018-01-01

We analyzed the performance of linear and nonlinear models to assess dynamic cerebral autoregulation (dCA) from spontaneous variations in healthy subjects and compared it with the use of two known maneuvers to abruptly change arterial blood pressure (BP): thigh cuffs and sit-to-stand. Cerebral blood flow velocity and BP were measured simultaneously at rest and while the maneuvers were performed in 20 healthy subjects. To analyze the spontaneous variations, we implemented two types of models using support vector machine (SVM): linear and nonlinear finite impulse response models. The classic autoregulation index (ARI) and the more recently proposed model-free ARI (mfARI) were used as measures of dCA. An ANOVA analysis was applied to compare the different methods and the coefficient of variation was calculated to evaluate their variability. There are differences between indexes, but not between models and maneuvers. The mfARI index with the sit-to-stand maneuver shows the least variability. Support vector machine modeling of spontaneous variation with the mfARI index could be used for the assessment of dCA as an alternative to maneuvers to introduce large BP fluctuations.

Superrotation charge and supertranslation hair on black holes

DOE PAGES

Hawking, Stephen W.; Perry, Malcolm J.; Strominger, Andrew

2017-05-31

It is shown that black hole spacetimes in classical Einstein gravity are characterized by, in addition to their ADM mass M, momentummore » $$\\vec{P}$$, angular momentum $$\\vec{J}$$ and boost charge $$\\vec{/k}$$ , an infinite head of supertranslation hair. Furthermore, the distinct black holes are distinguished by classical superrotation charges measured at infinity. Solutions with supertranslation hair are diffeomorphic to the Schwarzschild spacetime, but the diffeomorphisms are part of the BMS subgroup and act nontrivially on the physical phase space. It is shown that a black hole can be supertranslated by throwing in an asymmetric shock wave. We derive a leading-order Bondi-gauge expression for the linearized horizon supertranslation charge and shown to generate, via the Dirac bracket, supertranslations on the linearized phase space of gravitational excitations of the horizon. The considerations of this paper are largely classical augmented by comments on their implications for the quantum theory.« less

Superrotation charge and supertranslation hair on black holes

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

Hawking, Stephen W.; Perry, Malcolm J.; Strominger, Andrew

It is shown that black hole spacetimes in classical Einstein gravity are characterized by, in addition to their ADM mass M, momentummore » $$\\vec{P}$$, angular momentum $$\\vec{J}$$ and boost charge $$\\vec{/k}$$ , an infinite head of supertranslation hair. Furthermore, the distinct black holes are distinguished by classical superrotation charges measured at infinity. Solutions with supertranslation hair are diffeomorphic to the Schwarzschild spacetime, but the diffeomorphisms are part of the BMS subgroup and act nontrivially on the physical phase space. It is shown that a black hole can be supertranslated by throwing in an asymmetric shock wave. We derive a leading-order Bondi-gauge expression for the linearized horizon supertranslation charge and shown to generate, via the Dirac bracket, supertranslations on the linearized phase space of gravitational excitations of the horizon. The considerations of this paper are largely classical augmented by comments on their implications for the quantum theory.« less

A squeezed light source operated under high vacuum

PubMed Central

Wade, Andrew R.; Mansell, Georgia L.; Chua, Sheon S. Y.; Ward, Robert L.; Slagmolen, Bram J. J.; Shaddock, Daniel A.; McClelland, David E.

2015-01-01

Non-classical squeezed states of light are becoming increasingly important to a range of metrology and other quantum optics applications in cryptography, quantum computation and biophysics. Applications such as improving the sensitivity of advanced gravitational wave detectors and the development of space-based metrology and quantum networks will require robust deployable vacuum-compatible sources. To date non-linear photonics devices operated under high vacuum have been simple single pass systems, testing harmonic generation and the production of classically correlated photon pairs for space-based applications. Here we demonstrate the production under high-vacuum conditions of non-classical squeezed light with an observed 8.6 dB of quantum noise reduction down to 10 Hz. Demonstration of a resonant non-linear optical device, for the generation of squeezed light under vacuum, paves the way to fully exploit the advantages of in-vacuum operations, adapting this technology for deployment into new extreme environments. PMID:26657616

Towards the Fundamental Quantum Limit of Linear Measurements of Classical Signals

NASA Astrophysics Data System (ADS)

Miao, Haixing; Adhikari, Rana X.; Ma, Yiqiu; Pang, Belinda; Chen, Yanbei

2017-08-01

The quantum Cramér-Rao bound (QCRB) sets a fundamental limit for the measurement of classical signals with detectors operating in the quantum regime. Using linear-response theory and the Heisenberg uncertainty relation, we derive a general condition for achieving such a fundamental limit. When applied to classical displacement measurements with a test mass, this condition leads to an explicit connection between the QCRB and the standard quantum limit that arises from a tradeoff between the measurement imprecision and quantum backaction; the QCRB can be viewed as an outcome of a quantum nondemolition measurement with the backaction evaded. Additionally, we show that the test mass is more a resource for improving measurement sensitivity than a victim of the quantum backaction, which suggests a new approach to enhancing the sensitivity of a broad class of sensors. We illustrate these points with laser interferometric gravitational-wave detectors.

A squeezed light source operated under high vacuum

NASA Astrophysics Data System (ADS)

Wade, Andrew R.; Mansell, Georgia L.; Chua, Sheon S. Y.; Ward, Robert L.; Slagmolen, Bram J. J.; Shaddock, Daniel A.; McClelland, David E.

2015-12-01

Non-classical squeezed states of light are becoming increasingly important to a range of metrology and other quantum optics applications in cryptography, quantum computation and biophysics. Applications such as improving the sensitivity of advanced gravitational wave detectors and the development of space-based metrology and quantum networks will require robust deployable vacuum-compatible sources. To date non-linear photonics devices operated under high vacuum have been simple single pass systems, testing harmonic generation and the production of classically correlated photon pairs for space-based applications. Here we demonstrate the production under high-vacuum conditions of non-classical squeezed light with an observed 8.6 dB of quantum noise reduction down to 10 Hz. Demonstration of a resonant non-linear optical device, for the generation of squeezed light under vacuum, paves the way to fully exploit the advantages of in-vacuum operations, adapting this technology for deployment into new extreme environments.

Superrotation charge and supertranslation hair on black holes

NASA Astrophysics Data System (ADS)

Hawking, Stephen W.; Perry, Malcolm J.; Strominger, Andrew

2017-05-01

It is shown that black hole spacetimes in classical Einstein gravity are characterized by, in addition to their ADM mass M, momentum \\overrightarrow{P} , angular momentum \\overrightarrow{J} and boost charge \\overrightarrow{K} , an infinite head of supertranslation hair. The distinct black holes are distinguished by classical superrotation charges measured at infinity. Solutions with super-translation hair are diffeomorphic to the Schwarzschild spacetime, but the diffeomorphisms are part of the BMS subgroup and act nontrivially on the physical phase space. It is shown that a black hole can be supertranslated by throwing in an asymmetric shock wave. A leading-order Bondi-gauge expression is derived for the linearized horizon supertranslation charge and shown to generate, via the Dirac bracket, supertranslations on the linearized phase space of gravitational excitations of the horizon. The considerations of this paper are largely classical augmented by comments on their implications for the quantum theory.

Colombeau algebra as a mathematical tool for investigating step load and step deformation of systems of nonlinear springs and dashpots

NASA Astrophysics Data System (ADS)

Průša, Vít; Řehoř, Martin; Tůma, Karel

2017-02-01

The response of mechanical systems composed of springs and dashpots to a step input is of eminent interest in the applications. If the system is formed by linear elements, then its response is governed by a system of linear ordinary differential equations. In the linear case, the mathematical method of choice for the analysis of the response is the classical theory of distributions. However, if the system contains nonlinear elements, then the classical theory of distributions is of no use, since it is strictly limited to the linear setting. Consequently, a question arises whether it is even possible or reasonable to study the response of nonlinear systems to step inputs. The answer is positive. A mathematical theory that can handle the challenge is the so-called Colombeau algebra. Building on the abstract result by Průša and Rajagopal (Int J Non-Linear Mech 81:207-221, 2016), we show how to use the theory in the analysis of response of nonlinear spring-dashpot and spring-dashpot-mass systems.

Intensity-Curvature Measurement Approaches for the Diagnosis of Magnetic Resonance Imaging Brain Tumors.

PubMed

Ciulla, Carlo; Veljanovski, Dimitar; Rechkoska Shikoska, Ustijana; Risteski, Filip A

2015-11-01

This research presents signal-image post-processing techniques called Intensity-Curvature Measurement Approaches with application to the diagnosis of human brain tumors detected through Magnetic Resonance Imaging (MRI). Post-processing of the MRI of the human brain encompasses the following model functions: (i) bivariate cubic polynomial, (ii) bivariate cubic Lagrange polynomial, (iii) monovariate sinc, and (iv) bivariate linear. The following Intensity-Curvature Measurement Approaches were used: (i) classic-curvature, (ii) signal resilient to interpolation, (iii) intensity-curvature measure and (iv) intensity-curvature functional. The results revealed that the classic-curvature, the signal resilient to interpolation and the intensity-curvature functional are able to add additional information useful to the diagnosis carried out with MRI. The contribution to the MRI diagnosis of our study are: (i) the enhanced gray level scale of the tumor mass and the well-behaved representation of the tumor provided through the signal resilient to interpolation, and (ii) the visually perceptible third dimension perpendicular to the image plane provided through the classic-curvature and the intensity-curvature functional.

Intensity-Curvature Measurement Approaches for the Diagnosis of Magnetic Resonance Imaging Brain Tumors

PubMed Central

Ciulla, Carlo; Veljanovski, Dimitar; Rechkoska Shikoska, Ustijana; Risteski, Filip A.

2015-01-01

This research presents signal-image post-processing techniques called Intensity-Curvature Measurement Approaches with application to the diagnosis of human brain tumors detected through Magnetic Resonance Imaging (MRI). Post-processing of the MRI of the human brain encompasses the following model functions: (i) bivariate cubic polynomial, (ii) bivariate cubic Lagrange polynomial, (iii) monovariate sinc, and (iv) bivariate linear. The following Intensity-Curvature Measurement Approaches were used: (i) classic-curvature, (ii) signal resilient to interpolation, (iii) intensity-curvature measure and (iv) intensity-curvature functional. The results revealed that the classic-curvature, the signal resilient to interpolation and the intensity-curvature functional are able to add additional information useful to the diagnosis carried out with MRI. The contribution to the MRI diagnosis of our study are: (i) the enhanced gray level scale of the tumor mass and the well-behaved representation of the tumor provided through the signal resilient to interpolation, and (ii) the visually perceptible third dimension perpendicular to the image plane provided through the classic-curvature and the intensity-curvature functional. PMID:26644943

Quantum gap and spin-wave excitations in the Kitaev model on a triangular lattice

NASA Astrophysics Data System (ADS)

Avella, Adolfo; Di Ciolo, Andrea; Jackeli, George

2018-05-01

We study the effects of quantum fluctuations on the dynamical generation of a gap and on the evolution of the spin-wave spectra of a frustrated magnet on a triangular lattice with bond-dependent Ising couplings, analog of the Kitaev honeycomb model. The quantum fluctuations lift the subextensive degeneracy of the classical ground-state manifold by a quantum order-by-disorder mechanism. Nearest-neighbor chains remain decoupled and the surviving discrete degeneracy of the ground state is protected by a hidden model symmetry. We show how the four-spin interaction, emergent from the fluctuations, generates a spin gap shifting the nodal lines of the linear spin-wave spectrum to finite energies.

Towards classical spectrum generating algebras for f-deformations

NASA Astrophysics Data System (ADS)

Kullock, Ricardo; Latini, Danilo

2016-01-01

In this paper we revise the classical analog of f-oscillators, a generalization of q-oscillators given in Man'ko et al. (1997) [8], in the framework of classical spectrum generating algebras (SGA) introduced in Kuru and Negro (2008) [9]. We write down the deformed Poisson algebra characterizing the entire family of non-linear oscillators and construct its general solution algebraically. The latter, covering the full range of f-deformations, shows an energy dependence both in the amplitude and the frequency of the motion.

Novel modeling technique for the stator of traveling wave ultrasonic motors.

PubMed

Pons, José L; Rodríguez, Humberto; Ceres, Ramón; Calderón, Leopoldo

2003-11-01

Traveling wave ultrasonic motors (TWUM) are a promising type of piezoelectric transducers, which are based on the friction transmission of mechanical propagating waves. These waves are excited on the stator by using high Q piezoelectric ceramics. This article presents a modeling strategy, which allows for a quick and precise modal and forced analysis of the stator of TWUM. First-order shear deformation laminated plate theory is applied to annular subdomains (super-elements) of the stator. In addition to shear deformations, the model takes into account the effect of rotary inertia, the stiffness contribution of the teeth, and the linear varying thickness of the stator. Moreover, the formulation considers a more realistic function for the electric field inside the piezoelectric ceramic, i.e., a linear function, instead of the generally assumed constant electric field. The Ritz method is used to find an approximated solution for the dynamic equations. Finally, the modal response is obtained and compared against the results from classical simplified models and the finite element method. Thus, the high accuracy and short computation times of the novel strategy were demonstrated.

Riemannian multi-manifold modeling and clustering in brain networks

NASA Astrophysics Data System (ADS)

Slavakis, Konstantinos; Salsabilian, Shiva; Wack, David S.; Muldoon, Sarah F.; Baidoo-Williams, Henry E.; Vettel, Jean M.; Cieslak, Matthew; Grafton, Scott T.

2017-08-01

This paper introduces Riemannian multi-manifold modeling in the context of brain-network analytics: Brainnetwork time-series yield features which are modeled as points lying in or close to a union of a finite number of submanifolds within a known Riemannian manifold. Distinguishing disparate time series amounts thus to clustering multiple Riemannian submanifolds. To this end, two feature-generation schemes for brain-network time series are put forth. The first one is motivated by Granger-causality arguments and uses an auto-regressive moving average model to map low-rank linear vector subspaces, spanned by column vectors of appropriately defined observability matrices, to points into the Grassmann manifold. The second one utilizes (non-linear) dependencies among network nodes by introducing kernel-based partial correlations to generate points in the manifold of positivedefinite matrices. Based on recently developed research on clustering Riemannian submanifolds, an algorithm is provided for distinguishing time series based on their Riemannian-geometry properties. Numerical tests on time series, synthetically generated from real brain-network structural connectivity matrices, reveal that the proposed scheme outperforms classical and state-of-the-art techniques in clustering brain-network states/structures.

Quantum Theory of (H,H{Sub 2}) Scattering: Approximate Treatments of Reactive Scattering

DOE R&D Accomplishments Database

Tang, K. T.; Karplus, M.

1970-10-01

A quantum mechanical study is made of reactive scattering in the (H, H{sub 2}) system. The problem is formulated in terms of a form of the distorted-wave Born approximation (DWBA) suitable for collisions in which all particles have finite mass. For certain incident energies, differential and total cross sections, as well as other attributes of the reactive collisions, (e.g. reaction configuration), are determined. Two limiting models in the DWBA formulation are compared; in one, the molecule is unperturbed by the incoming atom and in the other, the molecule adiabatically follows the incoming atom. For thermal incident energies and semi-empirical interaction potential employed, the adiabatic model seems to be more appropriate. Since the DWBA method is too complicated for a general study of the (H, H{sub 2}) reaction, a much simpler approximation method, the ?linear model? is developed. This model is very different in concept from treatments in which the three atoms are constrained to move on a line throughout the collision. The present model includes the full three-dimensional aspect of the collision and it is only the evaluation of the transition matrix element itself that is simplified. It is found that the linear model, when appropriately normalized, gives results in good agreement with that of the DWBA method. By application of this model, the energy dependence, rotational state of dependence and other properties of the total and differential reactions cross sections are determined. These results of the quantum mechanical treatment are compared with the classical calculation for the same potential surface. The most important result is that, in agreement with the classical treatment, the differential cross sections are strongly backward peaked at low energies and shifts in the forward direction as the energy increases. Finally, the implications of the present calculations for a theory of chemical kinetics are discussed.

Bose-Einstein condensation of the classical axion field in cosmology?

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

Davidson, Sacha; Elmer, Martin, E-mail: s.davidson@ipnl.in2p3.fr, E-mail: m.elmer@ipnl.in2p3.fr

The axion is a motivated cold dark matter candidate, which it would be interesting to distinguish from weakly interacting massive particles. Sikivie has suggested that axions could behave differently during non-linear galaxy evolution, if they form a Bose-Einstein condensate, and argues that ''gravitational thermalisation'' drives them to a Bose-Einstein condensate during the radiation dominated era. Using classical equations of motion during linear structure formation, we explore whether the gravitational interactions of axions can generate enough entropy. At linear order in G{sub N}, we interpret that the principle activities of gravity are to expand the Universe and grow density fluctuations. Tomore » quantify the rate of entropy creation we use the anisotropic stress to estimate a short dissipation scale for axions which does not confirm previous estimates of their gravitational thermalisation rate.« less

Insight into efficient image registration techniques and the demons algorithm.

PubMed

Vercauteren, Tom; Pennec, Xavier; Malis, Ezio; Perchant, Aymeric; Ayache, Nicholas

2007-01-01

As image registration becomes more and more central to many biomedical imaging applications, the efficiency of the algorithms becomes a key issue. Image registration is classically performed by optimizing a similarity criterion over a given spatial transformation space. Even if this problem is considered as almost solved for linear registration, we show in this paper that some tools that have recently been developed in the field of vision-based robot control can outperform classical solutions. The adequacy of these tools for linear image registration leads us to revisit non-linear registration and allows us to provide interesting theoretical roots to the different variants of Thirion's demons algorithm. This analysis predicts a theoretical advantage to the symmetric forces variant of the demons algorithm. We show that, on controlled experiments, this advantage is confirmed, and yields a faster convergence.

Hydrodynamic model for conductivity in graphene.

PubMed

Mendoza, M; Herrmann, H J; Succi, S

2013-01-01

Based on the recently developed picture of an electronic ideal relativistic fluid at the Dirac point, we present an analytical model for the conductivity in graphene that is able to describe the linear dependence on the carrier density and the existence of a minimum conductivity. The model treats impurities as submerged rigid obstacles, forming a disordered medium through which graphene electrons flow, in close analogy with classical fluid dynamics. To describe the minimum conductivity, we take into account the additional carrier density induced by the impurities in the sample. The model, which predicts the conductivity as a function of the impurity fraction of the sample, is supported by extensive simulations for different values of ε, the dimensionless strength of the electric field, and provides excellent agreement with experimental data.

Aesthetic perception of visual textures: a holistic exploration using texture analysis, psychological experiment, and perception modeling.

PubMed

Liu, Jianli; Lughofer, Edwin; Zeng, Xianyi

2015-01-01

Modeling human aesthetic perception of visual textures is important and valuable in numerous industrial domains, such as product design, architectural design, and decoration. Based on results from a semantic differential rating experiment, we modeled the relationship between low-level basic texture features and aesthetic properties involved in human aesthetic texture perception. First, we compute basic texture features from textural images using four classical methods. These features are neutral, objective, and independent of the socio-cultural context of the visual textures. Then, we conduct a semantic differential rating experiment to collect from evaluators their aesthetic perceptions of selected textural stimuli. In semantic differential rating experiment, eights pairs of aesthetic properties are chosen, which are strongly related to the socio-cultural context of the selected textures and to human emotions. They are easily understood and connected to everyday life. We propose a hierarchical feed-forward layer model of aesthetic texture perception and assign 8 pairs of aesthetic properties to different layers. Finally, we describe the generation of multiple linear and non-linear regression models for aesthetic prediction by taking dimensionality-reduced texture features and aesthetic properties of visual textures as dependent and independent variables, respectively. Our experimental results indicate that the relationships between each layer and its neighbors in the hierarchical feed-forward layer model of aesthetic texture perception can be fitted well by linear functions, and the models thus generated can successfully bridge the gap between computational texture features and aesthetic texture properties.

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.

PET Pharmacokinetic Modelling

NASA Astrophysics Data System (ADS)

Müller-Schauenburg, Wolfgang; Reimold, Matthias

Positron Emission Tomography is a well-established technique that allows imaging and quantification of tissue properties in-vivo. The goal of pharmacokinetic modelling is to estimate physiological parameters, e.g. perfusion or receptor density from the measured time course of a radiotracer. After a brief overview of clinical application of PET, we summarize the fundamentals of modelling: distribution volume, Fick's principle of local balancing, extraction and perfusion, and how to calculate equilibrium data from measurements after bolus injection. Three fundamental models are considered: (i) the 1-tissue compartment model, e.g. for regional cerebral blood flow (rCBF) with the short-lived tracer [15O]water, (ii) the 2-tissue compartment model accounting for trapping (one exponential + constant), e.g. for glucose metabolism with [18F]FDG, (iii) the reversible 2-tissue compartment model (two exponentials), e.g. for receptor binding. Arterial blood sampling is required for classical PET modelling, but can often be avoided by comparing regions with specific binding with so called reference regions with negligible specific uptake, e.g. in receptor imaging. To estimate the model parameters, non-linear least square fits are the standard. Various linearizations have been proposed for rapid parameter estimation, e.g. on a pixel-by-pixel basis, for the prize of a bias. Such linear approaches exist for all three models; e.g. the PATLAK-plot for trapping substances like FDG, and the LOGAN-plot to obtain distribution volumes for reversibly binding tracers. The description of receptor modelling is dedicated to the approaches of the subsequent lecture (chapter) of Millet, who works in the tradition of Delforge with multiple-injection investigations.

Feedback control by online learning an inverse model.

PubMed

Waegeman, Tim; Wyffels, Francis; Schrauwen, Francis

2012-10-01

A model, predictor, or error estimator is often used by a feedback controller to control a plant. Creating such a model is difficult when the plant exhibits nonlinear behavior. In this paper, a novel online learning control framework is proposed that does not require explicit knowledge about the plant. This framework uses two learning modules, one for creating an inverse model, and the other for actually controlling the plant. Except for their inputs, they are identical. The inverse model learns by the exploration performed by the not yet fully trained controller, while the actual controller is based on the currently learned model. The proposed framework allows fast online learning of an accurate controller. The controller can be applied on a broad range of tasks with different dynamic characteristics. We validate this claim by applying our control framework on several control tasks: 1) the heating tank problem (slow nonlinear dynamics); 2) flight pitch control (slow linear dynamics); and 3) the balancing problem of a double inverted pendulum (fast linear and nonlinear dynamics). The results of these experiments show that fast learning and accurate control can be achieved. Furthermore, a comparison is made with some classical control approaches, and observations concerning convergence and stability are made.

Statistical modelling of networked human-automation performance using working memory capacity.

PubMed

Ahmed, Nisar; de Visser, Ewart; Shaw, Tyler; Mohamed-Ameen, Amira; Campbell, Mark; Parasuraman, Raja

2014-01-01

This study examines the challenging problem of modelling the interaction between individual attentional limitations and decision-making performance in networked human-automation system tasks. Analysis of real experimental data from a task involving networked supervision of multiple unmanned aerial vehicles by human participants shows that both task load and network message quality affect performance, but that these effects are modulated by individual differences in working memory (WM) capacity. These insights were used to assess three statistical approaches for modelling and making predictions with real experimental networked supervisory performance data: classical linear regression, non-parametric Gaussian processes and probabilistic Bayesian networks. It is shown that each of these approaches can help designers of networked human-automated systems cope with various uncertainties in order to accommodate future users by linking expected operating conditions and performance from real experimental data to observable cognitive traits like WM capacity. Practitioner Summary: Working memory (WM) capacity helps account for inter-individual variability in operator performance in networked unmanned aerial vehicle supervisory tasks. This is useful for reliable performance prediction near experimental conditions via linear models; robust statistical prediction beyond experimental conditions via Gaussian process models and probabilistic inference about unknown task conditions/WM capacities via Bayesian network models.

Computational model for simulation of sequences of helicity and angular momentum transfer in turbid tissue-like scattering medium (Conference Presentation)

NASA Astrophysics Data System (ADS)

Doronin, Alexander; Meglinski, Igor

2017-02-01

Current report considers development of a unified Monte Carlo (MC) -based computational model for simulation of propagation of Laguerre-Gaussian (LG) beams in turbid tissue-like scattering medium. With a primary goal to proof the concept of using complex light for tissue diagnosis we explore propagation of LG beams in comparison with Gaussian beams for both linear and circular polarization. MC simulations of radially and azimuthally polarized LG beams in turbid media have been performed, classic phenomena such as preservation of the orbital angular momentum, optical memory and helicity flip are observed, detailed comparison is presented and discussed.

Sea surface mean square slope from Ku-band backscatter data

NASA Technical Reports Server (NTRS)

Jackson, F. C.; Walton, W. T.; Hines, D. E.; Walter, B. A.; Peng, C. Y.

1992-01-01

A surface mean-square-slope parameter analysis is conducted for 14-GHz airborne radar altimeter near-nadir, quasi-specular backscatter data, which in raw form obtained by least-squares fitting of an optical scattering model to the return waveform show an approximately linear dependence over the 7-15 m/sec wind speed range. Slope data are used to draw inferences on the structure of the high-wavenumber portion of the spectrum. A directionally-integrated model height spectrum that encompasses wind speed-dependent k exp -5/2 and classical Phillips k exp -3 power laws subranges in the range of gravity waves is supported by the data.

Probability density of spatially distributed soil moisture inferred from crosshole georadar traveltime measurements

NASA Astrophysics Data System (ADS)

Linde, N.; Vrugt, J. A.

2009-04-01

Geophysical models are increasingly used in hydrological simulations and inversions, where they are typically treated as an artificial data source with known uncorrelated "data errors". The model appraisal problem in classical deterministic linear and non-linear inversion approaches based on linearization is often addressed by calculating model resolution and model covariance matrices. These measures offer only a limited potential to assign a more appropriate "data covariance matrix" for future hydrological applications, simply because the regularization operators used to construct a stable inverse solution bear a strong imprint on such estimates and because the non-linearity of the geophysical inverse problem is not explored. We present a parallelized Markov Chain Monte Carlo (MCMC) scheme to efficiently derive the posterior spatially distributed radar slowness and water content between boreholes given first-arrival traveltimes. This method is called DiffeRential Evolution Adaptive Metropolis (DREAM_ZS) with snooker updater and sampling from past states. Our inverse scheme does not impose any smoothness on the final solution, and uses uniform prior ranges of the parameters. The posterior distribution of radar slowness is converted into spatially distributed soil moisture values using a petrophysical relationship. To benchmark the performance of DREAM_ZS, we first apply our inverse method to a synthetic two-dimensional infiltration experiment using 9421 traveltimes contaminated with Gaussian errors and 80 different model parameters, corresponding to a model discretization of 0.3 m × 0.3 m. After this, the method is applied to field data acquired in the vadose zone during snowmelt. This work demonstrates that fully non-linear stochastic inversion can be applied with few limiting assumptions to a range of common two-dimensional tomographic geophysical problems. The main advantage of DREAM_ZS is that it provides a full view of the posterior distribution of spatially distributed soil moisture, which is key to appropriately treat geophysical parameter uncertainty and infer hydrologic models.

Predicting surface scatter using a linear systems formulation of non-paraxial scalar diffraction

NASA Astrophysics Data System (ADS)

Krywonos, Andrey

Scattering effects from rough surfaces are non-paraxial diffraction phenomena resulting from random phase variations in the reflected wavefront. The ability to predict these effects is important in a variety of applications including x-ray and EUV imaging, the design of stray light rejection systems, and reflection modeling for rendering realistic scenes and animations of physical objects in computer graphics. Rayleigh-Rice (small perturbation method) and Beckmann-Kirchoff (Kirchhoff approximation) theories are commonly used to predict surface scatter effects. In addition, Harvey and Shack developed a linear systems formulation of surface scatter phenomena in which the scattering behavior is characterized by a surface transfer function. This treatment provided insight and understanding not readily gleaned from the two previous theories, and has been incorporated into a variety of computer software packages (ASAP, Zemax, Tracepro). However, smooth surface and paraxial approximations have severely limited the range of applicability of each of the above theoretical treatments. In this dissertation, a linear systems formulation of non-paraxial scalar diffraction theory is first developed and then applied to sinusoidal phase gratings, resulting in diffraction efficiency predictions far more accurate than those provided by classical scalar theories. The application of the theory to these gratings was motivated by the fact that rough surfaces are frequently modeled as a superposition of sinusoidal surfaces of different amplitudes, periods, and orientations. The application of the non-paraxial scalar diffraction theory to surface scatter phenomena resulted first in a modified Beckmann-Kirchhoff surface scattering model, then a generalized Harvey-Shack theory, both of which produce accurate results for rougher surfaces than the Rayleigh-Rice theory and for larger incident and scattering angles than the classical Beckmann-Kirchhoff theory. These new developments enable the analysis and simplify the understanding of wide-angle scattering behavior from rough surfaces illuminated at large incident angles. In addition, they provide an improved BRDF (Bidirectional Reflectance Distribution Function) model, particularly for the smooth surface inverse scattering problem of determining surface power spectral density (PSD) curves from BRDF measurements.

Classical and all-floating FETI methods for the simulation of arterial tissues

PubMed Central

Augustin, Christoph M.; Holzapfel, Gerhard A.; Steinbach, Olaf

2015-01-01

High-resolution and anatomically realistic computer models of biological soft tissues play a significant role in the understanding of the function of cardiovascular components in health and disease. However, the computational effort to handle fine grids to resolve the geometries as well as sophisticated tissue models is very challenging. One possibility to derive a strongly scalable parallel solution algorithm is to consider finite element tearing and interconnecting (FETI) methods. In this study we propose and investigate the application of FETI methods to simulate the elastic behavior of biological soft tissues. As one particular example we choose the artery which is – as most other biological tissues – characterized by anisotropic and nonlinear material properties. We compare two specific approaches of FETI methods, classical and all-floating, and investigate the numerical behavior of different preconditioning techniques. In comparison to classical FETI, the all-floating approach has not only advantages concerning the implementation but in many cases also concerning the convergence of the global iterative solution method. This behavior is illustrated with numerical examples. We present results of linear elastic simulations to show convergence rates, as expected from the theory, and results from the more sophisticated nonlinear case where we apply a well-known anisotropic model to the realistic geometry of an artery. Although the FETI methods have a great applicability on artery simulations we will also discuss some limitations concerning the dependence on material parameters. PMID:26751957

Convective flows of generalized time-nonlocal nanofluids through a vertical rectangular channel

NASA Astrophysics Data System (ADS)

Ahmed, Najma; Vieru, Dumitru; Fetecau, Constantin; Shah, Nehad Ali

2018-05-01

Time-nonlocal generalized model of the natural convection heat transfer and nanofluid flows through a rectangular vertical channel with wall conditions of the Robin type are studied. The generalized mathematical model with time-nonlocality is developed by considering the fractional constitutive equations for the shear stress and thermal flux defined with the time-fractional Caputo derivative. The Caputo power-law non-local kernel provides the damping to the velocity and temperature gradient; therefore, transport processes are influenced by the histories at all past and present times. Analytical solutions for dimensionless velocity and temperature fields are obtained by using the Laplace transform coupled with the finite sine-cosine Fourier transform which is suitable to problems with boundary conditions of the Robin type. Particularizing the fractional thermal and velocity parameters, solutions for three simplified models are obtained (classical linear momentum equation with damped thermal flux; fractional shear stress constitutive equation with classical Fourier's law for thermal flux; classical shear stress and thermal flux constitutive equations). It is found that the thermal histories strongly influence the thermal transport for small values of time t. Also, the thermal transport can be enhanced if the thermal fractional parameter decreases or by increasing the nanoparticles' volume fraction. The velocity field is influenced on the one hand by the temperature of the fluid and on the other by the damping of the velocity gradient introduced by the fractional derivative. Also, the transport motions of the channel walls influence the motion of the fluid layers located near them.

Applied Time Domain Stability Margin Assessment for Nonlinear Time-Varying Systems

NASA Technical Reports Server (NTRS)

Kiefer, J. M.; Johnson, M. D.; Wall, J. H.; Dominguez, A.

2016-01-01

The baseline stability margins for NASA's Space Launch System (SLS) launch vehicle were generated via the classical approach of linearizing the system equations of motion and determining the gain and phase margins from the resulting frequency domain model. To improve the fidelity of the classical methods, the linear frequency domain approach can be extended by replacing static, memoryless nonlinearities with describing functions. This technique, however, does not address the time varying nature of the dynamics of a launch vehicle in flight. An alternative technique for the evaluation of the stability of the nonlinear launch vehicle dynamics along its trajectory is to incrementally adjust the gain and/or time delay in the time domain simulation until the system exhibits unstable behavior. This technique has the added benefit of providing a direct comparison between the time domain and frequency domain tools in support of simulation validation. This technique was implemented by using the Stability Aerospace Vehicle Analysis Tool (SAVANT) computer simulation to evaluate the stability of the SLS system with the Adaptive Augmenting Control (AAC) active and inactive along its ascent trajectory. The gains for which the vehicle maintains apparent time-domain stability defines the gain margins, and the time delay similarly defines the phase margin. This method of extracting the control stability margins from the time-domain simulation is relatively straightforward and the resultant margins can be compared to the linearized system results. The sections herein describe the techniques employed to extract the time-domain margins, compare the results between these nonlinear and the linear methods, and provide explanations for observed discrepancies. The SLS ascent trajectory was simulated with SAVANT and the classical linear stability margins were evaluated at one second intervals. The linear analysis was performed with the AAC algorithm disabled to attain baseline stability margins. At each time point, the system was linearized about the current operating point using Simulink's built-in solver. Each linearized system in time was evaluated for its rigid-body gain margin (high frequency gain margin), rigid-body phase margin, and aero gain margin (low frequency gain margin) for each control axis. Using the stability margins derived from the baseline linearization approach, the time domain derived stability margins were determined by executing time domain simulations in which axis-specific incremental gain and phase adjustments were made to the nominal system about the expected neutral stability point at specific flight times. The baseline stability margin time histories were used to shift the system gain to various values around the zero margin point such that a precise amount of expected gain margin was maintained throughout flight. When assessing the gain margins, the gain was applied starting at the time point under consideration, thereafter following the variation in the margin found in the linear analysis. When assessing the rigid-body phase margin, a constant time delay was applied to the system starting at the time point under consideration. If the baseline stability margins were correctly determined via the linear analysis, the time domain simulation results should contain unstable behavior at certain gain and phase values. Examples will be shown from repeated simulations with variable added gain and phase lag. Faithfulness of margins calculated from the linear analysis to the nonlinear system will be demonstrated.

[Scale Relativity Theory in living beings morphogenesis: fratal, determinism and chance].

PubMed

Chaline, J

2012-10-01

The Scale Relativity Theory has many biological applications from linear to non-linear and, from classical mechanics to quantum mechanics. Self-similar laws have been used as model for the description of a huge number of biological systems. Theses laws may explain the origin of basal life structures. Log-periodic behaviors of acceleration or deceleration can be applied to branching macroevolution, to the time sequences of major evolutionary leaps. The existence of such a law does not mean that the role of chance in evolution is reduced, but instead that randomness and contingency may occur within a framework which may itself be structured in a partly statistical way. The scale relativity theory can open new perspectives in evolution. Copyright © 2012 Elsevier Masson SAS. All rights reserved.

Feature extraction with deep neural networks by a generalized discriminant analysis.

PubMed

Stuhlsatz, André; Lippel, Jens; Zielke, Thomas

2012-04-01

We present an approach to feature extraction that is a generalization of the classical linear discriminant analysis (LDA) on the basis of deep neural networks (DNNs). As for LDA, discriminative features generated from independent Gaussian class conditionals are assumed. This modeling has the advantages that the intrinsic dimensionality of the feature space is bounded by the number of classes and that the optimal discriminant function is linear. Unfortunately, linear transformations are insufficient to extract optimal discriminative features from arbitrarily distributed raw measurements. The generalized discriminant analysis (GerDA) proposed in this paper uses nonlinear transformations that are learnt by DNNs in a semisupervised fashion. We show that the feature extraction based on our approach displays excellent performance on real-world recognition and detection tasks, such as handwritten digit recognition and face detection. In a series of experiments, we evaluate GerDA features with respect to dimensionality reduction, visualization, classification, and detection. Moreover, we show that GerDA DNNs can preprocess truly high-dimensional input data to low-dimensional representations that facilitate accurate predictions even if simple linear predictors or measures of similarity are used.

An analysis of a large dataset on immigrant integration in Spain. The Statistical Mechanics perspective on Social Action

NASA Astrophysics Data System (ADS)

Barra, Adriano; Contucci, Pierluigi; Sandell, Rickard; Vernia, Cecilia

2014-02-01

How does immigrant integration in a country change with immigration density? Guided by a statistical mechanics perspective we propose a novel approach to this problem. The analysis focuses on classical integration quantifiers such as the percentage of jobs (temporary and permanent) given to immigrants, mixed marriages, and newborns with parents of mixed origin. We find that the average values of different quantifiers may exhibit either linear or non-linear growth on immigrant density and we suggest that social action, a concept identified by Max Weber, causes the observed non-linearity. Using the statistical mechanics notion of interaction to quantitatively emulate social action, a unified mathematical model for integration is proposed and it is shown to explain both growth behaviors observed. The linear theory instead, ignoring the possibility of interaction effects would underestimate the quantifiers up to 30% when immigrant densities are low, and overestimate them as much when densities are high. The capacity to quantitatively isolate different types of integration mechanisms makes our framework a suitable tool in the quest for more efficient integration policies.

Space-time codependence of retinal ganglion cells can be explained by novel and separable components of their receptive fields.

PubMed

Cowan, Cameron S; Sabharwal, Jasdeep; Wu, Samuel M

2016-09-01

Reverse correlation methods such as spike-triggered averaging consistently identify the spatial center in the linear receptive fields (RFs) of retinal ganglion cells (GCs). However, the spatial antagonistic surround observed in classical experiments has proven more elusive. Tests for the antagonistic surround have heretofore relied on models that make questionable simplifying assumptions such as space-time separability and radial homogeneity/symmetry. We circumvented these, along with other common assumptions, and observed a linear antagonistic surround in 754 of 805 mouse GCs. By characterizing the RF's space-time structure, we found the overall linear RF's inseparability could be accounted for both by tuning differences between the center and surround and differences within the surround. Finally, we applied this approach to characterize spatial asymmetry in the RF surround. These results shed new light on the spatiotemporal organization of GC linear RFs and highlight a major contributor to its inseparability. © 2016 The Authors. Physiological Reports published by Wiley Periodicals, Inc. on behalf of the American Physiological Society and The Physiological Society.

Linear ultrasonic motor for absolute gravimeter.

PubMed

Jian, Yue; Yao, Zhiyuan; Silberschmidt, Vadim V

2017-05-01

Thanks to their compactness and suitability for vacuum applications, linear ultrasonic motors are considered as substitutes for classical electromagnetic motors as driving elements in absolute gravimeters. Still, their application is prevented by relatively low power output. To overcome this limitation and provide better stability, a V-type linear ultrasonic motor with a new clamping method is proposed for a gravimeter. In this paper, a mechanical model of stators with flexible clamping components is suggested, according to a design criterion for clamps of linear ultrasonic motors. After that, an effect of tangential and normal rigidity of the clamping components on mechanical output is studied. It is followed by discussion of a new clamping method with sufficient tangential rigidity and a capability to facilitate pre-load. Additionally, a prototype of the motor with the proposed clamping method was fabricated and the performance tests in vertical direction were implemented. Experimental results show that the suggested motor has structural stability and high dynamic performance, such as no-load speed of 1.4m/s and maximal thrust of 43N, meeting the requirements for absolute gravimeters. Copyright © 2017 Elsevier B.V. All rights reserved.

Single point dilution method for the quantitative analysis of antibodies to the gag24 protein of HIV-1.

PubMed

Palenzuela, D O; Benítez, J; Rivero, J; Serrano, R; Ganzó, O

1997-10-13

In the present work a concept proposed in 1992 by Dopotka and Giesendorf was applied to the quantitative analysis of antibodies to the p24 protein of HIV-1 in infected asymptomatic individuals and AIDS patients. Two approaches were analyzed, a linear model OD = b0 + b1.log(titer) and a nonlinear log(titer) = alpha.OD beta, similar to the Dopotka-Giesendorf's model. The above two proposed models adequately fit the dependence of the optical density values at a single point dilution, and titers achieved by the end point dilution method (EPDM). Nevertheless, the nonlinear model better fits the experimental data, according to residuals analysis. Classical EPDM was compared with the new single point dilution method (SPDM) using both models. The best correlation between titers calculated using both models and titers achieved by EPDM was obtained with the nonlinear model. The correlation coefficients for the nonlinear and linear models were r = 0.85 and r = 0.77, respectively. A new correction factor was introduced into the nonlinear model and this reduced the day-to-day variation of titer values. In general, SPDM saves time, reagents and is more precise and sensitive to changes in antibody levels, and therefore has a higher resolution than EPDM.

Fractal dimension and nonlinear dynamical processes

NASA Astrophysics Data System (ADS)

McCarty, Robert C.; Lindley, John P.

1993-11-01

Mandelbrot, Falconer and others have demonstrated the existence of dimensionally invariant geometrical properties of non-linear dynamical processes known as fractals. Barnsley defines fractal geometry as an extension of classical geometry. Such an extension, however, is not mathematically trivial Of specific interest to those engaged in signal processing is the potential use of fractal geometry to facilitate the analysis of non-linear signal processes often referred to as non-linear time series. Fractal geometry has been used in the modeling of non- linear time series represented by radar signals in the presence of ground clutter or interference generated by spatially distributed reflections around the target or a radar system. It was recognized by Mandelbrot that the fractal geometries represented by man-made objects had different dimensions than the geometries of the familiar objects that abound in nature such as leaves, clouds, ferns, trees, etc. The invariant dimensional property of non-linear processes suggests that in the case of acoustic signals (active or passive) generated within a dispersive medium such as the ocean environment, there exists much rich structure that will aid in the detection and classification of various objects, man-made or natural, within the medium.

Multistructure index in revealing complexity of regulatory mechanisms of human cardiovascular system at rest and orthostatic stress in healthy humans

NASA Astrophysics Data System (ADS)

Makowiec, Danuta; Graff, Beata; Struzik, Zbigniew R.

2017-02-01

Biological regulation is sufficiently complex to pose an enduring challenge for characterization of both its equilibrium and transient non-equilibrium dynamics. Two univariate but coupled observables, heart rate and systolic blood pressure, are commonly characterized in the benchmark example of the human cardiovascular regulatory system. Asymmetric distributions of accelerations and decelerations of heart rate, as well as rises and falls in systolic blood pressure, recorded in humans during a head-up tilt test provide insights into the dynamics of cardiovascular response to a rapid, controlled deregulation of the system's homeostasis. The baroreflex feedback loop is assumed to be the fundamental physiological mechanism for ensuring homeostatic blood supply to distant organs at rest and during orthostatic stress, captured in a classical beat-to-beat autoregressive model of baroreflex by de Boer et al. (1987). For model corroboration, a multistructure index statistic is proposed, seamlessly evaluating the size spectrum of magnitudes of neural reflexes such as baroreflex, responsible for maintaining the homeostatic dynamics. The multistructure index exposes a distinctly different dynamics of multiscale asymmetry between results obtained from real-life signals recorded from healthy subjects and those simulated using both the classical and perturbed versions of the model. Nonlinear effects observed suggest the pronounced presence of complex mechanisms resulting from baroreflex regulation when a human is at rest, which is aggravated in the system's response to orthostatic stress. Using our methodology of multistructure index, we therefore show a marked difference between model and real-life scenarios, which we attribute to multiscale asymmetry of non-linear origin in real-life signals, which we are not reproducible by the classical model.

Quantum annealing versus classical machine learning applied to a simplified computational biology problem

PubMed Central

Li, Richard Y.; Di Felice, Rosa; Rohs, Remo; Lidar, Daniel A.

2018-01-01

Transcription factors regulate gene expression, but how these proteins recognize and specifically bind to their DNA targets is still debated. Machine learning models are effective means to reveal interaction mechanisms. Here we studied the ability of a quantum machine learning approach to predict binding specificity. Using simplified datasets of a small number of DNA sequences derived from actual binding affinity experiments, we trained a commercially available quantum annealer to classify and rank transcription factor binding. The results were compared to state-of-the-art classical approaches for the same simplified datasets, including simulated annealing, simulated quantum annealing, multiple linear regression, LASSO, and extreme gradient boosting. Despite technological limitations, we find a slight advantage in classification performance and nearly equal ranking performance using the quantum annealer for these fairly small training data sets. Thus, we propose that quantum annealing might be an effective method to implement machine learning for certain computational biology problems. PMID:29652405

Thermal quantum time-correlation functions from classical-like dynamics

NASA Astrophysics Data System (ADS)

Hele, Timothy J. H.

2017-07-01

Thermal quantum time-correlation functions are of fundamental importance in quantum dynamics, allowing experimentally measurable properties such as reaction rates, diffusion constants and vibrational spectra to be computed from first principles. Since the exact quantum solution scales exponentially with system size, there has been considerable effort in formulating reliable linear-scaling methods involving exact quantum statistics and approximate quantum dynamics modelled with classical-like trajectories. Here, we review recent progress in the field with the development of methods including centroid molecular dynamics , ring polymer molecular dynamics (RPMD) and thermostatted RPMD (TRPMD). We show how these methods have recently been obtained from 'Matsubara dynamics', a form of semiclassical dynamics which conserves the quantum Boltzmann distribution. We also apply the Matsubara formalism to reaction rate theory, rederiving t → 0+ quantum transition-state theory (QTST) and showing that Matsubara-TST, like RPMD-TST, is equivalent to QTST. We end by surveying areas for future progress.

High-density amorphous ice: A path-integral simulation

NASA Astrophysics Data System (ADS)

Herrero, Carlos P.; Ramírez, Rafael

2012-09-01

Structural and thermodynamic properties of high-density amorphous (HDA) ice have been studied by path-integral molecular dynamics simulations in the isothermal-isobaric ensemble. Interatomic interactions were modeled by using the effective q-TIP4P/F potential for flexible water. Quantum nuclear motion is found to affect several observable properties of the amorphous solid. At low temperature (T = 50 K) the molar volume of HDA ice is found to increase by 6%, and the intramolecular O-H distance rises by 1.4% due to quantum motion. Peaks in the radial distribution function of HDA ice are broadened with respect to their classical expectancy. The bulk modulus, B, is found to rise linearly with the pressure, with a slope ∂B/∂P = 7.1. Our results are compared with those derived earlier from classical and path-integral simulations of HDA ice. We discuss similarities and discrepancies with those earlier simulations.

A comparison of portfolio selection models via application on ISE 100 index data

NASA Astrophysics Data System (ADS)

Altun, Emrah; Tatlidil, Hüseyin

2013-10-01

Markowitz Model, a classical approach to portfolio optimization problem, relies on two important assumptions: the expected return is multivariate normally distributed and the investor is risk averter. But this model has not been extensively used in finance. Empirical results show that it is very hard to solve large scale portfolio optimization problems with Mean-Variance (M-V)model. Alternative model, Mean Absolute Deviation (MAD) model which is proposed by Konno and Yamazaki [7] has been used to remove most of difficulties of Markowitz Mean-Variance model. MAD model don't need to assume that the probability of the rates of return is normally distributed and based on Linear Programming. Another alternative portfolio model is Mean-Lower Semi Absolute Deviation (M-LSAD), which is proposed by Speranza [3]. We will compare these models to determine which model gives more appropriate solution to investors.

Multiscale modeling and computation of optically manipulated nano devices

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

Bao, Gang, E-mail: baog@zju.edu.cn; Liu, Di, E-mail: richardl@math.msu.edu; Luo, Songting, E-mail: luos@iastate.edu

2016-07-01

We present a multiscale modeling and computational scheme for optical-mechanical responses of nanostructures. The multi-physical nature of the problem is a result of the interaction between the electromagnetic (EM) field, the molecular motion, and the electronic excitation. To balance accuracy and complexity, we adopt the semi-classical approach that the EM field is described classically by the Maxwell equations, and the charged particles follow the Schrödinger equations quantum mechanically. To overcome the numerical challenge of solving the high dimensional multi-component many-body Schrödinger equations, we further simplify the model with the Ehrenfest molecular dynamics to determine the motion of the nuclei, andmore » use the Time-Dependent Current Density Functional Theory (TD-CDFT) to calculate the excitation of the electrons. This leads to a system of coupled equations that computes the electromagnetic field, the nuclear positions, and the electronic current and charge densities simultaneously. In the regime of linear responses, the resonant frequencies initiating the out-of-equilibrium optical-mechanical responses can be formulated as an eigenvalue problem. A self-consistent multiscale method is designed to deal with the well separated space scales. The isomerization of azobenzene is presented as a numerical example.« less

Non-classical and potential symmetry analysis of Richard's equation for moisture flow in soil

NASA Astrophysics Data System (ADS)

Wiltshire, Ron; El-Kafri, Manal

2004-01-01

This paper focuses upon the derivation of the non-classical symmetries of Bluman and Cole as they apply to Richard's equation for water flow in an unsaturated uniform soil. It is shown that the determining equations for the non-classical case lead to four highly non-linear equations which have been solved in five particular cases. In each case the corresponding similarity ansatz has been derived and Richard's equation is reduced to an ordinary differential equation. Explicit solutions are produced when possible. Richard's equation is also expressed as a potential system and in reviewing the classical Lie solutions a new symmetry is derived together with its similarity ansatz. Determining equations are then produced for the potential system using the non-classical algorithm. This results in an under-determined set of equations and an example symmetry that reveals a missing classical case is presented. An example of a classical and a non-classical symmetry reduction applied to the infiltration of moisture in soil is presented. The condition for surface invariance is used to demonstrate the equivalence of a classical Lie and a potential symmetry.

Neural Networks and other Techniques for Fault Identification and Isolation of Aircraft Systems

NASA Technical Reports Server (NTRS)

Innocenti, M.; Napolitano, M.

2003-01-01

Fault identification, isolation, and accomodation have become critical issues in the overall performance of advanced aircraft systems. Neural Networks have shown to be a very attractive alternative to classic adaptation methods for identification and control of non-linear dynamic systems. The purpose of this paper is to show the improvements in neural network applications achievable through the use of learning algorithms more efficient than the classic Back-Propagation, and through the implementation of the neural schemes in parallel hardware. The results of the analysis of a scheme for Sensor Failure, Detection, Identification and Accommodation (SFDIA) using experimental flight data of a research aircraft model are presented. Conventional approaches to the problem are based on observers and Kalman Filters while more recent methods are based on neural approximators. The work described in this paper is based on the use of neural networks (NNs) as on-line learning non-linear approximators. The performances of two different neural architectures were compared. The first architecture is based on a Multi Layer Perceptron (MLP) NN trained with the Extended Back Propagation algorithm (EBPA). The second architecture is based on a Radial Basis Function (RBF) NN trained with the Extended-MRAN (EMRAN) algorithms. In addition, alternative methods for communications links fault detection and accomodation are presented, relative to multiple unmanned aircraft applications.

Interacting charges and the classical electron radius

NASA Astrophysics Data System (ADS)

De Luca, Roberto; Di Mauro, Marco; Faella, Orazio; Naddeo, Adele

2018-03-01

The equation of the motion of a point charge q repelled by a fixed point-like charge Q is derived and studied. In solving this problem useful concepts in classical and relativistic kinematics, in Newtonian mechanics and in non-linear ordinary differential equations are revised. The validity of the approximations is discussed from the physical point of view. In particular the classical electron radius emerges naturally from the requirement that the initial distance is large enough for the non-relativistic approximation to be valid. The relevance of this topic for undergraduate physics teaching is pointed out.

Quantum Neural Nets

NASA Technical Reports Server (NTRS)

Zak, Michail; Williams, Colin P.

1997-01-01

The capacity of classical neurocomputers is limited by the number of classical degrees of freedom which is roughly proportional to the size of the computer. By Contrast, a Hypothetical quantum neurocomputer can implement an exponentially large number of the degrees of freedom within the same size. In this paper an attempt is made to reconcile linear reversible structure of quantum evolution with nonlinear irreversible dynamics for neural nets.

Polar codes for achieving the classical capacity of a quantum channel

NASA Astrophysics Data System (ADS)

Guha, Saikat; Wilde, Mark

2012-02-01

We construct the first near-explicit, linear, polar codes that achieve the capacity for classical communication over quantum channels. The codes exploit the channel polarization phenomenon observed by Arikan for classical channels. Channel polarization is an effect in which one can synthesize a set of channels, by ``channel combining'' and ``channel splitting,'' in which a fraction of the synthesized channels is perfect for data transmission while the other fraction is completely useless for data transmission, with the good fraction equal to the capacity of the channel. Our main technical contributions are threefold. First, we demonstrate that the channel polarization effect occurs for channels with classical inputs and quantum outputs. We then construct linear polar codes based on this effect, and the encoding complexity is O(N log N), where N is the blocklength of the code. We also demonstrate that a quantum successive cancellation decoder works well, i.e., the word error rate decays exponentially with the blocklength of the code. For a quantum channel with binary pure-state outputs, such as a binary-phase-shift-keyed coherent-state optical communication alphabet, the symmetric Holevo information rate is in fact the ultimate channel capacity, which is achieved by our polar code.

Computing anticipatory systems with incursion and hyperincursion

NASA Astrophysics Data System (ADS)

Dubois, Daniel M.

1998-07-01

An anticipatory system is a system which contains a model of itself and/or of its environment in view of computing its present state as a function of the prediction of the model. With the concepts of incursion and hyperincursion, anticipatory discrete systems can be modelled, simulated and controlled. By definition an incursion, an inclusive or implicit recursion, can be written as: x(t+1)=F[…,x(t-1),x(t),x(t+1),…] where the value of a variable x(t+1) at time t+1 is a function of this variable at past, present and future times. This is an extension of recursion. Hyperincursion is an incursion with multiple solutions. For example, chaos in the Pearl-Verhulst map model: x(t+1)=a.x(t).[1-x(t)] is controlled by the following anticipatory incursive model: x(t+1)=a.x(t).[1-x(t+1)] which corresponds to the differential anticipatory equation: dx(t)/dt=a.x(t).[1-x(t+1)]-x(t). The main part of this paper deals with the discretisation of differential equation systems of linear and non-linear oscillators. The non-linear oscillator is based on the Lotka-Volterra equations model. The discretisation is made by incursion. The incursive discrete equation system gives the same stability condition than the original differential equations without numerical instabilities. The linearisation of the incursive discrete non-linear Lotka-Volterra equation system gives rise to the classical harmonic oscillator. The incursive discretisation of the linear oscillator is similar to define backward and forward discrete derivatives. A generalized complex derivative is then considered and applied to the harmonic oscillator. Non-locality seems to be a property of anticipatory systems. With some mathematical assumption, the Schrödinger quantum equation is derived for a particle in a uniform potential. Finally an hyperincursive system is given in the case of a neural stack memory.

Feedback control laws for highly maneuverable aircraft

NASA Technical Reports Server (NTRS)

Garrard, William L.; Balas, Gary J.

1995-01-01

During this year, we concentrated our efforts on the design of controllers for lateral/directional control using mu synthesis. This proved to be a more difficult task than we anticipated and we are still working on the designs. In the lateral-directional control problem, the inputs are pilot lateral stick and pedal commands and the outputs are roll rate about the velocity vector and side slip angle. The control effectors are ailerons, rudder deflection, and directional thrust vectoring vane deflection which produces a yawing moment about the body axis. Our math model does not contain any provision for thrust vectoring of rolling moment. This has resulted in limitations of performance at high angles of attack. During 1994-95, the following tasks for the lateral-directional controllers were accomplished: (1) Designed both inner and outer loop dynamic inversion controllers. These controllers are implemented using accelerometer outputs rather than an a priori model of the vehicle aerodynamics; (2) Used classical techniques to design controllers for the system linearized by dynamics inversion. These controllers acted to control roll rate and Dutch roll response; (3) Implemented the inner loop dynamic inversion and classical controllers on the six DOF simulation; (4) Developed a lateral-directional control allocation scheme based on minimizing required control effort among the ailerons, rudder, and directional thrust vectoring; and (5) Developed mu outer loop controllers combined with classical inner loop controllers.

Panel Flutter Emulation Using a Few Concentrated Forces

NASA Astrophysics Data System (ADS)

Dhital, Kailash; Han, Jae-Hung

2018-04-01

The objective of this paper is to study the feasibility of panel flutter emulation using a few concentrated forces. The concentrated forces are considered to be equivalent to aerodynamic forces. The equivalence is carried out using surface spline method and principle of virtual work. The structural modeling of the plate is based on the classical plate theory and the aerodynamic modeling is based on the piston theory. The present approach differs from the linear panel flutter analysis in scheming the modal aerodynamics forces with unchanged structural properties. The solutions for the flutter problem are obtained numerically using the standard eigenvalue procedure. A few concentrated forces were considered with an optimization effort to decide their optimal locations. The optimization process is based on minimizing the error between the flutter bounds from emulated and linear flutter analysis method. The emulated flutter results for the square plate of four different boundary conditions using six concentrated forces are obtained with minimal error to the reference value. The results demonstrated the workability and viability of using concentrated forces in emulating real panel flutter. In addition, the paper includes the parametric studies of linear panel flutter whose proper literatures are not available.

Mediation analysis when a continuous mediator is measured with error and the outcome follows a generalized linear model

PubMed Central

Valeri, Linda; Lin, Xihong; VanderWeele, Tyler J.

2014-01-01

Mediation analysis is a popular approach to examine the extent to which the effect of an exposure on an outcome is through an intermediate variable (mediator) and the extent to which the effect is direct. When the mediator is mis-measured the validity of mediation analysis can be severely undermined. In this paper we first study the bias of classical, non-differential measurement error on a continuous mediator in the estimation of direct and indirect causal effects in generalized linear models when the outcome is either continuous or discrete and exposure-mediator interaction may be present. Our theoretical results as well as a numerical study demonstrate that in the presence of non-linearities the bias of naive estimators for direct and indirect effects that ignore measurement error can take unintuitive directions. We then develop methods to correct for measurement error. Three correction approaches using method of moments, regression calibration and SIMEX are compared. We apply the proposed method to the Massachusetts General Hospital lung cancer study to evaluate the effect of genetic variants mediated through smoking on lung cancer risk. PMID:25220625

Transport spectroscopy of low disorder silicon tunnel barriers with and without Sb implants

DOE PAGES

Shirkhorshidian, A.; Bishop, N. C.; Dominguez, J.; ...

2015-04-30

We present transport measurements of silicon MOS split gate structures with and without Sb implants. We observe classical point contact (PC) behavior that is free of any pronounced unintentional resonances at liquid He temperatures. The implanted device has resonances superposed on the PC transport indicative of transport through the Sb donors. We fit the differential conductance to a rectangular tunnel barrier model with a linear barrier height dependence on source–drain voltage and non-linear dependence on gate bias. Effects such as Fowler–Nordheim (FN) tunneling and image charge barrier lowering (ICBL) are considered. Barrier heights and widths are estimated for the entiremore » range of relevant biases. The barrier heights at the locations of some of the resonances for the implanted tunnel barrier are between 15–20 meV, which are consistent with transport through shallow partially hybridized Sb donors. The dependence of width and barrier height on gate voltage is found to be linear over a wide range of gate bias in the split gate geometry but deviates considerably when the barrier becomes large and is not described completely by standard 1D models such as FN or ICBL effects.« less

Theoretical foundations of apparent-damping phenomena and nearly irreversible energy exchange in linear conservative systems.

PubMed

Carcaterra, A; Akay, A

2007-04-01

This paper discusses a class of unexpected irreversible phenomena that can develop in linear conservative systems and provides a theoretical foundation that explains the underlying principles. Recent studies have shown that energy can be introduced to a linear system with near irreversibility, or energy within a system can migrate to a subsystem nearly irreversibly, even in the absence of dissipation, provided that the system has a particular natural frequency distribution. The present work introduces a general theory that provides a mathematical foundation and a physical explanation for the near irreversibility phenomena observed and reported in previous publications. Inspired by the properties of probability distribution functions, the general formulation developed here is based on particular properties of harmonic series, which form the common basis of linear dynamic system models. The results demonstrate the existence of a special class of linear nondissipative dynamic systems that exhibit nearly irreversible energy exchange and possess a decaying impulse response. In addition to uncovering a new class of dynamic system properties, the results have far-reaching implications in engineering applications where classical vibration damping or absorption techniques may not be effective. Furthermore, the results also support the notion of nearly irreversible energy transfer in conservative linear systems, which until now has been a concept associated exclusively with nonlinear systems.

Fully compressible solutions for early stage Richtmyer–Meshkov instability

DOE PAGES

Margolin, Len G.; Reisner, Jon Michael

2016-10-27

Here, we will consider the effects of compressibility and viscosity on the early dynamics of the Richtmyer–Meshkov instability (RMI). In particular, we will combine theory, scaling, and high resolution simulation of RMI to probe the details of the initial compression and the subsequent viscous damping as a shock interacts with a density discontinuity. We will propose a refinement of the classic 1D model for the linear regime of RMI that, for small initial perturbation wavelengths, more accurately reproduces the 2D dynamics of a fully resolved numerical simulation.

Nonlinear dynamics of a semiquantum Hamiltonian in the vicinity of quantum unstable regimes

NASA Astrophysics Data System (ADS)

Kowalski, A. M.; Rossignoli, R.

2018-04-01

We examine the emergence of chaos in a non-linear model derived from a semiquantum Hamiltonian describing the coupling between a classical field and a quantum system. The latter corresponds to a bosonic version of a BCS-like Hamiltonian, and possesses stable and unstable regimes. The dynamics of the whole system is shown to be strongly influenced by the quantum subsystem. In particular, chaos is seen to arise in the vicinity of a quantum critical case, which separates the stable and unstable regimes of the bosonic system.

Catenaries in viscous fluid

NASA Astrophysics Data System (ADS)

Hanna, James; Chakrabarti, Brato

2015-11-01

Slender structures live in fluid flows across many scales, from towed instruments to plant blades to microfluidic valves. The present work details a simple model of a flexible structure in a uniform flow. We present analytical solutions for the translating, axially flowing equilibria of strings subjected to a uniform body force and linear drag forces. This is an extension of the classical catenaries to a five-parameter family of solutions, represented as trajectories in angle-curvature ``phase space.'' Limiting cases include neutrally buoyant towed cables and freely sedimenting flexible filaments. Now at University of California, San Diego.

Cosmological wheel of time: A classical perspective of f(R) gravity

NASA Astrophysics Data System (ADS)

Yadav, Bal Krishna; Verma, Murli Manohar

It is shown that the structures in the universe can be interpreted to show a closed wheel of time, rather than a straight arrow. An analysis in f(R) gravity model has been carried out to show that due to local observations, a small arc at any given spacetime point would invariably indicate an arrow of time from past to future, though on a quantum scale it is not a linear flow but a closed loop, a fact that can be examined through future observations.

Quantum state engineering of light with continuous-wave optical parametric oscillators.

PubMed

Morin, Olivier; Liu, Jianli; Huang, Kun; Barbosa, Felippe; Fabre, Claude; Laurat, Julien

2014-05-30

Engineering non-classical states of the electromagnetic field is a central quest for quantum optics(1,2). Beyond their fundamental significance, such states are indeed the resources for implementing various protocols, ranging from enhanced metrology to quantum communication and computing. A variety of devices can be used to generate non-classical states, such as single emitters, light-matter interfaces or non-linear systems(3). We focus here on the use of a continuous-wave optical parametric oscillator(3,4). This system is based on a non-linear χ(2) crystal inserted inside an optical cavity and it is now well-known as a very efficient source of non-classical light, such as single-mode or two-mode squeezed vacuum depending on the crystal phase matching. Squeezed vacuum is a Gaussian state as its quadrature distributions follow a Gaussian statistics. However, it has been shown that number of protocols require non-Gaussian states(5). Generating directly such states is a difficult task and would require strong χ(3) non-linearities. Another procedure, probabilistic but heralded, consists in using a measurement-induced non-linearity via a conditional preparation technique operated on Gaussian states. Here, we detail this generation protocol for two non-Gaussian states, the single-photon state and a superposition of coherent states, using two differently phase-matched parametric oscillators as primary resources. This technique enables achievement of a high fidelity with the targeted state and generation of the state in a well-controlled spatiotemporal mode.

General Linearized Theory of Quantum Fluctuations around Arbitrary Limit Cycles

NASA Astrophysics Data System (ADS)

Navarrete-Benlloch, Carlos; Weiss, Talitha; Walter, Stefan; de Valcárcel, Germán J.

2017-09-01

The theory of Gaussian quantum fluctuations around classical steady states in nonlinear quantum-optical systems (also known as standard linearization) is a cornerstone for the analysis of such systems. Its simplicity, together with its accuracy far from critical points or situations where the nonlinearity reaches the strong coupling regime, has turned it into a widespread technique, being the first method of choice in most works on the subject. However, such a technique finds strong practical and conceptual complications when one tries to apply it to situations in which the classical long-time solution is time dependent, a most prominent example being spontaneous limit-cycle formation. Here, we introduce a linearization scheme adapted to such situations, using the driven Van der Pol oscillator as a test bed for the method, which allows us to compare it with full numerical simulations. On a conceptual level, the scheme relies on the connection between the emergence of limit cycles and the spontaneous breaking of the symmetry under temporal translations. On the practical side, the method keeps the simplicity and linear scaling with the size of the problem (number of modes) characteristic of standard linearization, making it applicable to large (many-body) systems.

Chaotic sources of noise in machine acoustics

NASA Astrophysics Data System (ADS)

Moon, F. C., Prof.; Broschart, Dipl.-Ing. T.

1994-05-01

In this paper a model is posited for deterministic, random-like noise in machines with sliding rigid parts impacting linear continuous machine structures. Such problems occur in gear transmission systems. A mathematical model is proposed to explain the random-like structure-borne and air-borne noise from such systems when the input is a periodic deterministic excitation of the quasi-rigid impacting parts. An experimental study is presented which supports the model. A thin circular plate is impacted by a chaotically vibrating mass excited by a sinusoidal moving base. The results suggest that the plate vibrations might be predicted by replacing the chaotic vibrating mass with a probabilistic forcing function. Prechaotic vibrations of the impacting mass show classical period doubling phenomena.

A dielectric model of self-assembled monolayer interfaces by capacitive spectroscopy.

PubMed

Góes, Márcio S; Rahman, Habibur; Ryall, Joshua; Davis, Jason J; Bueno, Paulo R

2012-06-26

The presence of self-assembled monolayers at an electrode introduces capacitance and resistance contributions that can profoundly affect subsequently observed electronic characteristics. Despite the impact of this on any voltammetry, these contributions are not directly resolvable with any clarity by standard electrochemical means. A capacitive analysis of such interfaces (by capacitance spectroscopy), introduced here, enables a clean mapping of these features and additionally presents a means of studying layer polarizability and Cole-Cole relaxation effects. The resolved resistive term contributes directly to an intrinsic monolayer uncompensated resistance that has a linear dependence on the layer thickness. The dielectric model proposed is fully aligned with the classic Helmholtz plate capacitor model and additionally explains the inherently associated resistive features of molecular films.

Spherical collapse and virialization in f ( T ) gravities

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

Lin, Rui-Hui; Zhai, Xiang-Hua; Li, Xin-Zhou, E-mail: 1000379711@smail.shnu.edu.cn, E-mail: zhaixh@shnu.edu.cn, E-mail: kychz@shnu.edu.cn

2017-03-01

Using the classical top-hat profile, we study the non-linear growth of spherically symmetric density perturbation and structure formation in f ( T ) gravities. In particular, three concrete models, which have been tested against the observation of large-scale evolution and linear perturbation of the universe in the cosmological scenario, are investigated in this framework, covering both minimal and nonminimal coupling cases of f ( T ) gravities. Moreover, we consider the virialization of the overdense region in the models after they detach from the background expanding universe and turn around to collapse. We find that there are constraints in themore » magnitude and occurring epoch of the initial perturbation. The existence of these constraints indicates that a perturbation that is too weak or occurs too late will not be able to stop the expanding of the overdense region. The illustration of the evolution of the perturbation shows that in f ( T ) gravities, the initial perturbation within the constraints can eventually lead to clustering and form structure. The evolution also shows that nonminimal coupling models collapse slower than the minimal coupling one.« less

Boulder Dislodgement by Tsunamis and Storms: Version 2.0

NASA Astrophysics Data System (ADS)

Weiss, Robert

2016-04-01

In the past, boulder dislodgement by tsunami and storm waves has been approached with a simple threshold approach in which a boulder was moved if the sum of the acting forces on the boulder is larger than zero. The impulse theory taught us, however, that this criterion is not enough to explain particle dislodgement. We employ an adapted version of the Newton's Second Law of Motion (NSLM) in order to consider the essence of the impulse theory which is that the sum of the forces has to exceed a certain threshold for a certain period of time. Furthermore, a classical assumption is to consider linear waves. However, when waves travel toward the shore, they alter due to non-linear processes. We employ the TRIADS model to quantify that change and how it impacts boulder dislodgement. We present our results of the coupled model (adapted NSLM and TRIADS model). The results project a more complex picture of boulder transport by storms and tsunami. The following question arises: What information do we actually invert, and what does it tell us about the causative event?

Dynamics of f(R) gravity models and asymmetry of time

NASA Astrophysics Data System (ADS)

Verma, Murli Manohar; Yadav, Bal Krishna

We solve the field equations of modified gravity for f(R) model in metric formalism. Further, we obtain the fixed points of the dynamical system in phase-space analysis of f(R) models, both with and without the effects of radiation. The stability of these points is studied against the perturbations in a smooth spatial background by applying the conditions on the eigenvalues of the matrix obtained in the linearized first-order differential equations. Following this, these fixed points are used for analyzing the dynamics of the system during the radiation, matter and acceleration-dominated phases of the universe. Certain linear and quadratic forms of f(R) are determined from the geometrical and physical considerations and the behavior of the scale factor is found for those forms. Further, we also determine the Hubble parameter H(t), the Ricci scalar R and the scale factor a(t) for these cosmic phases. We show the emergence of an asymmetry of time from the dynamics of the scalar field exclusively owing to the f(R) gravity in the Einstein frame that may lead to an arrow of time at a classical level.

Should the SCOPA-COG be modified? A Rasch analysis perspective.

PubMed

Forjaz, M J; Frades-Payo, B; Rodriguez-Blazquez, C; Ayala, A; Martinez-Martin, P

2010-02-01

The SCales for Outcomes in PArkinson's disease-Cognition (SCOPA-COG) is a specific measure of cognitive function for Parkinson's disease (PD) patients. Previous studies, under the frame of the classic test theory, indicate satisfactory psychometric properties. The Rasch model, an item response theory approach, provides new information about the scale, as well as results in a linear scale. This study aims at analysing the SCOPA-COG according to the Rasch model and, on the basis of results, suggesting modification to the SCOPA-COG. Fit to the Rasch model was analysed using a sample of 384 PD patients. A good fit was obtained after rescoring for disordered thresholds. The person separation index, a reliability measure, was 0.83. Differential item functioning was observed by age for three items and by gender for one item. The SCOPA-COG is a unidimensional measure of global cognitive function in PD patients, with good scale targeting and no empirical evidence for use of the subscale scores. Its adequate reliability and internal construct validity were supported. The SCOPA-COG, with the proposed scoring scheme, generates true linear interval scores.

Electron kinetic effects on interferometry, polarimetry and Thomson scattering measurements in burning plasmas (invited).

PubMed

Mirnov, V V; Brower, D L; Den Hartog, D J; Ding, W X; Duff, J; Parke, E

2014-11-01

At anticipated high electron temperatures in ITER, the effects of electron thermal motion on Thomson scattering (TS), toroidal interferometer/polarimeter (TIP), and poloidal polarimeter (PoPola) diagnostics will be significant and must be accurately treated. The precision of the previous lowest order linear in τ = Te/mec(2) model may be insufficient; we present a more precise model with τ(2)-order corrections to satisfy the high accuracy required for ITER TIP and PoPola diagnostics. The linear model is extended from Maxwellian to a more general class of anisotropic electron distributions that allows us to take into account distortions caused by equilibrium current, ECRH, and RF current drive effects. The classical problem of the degree of polarization of incoherent Thomson scattered radiation is solved analytically exactly without any approximations for the full range of incident polarizations, scattering angles, and electron thermal motion from non-relativistic to ultra-relativistic. The results are discussed in the context of the possible use of the polarization properties of Thomson scattered light as a method of Te measurement relevant to ITER operational scenarios.

Modelling of a bridge-shaped nonlinear piezoelectric energy harvester

NASA Astrophysics Data System (ADS)

Gafforelli, G.; Xu, R.; Corigliano, A.; Kim, S. G.

2013-12-01

Piezoelectric MicroElectroMechanical Systems (MEMS) energy harvesting is an attractive technology for harvesting small magnitudes of energy from ambient vibrations. Increasing the operating frequency bandwidth of such devices is one of the major issues for real world applications. A MEMS-scale doubly clamped nonlinear beam resonator is designed and developed to demonstrate very wide bandwidth and high power density. In this paper a first complete theoretical discussion of nonlinear resonating piezoelectric energy harvesting is provided. The sectional behaviour of the beam is studied through the Classical Lamination Theory (CLT) specifically modified to introduce the piezoelectric coupling and nonlinear Green-Lagrange strain tensor. A lumped parameter model is built through Rayleigh-Ritz Method and the resulting nonlinear coupled equations are solved in the frequency domain through the Harmonic Balance Method (HBM). Finally, the influence of external load resistance on the dynamic behaviour is studied. The theoretical model shows that nonlinear resonant harvesters have much wider power bandwidth than that of linear resonators but their maximum power is still bounded by the mechanical damping as is the case for linear resonating harvesters.

Linear unsaturating magnetoresistance in disordered systems

NASA Astrophysics Data System (ADS)

Lai, Ying Tong; Lara, Silvia; Love, Cameron; Ramakrishnan, Navneeth; Adam, Shaffique

Theoretical works have shown that disordered systems exhibit classical magnetoresistance (MR). In this talk, we examine a variety of experimental systems that observe linear MR at high magnetic fields, including silver chalcogenides, graphene, graphite and Weyl semimetals. We show that a careful analysis of the magnitude of the MR, as well as the field strength at which the MR changes from quadratic to linear, reveal important properties of the system, such as the ratio of the root-mean-square fluctuations in the carrier density and the average carrier density. By looking at other properties such as the zero-field mobility, we show that this carrier density inhomogeneity is consistent with what is known about the microscopic impurities in these experiments. The application of this disorder-induced MR to a variety of different experimental scenarios underline the universality of these theoretical models. This work is supported by the Singapore National Research Foundation (NRF-NRFF2012-01) and the Singapore Ministry of Education and Yale-NUS College through Grant Number R-607-265-01312.

Numerical solution methods for viscoelastic orthotropic materials

NASA Technical Reports Server (NTRS)

Gramoll, K. C.; Dillard, D. A.; Brinson, H. F.

1988-01-01

Numerical solution methods for viscoelastic orthotropic materials, specifically fiber reinforced composite materials, are examined. The methods include classical lamination theory using time increments, direction solution of the Volterra Integral, Zienkiewicz's linear Prony series method, and a new method called Nonlinear Differential Equation Method (NDEM) which uses a nonlinear Prony series. The criteria used for comparison of the various methods include the stability of the solution technique, time step size stability, computer solution time length, and computer memory storage. The Volterra Integral allowed the implementation of higher order solution techniques but had difficulties solving singular and weakly singular compliance function. The Zienkiewicz solution technique, which requires the viscoelastic response to be modeled by a Prony series, works well for linear viscoelastic isotropic materials and small time steps. The new method, NDEM, uses a modified Prony series which allows nonlinear stress effects to be included and can be used with orthotropic nonlinear viscoelastic materials. The NDEM technique is shown to be accurate and stable for both linear and nonlinear conditions with minimal computer time.

Bayesian inference of radiation belt loss timescales.

NASA Astrophysics Data System (ADS)

Camporeale, E.; Chandorkar, M.

2017-12-01

Electron fluxes in the Earth's radiation belts are routinely studied using the classical quasi-linear radial diffusion model. Although this simplified linear equation has proven to be an indispensable tool in understanding the dynamics of the radiation belt, it requires specification of quantities such as the diffusion coefficient and electron loss timescales that are never directly measured. Researchers have so far assumed a-priori parameterisations for radiation belt quantities and derived the best fit using satellite data. The state of the art in this domain lacks a coherent formulation of this problem in a probabilistic framework. We present some recent progress that we have made in performing Bayesian inference of radial diffusion parameters. We achieve this by making extensive use of the theory connecting Gaussian Processes and linear partial differential equations, and performing Markov Chain Monte Carlo sampling of radial diffusion parameters. These results are important for understanding the role and the propagation of uncertainties in radiation belt simulations and, eventually, for providing a probabilistic forecast of energetic electron fluxes in a Space Weather context.

On Fluctuations of Eigenvalues of Random Band Matrices

NASA Astrophysics Data System (ADS)

Shcherbina, M.

2015-10-01

We consider the fluctuations of linear eigenvalue statistics of random band matrices whose entries have the form with i.i.d. possessing the th moment, where the function u has a finite support , so that M has only nonzero diagonals. The parameter b (called the bandwidth) is assumed to grow with n in a way such that . Without any additional assumptions on the growth of b we prove CLT for linear eigenvalue statistics for a rather wide class of test functions. Thus we improve and generalize the results of the previous papers (Jana et al., arXiv:1412.2445; Li et al. Random Matrices 2:04, 2013), where CLT was proven under the assumption . Moreover, we develop a method which allows to prove automatically the CLT for linear eigenvalue statistics of the smooth test functions for almost all classical models of random matrix theory: deformed Wigner and sample covariance matrices, sparse matrices, diluted random matrices, matrices with heavy tales etc.

The Kelvin-Helmholtz instability of boundary-layer plasmas in the kinetic regime

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

Steinbusch, Benedikt, E-mail: b.steinbusch@fz-juelich.de; Gibbon, Paul, E-mail: p.gibbon@fz-juelich.de; Department of Mathematics, Centre for Mathematical Plasma Astrophysics, Katholieke Universiteit Leuven

2016-05-15

The dynamics of the Kelvin-Helmholtz instability are investigated in the kinetic, high-frequency regime with a novel, two-dimensional, mesh-free tree code. In contrast to earlier studies which focused on specially prepared equilibrium configurations in order to compare with fluid theory, a more naturally occurring plasma-vacuum boundary layer is considered here with relevance to both space plasma and linear plasma devices. Quantitative comparisons of the linear phase are made between the fluid and kinetic models. After establishing the validity of this technique via comparison to linear theory and conventional particle-in-cell simulation for classical benchmark problems, a quantitative analysis of the more complexmore » magnetized plasma-vacuum layer is presented and discussed. It is found that in this scenario, the finite Larmor orbits of the ions result in significant departures from the effective shear velocity and width underlying the instability growth, leading to generally slower development and stronger nonlinear coupling between fast growing short-wavelength modes and longer wavelengths.« less

Classical multiparty computation using quantum resources

NASA Astrophysics Data System (ADS)

Clementi, Marco; Pappa, Anna; Eckstein, Andreas; Walmsley, Ian A.; Kashefi, Elham; Barz, Stefanie

2017-12-01

In this work, we demonstrate a way to perform classical multiparty computing among parties with limited computational resources. Our method harnesses quantum resources to increase the computational power of the individual parties. We show how a set of clients restricted to linear classical processing are able to jointly compute a nonlinear multivariable function that lies beyond their individual capabilities. The clients are only allowed to perform classical xor gates and single-qubit gates on quantum states. We also examine the type of security that can be achieved in this limited setting. Finally, we provide a proof-of-concept implementation using photonic qubits that allows four clients to compute a specific example of a multiparty function, the pairwise and.

A single-cell spiking model for the origin of grid-cell patterns

PubMed Central

Kempter, Richard

2017-01-01

Spatial cognition in mammals is thought to rely on the activity of grid cells in the entorhinal cortex, yet the fundamental principles underlying the origin of grid-cell firing are still debated. Grid-like patterns could emerge via Hebbian learning and neuronal adaptation, but current computational models remained too abstract to allow direct confrontation with experimental data. Here, we propose a single-cell spiking model that generates grid firing fields via spike-rate adaptation and spike-timing dependent plasticity. Through rigorous mathematical analysis applicable in the linear limit, we quantitatively predict the requirements for grid-pattern formation, and we establish a direct link to classical pattern-forming systems of the Turing type. Our study lays the groundwork for biophysically-realistic models of grid-cell activity. PMID:28968386

Hydrodynamic Model for Conductivity in Graphene

PubMed Central

Mendoza, M.; Herrmann, H. J.; Succi, S.

2013-01-01

Based on the recently developed picture of an electronic ideal relativistic fluid at the Dirac point, we present an analytical model for the conductivity in graphene that is able to describe the linear dependence on the carrier density and the existence of a minimum conductivity. The model treats impurities as submerged rigid obstacles, forming a disordered medium through which graphene electrons flow, in close analogy with classical fluid dynamics. To describe the minimum conductivity, we take into account the additional carrier density induced by the impurities in the sample. The model, which predicts the conductivity as a function of the impurity fraction of the sample, is supported by extensive simulations for different values of ε, the dimensionless strength of the electric field, and provides excellent agreement with experimental data. PMID:23316277

The Box-Cox power transformation on nursing sensitive indicators: Does it matter if structural effects are omitted during the estimation of the transformation parameter?

PubMed Central

2011-01-01

Background Many nursing and health related research studies have continuous outcome measures that are inherently non-normal in distribution. The Box-Cox transformation provides a powerful tool for developing a parsimonious model for data representation and interpretation when the distribution of the dependent variable, or outcome measure, of interest deviates from the normal distribution. The objectives of this study was to contrast the effect of obtaining the Box-Cox power transformation parameter and subsequent analysis of variance with or without a priori knowledge of predictor variables under the classic linear or linear mixed model settings. Methods Simulation data from a 3 × 4 factorial treatments design, along with the Patient Falls and Patient Injury Falls from the National Database of Nursing Quality Indicators (NDNQI®) for the 3rd quarter of 2007 from a convenience sample of over one thousand US hospitals were analyzed. The effect of the nonlinear monotonic transformation was contrasted in two ways: a) estimating the transformation parameter along with factors with potential structural effects, and b) estimating the transformation parameter first and then conducting analysis of variance for the structural effect. Results Linear model ANOVA with Monte Carlo simulation and mixed models with correlated error terms with NDNQI examples showed no substantial differences on statistical tests for structural effects if the factors with structural effects were omitted during the estimation of the transformation parameter. Conclusions The Box-Cox power transformation can still be an effective tool for validating statistical inferences with large observational, cross-sectional, and hierarchical or repeated measure studies under the linear or the mixed model settings without prior knowledge of all the factors with potential structural effects. PMID:21854614

The Box-Cox power transformation on nursing sensitive indicators: does it matter if structural effects are omitted during the estimation of the transformation parameter?

PubMed

Hou, Qingjiang; Mahnken, Jonathan D; Gajewski, Byron J; Dunton, Nancy

2011-08-19

Many nursing and health related research studies have continuous outcome measures that are inherently non-normal in distribution. The Box-Cox transformation provides a powerful tool for developing a parsimonious model for data representation and interpretation when the distribution of the dependent variable, or outcome measure, of interest deviates from the normal distribution. The objectives of this study was to contrast the effect of obtaining the Box-Cox power transformation parameter and subsequent analysis of variance with or without a priori knowledge of predictor variables under the classic linear or linear mixed model settings. Simulation data from a 3 × 4 factorial treatments design, along with the Patient Falls and Patient Injury Falls from the National Database of Nursing Quality Indicators (NDNQI® for the 3rd quarter of 2007 from a convenience sample of over one thousand US hospitals were analyzed. The effect of the nonlinear monotonic transformation was contrasted in two ways: a) estimating the transformation parameter along with factors with potential structural effects, and b) estimating the transformation parameter first and then conducting analysis of variance for the structural effect. Linear model ANOVA with Monte Carlo simulation and mixed models with correlated error terms with NDNQI examples showed no substantial differences on statistical tests for structural effects if the factors with structural effects were omitted during the estimation of the transformation parameter. The Box-Cox power transformation can still be an effective tool for validating statistical inferences with large observational, cross-sectional, and hierarchical or repeated measure studies under the linear or the mixed model settings without prior knowledge of all the factors with potential structural effects.

A characterization of linearly repetitive cut and project sets

NASA Astrophysics Data System (ADS)

Haynes, Alan; Koivusalo, Henna; Walton, James

2018-02-01

For the development of a mathematical theory which can be used to rigorously investigate physical properties of quasicrystals, it is necessary to understand regularity of patterns in special classes of aperiodic point sets in Euclidean space. In one dimension, prototypical mathematical models for quasicrystals are provided by Sturmian sequences and by point sets generated by substitution rules. Regularity properties of such sets are well understood, thanks mostly to well known results by Morse and Hedlund, and physicists have used this understanding to study one dimensional random Schrödinger operators and lattice gas models. A key fact which plays an important role in these problems is the existence of a subadditive ergodic theorem, which is guaranteed when the corresponding point set is linearly repetitive. In this paper we extend the one-dimensional model to cut and project sets, which generalize Sturmian sequences in higher dimensions, and which are frequently used in mathematical and physical literature as models for higher dimensional quasicrystals. By using a combination of algebraic, geometric, and dynamical techniques, together with input from higher dimensional Diophantine approximation, we give a complete characterization of all linearly repetitive cut and project sets with cubical windows. We also prove that these are precisely the collection of such sets which satisfy subadditive ergodic theorems. The results are explicit enough to allow us to apply them to known classical models, and to construct linearly repetitive cut and project sets in all pairs of dimensions and codimensions in which they exist. Research supported by EPSRC grants EP/L001462, EP/J00149X, EP/M023540. HK also gratefully acknowledges the support of the Osk. Huttunen foundation.

Quantum simulation from the bottom up: the case of rebits

NASA Astrophysics Data System (ADS)

Enshan Koh, Dax; Yuezhen Niu, Murphy; Yoder, Theodore J.

2018-05-01

Typically, quantum mechanics is thought of as a linear theory with unitary evolution governed by the Schrödinger equation. While this is technically true and useful for a physicist, with regards to computation it is an unfortunately narrow point of view. Just as a classical computer can simulate highly nonlinear functions of classical states, so too can the more general quantum computer simulate nonlinear evolutions of quantum states. We detail one particular simulation of nonlinearity on a quantum computer, showing how the entire class of -unitary evolutions (on n qubits) can be simulated using a unitary, real-amplitude quantum computer (consisting of n  +  1 qubits in total). These operators can be represented as the sum of a linear and antilinear operator, and add an intriguing new set of nonlinear quantum gates to the toolbox of the quantum algorithm designer. Furthermore, a subgroup of these nonlinear evolutions, called the -Cliffords, can be efficiently classically simulated, by making use of the fact that Clifford operators can simulate non-Clifford (in fact, non-linear) operators. This perspective of using the physical operators that we have to simulate non-physical ones that we do not is what we call bottom-up simulation, and we give some examples of its broader implications.

On new non-modal hydrodynamic stability modes and resulting non-exponential growth rates - a Lie symmetry approach

NASA Astrophysics Data System (ADS)

Oberlack, Martin; Nold, Andreas; Sanjon, Cedric Wilfried; Wang, Yongqi; Hau, Jan

2016-11-01

Classical hydrodynamic stability theory for laminar shear flows, no matter if considering long-term stability or transient growth, is based on the normal-mode ansatz, or, in other words, on an exponential function in space (stream-wise direction) and time. Recently, it became clear that the normal mode ansatz and the resulting Orr-Sommerfeld equation is based on essentially three fundamental symmetries of the linearized Euler and Navier-Stokes equations: translation in space and time and scaling of the dependent variable. Further, Kelvin-mode of linear shear flows seemed to be an exception in this context as it admits a fourth symmetry resulting in the classical Kelvin mode which is rather different from normal-mode. However, very recently it was discovered that most of the classical canonical shear flows such as linear shear, Couette, plane and round Poiseuille, Taylor-Couette, Lamb-Ossen vortex or asymptotic suction boundary layer admit more symmetries. This, in turn, led to new problem specific non-modal ansatz functions. In contrast to the exponential growth rate in time of the modal-ansatz, the new non-modal ansatz functions usually lead to an algebraic growth or decay rate, while for the asymptotic suction boundary layer a double-exponential growth or decay is observed.

The role of molecular conformation and polarizable embedding for one- and two-photon absorption of disperse orange 3 in solution.

PubMed

Silva, Daniel L; Murugan, N Arul; Kongsted, Jacob; Rinkevicius, Zilvinas; Canuto, Sylvio; Ågren, Hans

2012-07-19

Solvent effects on the one- and two-photon absorption (1PA and 2PA) of disperse orange 3 (DO3) in dimethyl sulfoxide (DMSO) are studied using a discrete polarizable embedding (PE) response theory. The scheme comprises a quantum region containing the chromophore and an atomically granulated classical region for the solvent accounting for full interactions within and between the two regions. Either classical molecular dynamics (MD) or hybrid Car-Parrinello (CP) quantum/classical (QM/MM) molecular dynamics simulations are employed to describe the solvation of DO3 in DMSO, allowing for an analysis of the effect of the intermolecular short-range repulsion, long-range attraction, and electrostatic interactions on the conformational changes of the chromophore and also the effect of the solute-solvent polarization. PE linear response calculations are performed to verify the character, solvatochromic shift, and overlap of the two lowest energy transitions responsible for the linear absorption spectrum of DO3 in DMSO in the visible spectral region. Results of the PE linear and quadratic response calculations, performed using uncorrelated solute-solvent configurations sampled from either the classical or hybrid CP QM/MM MD simulations, are used to estimate the width of the line shape function of the two electronic lowest energy excited states, which allow a prediction of the 2PA cross-sections without the use of empirical parameters. Appropriate exchange-correlation functionals have been employed in order to describe the charge-transfer process following the electronic transitions of the chromophore in solution.

Avoiding Communication in Dense Linear Algebra

DTIC Science & Technology

2013-08-16

Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.1.1 Asymptotic Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . 6...and parallelizing Strassen’s matrix multiplication algorithm (Chapter 11). 6 Chapter 2 Preliminaries 2.1 Notation and Definitions In this section we...between computations and algo- rithms). The following definition is based on [56]: Definition 2.1. A classical algorithm in linear algebra is one that

Linear Response Laws and Causality in Electrodynamics

ERIC Educational Resources Information Center

Yuffa, Alex J.; Scales, John A.

2012-01-01

Linear response laws and causality (the effect cannot precede the cause) are of fundamental importance in physics. In the context of classical electrodynamics, students often have a difficult time grasping these concepts because the physics is obscured by the intermingling of the time and frequency domains. In this paper, we analyse the linear…

A moist Boussinesq shallow water equations set for testing atmospheric models

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

Zerroukat, M., E-mail: mohamed.zerroukat@metoffice.gov.uk; Allen, T.

The shallow water equations have long been used as an initial test for numerical methods applied to atmospheric models with the test suite of Williamson et al. being used extensively for validating new schemes and assessing their accuracy. However the lack of physics forcing within this simplified framework often requires numerical techniques to be reworked when applied to fully three dimensional models. In this paper a novel two-dimensional shallow water equations system that retains moist processes is derived. This system is derived from three-dimensional Boussinesq approximation of the hydrostatic Euler equations where, unlike the classical shallow water set, we allowmore » the density to vary slightly with temperature. This results in extra (or buoyancy) terms for the momentum equations, through which a two-way moist-physics dynamics feedback is achieved. The temperature and moisture variables are advected as separate tracers with sources that interact with the mean-flow through a simplified yet realistic bulk moist-thermodynamic phase-change model. This moist shallow water system provides a unique tool to assess the usually complex and highly non-linear dynamics–physics interactions in atmospheric models in a simple yet realistic way. The full non-linear shallow water equations are solved numerically on several case studies and the results suggest quite realistic interaction between the dynamics and physics and in particular the generation of cloud and rain. - Highlights: • Novel shallow water equations which retains moist processes are derived from the three-dimensional hydrostatic Boussinesq equations. • The new shallow water set can be seen as a more general one, where the classical equations are a special case of these equations. • This moist shallow water system naturally allows a feedback mechanism from the moist physics increments to the momentum via buoyancy. • Like full models, temperature and moistures are advected as tracers that interact through a simplified yet realistic phase-change model. • This model is a unique tool to test numerical methods for atmospheric models, and physics–dynamics coupling, in a very realistic and simple way.« less

Creating Very True Quantum Algorithms for Quantum Energy Based Computing

NASA Astrophysics Data System (ADS)

Nagata, Koji; Nakamura, Tadao; Geurdes, Han; Batle, Josep; Abdalla, Soliman; Farouk, Ahmed; Diep, Do Ngoc

2018-04-01

An interpretation of quantum mechanics is discussed. It is assumed that quantum is energy. An algorithm by means of the energy interpretation is discussed. An algorithm, based on the energy interpretation, for fast determining a homogeneous linear function f( x) := s. x = s 1 x 1 + s 2 x 2 + ⋯ + s N x N is proposed. Here x = ( x 1, … , x N ), x j ∈ R and the coefficients s = ( s 1, … , s N ), s j ∈ N. Given the interpolation values (f(1), f(2),...,f(N))=ěc {y}, the unknown coefficients s = (s1(ěc {y}),\\dots , sN(ěc {y})) of the linear function shall be determined, simultaneously. The speed of determining the values is shown to outperform the classical case by a factor of N. Our method is based on the generalized Bernstein-Vazirani algorithm to qudit systems. Next, by using M parallel quantum systems, M homogeneous linear functions are determined, simultaneously. The speed of obtaining the set of M homogeneous linear functions is shown to outperform the classical case by a factor of N × M.

Creating Very True Quantum Algorithms for Quantum Energy Based Computing

NASA Astrophysics Data System (ADS)

Nagata, Koji; Nakamura, Tadao; Geurdes, Han; Batle, Josep; Abdalla, Soliman; Farouk, Ahmed; Diep, Do Ngoc

2017-12-01

An interpretation of quantum mechanics is discussed. It is assumed that quantum is energy. An algorithm by means of the energy interpretation is discussed. An algorithm, based on the energy interpretation, for fast determining a homogeneous linear function f(x) := s.x = s 1 x 1 + s 2 x 2 + ⋯ + s N x N is proposed. Here x = (x 1, … , x N ), x j ∈ R and the coefficients s = (s 1, … , s N ), s j ∈ N. Given the interpolation values (f(1), f(2),...,f(N))=ěc {y}, the unknown coefficients s = (s1(ěc {y}),\\dots , sN(ěc {y})) of the linear function shall be determined, simultaneously. The speed of determining the values is shown to outperform the classical case by a factor of N. Our method is based on the generalized Bernstein-Vazirani algorithm to qudit systems. Next, by using M parallel quantum systems, M homogeneous linear functions are determined, simultaneously. The speed of obtaining the set of M homogeneous linear functions is shown to outperform the classical case by a factor of N × M.

Deep Drawing Simulations With Different Polycrystalline Models

NASA Astrophysics Data System (ADS)

Duchêne, Laurent; de Montleau, Pierre; Bouvier, Salima; Habraken, Anne Marie

2004-06-01

The goal of this research is to study the anisotropic material behavior during forming processes, represented by both complex yield loci and kinematic-isotropic hardening models. A first part of this paper describes the main concepts of the `Stress-strain interpolation' model that has been implemented in the non-linear finite element code Lagamine. This model consists of a local description of the yield locus based on the texture of the material through the full constraints Taylor's model. The texture evolution due to plastic deformations is computed throughout the FEM simulations. This `local yield locus' approach was initially linked to the classical isotropic Swift hardening law. Recently, a more complex hardening model was implemented: the physically-based microstructural model of Teodosiu. It takes into account intergranular heterogeneity due to the evolution of dislocation structures, that affects isotropic and kinematic hardening. The influence of the hardening model is compared to the influence of the texture evolution thanks to deep drawing simulations.

Past, present and prospect of an Artificial Intelligence (AI) based model for sediment transport prediction

NASA Astrophysics Data System (ADS)

Afan, Haitham Abdulmohsin; El-shafie, Ahmed; Mohtar, Wan Hanna Melini Wan; Yaseen, Zaher Mundher

2016-10-01

An accurate model for sediment prediction is a priority for all hydrological researchers. Many conventional methods have shown an inability to achieve an accurate prediction of suspended sediment. These methods are unable to understand the behaviour of sediment transport in rivers due to the complexity, noise, non-stationarity, and dynamism of the sediment pattern. In the past two decades, Artificial Intelligence (AI) and computational approaches have become a remarkable tool for developing an accurate model. These approaches are considered a powerful tool for solving any non-linear model, as they can deal easily with a large number of data and sophisticated models. This paper is a review of all AI approaches that have been applied in sediment modelling. The current research focuses on the development of AI application in sediment transport. In addition, the review identifies major challenges and opportunities for prospective research. Throughout the literature, complementary models superior to classical modelling.

Recurrence theorems: A unified account

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

Wallace, David, E-mail: david.wallace@balliol.ox.ac.uk

I discuss classical and quantum recurrence theorems in a unified manner, treating both as generalisations of the fact that a system with a finite state space only has so many places to go. Along the way, I prove versions of the recurrence theorem applicable to dynamics on linear and metric spaces and make some comments about applications of the classical recurrence theorem in the foundations of statistical mechanics.

Equivalence-point electromigration acid-base titration via moving neutralization boundary electrophoresis.

PubMed

Yang, Qing; Fan, Liu-Yin; Huang, Shan-Sheng; Zhang, Wei; Cao, Cheng-Xi

2011-04-01

In this paper, we developed a novel method of acid-base titration, viz. the electromigration acid-base titration (EABT), via a moving neutralization boundary (MNR). With HCl and NaOH as the model strong acid and base, respectively, we conducted the experiments on the EABT via the method of moving neutralization boundary for the first time. The experiments revealed that (i) the concentration of agarose gel, the voltage used and the content of background electrolyte (KCl) had evident influence on the boundary movement; (ii) the movement length was a function of the running time under the constant acid and base concentrations; and (iii) there was a good linearity between the length and natural logarithmic concentration of HCl under the optimized conditions, and the linearity could be used to detect the concentration of acid. The experiments further manifested that (i) the RSD values of intra-day and inter-day runs were less than 1.59 and 3.76%, respectively, indicating similar precision and stability in capillary electrophoresis or HPLC; (ii) the indicators with different pK(a) values had no obvious effect on EABT, distinguishing strong influence on the judgment of equivalence-point titration in the classic one; and (iii) the constant equivalence-point titration always existed in the EABT, rather than the classic volumetric analysis. Additionally, the EABT could be put to good use for the determination of actual acid concentrations. The experimental results achieved herein showed a new general guidance for the development of classic volumetric analysis and element (e.g. nitrogen) content analysis in protein chemistry. Copyright © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

On solutions of the fifth-order dispersive equations with porous medium type non-linearity

NASA Astrophysics Data System (ADS)

Kocak, Huseyin; Pinar, Zehra

2018-07-01

In this work, we focus on obtaining the exact solutions of the fifth-order semi-linear and non-linear dispersive partial differential equations, which have the second-order diffusion-like (porous-type) non-linearity. The proposed equations were not studied in the literature in the sense of the exact solutions. We reveal solutions of the proposed equations using the classical Riccati equations method. The obtained exact solutions, which can play a key role to simulate non-linear waves in the medium with dispersion and diffusion, are illustrated and discussed in details.

High-order harmonic generation from highly excited states in acetylene

NASA Astrophysics Data System (ADS)

Mulholland, Peter; Dundas, Daniel

2018-04-01

High-order harmonic generation (HHG) from aligned acetylene molecules interacting with mid infra-red (IR), linearly polarized laser pulses is studied theoretically using a mixed quantum-classical approach in which the electrons are described using time-dependent density-functional theory while the ions are treated classically. We find that for molecules aligned perpendicular to the laser polarization axis, HHG arises from the highest-occupied molecular orbital (HOMO), while for molecules aligned along the laser polarization axis, HHG is dominated by the HOMO-1. In the parallel orientation we observe a double plateau with an inner plateau that is produced by ionization from and recombination back to an autoionizing state. Two pieces of evidence support this idea. First, by choosing a suitably tuned vacuum ultraviolet pump pulse that directly excites the autoionizing state we observe a dramatic enhancement of all harmonics in the inner plateau. Second, in certain circumstances, the position of the inner plateau cutoff does not agree with the classical three-step model. We show that this discrepancy can be understood in terms of a minimum in the dipole recombination matrix element from the continuum to the autoionizing state.

Efficient spectral computation of the stationary states of rotating Bose-Einstein condensates by preconditioned nonlinear conjugate gradient methods

NASA Astrophysics Data System (ADS)

Antoine, Xavier; Levitt, Antoine; Tang, Qinglin

2017-08-01

We propose a preconditioned nonlinear conjugate gradient method coupled with a spectral spatial discretization scheme for computing the ground states (GS) of rotating Bose-Einstein condensates (BEC), modeled by the Gross-Pitaevskii Equation (GPE). We first start by reviewing the classical gradient flow (also known as imaginary time (IMT)) method which considers the problem from the PDE standpoint, leading to numerically solve a dissipative equation. Based on this IMT equation, we analyze the forward Euler (FE), Crank-Nicolson (CN) and the classical backward Euler (BE) schemes for linear problems and recognize classical power iterations, allowing us to derive convergence rates. By considering the alternative point of view of minimization problems, we propose the preconditioned steepest descent (PSD) and conjugate gradient (PCG) methods for the GS computation of the GPE. We investigate the choice of the preconditioner, which plays a key role in the acceleration of the convergence process. The performance of the new algorithms is tested in 1D, 2D and 3D. We conclude that the PCG method outperforms all the previous methods, most particularly for 2D and 3D fast rotating BECs, while being simple to implement.

Application of various FLD modelling approaches

NASA Astrophysics Data System (ADS)

Banabic, D.; Aretz, H.; Paraianu, L.; Jurco, P.

2005-07-01

This paper focuses on a comparison between different modelling approaches to predict the forming limit diagram (FLD) for sheet metal forming under a linear strain path using the recently introduced orthotropic yield criterion BBC2003 (Banabic D et al 2005 Int. J. Plasticity 21 493-512). The FLD models considered here are a finite element based approach, the well known Marciniak-Kuczynski model, the modified maximum force criterion according to Hora et al (1996 Proc. Numisheet'96 Conf. (Dearborn/Michigan) pp 252-6), Swift's diffuse (Swift H W 1952 J. Mech. Phys. Solids 1 1-18) and Hill's classical localized necking approach (Hill R 1952 J. Mech. Phys. Solids 1 19-30). The FLD of an AA5182-O aluminium sheet alloy has been determined experimentally in order to quantify the predictive capabilities of the models mentioned above.

Falling paper: Navier-Stokes solutions, model of fluid forces, and center of mass elevation.

PubMed

Pesavento, Umberto; Wang, Z Jane

2004-10-01

We investigate the problem of falling paper by solving the two dimensional Navier-Stokes equations subject to the motion of a free-falling body at Reynolds numbers around 10(3). The aerodynamic lift on a tumbling plate is found to be dominated by the product of linear and angular velocities rather than velocity squared, as appropriate for an airfoil. This coupling between translation and rotation provides a mechanism for a brief elevation of center of mass near the cusplike turning points. The Navier-Stokes solutions further provide the missing quantity in the classical theory of lift, the instantaneous circulation, and suggest a revised model for the fluid forces.

Mathematical Modeling of Torsional Surface Wave Propagation in a Non-Homogeneous Transverse Isotropic Elastic Solid Semi-Infinite Medium Under a Layer

NASA Astrophysics Data System (ADS)

Sethi, M.; Sharma, A.; Vasishth, A.

2017-05-01

The present paper deals with the mathematical modeling of the propagation of torsional surface waves in a non-homogeneous transverse isotropic elastic half-space under a rigid layer. Both rigidities and density of the half-space are assumed to vary inversely linearly with depth. Separation of variable method has been used to get the analytical solutions for the dispersion equation of the torsional surface waves. Also, the effects of nonhomogeneities on the phase velocity of torsional surface waves have been shown graphically. Also, dispersion equations have been derived for some particular cases, which are in complete agreement with some classical results.

Experimental evidence of symmetry-breaking supercritical transition in pipe flow of shear-thinning fluids

NASA Astrophysics Data System (ADS)

Wen, Chaofan; Poole, Robert J.; Willis, Ashley P.; Dennis, David J. C.

2017-03-01

Experimental results reveal that the asymmetric flow of shear-thinning fluid through a cylindrical pipe, which was previously associated with the laminar-turbulent transition process, appears to have the characteristics of a nonhysteretic, supercritical instability of the laminar base state. Contrary to what was previously believed, classical transition is found to be responsible for returning symmetry to the flow. An absence of evidence of the instability in simulations (either linear or nonlinear) suggests that an element of physics is lacking in the commonly used rheological model for inelastic shear-thinning fluids. These unexpected discoveries raise new questions regarding the stability of these practically important fluids and how they can be successfully modeled.

Poisson structure on a space with linear SU(2) fuzziness

NASA Astrophysics Data System (ADS)

Khorrami, Mohammad; Fatollahi, Amir H.; Shariati, Ahmad

2009-07-01

The Poisson structure is constructed for a model in which spatial coordinates of configuration space are noncommutative and satisfy the commutation relations of a Lie algebra. The case is specialized to that of the group SU(2), for which the counterpart of the angular momentum as well as the Euler parametrization of the phase space are introduced. SU(2)-invariant classical systems are discussed, and it is observed that the path of particle can be obtained by the solution of a first-order equation, as the case with such models on commutative spaces. The examples of free particle, rotationally invariant potentials, and specially the isotropic harmonic oscillator are investigated in more detail.

High Reynolds number analysis of flat plate and separated afterbody flow using non-linear turbulence models

NASA Technical Reports Server (NTRS)

Carlson, John R.

1996-01-01

The ability of the three-dimensional Navier-Stokes method, PAB3D, to simulate the effect of Reynolds number variation using non-linear explicit algebraic Reynolds stress turbulence modeling was assessed. Subsonic flat plate boundary-layer flow parameters such as normalized velocity distributions, local and average skin friction, and shape factor were compared with DNS calculations and classical theory at various local Reynolds numbers up to 180 million. Additionally, surface pressure coefficient distributions and integrated drag predictions on an axisymmetric nozzle afterbody were compared with experimental data from 10 to 130 million Reynolds number. The high Reynolds data was obtained from the NASA Langley 0.3m Transonic Cryogenic Tunnel. There was generally good agreement of surface static pressure coefficients between the CFD and measurement. The change in pressure coefficient distributions with varying Reynolds number was similar to the experimental data trends, though slightly over-predicting the effect. The computational sensitivity of viscous modeling and turbulence modeling are shown. Integrated afterbody pressure drag was typically slightly lower than the experimental data. The change in afterbody pressure drag with Reynolds number was small both experimentally and computationally, even though the shape of the distribution was somewhat modified with Reynolds number.

A non-linear data mining parameter selection algorithm for continuous variables

PubMed Central

Razavi, Marianne; Brady, Sean

2017-01-01

In this article, we propose a new data mining algorithm, by which one can both capture the non-linearity in data and also find the best subset model. To produce an enhanced subset of the original variables, a preferred selection method should have the potential of adding a supplementary level of regression analysis that would capture complex relationships in the data via mathematical transformation of the predictors and exploration of synergistic effects of combined variables. The method that we present here has the potential to produce an optimal subset of variables, rendering the overall process of model selection more efficient. This algorithm introduces interpretable parameters by transforming the original inputs and also a faithful fit to the data. The core objective of this paper is to introduce a new estimation technique for the classical least square regression framework. This new automatic variable transformation and model selection method could offer an optimal and stable model that minimizes the mean square error and variability, while combining all possible subset selection methodology with the inclusion variable transformations and interactions. Moreover, this method controls multicollinearity, leading to an optimal set of explanatory variables. PMID:29131829

Disease Progression Modeling to Evaluate the Effects of Enzyme Replacement Therapy on Kidney Function in Adult Patients with the Classic Phenotype of Fabry Disease.

PubMed

Nowak, Albina; Koch, Gilbert; Huynh-Do, Uyen; Siegenthaler, Martin; Marti, Hans-Peter; Pfister, Marc

2017-01-01

Fabry disease (FD) is a rare inherited lysosomal storage disease with common and serious kidney complications. Enzyme replacement therapies (ERT) with agalsidase-α and -β were investigated to characterize their therapeutic effect on kidney function in FD patients with Classic phenotype. The prospective FD cohort consisted of 98 genetically confirmed patients (females, n = 61, males, n = 37). The median [interquartile range] follow-up time (time difference from first to last visit) was 9 [6, 12] years. The median age of ERT start was 36 [21 - 54] years for females and 39 [28 - 49] years for males. A disease progression model was developed to (i) characterize the time course of estimated glomerular filtration rate (eGFR) and (ii) evaluate therapeutic effects of ERT on kidney function. Change in eGFR over time was best described by the linear model. Females had stable kidney function with and without ERT (eGFR slopes of -0.07 ml/min/1.73m^2 per year and 0.52 ml/min/1.73m^2 per year, respectively). Males with ERT showed an eGFR decrease of -3.07 ml/min/1.73m^2 per year. Mathematical disease progression modeling indicates that there is no clear therapeutic effect of ERT on kidney function in adult patients with Classic Phenotype of FD. Interpretation of these findings should take into account that the study is not randomized and lacks a placebo controlled group. Further investigations are warranted to clarify whether earlier ERT initiation before 18 years of age, higher ERT dose or more intensive therapies can preserve kidney function. © 2017 The Author(s)Published by S. Karger AG, Basel.

Electrophoresis in strong electric fields.

PubMed

Barany, Sandor

2009-01-01

Two kinds of non-linear electrophoresis (ef) that can be detected in strong electric fields (several hundred V/cm) are considered. The first ("classical" non-linear ef) is due to the interaction of the outer field with field-induced ionic charges in the electric double layer (EDL) under conditions, when field-induced variations of electrolyte concentration remain to be small comparatively to its equilibrium value. According to the Shilov theory, the non-linear component of the electrophoretic velocity for dielectric particles is proportional to the cubic power of the applied field strength (cubic electrophoresis) and to the second power of the particles radius; it is independent of the zeta-potential but is determined by the surface conductivity of particles. The second one, the so-called "superfast electrophoresis" is connected with the interaction of a strong outer field with a secondary diffuse layer of counterions (space charge) that is induced outside the primary (classical) diffuse EDL by the external field itself because of concentration polarization. The Dukhin-Mishchuk theory of "superfast electrophoresis" predicts quadratic dependence of the electrophoretic velocity of unipolar (ionically or electronically) conducting particles on the external field gradient and linear dependence on the particle's size in strong electric fields. These are in sharp contrast to the laws of classical electrophoresis (no dependence of V(ef) on the particle's size and linear dependence on the electric field gradient). A new method to measure the ef velocity of particles in strong electric fields is developed that is based on separation of the effects of sedimentation and electrophoresis using videoimaging and a new flowcell and use of short electric pulses. To test the "classical" non-linear electrophoresis, we have measured the ef velocity of non-conducting polystyrene, aluminium-oxide and (semiconductor) graphite particles as well as Saccharomice cerevisiae yeast cells as a function of the electric field strength, particle size, electrolyte concentration and the adsorbed polymer amount. It has been shown that the electrophoretic velocity of the particles/cells increases with field strength linearly up to about 100 and 200 V/cm (for cells) without and with adsorbed polymers both in pure water and in electrolyte solutions. In line with the theoretical predictions, in stronger fields substantial non-linear effects were recorded (V(ef)~E(3)). The ef velocity of unipolar ion-type conducting (ion-exchanger particles and fibres), electron-type conducting (magnesium and Mg/Al alloy) and semiconductor particles (graphite, activated carbon, pyrite, molybdenite) increases significantly with the electric field (V(ef)~E(2)) and the particle's size but is almost independent of the ionic strength. These trends are inconsistent with Smoluchowski's equation for dielectric particles, but are consistent with the Dukhin-Mishchuk theory of superfast electrophoresis.

Classical theory of atom-surface scattering: The rainbow effect

NASA Astrophysics Data System (ADS)

Miret-Artés, Salvador; Pollak, Eli

2012-07-01

The scattering of heavy atoms and molecules from surfaces is oftentimes dominated by classical mechanics. A large body of experiments have gathered data on the angular distributions of the scattered species, their energy loss distribution, sticking probability, dependence on surface temperature and more. For many years these phenomena have been considered theoretically in the framework of the “washboard model” in which the interaction of the incident particle with the surface is described in terms of hard wall potentials. Although this class of models has helped in elucidating some of the features it left open many questions such as: true potentials are clearly not hard wall potentials, it does not provide a realistic framework for phonon scattering, and it cannot explain the incident angle and incident energy dependence of rainbow scattering, nor can it provide a consistent theory for sticking. In recent years we have been developing a classical perturbation theory approach which has provided new insight into the dynamics of atom-surface scattering. The theory includes both surface corrugation as well as interaction with surface phonons in terms of harmonic baths which are linearly coupled to the system coordinates. This model has been successful in elucidating many new features of rainbow scattering in terms of frictions and bath fluctuations or noise. It has also given new insight into the origins of asymmetry in atomic scattering from surfaces. New phenomena deduced from the theory include friction induced rainbows, energy loss rainbows, a theory of super-rainbows, and more. In this review we present the classical theory of atom-surface scattering as well as extensions and implications for semiclassical scattering and the further development of a quantum theory of surface scattering. Special emphasis is given to the inversion of scattering data into information on the particle-surface interactions.

Validation of Bayesian analysis of compartmental kinetic models in medical imaging.

PubMed

Sitek, Arkadiusz; Li, Quanzheng; El Fakhri, Georges; Alpert, Nathaniel M

2016-10-01

Kinetic compartmental analysis is frequently used to compute physiologically relevant quantitative values from time series of images. In this paper, a new approach based on Bayesian analysis to obtain information about these parameters is presented and validated. The closed-form of the posterior distribution of kinetic parameters is derived with a hierarchical prior to model the standard deviation of normally distributed noise. Markov chain Monte Carlo methods are used for numerical estimation of the posterior distribution. Computer simulations of the kinetics of F18-fluorodeoxyglucose (FDG) are used to demonstrate drawing statistical inferences about kinetic parameters and to validate the theory and implementation. Additionally, point estimates of kinetic parameters and covariance of those estimates are determined using the classical non-linear least squares approach. Posteriors obtained using methods proposed in this work are accurate as no significant deviation from the expected shape of the posterior was found (one-sided P>0.08). It is demonstrated that the results obtained by the standard non-linear least-square methods fail to provide accurate estimation of uncertainty for the same data set (P<0.0001). The results of this work validate new methods for a computer simulations of FDG kinetics. Results show that in situations where the classical approach fails in accurate estimation of uncertainty, Bayesian estimation provides an accurate information about the uncertainties in the parameters. Although a particular example of FDG kinetics was used in the paper, the methods can be extended for different pharmaceuticals and imaging modalities. Copyright © 2016 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.

Tug-of-war between classical and multicenter bonds in H-(Be)n-H species

NASA Astrophysics Data System (ADS)

Lundell, Katie A.; Boldyrev, Alexander I.

2018-05-01

Quantum chemical calculations were performed for beryllium homocatenated compounds [H-(Be)n-H]. Global minimum structures were found using machine searches (Coalescence Kick method) with density functional theory. Chemical bonding analysis was performed with the Adaptive Natural Density Partitioning method. It was found that H-(Be)2-H and H-(Be)3-H clusters are linear with classical two-center two-electron bonds, while for n > 3, three-dimensional structures are more stable with multicenter bonding. Thus, at n = 4, multicenter bonding wins the tug-of-war vs. the classical bonding.

Classical r-matrices for the generalised Chern–Simons formulation of 3d gravity

NASA Astrophysics Data System (ADS)

Osei, Prince K.; Schroers, Bernd J.

2018-04-01

We study the conditions for classical r-matrices to be compatible with the generalised Chern–Simons action for 3d gravity. Compatibility means solving the classical Yang–Baxter equations with a prescribed symmetric part for each of the real Lie algebras and bilinear pairings arising in the generalised Chern–Simons action. We give a new construction of r-matrices via a generalised complexification and derive a non-linear set of matrix equations determining the most general compatible r-matrix. We exhibit new families of solutions and show that they contain some known r-matrices for special parameter values.

Quantum correction to classical gravitational interaction between two polarizable objects

NASA Astrophysics Data System (ADS)

Wu, Puxun; Hu, Jiawei; Yu, Hongwei

2016-12-01

When gravity is quantized, there inevitably exist quantum gravitational vacuum fluctuations which induce quadrupole moments in gravitationally polarizable objects and produce a quantum correction to the classical Newtonian interaction between them. Here, based upon linearized quantum gravity and the leading-order perturbation theory, we study, from a quantum field-theoretic prospect, this quantum correction between a pair of gravitationally polarizable objects treated as two-level harmonic oscillators. We find that the interaction potential behaves like r-11 in the retarded regime and r-10 in the near regime. Our result agrees with what were recently obtained in different approaches. Our study seems to indicate that linearized quantum gravity is robust in dealing with quantum gravitational effects at low energies.

Understanding the breakdown of classic two-phase theory and spray atomization at engine-relevant conditions

NASA Astrophysics Data System (ADS)

Dahms, Rainer N.

2016-04-01

A generalized framework for multi-component liquid injections is presented to understand and predict the breakdown of classic two-phase theory and spray atomization at engine-relevant conditions. The analysis focuses on the thermodynamic structure and the immiscibility state of representative gas-liquid interfaces. The most modern form of Helmholtz energy mixture state equation is utilized which exhibits a unique and physically consistent behavior over the entire two-phase regime of fluid densities. It is combined with generalized models for non-linear gradient theory and for liquid injections to quantify multi-component two-phase interface structures in global thermal equilibrium. Then, the Helmholtz free energy is minimized which determines the interfacial species distribution as a consequence. This minimal free energy state is demonstrated to validate the underlying assumptions of classic two-phase theory and spray atomization. However, under certain engine-relevant conditions for which corroborating experimental data are presented, this requirement for interfacial thermal equilibrium becomes unsustainable. A rigorously derived probability density function quantifies the ability of the interface to develop internal spatial temperature gradients in the presence of significant temperature differences between injected liquid and ambient gas. Then, the interface can no longer be viewed as an isolated system at minimal free energy. Instead, the interfacial dynamics become intimately connected to those of the separated homogeneous phases. Hence, the interface transitions toward a state in local equilibrium whereupon it becomes a dense-fluid mixing layer. A new conceptual view of a transitional liquid injection process emerges from a transition time scale analysis. Close to the nozzle exit, the two-phase interface still remains largely intact and more classic two-phase processes prevail as a consequence. Further downstream, however, the transition to dense-fluid mixing generally occurs before the liquid length is reached. The significance of the presented modeling expressions is established by a direct comparison to a reduced model, which utilizes widely applied approximations but fundamentally fails to capture the physical complexity discussed in this paper.

Quantum computation with classical light: Implementation of the Deutsch-Jozsa algorithm

NASA Astrophysics Data System (ADS)

Perez-Garcia, Benjamin; McLaren, Melanie; Goyal, Sandeep K.; Hernandez-Aranda, Raul I.; Forbes, Andrew; Konrad, Thomas

2016-05-01

We propose an optical implementation of the Deutsch-Jozsa Algorithm using classical light in a binary decision-tree scheme. Our approach uses a ring cavity and linear optical devices in order to efficiently query the oracle functional values. In addition, we take advantage of the intrinsic Fourier transforming properties of a lens to read out whether the function given by the oracle is balanced or constant.

Linear and angular coherence momenta in the classical second-order coherence theory of vector electromagnetic fields.

PubMed

Wang, Wei; Takeda, Mitsuo

2006-09-01

A new concept of vector and tensor densities is introduced into the general coherence theory of vector electromagnetic fields that is based on energy and energy-flow coherence tensors. Related coherence conservation laws are presented in the form of continuity equations that provide new insights into the propagation of second-order correlation tensors associated with stationary random classical electromagnetic fields.

Jointly modeling longitudinal proportional data and survival times with an application to the quality of life data in a breast cancer trial.

PubMed

Song, Hui; Peng, Yingwei; Tu, Dongsheng

2017-04-01

Motivated by the joint analysis of longitudinal quality of life data and recurrence free survival times from a cancer clinical trial, we present in this paper two approaches to jointly model the longitudinal proportional measurements, which are confined in a finite interval, and survival data. Both approaches assume a proportional hazards model for the survival times. For the longitudinal component, the first approach applies the classical linear mixed model to logit transformed responses, while the second approach directly models the responses using a simplex distribution. A semiparametric method based on a penalized joint likelihood generated by the Laplace approximation is derived to fit the joint model defined by the second approach. The proposed procedures are evaluated in a simulation study and applied to the analysis of breast cancer data motivated this research.

Global/local stress analysis of composite panels

NASA Technical Reports Server (NTRS)

Ransom, Jonathan B.; Knight, Norman F., Jr.

1989-01-01

A method for performing a global/local stress analysis is described, and its capabilities are demonstrated. The method employs spline interpolation functions which satisfy the linear plate bending equation to determine displacements and rotations from a global model which are used as boundary conditions for the local model. Then, the local model is analyzed independent of the global model of the structure. This approach can be used to determine local, detailed stress states for specific structural regions using independent, refined local models which exploit information from less-refined global models. The method presented is not restricted to having a priori knowledge of the location of the regions requiring local detailed stress analysis. This approach also reduces the computational effort necessary to obtain the detailed stress state. Criteria for applying the method are developed. The effectiveness of the method is demonstrated using a classical stress concentration problem and a graphite-epoxy blade-stiffened panel with a discontinuous stiffener.

Global/local stress analysis of composite structures. M.S. Thesis

NASA Technical Reports Server (NTRS)

Ransom, Jonathan B.

1989-01-01

A method for performing a global/local stress analysis is described and its capabilities are demonstrated. The method employs spline interpolation functions which satisfy the linear plate bending equation to determine displacements and rotations from a global model which are used as boundary conditions for the local model. Then, the local model is analyzed independent of the global model of the structure. This approach can be used to determine local, detailed stress states for specific structural regions using independent, refined local models which exploit information from less-refined global models. The method presented is not restricted to having a priori knowledge of the location of the regions requiring local detailed stress analysis. This approach also reduces the computational effort necessary to obtain the detailed stress state. Criteria for applying the method are developed. The effectiveness of the method is demonstrated using a classical stress concentration problem and a graphite-epoxy blade-stiffened panel with a discontinuous stiffener.

Couple stress theory of curved rods. 2-D, high order, Timoshenko's and Euler-Bernoulli models

NASA Astrophysics Data System (ADS)

Zozulya, V. V.

2017-01-01

New models for plane curved rods based on linear couple stress theory of elasticity have been developed.2-D theory is developed from general 2-D equations of linear couple stress elasticity using a special curvilinear system of coordinates related to the middle line of the rod as well as special hypothesis based on assumptions that take into account the fact that the rod is thin. High order theory is based on the expansion of the equations of the theory of elasticity into Fourier series in terms of Legendre polynomials. First, stress and strain tensors, vectors of displacements and rotation along with body forces have been expanded into Fourier series in terms of Legendre polynomials with respect to a thickness coordinate.Thereby, all equations of elasticity including Hooke's law have been transformed to the corresponding equations for Fourier coefficients. Then, in the same way as in the theory of elasticity, a system of differential equations in terms of displacements and boundary conditions for Fourier coefficients have been obtained. Timoshenko's and Euler-Bernoulli theories are based on the classical hypothesis and the 2-D equations of linear couple stress theory of elasticity in a special curvilinear system. The obtained equations can be used to calculate stress-strain and to model thin walled structures in macro, micro and nano scales when taking into account couple stress and rotation effects.

DCJ-indel and DCJ-substitution distances with distinct operation costs

PubMed Central

2013-01-01

Background Classical approaches to compute the genomic distance are usually limited to genomes with the same content and take into consideration only rearrangements that change the organization of the genome (i.e. positions and orientation of pieces of DNA, number and type of chromosomes, etc.), such as inversions, translocations, fusions and fissions. These operations are generically represented by the double-cut and join (DCJ) operation. The distance between two genomes, in terms of number of DCJ operations, can be computed in linear time. In order to handle genomes with distinct contents, also insertions and deletions of fragments of DNA – named indels – must be allowed. More powerful than an indel is a substitution of a fragment of DNA by another fragment of DNA. Indels and substitutions are called content-modifying operations. It has been shown that both the DCJ-indel and the DCJ-substitution distances can also be computed in linear time, assuming that the same cost is assigned to any DCJ or content-modifying operation. Results In the present study we extend the DCJ-indel and the DCJ-substitution models, considering that the content-modifying cost is distinct from and upper bounded by the DCJ cost, and show that the distance in both models can still be computed in linear time. Although the triangular inequality can be disrupted in both models, we also show how to efficiently fix this problem a posteriori. PMID:23879938

Classical and quantum non-linear optical applications using the Mach-Zehnder interferometer

NASA Astrophysics Data System (ADS)

Prescod, Andru

Mach Zehnder (MZ) modulators are widely employed in a variety of applications, such as optical communications, optical imaging, metrology and encryption. In this dissertation, we explore two non-linear MZ applications; one classified as classical and one as quantum, in which the Mach Zehnder interferometer is used. In the first application, a classical non-linear application, we introduce and study a new electro-optic highly linear (e.g., >130 dB) modulator configuration. This modulator makes use of a phase modulator (PM) in one arm of the MZ interferometer (MZI) and a ring resonator (RR) located on the other arm. The modulator performance is obtained through the control of a combination of internal and external parameters. These parameters include the RR-coupling ratio (internal parameter); the RF power split ratio and the RF phase bias (external parameters). Results show the unique and superior features, such as high linearity (SFDR˜133 dB), modulation bandwidth extension (as much as 70%) over the previously proposed and demonstrated Resonator-Assisted Mach Zehnder (RAMZ) design. Furthermore the proposed electro-optic modulator of this dissertation also provides an inherent SFDR compensation capability, even in cases where a significant waveguide optical loss exists. This design also shows potential for increased flexibility, practicality and ease of use. In the second application, a quantum non-linear application, we experimentally demonstrate quantum optical coherence tomography (QOCT) using a type II non-linear crystal (periodically-poled potassium titanyl phosphate (KTiOPO4) or PPKTP). There have been several publications discussing the merits and disadvantages of QOCT compared to OCT and other imaging techniques. First, we discuss the issues and solutions for increasing the efficiency of the quantum entangled photons. Second, we use a free space QOCT experiment to generate a high flux of these quantum entangled photons in two orthogonal polarizations, by parametric down-conversion. Third, by ensuring that these down-converted photons have the same frequency, spatial-temporal mode, and the same polarization when they interfere at a beam splitter, quantum interference should occur. Quantum interference of these entangled photons enables high resolution probing of dispersive samples.

Linear Quantitative Profiling Method Fast Monitors Alkaloids of Sophora Flavescens That Was Verified by Tri-Marker Analyses.

PubMed

Hou, Zhifei; Sun, Guoxiang; Guo, Yong

2016-01-01

The present study demonstrated the use of the Linear Quantitative Profiling Method (LQPM) to evaluate the quality of Alkaloids of Sophora flavescens (ASF) based on chromatographic fingerprints in an accurate, economical and fast way. Both linear qualitative and quantitative similarities were calculated in order to monitor the consistency of the samples. The results indicate that the linear qualitative similarity (LQLS) is not sufficiently discriminating due to the predominant presence of three alkaloid compounds (matrine, sophoridine and oxymatrine) in the test samples; however, the linear quantitative similarity (LQTS) was shown to be able to obviously identify the samples based on the difference in the quantitative content of all the chemical components. In addition, the fingerprint analysis was also supported by the quantitative analysis of three marker compounds. The LQTS was found to be highly correlated to the contents of the marker compounds, indicating that quantitative analysis of the marker compounds may be substituted with the LQPM based on the chromatographic fingerprints for the purpose of quantifying all chemicals of a complex sample system. Furthermore, once reference fingerprint (RFP) developed from a standard preparation in an immediate detection way and the composition similarities calculated out, LQPM could employ the classical mathematical model to effectively quantify the multiple components of ASF samples without any chemical standard.

Wing Leading Edge RCC Rapid Response Damage Prediction Tool (IMPACT2)

NASA Technical Reports Server (NTRS)

Clark, Robert; Cottter, Paul; Michalopoulos, Constantine

2013-01-01

This rapid response computer program predicts Orbiter Wing Leading Edge (WLE) damage caused by ice or foam impact during a Space Shuttle launch (Program "IMPACT2"). The program was developed after the Columbia accident in order to assess quickly WLE damage due to ice, foam, or metal impact (if any) during a Shuttle launch. IMPACT2 simulates an impact event in a few minutes for foam impactors, and in seconds for ice and metal impactors. The damage criterion is derived from results obtained from one sophisticated commercial program, which requires hours to carry out simulations of the same impact events. The program was designed to run much faster than the commercial program with prediction of projectile threshold velocities within 10 to 15% of commercial-program values. The mathematical model involves coupling of Orbiter wing normal modes of vibration to nonlinear or linear springmass models. IMPACT2 solves nonlinear or linear impact problems using classical normal modes of vibration of a target, and nonlinear/ linear time-domain equations for the projectile. Impact loads and stresses developed in the target are computed as functions of time. This model is novel because of its speed of execution. A typical model of foam, or other projectile characterized by material nonlinearities, impacting an RCC panel is executed in minutes instead of hours needed by the commercial programs. Target damage due to impact can be assessed quickly, provided that target vibration modes and allowable stress are known.

Plate and butt-weld stresses beyond elastic limit, material and structural modeling

NASA Technical Reports Server (NTRS)

Verderaime, V.

1991-01-01

Ultimate safety factors of high performance structures depend on stress behavior beyond the elastic limit, a region not too well understood. An analytical modeling approach was developed to gain fundamental insights into inelastic responses of simple structural elements. Nonlinear material properties were expressed in engineering stresses and strains variables and combined with strength of material stress and strain equations similar to numerical piece-wise linear method. Integrations are continuous which allows for more detailed solutions. Included with interesting results are the classical combined axial tension and bending load model and the strain gauge conversion to stress beyond the elastic limit. Material discontinuity stress factors in butt-welds were derived. This is a working-type document with analytical methods and results applicable to all industries of high reliability structures.

Interaction with a field: a simple integrable model with backreaction

NASA Astrophysics Data System (ADS)

Mouchet, Amaury

2008-09-01

The classical model of an oscillator linearly coupled to a string captures, for a low price in technique, many general features of more realistic models for describing a particle interacting with a field or an atom in an electromagnetic cavity. The scattering matrix and the asymptotic in and out-waves on the string can be computed exactly and the phenomenon of resonant scattering can be introduced in the simplest way. The dissipation induced by the coupling of the oscillator to the string can be studied completely. In the case of a d'Alembert string, the backreaction leads to an Abraham-Lorentz-Dirac-like equation. In the case of a Klein-Gordon string, one can see explicitly how radiation governs the (meta)stability of the (quasi)bounded mode.

Quantum computation for solving linear systems

NASA Astrophysics Data System (ADS)

Cao, Yudong

Quantum computation is a subject born out of the combination between physics and computer science. It studies how the laws of quantum mechanics can be exploited to perform computations much more efficiently than current computers (termed classical computers as oppose to quantum computers). The thesis starts by introducing ideas from quantum physics and theoretical computer science and based on these ideas, introducing the basic concepts in quantum computing. These introductory discussions are intended for non-specialists to obtain the essential knowledge needed for understanding the new results presented in the subsequent chapters. After introducing the basics of quantum computing, we focus on the recently proposed quantum algorithm for linear systems. The new results include i) special instances of quantum circuits that can be implemented using current experimental resources; ii) detailed quantum algorithms that are suitable for a broader class of linear systems. We show that for some particular problems the quantum algorithm is able to achieve exponential speedup over their classical counterparts.

Exact Solutions for Stokes' Flow of a Non-Newtonian Nanofluid Model: A Lie Similarity Approach

NASA Astrophysics Data System (ADS)

Aziz, Taha; Aziz, A.; Khalique, C. M.

2016-07-01

The fully developed time-dependent flow of an incompressible, thermodynamically compatible non-Newtonian third-grade nanofluid is investigated. The classical Stokes model is considered in which the flow is generated due to the motion of the plate in its own plane with an impulsive velocity. The Lie symmetry approach is utilised to convert the governing nonlinear partial differential equation into different linear and nonlinear ordinary differential equations. The reduced ordinary differential equations are then solved by using the compatibility and generalised group method. Exact solutions for the model equation are deduced in the form of closed-form exponential functions which are not available in the literature before. In addition, we also derived the conservation laws associated with the governing model. Finally, the physical features of the pertinent parameters are discussed in detail through several graphs.

Numerical methods for coupled fracture problems

NASA Astrophysics Data System (ADS)

Viesca, Robert C.; Garagash, Dmitry I.

2018-04-01

We consider numerical solutions in which the linear elastic response to an opening- or sliding-mode fracture couples with one or more processes. Classic examples of such problems include traction-free cracks leading to stress singularities or cracks with cohesive-zone strength requirements leading to non-singular stress distributions. These classical problems have characteristic square-root asymptotic behavior for stress, relative displacement, or their derivatives. Prior work has shown that such asymptotics lead to a natural quadrature of the singular integrals at roots of Chebyhsev polynomials of the first, second, third, or fourth kind. We show that such quadratures lead to convenient techniques for interpolation, differentiation, and integration, with the potential for spectral accuracy. We further show that these techniques, with slight amendment, may continue to be used for non-classical problems which lack the classical asymptotic behavior. We consider solutions to example problems of both the classical and non-classical variety (e.g., fluid-driven opening-mode fracture and fault shear rupture driven by thermal weakening), with comparisons to analytical solutions or asymptotes, where available.

Effective dynamics of a classical point charge

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

Polonyi, Janos, E-mail: polonyi@iphc.cnrs.fr

2014-03-15

The effective Lagrangian of a point charge is derived by eliminating the electromagnetic field within the framework of the classical closed time path formalism. The short distance singularity of the electromagnetic field is regulated by an UV cutoff. The Abraham–Lorentz force is recovered and its similarity to quantum anomalies is underlined. The full cutoff-dependent linearized equation of motion is obtained, no runaway trajectories are found but the effective dynamics shows acausality if the cutoff is beyond the classical charge radius. The strength of the radiation reaction force displays a pole in its cutoff-dependence in a manner reminiscent of the Landau-polemore » of perturbative QED. Similarity between the dynamical breakdown of the time reversal invariance and dynamical symmetry breaking is pointed out. -- Highlights: •Extension of the classical action principle for dissipative systems. •New derivation of the Abraham–Lorentz force for a point charge. •Absence of a runaway solution of the Abraham–Lorentz force. •Acausality in classical electrodynamics. •Renormalization of classical electrodynamics of point charges.« less

Numerical Asymptotic Solutions Of Differential Equations

NASA Technical Reports Server (NTRS)

Thurston, Gaylen A.

1992-01-01

Numerical algorithms derived and compared with classical analytical methods. In method, expansions replaced with integrals evaluated numerically. Resulting numerical solutions retain linear independence, main advantage of asymptotic solutions.

Using dynamic N-mixture models to test cavity limitation on northern flying squirrel demographic parameters using experimental nest box supplementation.

PubMed

Priol, Pauline; Mazerolle, Marc J; Imbeau, Louis; Drapeau, Pierre; Trudeau, Caroline; Ramière, Jessica

2014-06-01

Dynamic N-mixture models have been recently developed to estimate demographic parameters of unmarked individuals while accounting for imperfect detection. We propose an application of the Dail and Madsen (2011: Biometrics, 67, 577-587) dynamic N-mixture model in a manipulative experiment using a before-after control-impact design (BACI). Specifically, we tested the hypothesis of cavity limitation of a cavity specialist species, the northern flying squirrel, using nest box supplementation on half of 56 trapping sites. Our main purpose was to evaluate the impact of an increase in cavity availability on flying squirrel population dynamics in deciduous stands in northwestern Québec with the dynamic N-mixture model. We compared abundance estimates from this recent approach with those from classic capture-mark-recapture models and generalized linear models. We compared apparent survival estimates with those from Cormack-Jolly-Seber (CJS) models. Average recruitment rate was 6 individuals per site after 4 years. Nevertheless, we found no effect of cavity supplementation on apparent survival and recruitment rates of flying squirrels. Contrary to our expectations, initial abundance was not affected by conifer basal area (food availability) and was negatively affected by snag basal area (cavity availability). Northern flying squirrel population dynamics are not influenced by cavity availability at our deciduous sites. Consequently, we suggest that this species should not be considered an indicator of old forest attributes in our study area, especially in view of apparent wide population fluctuations across years. Abundance estimates from N-mixture models were similar to those from capture-mark-recapture models, although the latter had greater precision. Generalized linear mixed models produced lower abundance estimates, but revealed the same relationship between abundance and snag basal area. Apparent survival estimates from N-mixture models were higher and less precise than those from CJS models. However, N-mixture models can be particularly useful to evaluate management effects on animal populations, especially for species that are difficult to detect in situations where individuals cannot be uniquely identified. They also allow investigating the effects of covariates at the site level, when low recapture rates would require restricting classic CMR analyses to a subset of sites with the most captures.

Thermodynamics versus Kinetics Dichotomy in the Linear Self-Assembly of Mixed Nanoblocks.

PubMed

Ruiz, L; Keten, S

2014-06-05

We report classical and replica exchange molecular dynamics simulations that establish the mechanisms underpinning the growth kinetics of a binary mix of nanorings that form striped nanotubes via self-assembly. A step-growth coalescence model captures the growth process of the nanotubes, which suggests that high aspect ratio nanostructures can grow by obeying the universal laws of self-similar coarsening, contrary to systems that grow through nucleation and elongation. Notably, striped patterns do not depend on specific growth mechanisms, but are governed by tempering conditions that control the likelihood of depropagation and fragmentation.

Quantum calculus of classical vortex images, integrable models and quantum states

NASA Astrophysics Data System (ADS)

Pashaev, Oktay K.

2016-10-01

From two circle theorem described in terms of q-periodic functions, in the limit q→1 we have derived the strip theorem and the stream function for N vortex problem. For regular N-vortex polygon we find compact expression for the velocity of uniform rotation and show that it represents a nonlinear oscillator. We describe q-dispersive extensions of the linear and nonlinear Schrodinger equations, as well as the q-semiclassical expansions in terms of Bernoulli and Euler polynomials. Different kind of q-analytic functions are introduced, including the pq-analytic and the golden analytic functions.

From Networks to Time Series

NASA Astrophysics Data System (ADS)

Shimada, Yutaka; Ikeguchi, Tohru; Shigehara, Takaomi

2012-10-01

In this Letter, we propose a framework to transform a complex network to a time series. The transformation from complex networks to time series is realized by the classical multidimensional scaling. Applying the transformation method to a model proposed by Watts and Strogatz [Nature (London) 393, 440 (1998)], we show that ring lattices are transformed to periodic time series, small-world networks to noisy periodic time series, and random networks to random time series. We also show that these relationships are analytically held by using the circulant-matrix theory and the perturbation theory of linear operators. The results are generalized to several high-dimensional lattices.

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.

Contact stresses in meshing spur gear teeth: Use of an incremental finite element procedure

NASA Technical Reports Server (NTRS)

Hsieh, Chih-Ming; Huston, Ronald L.; Oswald, Fred B.

1992-01-01

Contact stresses in meshing spur gear teeth are examined. The analysis is based upon an incremental finite element procedure that simultaneously determines the stresses in the contact region between the meshing teeth. The teeth themselves are modeled by two dimensional plain strain elements. Friction effects are included, with the friction forces assumed to obey Coulomb's law. The analysis assumes that the displacements are small and that the tooth materials are linearly elastic. The analysis procedure is validated by comparing its results with those for the classical two contacting semicylinders obtained from the Hertz method. Agreement is excellent.

Characterization of the dynamic behaviour of flax fibre reinforced composites using vibration measurements

NASA Astrophysics Data System (ADS)

El-Hafidi, Ali; Birame Gning, Papa; Piezel, Benoit; Fontaine, Stéphane

2017-10-01

Experimental and numerical methods to identify the linear viscoelastic properties of flax fibre reinforced epoxy (FFRE) composite are presented in this study. The method relies on the evolution of storage modulus and loss factor as observed through the frequency response. Free-free symmetrically guided beams were excited on the dynamic range of 10 Hz to 4 kHz with a swept sine excitation focused around their first modes. A fractional derivative Zener model has been identified to predict the complex moduli. A modified ply constitutive law has been then implemented in a classical laminates theory calculation (CLT) routine.

A constrained robust least squares approach for contaminant release history identification

NASA Astrophysics Data System (ADS)

Sun, Alexander Y.; Painter, Scott L.; Wittmeyer, Gordon W.

2006-04-01

Contaminant source identification is an important type of inverse problem in groundwater modeling and is subject to both data and model uncertainty. Model uncertainty was rarely considered in the previous studies. In this work, a robust framework for solving contaminant source recovery problems is introduced. The contaminant source identification problem is first cast into one of solving uncertain linear equations, where the response matrix is constructed using a superposition technique. The formulation presented here is general and is applicable to any porous media flow and transport solvers. The robust least squares (RLS) estimator, which originated in the field of robust identification, directly accounts for errors arising from model uncertainty and has been shown to significantly reduce the sensitivity of the optimal solution to perturbations in model and data. In this work, a new variant of RLS, the constrained robust least squares (CRLS), is formulated for solving uncertain linear equations. CRLS allows for additional constraints, such as nonnegativity, to be imposed. The performance of CRLS is demonstrated through one- and two-dimensional test problems. When the system is ill-conditioned and uncertain, it is found that CRLS gave much better performance than its classical counterpart, the nonnegative least squares. The source identification framework developed in this work thus constitutes a reliable tool for recovering source release histories in real applications.

Classification of longitudinal data through a semiparametric mixed-effects model based on lasso-type estimators.

PubMed

Arribas-Gil, Ana; De la Cruz, Rolando; Lebarbier, Emilie; Meza, Cristian

2015-06-01

We propose a classification method for longitudinal data. The Bayes classifier is classically used to determine a classification rule where the underlying density in each class needs to be well modeled and estimated. This work is motivated by a real dataset of hormone levels measured at the early stages of pregnancy that can be used to predict normal versus abnormal pregnancy outcomes. The proposed model, which is a semiparametric linear mixed-effects model (SLMM), is a particular case of the semiparametric nonlinear mixed-effects class of models (SNMM) in which finite dimensional (fixed effects and variance components) and infinite dimensional (an unknown function) parameters have to be estimated. In SNMM's maximum likelihood estimation is performed iteratively alternating parametric and nonparametric procedures. However, if one can make the assumption that the random effects and the unknown function interact in a linear way, more efficient estimation methods can be used. Our contribution is the proposal of a unified estimation procedure based on a penalized EM-type algorithm. The Expectation and Maximization steps are explicit. In this latter step, the unknown function is estimated in a nonparametric fashion using a lasso-type procedure. A simulation study and an application on real data are performed. © 2015, The International Biometric Society.

Multimode Bose-Hubbard model for quantum dipolar gases in confined geometries

NASA Astrophysics Data System (ADS)

Cartarius, Florian; Minguzzi, Anna; Morigi, Giovanna

2017-06-01

We theoretically consider ultracold polar molecules in a wave guide. The particles are bosons: They experience a periodic potential due to an optical lattice oriented along the wave guide and are polarized by an electric field orthogonal to the guide axis. The array is mechanically unstable by opening the transverse confinement in the direction orthogonal to the polarizing electric field and can undergo a transition to a double-chain (zigzag) structure. For this geometry we derive a multimode generalized Bose-Hubbard model for determining the quantum phases of the gas at the mechanical instability, taking into account the quantum fluctuations in all directions of space. Our model limits the dimension of the numerically relevant Hilbert subspace by means of an appropriate decomposition of the field operator, which is obtained from a field theoretical model of the linear-zigzag instability. We determine the phase diagrams of small systems using exact diagonalization and find that, even for tight transverse confinement, the aspect ratio between the two transverse trap frequencies controls not only the classical but also the quantum properties of the ground state in a nontrivial way. Convergence tests at the linear-zigzag instability demonstrate that our multimode generalized Bose-Hubbard model can catch the essential features of the quantum phases of dipolar gases in confined geometries with a limited computational effort.

Implementation of a channelized Hotelling observer model to assess image quality of x-ray angiography systems.

PubMed

Favazza, Christopher P; Fetterly, Kenneth A; Hangiandreou, Nicholas J; Leng, Shuai; Schueler, Beth A

2015-01-01

Evaluation of flat-panel angiography equipment through conventional image quality metrics is limited by the scope of standard spatial-domain image quality metric(s), such as contrast-to-noise ratio and spatial resolution, or by restricted access to appropriate data to calculate Fourier domain measurements, such as modulation transfer function, noise power spectrum, and detective quantum efficiency. Observer models have been shown capable of overcoming these limitations and are able to comprehensively evaluate medical-imaging systems. We present a spatial domain-based channelized Hotelling observer model to calculate the detectability index (DI) of our different sized disks and compare the performance of different imaging conditions and angiography systems. When appropriate, changes in DIs were compared to expectations based on the classical Rose model of signal detection to assess linearity of the model with quantum signal-to-noise ratio (SNR) theory. For these experiments, the estimated uncertainty of the DIs was less than 3%, allowing for precise comparison of imaging systems or conditions. For most experimental variables, DI changes were linear with expectations based on quantum SNR theory. DIs calculated for the smallest objects demonstrated nonlinearity with quantum SNR theory due to system blur. Two angiography systems with different detector element sizes were shown to perform similarly across the majority of the detection tasks.

Modeling daily soil temperature over diverse climate conditions in Iran—a comparison of multiple linear regression and support vector regression techniques

NASA Astrophysics Data System (ADS)

Delbari, Masoomeh; Sharifazari, Salman; Mohammadi, Ehsan

2018-02-01

The knowledge of soil temperature at different depths is important for agricultural industry and for understanding climate change. The aim of this study is to evaluate the performance of a support vector regression (SVR)-based model in estimating daily soil temperature at 10, 30 and 100 cm depth at different climate conditions over Iran. The obtained results were compared to those obtained from a more classical multiple linear regression (MLR) model. The correlation sensitivity for the input combinations and periodicity effect were also investigated. Climatic data used as inputs to the models were minimum and maximum air temperature, solar radiation, relative humidity, dew point, and the atmospheric pressure (reduced to see level), collected from five synoptic stations Kerman, Ahvaz, Tabriz, Saghez, and Rasht located respectively in the hyper-arid, arid, semi-arid, Mediterranean, and hyper-humid climate conditions. According to the results, the performance of both MLR and SVR models was quite well at surface layer, i.e., 10-cm depth. However, SVR performed better than MLR in estimating soil temperature at deeper layers especially 100 cm depth. Moreover, both models performed better in humid climate condition than arid and hyper-arid areas. Further, adding a periodicity component into the modeling process considerably improved the models' performance especially in the case of SVR.

A new modal superposition method for nonlinear vibration analysis of structures using hybrid mode shapes

NASA Astrophysics Data System (ADS)

Ferhatoglu, Erhan; Cigeroglu, Ender; Özgüven, H. Nevzat

2018-07-01

In this paper, a new modal superposition method based on a hybrid mode shape concept is developed for the determination of steady state vibration response of nonlinear structures. The method is developed specifically for systems having nonlinearities where the stiffness of the system may take different limiting values. Stiffness variation of these nonlinear systems enables one to define different linear systems corresponding to each value of the limiting equivalent stiffness. Moreover, the response of the nonlinear system is bounded by the confinement of these linear systems. In this study, a modal superposition method utilizing novel hybrid mode shapes which are defined as linear combinations of the modal vectors of the limiting linear systems is proposed to determine periodic response of nonlinear systems. In this method the response of the nonlinear system is written in terms of hybrid modes instead of the modes of the underlying linear system. This provides decrease of the number of modes that should be retained for an accurate solution, which in turn reduces the number of nonlinear equations to be solved. In this way, computational time for response calculation is directly curtailed. In the solution, the equations of motion are converted to a set of nonlinear algebraic equations by using describing function approach, and the numerical solution is obtained by using Newton's method with arc-length continuation. The method developed is applied on two different systems: a lumped parameter model and a finite element model. Several case studies are performed and the accuracy and computational efficiency of the proposed modal superposition method with hybrid mode shapes are compared with those of the classical modal superposition method which utilizes the mode shapes of the underlying linear system.

Application of Linear Discriminant Analysis in Dimensionality Reduction for Hand Motion Classification

NASA Astrophysics Data System (ADS)

Phinyomark, A.; Hu, H.; Phukpattaranont, P.; Limsakul, C.

2012-01-01

The classification of upper-limb movements based on surface electromyography (EMG) signals is an important issue in the control of assistive devices and rehabilitation systems. Increasing the number of EMG channels and features in order to increase the number of control commands can yield a high dimensional feature vector. To cope with the accuracy and computation problems associated with high dimensionality, it is commonplace to apply a processing step that transforms the data to a space of significantly lower dimensions with only a limited loss of useful information. Linear discriminant analysis (LDA) has been successfully applied as an EMG feature projection method. Recently, a number of extended LDA-based algorithms have been proposed, which are more competitive in terms of both classification accuracy and computational costs/times with classical LDA. This paper presents the findings of a comparative study of classical LDA and five extended LDA methods. From a quantitative comparison based on seven multi-feature sets, three extended LDA-based algorithms, consisting of uncorrelated LDA, orthogonal LDA and orthogonal fuzzy neighborhood discriminant analysis, produce better class separability when compared with a baseline system (without feature projection), principle component analysis (PCA), and classical LDA. Based on a 7-dimension time domain and time-scale feature vectors, these methods achieved respectively 95.2% and 93.2% classification accuracy by using a linear discriminant classifier.

Notes on quantitative structure-properties relationships (QSPR) (1): A discussion on a QSPR dimensionality paradox (QSPR DP) and its quantum resolution.

PubMed

Carbó-Dorca, Ramon; Gallegos, Ana; Sánchez, Angel J

2009-05-01

Classical quantitative structure-properties relationship (QSPR) statistical techniques unavoidably present an inherent paradoxical computational context. They rely on the definition of a Gram matrix in descriptor spaces, which is used afterwards to reduce the original dimension via several possible kinds of algebraic manipulations. From there, effective models for the computation of unknown properties of known molecular structures are obtained. However, the reduced descriptor dimension causes linear dependence within the set of discrete vector molecular representations, leading to positive semi-definite Gram matrices in molecular spaces. To resolve this QSPR dimensionality paradox (QSPR DP) here is proposed to adopt as starting point the quantum QSPR (QQSPR) computational framework perspective, where density functions act as infinite dimensional descriptors. The fundamental QQSPR equation, deduced from employing quantum expectation value numerical evaluation, can be approximately solved in order to obtain models exempt of the QSPR DP. The substitution of the quantum similarity matrix by an empirical Gram matrix in molecular spaces, build up with the original non manipulated discrete molecular descriptor vectors, permits to obtain classical QSPR models with the same characteristics as in QQSPR, that is: possessing a certain degree of causality and explicitly independent of the descriptor dimension. 2008 Wiley Periodicals, Inc.

Viscous propulsion in active transversely isotropic media

NASA Astrophysics Data System (ADS)

Cupples, Gemma; Dyson, Rosemary; Smith, David

2017-11-01

Taylor's swimming sheet is a classical model of microscale propulsion and pumping. Many biological fluids and substances are fibrous, having a preferred direction in their microstructure; for example cervical mucus. To understand how these effects modify viscous propulsion, we extend Taylor's classical model of small-amplitude viscous propulsion of a `swimming sheet' via the transversely-isotropic fluid model of Ericksen, which is linear in strain rate and possesses a distinguished direction. The energetic costs of swimming are significantly altered by all rheological parameters and the initial fibre angle. Propulsion in a passive transversely-isotropic fluid enhances mean rate of working, independent of the initial fibre orientation. In this regime the mean swimming velocity is unchanged from the Newtonian case. The effect of fibre tension, or alternatively a stresslet characterising an active fluid, is also considered. This stress introduces an angular dependence and dramatically changes the streamlines and flow field; fibres aligned with the swimming direction increase the energetic demands of the sheet. The constant fibre stress may result in a reversal of the mean swimming velocity and a negative mean rate of working if sufficiently large relative to the other parameters. Funding is provided by a Biotechnology and Biological Sciences Research Council (BBSRC) Industrial CASE Studentship (BB/L015587/1).

Equilibrium and initial linear stability analysis of liquid metal falling film flows in a varying spanwise magnetic field

NASA Astrophysics Data System (ADS)

Gao, D.; Morley, N. B.

2002-12-01

A 2D model for MHD free surface flow in a spanwise field is developed. The model, designed to simulate film flows of liquid metals in future thermo­nuclear fusion reactors, considers an applied spanwise magnetic field with spatial and temporal variation and an applied streamwise external current. A special case - a thin falling film flow in spanwise magnetic field with constant gradient and constant applied external streamwise current, is here investigated in depth to gain insight into the behavior of the MHD film flow. The fully developed flow solution is derived and initial linear stability analysis is performed for this special case. It is seen that the velocity profile is significantly changed due to the presence of the MHD effect, resulting in the free surface analog of the classic M-shape velocity profile seen in developing pipe flows in a field gradient. The field gradient is also seen to destabilize the film flow under most conditions. The effect of external current depends on the relative direction of the field gradient to the current direction. By controlling the magnitude of an external current, it is possible to obtain a linearly stable falling film under these magnetic field conditions. Tables 1, Figs 12, Refs 20.

Feedback stabilization of an oscillating vertical cylinder by POD Reduced-Order Model

NASA Astrophysics Data System (ADS)

Tissot, Gilles; Cordier, Laurent; Noack, Bernd R.

2015-01-01

The objective is to demonstrate the use of reduced-order models (ROM) based on proper orthogonal decomposition (POD) to stabilize the flow over a vertically oscillating circular cylinder in the laminar regime (Reynolds number equal to 60). The 2D Navier-Stokes equations are first solved with a finite element method, in which the moving cylinder is introduced via an ALE method. Since in fluid-structure interaction, the POD algorithm cannot be applied directly, we implemented the fictitious domain method of Glowinski et al. [1] where the solid domain is treated as a fluid undergoing an additional constraint. The POD-ROM is classically obtained by projecting the Navier-Stokes equations onto the first POD modes. At this level, the cylinder displacement is enforced in the POD-ROM through the introduction of Lagrange multipliers. For determining the optimal vertical velocity of the cylinder, a linear quadratic regulator framework is employed. After linearization of the POD-ROM around the steady flow state, the optimal linear feedback gain is obtained as solution of a generalized algebraic Riccati equation. Finally, when the optimal feedback control is applied, it is shown that the flow converges rapidly to the steady state. In addition, a vanishing control is obtained proving the efficiency of the control approach.

Application of variational and Galerkin equations to linear and nonlinear finite element analysis

NASA Technical Reports Server (NTRS)

Yu, Y.-Y.

1974-01-01

The paper discusses the application of the variational equation to nonlinear finite element analysis. The problem of beam vibration with large deflection is considered. The variational equation is shown to be flexible in both the solution of a general problem and in the finite element formulation. Difficulties are shown to arise when Galerkin's equations are used in the consideration of the finite element formulation of two-dimensional linear elasticity and of the linear classical beam.

Multilevel Preconditioners for Reaction-Diffusion Problems with Discontinuous Coefficients

DOE PAGES

Kolev, Tzanio V.; Xu, Jinchao; Zhu, Yunrong

2015-08-23

In this study, we extend some of the multilevel convergence results obtained by Xu and Zhu, to the case of second order linear reaction-diffusion equations. Specifically, we consider the multilevel preconditioners for solving the linear systems arising from the linear finite element approximation of the problem, where both diffusion and reaction coefficients are piecewise-constant functions. We discuss in detail the influence of both the discontinuous reaction and diffusion coefficients to the performance of the classical BPX and multigrid V-cycle preconditioner.

On the relationship between the classical Dicke-Jaynes-Cummings-Gaudin model and the nonlinear Schroedinger equation

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

Du, Dianlou; Geng, Xue

2013-05-15

In this paper, the relationship between the classical Dicke-Jaynes-Cummings-Gaudin (DJCG) model and the nonlinear Schroedinger (NLS) equation is studied. It is shown that the classical DJCG model is equivalent to a stationary NLS equation. Moreover, the standard NLS equation can be solved by the classical DJCG model and a suitably chosen higher order flow. Further, it is also shown that classical DJCG model can be transformed into the classical Gaudin spin model in an external magnetic field through a deformation of Lax matrix. Finally, the separated variables are constructed on the common level sets of Casimir functions and the generalizedmore » action-angle coordinates are introduced via the Hamilton-Jacobi equation.« less

A Regression Framework for Effect Size Assessments in Longitudinal Modeling of Group Differences

PubMed Central

Feingold, Alan

2013-01-01

The use of growth modeling analysis (GMA)--particularly multilevel analysis and latent growth modeling--to test the significance of intervention effects has increased exponentially in prevention science, clinical psychology, and psychiatry over the past 15 years. Model-based effect sizes for differences in means between two independent groups in GMA can be expressed in the same metric (Cohen’s d) commonly used in classical analysis and meta-analysis. This article first reviews conceptual issues regarding calculation of d for findings from GMA and then introduces an integrative framework for effect size assessments that subsumes GMA. The new approach uses the structure of the linear regression model, from which effect sizes for findings from diverse cross-sectional and longitudinal analyses can be calculated with familiar statistics, such as the regression coefficient, the standard deviation of the dependent measure, and study duration. PMID:23956615

Predicting perceptual quality of images in realistic scenario using deep filter banks

NASA Astrophysics Data System (ADS)

Zhang, Weixia; Yan, Jia; Hu, Shiyong; Ma, Yang; Deng, Dexiang

2018-03-01

Classical image perceptual quality assessment models usually resort to natural scene statistic methods, which are based on an assumption that certain reliable statistical regularities hold on undistorted images and will be corrupted by introduced distortions. However, these models usually fail to accurately predict degradation severity of images in realistic scenarios since complex, multiple, and interactive authentic distortions usually appear on them. We propose a quality prediction model based on convolutional neural network. Quality-aware features extracted from filter banks of multiple convolutional layers are aggregated into the image representation. Furthermore, an easy-to-implement and effective feature selection strategy is used to further refine the image representation and finally a linear support vector regression model is trained to map image representation into images' subjective perceptual quality scores. The experimental results on benchmark databases present the effectiveness and generalizability of the proposed model.

On the derivation of linear irreversible thermodynamics for classical fluids

PubMed Central

Theodosopulu, M.; Grecos, A.; Prigogine, I.

1978-01-01

We consider the microscopic derivation of the linearized hydrodynamic equations for an arbitrary simple fluid. Our discussion is based on the concept of hydrodynamical modes, and use is made of the ideas and methods of the theory of subdynamics. We also show that this analysis leads to the Gibbs relation for the entropy of the system. PMID:16592516

Feature Extraction of High-Dimensional Structures for Exploratory Analytics

DTIC Science & Technology

2013-04-01

Comparison of Euclidean vs. geodesic distance. LDRs use metric based on the Euclidean distance between two points, while the NLDRs are based on...geodesic distance. An NLDR successfully unrolls the curved manifold, whereas an LDR fails. ...........................3 1 1. Introduction An...and classical metric multidimensional scaling, are a linear DR ( LDR ). An LDR is based on a linear combination of

Lagrangians and Euler morphisms from connections on the frame bundle

NASA Astrophysics Data System (ADS)

Kurek, J.; Mikulski, W. M.

2011-07-01

We classify all natural operators transforming torsion free classical linear connections ∇ on m-dimensional manifolds M into r-th order Lagrangians λ(∇) and Euler morphisms E(∇) on the linear frame bundle P1M. We also briefly write how this classification result can be generalized on higher order frame bundles PkM instead of P1M.

Meissner effect in normal-superconducting proximity-contact double layers

NASA Astrophysics Data System (ADS)

Higashitani, Seiji; Nagai, Katsuhiko

1995-02-01

The Meissner effect in normal-superconducting proximity-contact double layers is discussed in the clean limit. The diamagnetic current is calculated using the quasi-classical Green's function. We obtain the quasi-classical Green's function linear in the vector potential in the proximity-contact double layers with a finite reflection coefficient at the interface. It is found that the diamagnetic current in the clean normal layer is constant in space, therefore, the magnetic field linearly decreases in the clean normal layer. We give an explicit expression for the screening length in the clean normal layer and study its temperature dependence. We show that the temperature dependence in the clean normal layer is considerably different from that in the dirty normal layer and agrees with a recent experiment in Au-Nb system.

Topology Counts: Force Distributions in Circular Spring Networks.

PubMed

Heidemann, Knut M; Sageman-Furnas, Andrew O; Sharma, Abhinav; Rehfeldt, Florian; Schmidt, Christoph F; Wardetzky, Max

2018-02-09

Filamentous polymer networks govern the mechanical properties of many biological materials. Force distributions within these networks are typically highly inhomogeneous, and, although the importance of force distributions for structural properties is well recognized, they are far from being understood quantitatively. Using a combination of probabilistic and graph-theoretical techniques, we derive force distributions in a model system consisting of ensembles of random linear spring networks on a circle. We show that characteristic quantities, such as the mean and variance of the force supported by individual springs, can be derived explicitly in terms of only two parameters: (i) average connectivity and (ii) number of nodes. Our analysis shows that a classical mean-field approach fails to capture these characteristic quantities correctly. In contrast, we demonstrate that network topology is a crucial determinant of force distributions in an elastic spring network. Our results for 1D linear spring networks readily generalize to arbitrary dimensions.

Nonlinear versus Ordinary Adaptive Control of Continuous Stirred-Tank Reactor

PubMed Central

Dostal, Petr

2015-01-01

Unfortunately, the major group of the systems in industry has nonlinear behavior and control of such processes with conventional control approaches with fixed parameters causes problems and suboptimal or unstable control results. An adaptive control is one way to how we can cope with nonlinearity of the system. This contribution compares classic adaptive control and its modification with Wiener system. This configuration divides nonlinear controller into the dynamic linear part and the static nonlinear part. The dynamic linear part is constructed with the use of polynomial synthesis together with the pole-placement method and the spectral factorization. The static nonlinear part uses static analysis of the controlled plant for introducing the mathematical nonlinear description of the relation between the controlled output and the change of the control input. Proposed controller is tested by the simulations on the mathematical model of the continuous stirred-tank reactor with cooling in the jacket as a typical nonlinear system. PMID:26346878

Non-Classical Smoothening of Nano-Scale Surface Corrugations

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

Aziz, Michael J.; Chason, Eric; Erlebacher, Jonah

1999-05-20

We report the first experimental observation of non-classical morphological equilibration of a corrugated crystalline surface. Periodic rippled structures with wavelengths of 290-550 nm were made on Si(OO1) by sputter rippling and then annealed at 650 - 750 °C. In contrast to the classical exponential decay with time, the ripple amplitude, A {lambda}(t), followed an inverse linear decay, A {lambda}(t)= A {lambda}(0)/(1 +k {lambda}t), agreeing with a prediction of Ozdemir and Zangwill. We measure the activation energy for surface relaxation to be 1.6±0.2 eV, consistent with an interpretation that dimers mediate transport.

Hydrostatic Stress Effect on the Yield Behavior of Inconel 100

NASA Technical Reports Server (NTRS)

Allen, Phillip A.; Wilson, Christopher D.

2003-01-01

Classical metal plasticity theory assumes that hydrostatic stress has negligible effect on the yield and postyield behavior of metals. Recent reexaminations of classical theory have revealed a significant effect of hydrostatic stress on the yield behavior of various geometries. Fatigue tests and nonlinear finite element analyses (FEA) of Inconel 100 (IN100) equal-arm bend specimens and new monotonic tests and nonlinear finite element analyses of IN100 smooth tension, smooth compression, and double-edge notch tension (DENT) test specimens have revealed the effect of internal hydrostatic tensile stresses on yielding. Nonlinear FEA using the von Mises (yielding is independent of hydrostatic stress) and the Drucker-Prager (yielding is linearly dependent on hydrostatic stress) yield functions were performed. A new FEA constitutive model was developed that incorporates a pressure-dependent yield function with combined multilinear kinematic and multilinear isotropic hardening using the ABAQUS user subroutine (UMAT) utility. In all monotonic tensile test cases, the von Mises constitutive model, overestimated the load for a given displacement or strain. Considering the failure displacements or strains for the DENT specimen, the Drucker-Prager FEM s predicted loads that were approximately 3% lower than the von Mises values. For the failure loads, the Drucker Prager FEM s predicted strains that were up to 35% greater than the von Mises values. Both the Drucker-Prager model and the von Mises model performed equally-well in simulating the equal-arm bend fatigue test.

Quantum annealing versus classical machine learning applied to a simplified computational biology problem

NASA Astrophysics Data System (ADS)

Li, Richard Y.; Di Felice, Rosa; Rohs, Remo; Lidar, Daniel A.

2018-03-01

Transcription factors regulate gene expression, but how these proteins recognize and specifically bind to their DNA targets is still debated. Machine learning models are effective means to reveal interaction mechanisms. Here we studied the ability of a quantum machine learning approach to classify and rank binding affinities. Using simplified data sets of a small number of DNA sequences derived from actual binding affinity experiments, we trained a commercially available quantum annealer to classify and rank transcription factor binding. The results were compared to state-of-the-art classical approaches for the same simplified data sets, including simulated annealing, simulated quantum annealing, multiple linear regression, LASSO, and extreme gradient boosting. Despite technological limitations, we find a slight advantage in classification performance and nearly equal ranking performance using the quantum annealer for these fairly small training data sets. Thus, we propose that quantum annealing might be an effective method to implement machine learning for certain computational biology problems.

Space-time models based on random fields with local interactions

NASA Astrophysics Data System (ADS)

Hristopulos, Dionissios T.; Tsantili, Ivi C.

2016-08-01

The analysis of space-time data from complex, real-life phenomena requires the use of flexible and physically motivated covariance functions. In most cases, it is not possible to explicitly solve the equations of motion for the fields or the respective covariance functions. In the statistical literature, covariance functions are often based on mathematical constructions. In this paper, we propose deriving space-time covariance functions by solving “effective equations of motion”, which can be used as statistical representations of systems with diffusive behavior. In particular, we propose to formulate space-time covariance functions based on an equilibrium effective Hamiltonian using the linear response theory. The effective space-time dynamics is then generated by a stochastic perturbation around the equilibrium point of the classical field Hamiltonian leading to an associated Langevin equation. We employ a Hamiltonian which extends the classical Gaussian field theory by including a curvature term and leads to a diffusive Langevin equation. Finally, we derive new forms of space-time covariance functions.

New modified multi-level residue harmonic balance method for solving nonlinearly vibrating double-beam problem

NASA Astrophysics Data System (ADS)

Rahman, Md. Saifur; Lee, Yiu-Yin

2017-10-01

In this study, a new modified multi-level residue harmonic balance method is presented and adopted to investigate the forced nonlinear vibrations of axially loaded double beams. Although numerous nonlinear beam or linear double-beam problems have been tackled and solved, there have been few studies of this nonlinear double-beam problem. The geometric nonlinear formulations for a double-beam model are developed. The main advantage of the proposed method is that a set of decoupled nonlinear algebraic equations is generated at each solution level. This heavily reduces the computational effort compared with solving the coupled nonlinear algebraic equations generated in the classical harmonic balance method. The proposed method can generate the higher-level nonlinear solutions that are neglected by the previous modified harmonic balance method. The results from the proposed method agree reasonably well with those from the classical harmonic balance method. The effects of damping, axial force, and excitation magnitude on the nonlinear vibrational behaviour are examined.

Compressive Spectral Method for the Simulation of the Nonlinear Gravity Waves

PubMed Central

Bayındır, Cihan

2016-01-01

In this paper an approach for decreasing the computational effort required for the spectral simulations of the fully nonlinear ocean waves is introduced. The proposed approach utilizes the compressive sampling algorithm and depends on the idea of using a smaller number of spectral components compared to the classical spectral method. After performing the time integration with a smaller number of spectral components and using the compressive sampling technique, it is shown that the ocean wave field can be reconstructed with a significantly better efficiency compared to the classical spectral method. For the sparse ocean wave model in the frequency domain the fully nonlinear ocean waves with Jonswap spectrum is considered. By implementation of a high-order spectral method it is shown that the proposed methodology can simulate the linear and the fully nonlinear ocean waves with negligible difference in the accuracy and with a great efficiency by reducing the computation time significantly especially for large time evolutions. PMID:26911357

Structure and coherence of reasoning ability in Down Syndrome adults and typically developing children.

PubMed

Natsopoulo, D; Christou, C; Koutselini, M; Raftopoulos, A; Karefillidou, C

2002-01-01

The present study investigates the ability of Down Syndrome (DS) adults to reason: (a) deductively with transitivity (linear and reverse relations) and categorical syllogisms (all-some relations); (b) inductively with classical verbal analogies and non-verbal analogical reasoning (Raven's Coloured Progressive Matrices); and (c) to retain information in short-term memory. The results have shown that: (i) The Down Syndrome adults did not differ from typically developing children, matched on expressive and verbal ability, in transitivity and non-verbal analogical thinking; (ii) they differed in categorical reasoning, classical verbal analogies and short-term memory. Application of a structural model demonstrated that, despite differences in slope means in the three measures, the structure of functioning within-and-across all domains of cognition tests and its growth pattern, equally reliable and coherent, goes in parallel for the Down Syndrome adults and the typically developing children. The results are discussed within the context of the two-group developmental and difference approach.

The Prediction Properties of Inverse and Reverse Regression for the Simple Linear Calibration Problem

NASA Technical Reports Server (NTRS)

Parker, Peter A.; Geoffrey, Vining G.; Wilson, Sara R.; Szarka, John L., III; Johnson, Nels G.

2010-01-01

The calibration of measurement systems is a fundamental but under-studied problem within industrial statistics. The origins of this problem go back to basic chemical analysis based on NIST standards. In today's world these issues extend to mechanical, electrical, and materials engineering. Often, these new scenarios do not provide "gold standards" such as the standard weights provided by NIST. This paper considers the classic "forward regression followed by inverse regression" approach. In this approach the initial experiment treats the "standards" as the regressor and the observed values as the response to calibrate the instrument. The analyst then must invert the resulting regression model in order to use the instrument to make actual measurements in practice. This paper compares this classical approach to "reverse regression," which treats the standards as the response and the observed measurements as the regressor in the calibration experiment. Such an approach is intuitively appealing because it avoids the need for the inverse regression. However, it also violates some of the basic regression assumptions.

Lagrangian geometrical optics of nonadiabatic vector waves and spin particles

DOE PAGES

Ruiz, D. E.; Dodin, I. Y.

2015-07-29

Linear vector waves, both quantum and classical, experience polarization-driven bending of ray trajectories and polarization dynamics that can be interpreted as the precession of the "wave spin". Here, both phenomena are governed by an effective gauge Hamiltonian vanishing in leading-order geometrical optics. This gauge Hamiltonian can be recognized as a generalization of the Stern-Gerlach Hamiltonian that is commonly known for spin-1/2 quantum particles. The corresponding reduced Lagrangians for continuous nondissipative waves and their geometrical-optics rays are derived from the fundamental wave Lagrangian. The resulting Euler-Lagrange equations can describe simultaneous interactions of N resonant modes, where N is arbitrary, and leadmore » to equations for the wave spin, which happens to be an (N 2 - 1)-dimensional spin vector. As a special case, classical equations for a Dirac particle (N = 2) are deduced formally, without introducing additional postulates or interpretations, from the Dirac quantum Lagrangian with the Pauli term. The model reproduces the Bargmann-Michel-Telegdi equations with added Stern-Gerlach force.« less

Symmetry aspects in emergent quantum mechanics

NASA Astrophysics Data System (ADS)

Elze, Hans-Thomas

2009-06-01

We discuss an explicit realization of the dissipative dynamics anticipated in the proof of 't Hooft's existence theorem, which states that 'For any quantum system there exists at least one deterministic model that reproduces all its dynamics after prequantization'. - There is an energy-parity symmetry hidden in the Liouville equation, which mimics the Kaplan-Sundrum protective symmetry for the cosmological constant. This symmetry may be broken by the coarse-graining inherent in physics at scales much larger than the Planck length. We correspondingly modify classical ensemble theory by incorporating dissipative fluctuations (information loss) - which are caused by discrete spacetime continually 'measuring' matter. In this way, aspects of quantum mechanics, such as the von Neumann equation, including a Lindblad term, arise dynamically and expectations of observables agree with the Born rule. However, the resulting quantum coherence is accompanied by an intrinsic decoherence and continuous localization mechanism. Our proposal leads towards a theory that is linear and local at the quantum mechanical level, but the relation to the underlying classical degrees of freedom is nonlocal.

Multi-species coexistence in Lotka-Volterra competitive systems with crowding effects.

PubMed

Gavina, Maica Krizna A; Tahara, Takeru; Tainaka, Kei-Ichi; Ito, Hiromu; Morita, Satoru; Ichinose, Genki; Okabe, Takuya; Togashi, Tatsuya; Nagatani, Takashi; Yoshimura, Jin

2018-01-19

Classical Lotka-Volterra (LV) competition equation has shown that coexistence of competitive species is only possible when intraspecific competition is stronger than interspecific competition, i.e., the species inhibit their own growth more than the growth of the other species. Note that density effect is assumed to be linear in a classical LV equation. In contrast, in wild populations we can observed that mortality rate often increases when population density is very high, known as crowding effects. Under this perspective, the aggregation models of competitive species have been developed, adding the additional reduction in growth rates at high population densities. This study shows that the coexistence of a few species is promoted. However, an unsolved question is the coexistence of many competitive species often observed in natural communities. Here, we build an LV competition equation with a nonlinear crowding effect. Our results show that under a weak crowding effect, stable coexistence of many species becomes plausible, unlike the previous aggregation model. An analysis indicates that increased mortality rate under high density works as elevated intraspecific competition leading to the coexistence. This may be another mechanism for the coexistence of many competitive species leading high species diversity in nature.

Twin lead ballistic conductor based on nanoribbon edge transport

NASA Astrophysics Data System (ADS)

Konôpka, Martin; Dieška, Peter

2018-03-01

If a device like a graphene nanoribbon (GNR) has all its four corners attached to electric current leads, the device becomes a quantum junction through which two electrical circuits can interact. We study such system theoretically for stationary currents. The 4-point energy-dependent conductance matrix of the nanostructure and the classical resistors in the circuits are parameters of the model. The two bias voltages in the circuits are the control variables of the studied system while the electrochemical potentials at the device's terminals are non-trivially dependent on the voltages. For the special case of the linear-response regime analytical formulae for the operation of the coupled quantum-classical device are derived and applied. For higher bias voltages numerical solutions are obtained. The effects of non-equilibrium Fermi levels are captured using a recursive algorithm in which self-consistency between the electrochemical potentials and the currents is reached within few iterations. The developed approach allows to study scenarios ranging from independent circuits to strongly coupled ones. For the chosen model of the GNR with highly conductive zigzag edges we determine the regime in which the single device carries two almost independent currents.

Bayesian model reduction and empirical Bayes for group (DCM) studies

PubMed Central

Friston, Karl J.; Litvak, Vladimir; Oswal, Ashwini; Razi, Adeel; Stephan, Klaas E.; van Wijk, Bernadette C.M.; Ziegler, Gabriel; Zeidman, Peter

2016-01-01

This technical note describes some Bayesian procedures for the analysis of group studies that use nonlinear models at the first (within-subject) level – e.g., dynamic causal models – and linear models at subsequent (between-subject) levels. Its focus is on using Bayesian model reduction to finesse the inversion of multiple models of a single dataset or a single (hierarchical or empirical Bayes) model of multiple datasets. These applications of Bayesian model reduction allow one to consider parametric random effects and make inferences about group effects very efficiently (in a few seconds). We provide the relatively straightforward theoretical background to these procedures and illustrate their application using a worked example. This example uses a simulated mismatch negativity study of schizophrenia. We illustrate the robustness of Bayesian model reduction to violations of the (commonly used) Laplace assumption in dynamic causal modelling and show how its recursive application can facilitate both classical and Bayesian inference about group differences. Finally, we consider the application of these empirical Bayesian procedures to classification and prediction. PMID:26569570

Optimization of the Bridgman crystal growth process

NASA Astrophysics Data System (ADS)

Margulies, M.; Witomski, P.; Duffar, T.

2004-05-01

A numerical optimization method of the vertical Bridgman growth configuration is presented and developed. It permits to optimize the furnace temperature field and the pulling rate versus time in order to decrease the radial thermal gradients in the sample. Some constraints are also included in order to insure physically realistic results. The model includes the two classical non-linearities associated to crystal growth processes, the radiative thermal exchange and the release of latent heat at the solid-liquid interface. The mathematical analysis and development of the problem is shortly described. On some examples, it is shown that the method works in a satisfactory way; however the results are dependent on the numerical parameters. Improvements of the optimization model, on the physical and numerical point of view, are suggested.

Poisson sigma models, reduction and nonlinear gauge theories

NASA Astrophysics Data System (ADS)

Signori, Daniele

This dissertation comprises two main lines of research. Firstly, we study non-linear gauge theories for principal bundles, where the structure group is replaced by a Lie groupoid. We follow the approach of Moerdijk-Mrcun and establish its relation with the existing physics literature. In particular, we derive a new formula for the gauge transformation which closely resembles and generalizes the classical formulas found in Yang Mills gauge theories. Secondly, we give a field theoretic interpretation of the of the BRST (Becchi-Rouet-Stora-Tyutin) and BFV (Batalin-Fradkin-Vilkovisky) methods for the reduction of coisotropic submanifolds of Poisson manifolds. The generalized Poisson sigma models that we define are related to the quantization deformation problems of coisotropic submanifolds using homotopical algebras.

Supersymmetry and fermionic modes in an oscillon background

NASA Astrophysics Data System (ADS)

Correa, R. A. C.; Ospedal, L. P. R.; de Paula, W.; Helayël-Neto, J. A.

2018-05-01

The excitations referred to as oscillons are long-lived time-dependent field configurations which emerge dynamically from non-linear field theories. Such long-lived solutions are of interest in applications that include systems of Condensed Matter Physics, the Standard Model of Particle Physics, Lorentz-symmetry violating scenarios and Cosmology. In this work, we show how oscillons may be accommodated in a supersymmetric scenario. We adopt as our framework simple (N = 1) supersymmetry in D = 1 + 1 dimensions. We focus on the bosonic sector with oscillon configurations and their (classical) effects on the corresponding fermionic modes, (supersymmetric) partners of the oscillons. The particular model we adopt to pursue our investigation displays cubic superfield which, in the physical scalar sector, corresponds to the usual quartic self-coupling.

The optimal location of piezoelectric actuators and sensors for vibration control of plates

NASA Astrophysics Data System (ADS)

Kumar, K. Ramesh; Narayanan, S.

2007-12-01

This paper considers the optimal placement of collocated piezoelectric actuator-sensor pairs on a thin plate using a model-based linear quadratic regulator (LQR) controller. LQR performance is taken as objective for finding the optimal location of sensor-actuator pairs. The problem is formulated using the finite element method (FEM) as multi-input-multi-output (MIMO) model control. The discrete optimal sensor and actuator location problem is formulated in the framework of a zero-one optimization problem. A genetic algorithm (GA) is used to solve the zero-one optimization problem. Different classical control strategies like direct proportional feedback, constant-gain negative velocity feedback and the LQR optimal control scheme are applied to study the control effectiveness.

On the usefulness of 'what' and 'where' pathways in vision.

PubMed

de Haan, Edward H F; Cowey, Alan

2011-10-01

The primate visual brain is classically portrayed as a large number of separate 'maps', each dedicated to the processing of specific visual cues, such as colour, motion or faces and their many features. In order to understand this fractionated architecture, the concept of cortical 'pathways' or 'streams' was introduced. In the currently prevailing view, the different maps are organised hierarchically into two major pathways, one involved in recognition and memory (the ventral stream or 'what' pathway) and the other in the programming of action (the dorsal stream or 'where' pathway). In this review, we question this heuristically influential but potentially misleading linear hierarchical pathway model and argue instead for a 'patchwork' or network model. Copyright © 2011 Elsevier Ltd. All rights reserved.

Transient pressure analysis of a volume fracturing well in fractured tight oil reservoirs

NASA Astrophysics Data System (ADS)

Lu, Cheng; Wang, Jiahang; Zhang, Cong; Cheng, Minhua; Wang, Xiaodong; Dong, Wenxiu; Zhou, Yingfang

2017-12-01

This paper presents a semi-analytical model to simulate transient pressure curves for a vertical well with a reconstructed fracture network in fractured tight oil reservoirs. In the proposed model, the reservoir is a composite system and contains two regions. The inner region is described as a formation with a finite conductivity hydraulic fracture network and the flow in the fracture is assumed to be linear, while the outer region is modeled using the classical Warren-Root model where radial flow is applied. The transient pressure curves of a vertical well in the proposed reservoir model are calculated semi-analytically using the Laplace transform and Stehfest numerical inversion. As shown in the type curves, the flow is divided into several regimes: (a) linear flow in artificial main fractures; (b) coupled boundary flow; (c) early linear flow in a fractured formation; (d) mid radial flow in the semi-fractures of the formation; (e) mid radial flow or pseudo steady flow; (f) mid cross-flow; (g) closed boundary flow. Based on our newly proposed model, the effects of some sensitive parameters, such as elastic storativity ratio, cross-flow coefficient, fracture conductivity and skin factor, on the type curves were also analyzed extensively. The simulated type curves show that for a vertical fractured well in a tight reservoir, the elastic storativity ratios and crossflow coefficients affect the time and the degree of crossflow respectively. The pressure loss increases with an increase in the fracture conductivity. To a certain extent, the effect of the fracture conductivity is more obvious than that of the half length of the fracture on improving the production effect. With an increase in the wellbore storage coefficient, the fluid compressibility is so large that it might cover the early stage fracturing characteristics. Linear or bilinear flow may not be recognized, and the pressure and pressure derivative gradually shift to the right. With an increase in the skin effect, the pressure loss increases gradually.

Physical aspects of heat generation/absorption in the second grade fluid flow due to Riga plate: Application of Cattaneo-Christov approach

NASA Astrophysics Data System (ADS)

Anjum, Aisha; Mir, N. A.; Farooq, M.; Javed, M.; Ahmad, S.; Malik, M. Y.; Alshomrani, A. S.

2018-06-01

The present article concentrates on thermal stratification in the flow of second grade fluid past a Riga plate with linear stretching towards a stagnation region. Heat transfer phenomenon is disclosed with heat generation/absorption. Riga plate is known as electromagnetic actuator which comprises of permanent magnets and alternating electrodes placed on a plane surface. Cattaneo-Christov heat flux model is implemented to analyze the features of heat transfer. This new heat flux model is the generalization of classical Fourier's law with the contribution of thermal relaxation time. For the first time heat generation/absorption effect is computed with non-Fourier's law of heat conduction (i.e., Cattaneo-Christov heat flux model). Transformations are used to obtain the governing non-linear ordinary differential equations. Approximate convergent solutions are developed for the non-dimensionalized governing problems. Physical features of velocity and temperature distributions are graphically analyzed corresponding to various parameters in 2D and 3D. It is noted that velocity field enhances with an increment of modified Hartman number while it reduces with increasing variable thickness parameter. Increment in modified heat generation parameter results in reduction of temperature field.

Electroencephalography (EEG) forward modeling via H(div) finite element sources with focal interpolation.

PubMed

Pursiainen, S; Vorwerk, J; Wolters, C H

2016-12-21

The goal of this study is to develop focal, accurate and robust finite element method (FEM) based approaches which can predict the electric potential on the surface of the computational domain given its structure and internal primary source current distribution. While conducting an EEG evaluation, the placement of source currents to the geometrically complex grey matter compartment is a challenging but necessary task to avoid forward errors attributable to tissue conductivity jumps. Here, this task is approached via a mathematically rigorous formulation, in which the current field is modeled via divergence conforming H(div) basis functions. Both linear and quadratic functions are used while the potential field is discretized via the standard linear Lagrangian (nodal) basis. The resulting model includes dipolar sources which are interpolated into a random set of positions and orientations utilizing two alternative approaches: the position based optimization (PBO) and the mean position/orientation (MPO) method. These results demonstrate that the present dipolar approach can reach or even surpass, at least in some respects, the accuracy of two classical reference methods, the partial integration (PI) and St. Venant (SV) approach which utilize monopolar loads instead of dipolar currents.

Optical choppers with rotational elements: modeling, design and prototypes

NASA Astrophysics Data System (ADS)

Duma, Virgil-Florin; Cira, Octavian; Demian, Dorin

2017-05-01

We present a brief overview of our contributions regarding the analysis and design of optical choppers. Their applications range numerous domains, from optical sensing in radiometry or telescopes to laser manufacturing and biomedical imaging - for example for the controlled attenuation of light, the elimination of selected spectral domains, or the switching of optical paths. While these aspects are pointed out, the paper describes our analysis, modeling, and manufacturing of prototypes for choppers with: (a) wheels with windows with linear margins; (b) wheels with windows with non-linear margins (semi-circular or elliptical), outward or inward; (c) rotational shafts with different shapes, with slits or with holes. While variant (a) represents classical choppers, variant (b) represents the "eclipse" choppers that we have developed and also patented for the solution with two adjustable wheels that can produce circular windows. Variant (c), of choppers with shafts is also a patent application. Their transmission functions are discussed, for the shape of the laser pulses produced and for the attenuation coefficients obtained. While this discussion has been completed analytically for top-hat laser beams, it has been modeled using simulations for Gaussian and Bessel beams. Design, manufacturing aspects, and prototypes of the different chopper configurations complete the presentation.

Knowledge diffusion in complex networks by considering time-varying information channels

NASA Astrophysics Data System (ADS)

Zhu, He; Ma, Jing

2018-03-01

In this article, based on a model of epidemic spreading, we explore the knowledge diffusion process with an innovative mechanism for complex networks by considering time-varying information channels. To cover the knowledge diffusion process in homogeneous and heterogeneous networks, two types of networks (the BA network and the ER network) are investigated. The mean-field theory is used to theoretically draw the knowledge diffusion threshold. Numerical simulation demonstrates that the knowledge diffusion threshold is almost linearly correlated with the mean of the activity rate. In addition, under the influence of the activity rate and distinct from the classic Susceptible-Infected-Susceptible (SIS) model, the density of knowers almost linearly grows with the spreading rate. Finally, in consideration of the ubiquitous mechanism of innovation, we further study the evolution of knowledge in our proposed model. The results suggest that compared with the effect of the spreading rate, the average knowledge version of the population is affected more by the innovation parameter and the mean of the activity rate. Furthermore, in the BA network, the average knowledge version of individuals with higher degree is always newer than those with lower degree.

Electron kinetic effects on interferometry, polarimetry and Thomson scattering measurements in burning plasmas (invited)

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

Mirnov, V. V.; Hartog, D. J. Den; Duff, J.

2014-11-15

At anticipated high electron temperatures in ITER, the effects of electron thermal motion on Thomson scattering (TS), toroidal interferometer/polarimeter (TIP), and poloidal polarimeter (PoPola) diagnostics will be significant and must be accurately treated. The precision of the previous lowest order linear in τ = T{sub e}/m{sub e}c{sup 2} model may be insufficient; we present a more precise model with τ{sup 2}-order corrections to satisfy the high accuracy required for ITER TIP and PoPola diagnostics. The linear model is extended from Maxwellian to a more general class of anisotropic electron distributions that allows us to take into account distortions caused bymore » equilibrium current, ECRH, and RF current drive effects. The classical problem of the degree of polarization of incoherent Thomson scattered radiation is solved analytically exactly without any approximations for the full range of incident polarizations, scattering angles, and electron thermal motion from non-relativistic to ultra-relativistic. The results are discussed in the context of the possible use of the polarization properties of Thomson scattered light as a method of T{sub e} measurement relevant to ITER operational scenarios.« less

Linear and nonlinear ion-acoustic waves in nonrelativistic quantum plasmas with arbitrary degeneracy.

PubMed

Haas, Fernando; Mahmood, Shahzad

2015-11-01

Linear and nonlinear ion-acoustic waves are studied in a fluid model for nonrelativistic, unmagnetized quantum plasma with electrons with an arbitrary degeneracy degree. The equation of state for electrons follows from a local Fermi-Dirac distribution function and applies equally well both to fully degenerate and classical, nondegenerate limits. Ions are assumed to be cold. Quantum diffraction effects through the Bohm potential are also taken into account. A general coupling parameter valid for dilute and dense plasmas is proposed. The linear dispersion relation of the ion-acoustic waves is obtained and the ion-acoustic speed is discussed for the limiting cases of extremely dense or dilute systems. In the long-wavelength limit, the results agree with quantum kinetic theory. Using the reductive perturbation method, the appropriate Korteweg-de Vries equation for weakly nonlinear solutions is obtained and the corresponding soliton propagation is analyzed. It is found that soliton hump and dip structures are formed depending on the value of the quantum parameter for the degenerate electrons, which affect the phase velocities in the dispersive medium.

Linear and nonlinear ion-acoustic waves in nonrelativistic quantum plasmas with arbitrary degeneracy

NASA Astrophysics Data System (ADS)

Haas, Fernando; Mahmood, Shahzad

2015-11-01

Linear and nonlinear ion-acoustic waves are studied in a fluid model for nonrelativistic, unmagnetized quantum plasma with electrons with an arbitrary degeneracy degree. The equation of state for electrons follows from a local Fermi-Dirac distribution function and applies equally well both to fully degenerate and classical, nondegenerate limits. Ions are assumed to be cold. Quantum diffraction effects through the Bohm potential are also taken into account. A general coupling parameter valid for dilute and dense plasmas is proposed. The linear dispersion relation of the ion-acoustic waves is obtained and the ion-acoustic speed is discussed for the limiting cases of extremely dense or dilute systems. In the long-wavelength limit, the results agree with quantum kinetic theory. Using the reductive perturbation method, the appropriate Korteweg-de Vries equation for weakly nonlinear solutions is obtained and the corresponding soliton propagation is analyzed. It is found that soliton hump and dip structures are formed depending on the value of the quantum parameter for the degenerate electrons, which affect the phase velocities in the dispersive medium.

Molecular dynamics study of Al and Ni 3Al sputtering by Al clusters bombardment

NASA Astrophysics Data System (ADS)

Zhurkin, Eugeni E.; Kolesnikov, Anton S.

2002-06-01

The sputtering of Al and Ni 3Al (1 0 0) surfaces induced by impact of Al ions and Al N clusters ( N=2,4,6,9,13,55) with energies of 100 and 500 eV/atom is studied at atomic scale by means of classical molecular dynamics (MD). The MD code we used implements many-body tight binding potential splined to ZBL at short distances. Special attention has been paid to model dense cascades: we used quite big computation cells with lateral periodic and damped boundary conditions. In addition, long simulation times (10-25 ps) and representative statistics (up to 1000 runs per each case) were considered. The total sputtering yields, energy and time spectrums of sputtered particles, as well as preferential sputtering of compound target were analyzed, both in the linear and non-linear regimes. The significant "cluster enhancement" of sputtering yield was found for cluster sizes N⩾13. In parallel, we estimated collision cascade features depending on cluster size in order to interpret the nature of observed non-linear effects.

Multi-linear sparse reconstruction for SAR imaging based on higher-order SVD

NASA Astrophysics Data System (ADS)

Gao, Yu-Fei; Gui, Guan; Cong, Xun-Chao; Yang, Yue; Zou, Yan-Bin; Wan, Qun

2017-12-01

This paper focuses on the spotlight synthetic aperture radar (SAR) imaging for point scattering targets based on tensor modeling. In a real-world scenario, scatterers usually distribute in the block sparse pattern. Such a distribution feature has been scarcely utilized by the previous studies of SAR imaging. Our work takes advantage of this structure property of the target scene, constructing a multi-linear sparse reconstruction algorithm for SAR imaging. The multi-linear block sparsity is introduced into higher-order singular value decomposition (SVD) with a dictionary constructing procedure by this research. The simulation experiments for ideal point targets show the robustness of the proposed algorithm to the noise and sidelobe disturbance which always influence the imaging quality of the conventional methods. The computational resources requirement is further investigated in this paper. As a consequence of the algorithm complexity analysis, the present method possesses the superiority on resource consumption compared with the classic matching pursuit method. The imaging implementations for practical measured data also demonstrate the effectiveness of the algorithm developed in this paper.

Development of Curved-Plate Elements for the Exact Buckling Analysis of Composite Plate Assemblies Including Transverse Shear Effects

NASA Technical Reports Server (NTRS)

McGowan, David M.; Anderson, Melvin S.

1998-01-01

The analytical formulation of curved-plate non-linear equilibrium equations that include transverse-shear-deformation effects is presented. A unified set of non-linear strains that contains terms from both physical and tensorial strain measures is used. Using several simplifying assumptions, linearized, stability equations are derived that describe the response of the plate just after bifurcation buckling occurs. These equations are then modified to allow the plate reference surface to be located a distance z(c), from the centroid surface which is convenient for modeling stiffened-plate assemblies. The implementation of the new theory into the VICONOPT buckling and vibration analysis and optimum design program code is described. Either classical plate theory (CPT) or first-order shear-deformation plate theory (SDPT) may be selected in VICONOPT. Comparisons of numerical results for several example problems with different loading states are made. Results from the new curved-plate analysis compare well with closed-form solution results and with results from known example problems in the literature. Finally, a design-optimization study of two different cylindrical shells subject to uniform axial compression is presented.

Exploring Divisibility and Summability of 'Photon' Wave Packets in Nonlinear Optical Phenomena

NASA Technical Reports Server (NTRS)

Prasad, Narasimha; Roychoudhuri, Chandrasekhar

2009-01-01

Formulations for second and higher harmonic frequency up and down conversions, as well as multi photon processes directly assume summability and divisibility of photons. Quantum mechanical (QM) interpretations are completely congruent with these assumptions. However, for linear optical phenomena (interference, diffraction, refraction, material dispersion, spectral dispersion, etc.), we have a profound dichotomy. Most optical engineers innovate and analyze all optical instruments by propagating pure classical electromagnetic (EM) fields using Maxwell s equations and gives only lip-service to the concept "indivisible light quanta". Further, irrespective of linearity or nonlinearity of the phenomena, the final results are always registered through some photo-electric or photo-chemical effects. This is mathematically well modeled by a quadratic action (energy absorption) relation. Since QM does not preclude divisibility or summability of photons in nonlinear & multi-photon effects, it cannot have any foundational reason against these same possibilities in linear optical phenomena. It implies that we must carefully revisit the fundamental roots behind all light-matter interaction processes and understand the common origin of "graininess" and "discreteness" of light energy.

Bayesian Inference for the Stereotype Regression Model: Application to a Case-control Study of Prostate Cancer

PubMed Central

Ahn, Jaeil; Mukherjee, Bhramar; Banerjee, Mousumi; Cooney, Kathleen A.

2011-01-01

Summary The stereotype regression model for categorical outcomes, proposed by Anderson (1984) is nested between the baseline category logits and adjacent category logits model with proportional odds structure. The stereotype model is more parsimonious than the ordinary baseline-category (or multinomial logistic) model due to a product representation of the log odds-ratios in terms of a common parameter corresponding to each predictor and category specific scores. The model could be used for both ordered and unordered outcomes. For ordered outcomes, the stereotype model allows more flexibility than the popular proportional odds model in capturing highly subjective ordinal scaling which does not result from categorization of a single latent variable, but are inherently multidimensional in nature. As pointed out by Greenland (1994), an additional advantage of the stereotype model is that it provides unbiased and valid inference under outcome-stratified sampling as in case-control studies. In addition, for matched case-control studies, the stereotype model is amenable to classical conditional likelihood principle, whereas there is no reduction due to sufficiency under the proportional odds model. In spite of these attractive features, the model has been applied less, as there are issues with maximum likelihood estimation and likelihood based testing approaches due to non-linearity and lack of identifiability of the parameters. We present comprehensive Bayesian inference and model comparison procedure for this class of models as an alternative to the classical frequentist approach. We illustrate our methodology by analyzing data from The Flint Men’s Health Study, a case-control study of prostate cancer in African-American men aged 40 to 79 years. We use clinical staging of prostate cancer in terms of Tumors, Nodes and Metastatsis (TNM) as the categorical response of interest. PMID:19731262

Quantum Bayesian networks with application to games displaying Parrondo's paradox

NASA Astrophysics Data System (ADS)

Pejic, Michael

Bayesian networks and their accompanying graphical models are widely used for prediction and analysis across many disciplines. We will reformulate these in terms of linear maps. This reformulation will suggest a natural extension, which we will show is equivalent to standard textbook quantum mechanics. Therefore, this extension will be termed quantum. However, the term quantum should not be taken to imply this extension is necessarily only of utility in situations traditionally thought of as in the domain of quantum mechanics. In principle, it may be employed in any modelling situation, say forecasting the weather or the stock market---it is up to experiment to determine if this extension is useful in practice. Even restricting to the domain of quantum mechanics, with this new formulation the advantages of Bayesian networks can be maintained for models incorporating quantum and mixed classical-quantum behavior. The use of these will be illustrated by various basic examples. Parrondo's paradox refers to the situation where two, multi-round games with a fixed winning criteria, both with probability greater than one-half for one player to win, are combined. Using a possibly biased coin to determine the rule to employ for each round, paradoxically, the previously losing player now wins the combined game with probabilitygreater than one-half. Using the extended Bayesian networks, we will formulate and analyze classical observed, classical hidden, and quantum versions of a game that displays this paradox, finding bounds for the discrepancy from naive expectations for the occurrence of the paradox. A quantum paradox inspired by Parrondo's paradox will also be analyzed. We will prove a bound for the discrepancy from naive expectations for this paradox as well. Games involving quantum walks that achieve this bound will be presented.

Reproducing the nonlinear dynamic behavior of a structured beam with a generalized continuum model

NASA Astrophysics Data System (ADS)

Vila, J.; Fernández-Sáez, J.; Zaera, R.

2018-04-01

In this paper we study the coupled axial-transverse nonlinear vibrations of a kind of one dimensional structured solids by application of the so called Inertia Gradient Nonlinear continuum model. To show the accuracy of this axiomatic model, previously proposed by the authors, its predictions are compared with numeric results from a previously defined finite discrete chain of lumped masses and springs, for several number of particles. A continualization of the discrete model equations based on Taylor series allowed us to set equivalent values of the mechanical properties in both discrete and axiomatic continuum models. Contrary to the classical continuum model, the inertia gradient nonlinear continuum model used herein is able to capture scale effects, which arise for modes in which the wavelength is comparable to the characteristic distance of the structured solid. The main conclusion of the work is that the proposed generalized continuum model captures the scale effects in both linear and nonlinear regimes, reproducing the behavior of the 1D nonlinear discrete model adequately.

Wing box transonic-flutter suppression using piezoelectric self-sensing actuators attached to skin

NASA Astrophysics Data System (ADS)

Otiefy, R. A. H.; Negm, H. M.

2010-12-01

The main objective of this research is to study the capability of piezoelectric (PZT) self-sensing actuators to suppress the transonic wing box flutter, which is a flow-structure interaction phenomenon. The unsteady general frequency modified transonic small disturbance (TSD) equation is used to model the transonic flow about the wing. The wing box structure and piezoelectric actuators are modeled using the equivalent plate method, which is based on the first order shear deformation plate theory (FSDPT). The piezoelectric actuators are bonded to the skin. The optimal electromechanical coupling conditions between the piezoelectric actuators and the wing are collected from previous work. Three main different control strategies, a linear quadratic Gaussian (LQG) which combines the linear quadratic regulator (LQR) with the Kalman filter estimator (KFE), an optimal static output feedback (SOF), and a classic feedback controller (CFC), are studied and compared. The optimum actuator and sensor locations are determined using the norm of feedback control gains (NFCG) and norm of Kalman filter estimator gains (NKFEG) respectively. A genetic algorithm (GA) optimization technique is used to calculate the controller and estimator parameters to achieve a target response.

Long term cavity closure in salt using a Carreau viscosity model.

NASA Astrophysics Data System (ADS)

Cornet, Jan; Dabrowski, Marcin; Schmid, Daniel

2017-04-01

The problem of a pressurized hole in an infinite homogenous body is one of the most classical problems in geoscience. The solution is well-known when the rheology is linear but becomes much more complicated when applied to formations such as salt that can behave nonlinearly. Defining a constitutive law for the steady state deformation of salt is already a challenge and we rely on two deformation mechanisms - dislocation creep and pressure solution - to do that. More precisely, we use a Carreau model for viscosity to take into account in a single and smooth manner a linear and a nonlinear process. We use this rheology to revisit the classical two-dimensional problem of a pressurized cylindrical hole in an infinite and homogeneous body under general far field loads. We are interested in characterizing the maximum closure velocity at the rim. We provide analytical solutions for pressure and far field pure shear loads and we give a proxy for the general case based on the two end members. Using this general approach, we show that adding pressure solution to the constitutive law is especially important when studying long term hole closure under low pressure loads or when the grain size is in the order of 0.1 mm. Only considering dislocation creep can lead to underestimating the closure velocity by several orders of magnitude. Adding far field shear stress also dramatically enhances hole closure. The stress situation in salt bodies is often considered as isotropic but some shear exists at the interface between moving salt bodies and cap rock so pressurized holes in these regions experience increased closure. The analytical approach adopted in this study enables us to better understand the influence of all the input parameters on hole closure in salt.

Evolution of stochastic demography with life history tradeoffs in density-dependent age-structured populations.

PubMed

Lande, Russell; Engen, Steinar; Sæther, Bernt-Erik

2017-10-31

We analyze the stochastic demography and evolution of a density-dependent age- (or stage-) structured population in a fluctuating environment. A positive linear combination of age classes (e.g., weighted by body mass) is assumed to act as the single variable of population size, [Formula: see text], exerting density dependence on age-specific vital rates through an increasing function of population size. The environment fluctuates in a stationary distribution with no autocorrelation. We show by analysis and simulation of age structure, under assumptions often met by vertebrate populations, that the stochastic dynamics of population size can be accurately approximated by a univariate model governed by three key demographic parameters: the intrinsic rate of increase and carrying capacity in the average environment, [Formula: see text] and [Formula: see text], and the environmental variance in population growth rate, [Formula: see text] Allowing these parameters to be genetically variable and to evolve, but assuming that a fourth parameter, [Formula: see text], measuring the nonlinearity of density dependence, remains constant, the expected evolution maximizes [Formula: see text] This shows that the magnitude of environmental stochasticity governs the classical trade-off between selection for higher [Formula: see text] versus higher [Formula: see text] However, selection also acts to decrease [Formula: see text], so the simple life-history trade-off between [Formula: see text]- and [Formula: see text]-selection may be obscured by additional trade-offs between them and [Formula: see text] Under the classical logistic model of population growth with linear density dependence ([Formula: see text]), life-history evolution in a fluctuating environment tends to maximize the average population size. Published under the PNAS license.

Expanded Very Large Array Nova Project Observations of the Classical Nova V1723 Aquilae

NASA Astrophysics Data System (ADS)

Krauss, Miriam I.; Chomiuk, Laura; Rupen, Michael; Roy, Nirupam; Mioduszewski, Amy J.; Sokoloski, J. L.; Nelson, Thomas; Mukai, Koji; Bode, M. F.; Eyres, S. P. S.; O'Brien, T. J.

2011-09-01

We present radio light curves and spectra of the classical nova V1723 Aql obtained with the Expanded Very Large Array (EVLA). This is the first paper to showcase results from the EVLA Nova Project, which comprises a team of observers and theorists utilizing the greatly enhanced sensitivity and frequency coverage of EVLA radio observations, along with observations at other wavelengths, to reach a deeper understanding of the energetics, morphology, and temporal characteristics of nova explosions. Our observations of V1723 Aql span 1-37 GHz in frequency, and we report on data from 14 to 175 days following the time of the nova explosion. The broad frequency coverage and frequent monitoring show that the radio behavior of V1723 Aql does not follow the classic Hubble-flow model of homologous spherically expanding thermal ejecta. The spectra are always at least partially optically thin, and the flux rises on faster timescales than can be reproduced with linear expansion. Therefore, any description of the underlying physical processes must go beyond this simple picture. The unusual spectral properties and light curve evolution might be explained by multiple emitting regions or shocked material. Indeed, X-ray observations from Swift reveal that shocks are likely present.

Cavity QED at the quantum-classical boundary

NASA Astrophysics Data System (ADS)

Fink, J. M.; Steffen, L.; Bishop, L. S.; Wallraff, A.

2010-03-01

The quantum limit of cavity QED is characterized by a well resolved vacuum Rabi mode splitting spectrum. If the number of excitations n in the resonantly coupled matter-light system is increased from one, the nonlinear √n scaling of the dressed eigenstates is observed [1]. At very large photon numbers the transmission spectrum turns into a single Lorentzian line as expected from the correspondence principle. This classical limit emerges when the occupancy of the low energy dressed states is increased until the quantum nonlinearity of the available transitions becomes small compared to dephasing and relaxation rates [2]. We explore this quantum-classical crossover in a circuit QED system where we vary the thermal occupation of the resonator by 5 orders of magnitude using a quasi-thermal noise source. From vacuum Rabi spectra measured in linear response and from time resolved vacuum Rabi oscillation measurements we consistently extract cavity field temperatures between 100 mK and 10 K using a master equation model. The presented experimental approach is useful to determine the thermal occupation of a quantum system and offers the possibility to study entanglement and decoherence at elevated temperatures. [1] J. M. Fink et al. Nature 454, 315 (2008). [2] I. Rau, et al. Phys. Rev. B 70, 054521 (2004).

Expanded Very Large Array Nova Project Observations of the Classical NovaV1723 Aquilae

NASA Technical Reports Server (NTRS)

Krauss, Miriam I.; Chomiuk, Laura; Rupen, Michael; Roy, Nirupam; Mioduszewski, Amy J.; Sokoloski, J. L.; Nelson, Thomas; Mukai, Koji; Bode, M. F.; Eyres, S. P. S.;

Music preferences with hearing aids: effects of signal properties, compression settings, and listener characteristics.

PubMed

Croghan, Naomi B H; Arehart, Kathryn H; Kates, James M

2014-01-01

Current knowledge of how to design and fit hearing aids to optimize music listening is limited. Many hearing-aid users listen to recorded music, which often undergoes compression limiting (CL) in the music industry. Therefore, hearing-aid users may experience twofold effects of compression when listening to recorded music: music-industry CL and hearing-aid wide dynamic-range compression (WDRC). The goal of this study was to examine the roles of input-signal properties, hearing-aid processing, and individual variability in the perception of recorded music, with a focus on the effects of dynamic-range compression. A group of 18 experienced hearing-aid users made paired-comparison preference judgments for classical and rock music samples using simulated hearing aids. Music samples were either unprocessed before hearing-aid input or had different levels of music-industry CL. Hearing-aid conditions included linear gain and individually fitted WDRC. Combinations of four WDRC parameters were included: fast release time (50 msec), slow release time (1,000 msec), three channels, and 18 channels. Listeners also completed several psychophysical tasks. Acoustic analyses showed that CL and WDRC reduced temporal envelope contrasts, changed amplitude distributions across the acoustic spectrum, and smoothed the peaks of the modulation spectrum. Listener judgments revealed that fast WDRC was least preferred for both genres of music. For classical music, linear processing and slow WDRC were equally preferred, and the main effect of number of channels was not significant. For rock music, linear processing was preferred over slow WDRC, and three channels were preferred to 18 channels. Heavy CL was least preferred for classical music, but the amount of CL did not change the patterns of WDRC preferences for either genre. Auditory filter bandwidth as estimated from psychophysical tuning curves was associated with variability in listeners' preferences for classical music. Fast, multichannel WDRC often leads to poor music quality, whereas linear processing or slow WDRC are generally preferred. Furthermore, the effect of WDRC is more important for music preferences than music-industry CL applied to signals before the hearing-aid input stage. Variability in hearing-aid users' perceptions of music quality may be partially explained by frequency resolution abilities.

Phase space explorations in time dependent density functional theory

NASA Astrophysics Data System (ADS)

Rajam, Aruna K.

Time dependent density functional theory (TDDFT) is one of the useful tools for the study of the dynamic behavior of correlated electronic systems under the influence of external potentials. The success of this formally exact theory practically relies on approximations for the exchange-correlation potential which is a complicated functional of the co-ordinate density, non-local in space and time. Adiabatic approximations (such as ALDA), which are local in time, are most commonly used in the increasing applications of the field. Going beyond ALDA, has been proved difficult leading to mathematical inconsistencies. We explore the regions where the theory faces challenges, and try to answer some of them via the insights from two electron model systems. In this thesis work we propose a phase-space extension of the TDDFT. We want to answer the challenges the theory is facing currently by exploring the one-body phase-space. We give a general introduction to this theory and its mathematical background in the first chapter. In second chapter, we carryout a detailed study of instantaneous phase-space densities and argue that the functionals of distributions can be a better alternative to the nonlocality issue of the exchange-correlation potentials. For this we study in detail the interacting and the non-interacting phase-space distributions for Hookes atom model. The applicability of ALDA-based TDDFT for the dynamics in strongfields can become severely problematic due to the failure of single-Slater determinant picture.. In the third chapter, we analyze how the phase-space distributions can shine some light into this problem. We do a comparative study of Kohn-Sham and interacting phase-space and momentum distributions for single ionization and double ionization systems. Using a simple model of two-electron systems, we have showed that the momentum distribution computed directly from the exact KS system contains spurious oscillations: a non-classical description of the essentially classical two-electron dynamics. In Time dependent density matrix functional theory (TDDMFT), the evolution scheme of the 1RDM (first order reduced density matrix) contains second-order reduced density matrix (2RDM), which has to be expressed in terms of 1RDMs. Any non-correlated approximations (Hartree-Fock) for 2RDM would fail to capture the natural occupations of the system. In our fourth chapter, we show that by applying the quasi-classical and semi-classical approximations one can capture the natural occupations of the excited systems. We study a time-dependent Moshinsky atom model for this. The fifth chapter contains a comparative work on the existing non-local exchange-correlation kernels that are based on current density response frame work and the co-moving frame work. We show that the two approaches though coinciding with each other in linear response regime, actually turn out to be different in non-linear regime.

High-Order Accurate Solutions to the Helmholtz Equation in the Presence of Boundary Singularities

DTIC Science & Technology

2015-03-31

FD scheme is only consistent for classical solutions of the PDE . For this reason, we implement the method of singularity subtraction as a means for...regularity due to the boundary conditions. This is because the FD scheme is only consistent for classical solutions of the PDE . For this reason, we...Introduction In the present work, we develop a high-order numerical method for solving linear elliptic PDEs with well-behaved variable coefficients on

Asymptotics of quasi-classical localized states in 2D system of charged hard-core bosons

NASA Astrophysics Data System (ADS)

Panov, Yu. D.; Moskvin, A. S.

2018-05-01

The continuous quasi-classical two-sublattice approximation is constructed for the 2D system of charged hard-core bosons to explore metastable inhomogeneous states analogous to inhomogeneous localized excitations in magnetic systems. The types of localized excitations are determined by asymptotic analysis and compared with numerical results. Depending on the homogeneous ground state, the excitations are the ferro and antiferro type vortices, the skyrmion-like topological excitations or linear domain walls.

The Physics of Vibration

NASA Astrophysics Data System (ADS)

Pippard, A. B.

1989-11-01

The study of vibration in physical systems is an important part of almost all fields in physics and engineering. This work, originally published in two volumes, examines the classical aspects in Part I and the quantum oscillator in Part II. The classical linear vibrator is treated first and the underlying unity of all linear oscillations in electrical, mechanical and acoustic systems is emphasized. Following this the book turns to the treatment of nonlinear vibrations, a field with which engineers and physicists are generally less familiar. In Part II the emphasis turns to quantum systems, that is those systems which can only be adequately described by quantum mechanics. The treatment concentrates on vibrations in atoms and molecules and their interaction with electromagnetic radiation. The similarities of classical and quantum methods are stressed and the limits of the classical treatment are examined. Throughout the book, each phenomenon discussed is illustrated with many examples and theory and experiment are compared. Although the reader may find that the physics discussed is demanding and the concepts are subtle in places, all mathematics used is familiar to both engineers and experimental scientists. Although not a textbook this is a useful introduction to the more advanced mathematical treatment of vibrations as it bridges the gap between the basic principles and more specialized concepts. It will be of great interest to advanced undergraduates and postgraduates as well as applied mathematicians, physicists and engineers in university and industry.

Periodic solutions of second-order nonlinear difference equations containing a small parameter. II - Equivalent linearization

NASA Technical Reports Server (NTRS)

Mickens, R. E.

1985-01-01

The classical method of equivalent linearization is extended to a particular class of nonlinear difference equations. It is shown that the method can be used to obtain an approximation of the periodic solutions of these equations. In particular, the parameters of the limit cycle and the limit points can be determined. Three examples illustrating the method are presented.

An O({radical}nL) primal-dual affine scaling algorithm for linear programming

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

Huang, Siming

1994-12-31

We present a new primal-dual affine scaling algorithm for linear programming. The search direction of the algorithm is a combination of classical affine scaling direction of Dikin and a recent new affine scaling direction of Jansen, Roos and Terlaky. The algorithm has an iteration complexity of O({radical}nL), comparing to O(nL) complexity of Jansen, Roos and Terlaky.

Intelligent Distributed Systems

DTIC Science & Technology

2015-10-23

periodic gossiping algorithms by using convex combination rules rather than standard averaging rules. On a ring graph, we have discovered how to sequence...the gossips within a period to achieve the best possible convergence rate and we have related this optimal value to the classic edge coloring problem...consensus. There are three different approaches to distributed averaging: linear iterations, gossiping , and dou- ble linear iterations which are also known as

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)

A parallel competitive Particle Swarm Optimization for non-linear first arrival traveltime tomography and uncertainty quantification

NASA Astrophysics Data System (ADS)

Luu, Keurfon; Noble, Mark; Gesret, Alexandrine; Belayouni, Nidhal; Roux, Pierre-François

2018-04-01

Seismic traveltime tomography is an optimization problem that requires large computational efforts. Therefore, linearized techniques are commonly used for their low computational cost. These local optimization methods are likely to get trapped in a local minimum as they critically depend on the initial model. On the other hand, global optimization methods based on MCMC are insensitive to the initial model but turn out to be computationally expensive. Particle Swarm Optimization (PSO) is a rather new global optimization approach with few tuning parameters that has shown excellent convergence rates and is straightforwardly parallelizable, allowing a good distribution of the workload. However, while it can traverse several local minima of the evaluated misfit function, classical implementation of PSO can get trapped in local minima at later iterations as particles inertia dim. We propose a Competitive PSO (CPSO) to help particles to escape from local minima with a simple implementation that improves swarm's diversity. The model space can be sampled by running the optimizer multiple times and by keeping all the models explored by the swarms in the different runs. A traveltime tomography algorithm based on CPSO is successfully applied on a real 3D data set in the context of induced seismicity.

Modeling of inactivation of surface borne microorganisms occurring on seeds by cold atmospheric plasma (CAP)

NASA Astrophysics Data System (ADS)

Mitra, Anindita; Li, Y.-F.; Shimizu, T.; Klämpfl, Tobias; Zimmermann, J. L.; Morfill, G. E.

2012-10-01

Cold Atmospheric Plasma (CAP) is a fast, low cost, simple, easy to handle technology for biological application. Our group has developed a number of different CAP devices using the microwave technology and the surface micro discharge (SMD) technology. In this study, FlatPlaSter2.0 at different time intervals (0.5 to 5 min) is used for microbial inactivation. There is a continuous demand for deactivation of microorganisms associated with raw foods/seeds without loosing their properties. This research focuses on the kinetics of CAP induced microbial inactivation of naturally growing surface microorganisms on seeds. The data were assessed for log- linear and non-log-linear models for survivor curves as a function of time. The Weibull model showed the best fitting performance of the data. No shoulder and tail was observed. The models are focused in terms of the number of log cycles reduction rather than on classical D-values with statistical measurements. The viability of seeds was not affected for CAP treatment times up to 3 min with our device. The optimum result was observed at 1 min with increased percentage of germination from 60.83% to 89.16% compared to the control. This result suggests the advantage and promising role of CAP in food industry.

Modeling Music Emotion Judgments Using Machine Learning Methods

PubMed Central

Vempala, Naresh N.; Russo, Frank A.

2018-01-01

Emotion judgments and five channels of physiological data were obtained from 60 participants listening to 60 music excerpts. Various machine learning (ML) methods were used to model the emotion judgments inclusive of neural networks, linear regression, and random forests. Input for models of perceived emotion consisted of audio features extracted from the music recordings. Input for models of felt emotion consisted of physiological features extracted from the physiological recordings. Models were trained and interpreted with consideration of the classic debate in music emotion between cognitivists and emotivists. Our models supported a hybrid position wherein emotion judgments were influenced by a combination of perceived and felt emotions. In comparing the different ML approaches that were used for modeling, we conclude that neural networks were optimal, yielding models that were flexible as well as interpretable. Inspection of a committee machine, encompassing an ensemble of networks, revealed that arousal judgments were predominantly influenced by felt emotion, whereas valence judgments were predominantly influenced by perceived emotion. PMID:29354080

Modeling Music Emotion Judgments Using Machine Learning Methods.

PubMed

Vempala, Naresh N; Russo, Frank A

2017-01-01

Emotion judgments and five channels of physiological data were obtained from 60 participants listening to 60 music excerpts. Various machine learning (ML) methods were used to model the emotion judgments inclusive of neural networks, linear regression, and random forests. Input for models of perceived emotion consisted of audio features extracted from the music recordings. Input for models of felt emotion consisted of physiological features extracted from the physiological recordings. Models were trained and interpreted with consideration of the classic debate in music emotion between cognitivists and emotivists. Our models supported a hybrid position wherein emotion judgments were influenced by a combination of perceived and felt emotions. In comparing the different ML approaches that were used for modeling, we conclude that neural networks were optimal, yielding models that were flexible as well as interpretable. Inspection of a committee machine, encompassing an ensemble of networks, revealed that arousal judgments were predominantly influenced by felt emotion, whereas valence judgments were predominantly influenced by perceived emotion.

Dynamical insurance models with investment: Constrained singular problems for integrodifferential equations

NASA Astrophysics Data System (ADS)

Belkina, T. A.; Konyukhova, N. B.; Kurochkin, S. V.

2016-01-01

Previous and new results are used to compare two mathematical insurance models with identical insurance company strategies in a financial market, namely, when the entire current surplus or its constant fraction is invested in risky assets (stocks), while the rest of the surplus is invested in a risk-free asset (bank account). Model I is the classical Cramér-Lundberg risk model with an exponential claim size distribution. Model II is a modification of the classical risk model (risk process with stochastic premiums) with exponential distributions of claim and premium sizes. For the survival probability of an insurance company over infinite time (as a function of its initial surplus), there arise singular problems for second-order linear integrodifferential equations (IDEs) defined on a semiinfinite interval and having nonintegrable singularities at zero: model I leads to a singular constrained initial value problem for an IDE with a Volterra integral operator, while II model leads to a more complicated nonlocal constrained problem for an IDE with a non-Volterra integral operator. A brief overview of previous results for these two problems depending on several positive parameters is given, and new results are presented. Additional results are concerned with the formulation, analysis, and numerical study of "degenerate" problems for both models, i.e., problems in which some of the IDE parameters vanish; moreover, passages to the limit with respect to the parameters through which we proceed from the original problems to the degenerate ones are singular for small and/or large argument values. Such problems are of mathematical and practical interest in themselves. Along with insurance models without investment, they describe the case of surplus completely invested in risk-free assets, as well as some noninsurance models of surplus dynamics, for example, charity-type models.

The Nature of Quantum Truth: Logic, Set Theory, & Mathematics in the Context of Quantum Theory

NASA Astrophysics Data System (ADS)

Frey, Kimberly

The purpose of this dissertation is to construct a radically new type of mathematics whose underlying logic differs from the ordinary classical logic used in standard mathematics, and which we feel may be more natural for applications in quantum mechanics. Specifically, we begin by constructing a first order quantum logic, the development of which closely parallels that of ordinary (classical) first order logic --- the essential differences are in the nature of the logical axioms, which, in our construction, are motivated by quantum theory. After showing that the axiomatic first order logic we develop is sound and complete (with respect to a particular class of models), this logic is then used as a foundation on which to build (axiomatic) mathematical systems --- and we refer to the resulting new mathematics as "quantum mathematics." As noted above, the hope is that this form of mathematics is more natural than classical mathematics for the description of quantum systems, and will enable us to address some foundational aspects of quantum theory which are still troublesome --- e.g. the measurement problem --- as well as possibly even inform our thinking about quantum gravity. After constructing the underlying logic, we investigate properties of several mathematical systems --- e.g. axiom systems for abstract algebras, group theory, linear algebra, etc. --- in the presence of this quantum logic. In the process, we demonstrate that the resulting quantum mathematical systems have some strange, but very interesting features, which indicates a richness in the structure of mathematics that is classically inaccessible. Moreover, some of these features do indeed suggest possible applications to foundational questions in quantum theory. We continue our investigation of quantum mathematics by constructing an axiomatic quantum set theory, which we show satisfies certain desirable criteria. Ultimately, we hope that such a set theory will lead to a foundation for quantum mathematics in a sense which parallels the foundational role of classical set theory in classical mathematics. One immediate application of the quantum set theory we develop is to provide a foundation on which to construct quantum natural numbers, which are the quantum analog of the classical counting numbers. It turns out that in a special class of models, there exists a 1-1 correspondence between the quantum natural numbers and bounded observables in quantum theory whose eigenvalues are (ordinary) natural numbers. This 1-1 correspondence is remarkably satisfying, and not only gives us great confidence in our quantum set theory, but indicates the naturalness of such models for quantum theory itself. We go on to develop a Peano-like arithmetic for these new "numbers," as well as consider some of its consequences. Finally, we conclude by summarizing our results, and discussing directions for future work.

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.

Time-frequency analysis of neuronal populations with instantaneous resolution based on noise-assisted multivariate empirical mode decomposition.

PubMed

Alegre-Cortés, J; Soto-Sánchez, C; Pizá, Á G; Albarracín, A L; Farfán, F D; Felice, C J; Fernández, E

2016-07-15

Linear analysis has classically provided powerful tools for understanding the behavior of neural populations, but the neuron responses to real-world stimulation are nonlinear under some conditions, and many neuronal components demonstrate strong nonlinear behavior. In spite of this, temporal and frequency dynamics of neural populations to sensory stimulation have been usually analyzed with linear approaches. In this paper, we propose the use of Noise-Assisted Multivariate Empirical Mode Decomposition (NA-MEMD), a data-driven template-free algorithm, plus the Hilbert transform as a suitable tool for analyzing population oscillatory dynamics in a multi-dimensional space with instantaneous frequency (IF) resolution. The proposed approach was able to extract oscillatory information of neurophysiological data of deep vibrissal nerve and visual cortex multiunit recordings that were not evidenced using linear approaches with fixed bases such as the Fourier analysis. Texture discrimination analysis performance was increased when Noise-Assisted Multivariate Empirical Mode plus Hilbert transform was implemented, compared to linear techniques. Cortical oscillatory population activity was analyzed with precise time-frequency resolution. Similarly, NA-MEMD provided increased time-frequency resolution of cortical oscillatory population activity. Noise-Assisted Multivariate Empirical Mode Decomposition plus Hilbert transform is an improved method to analyze neuronal population oscillatory dynamics overcoming linear and stationary assumptions of classical methods. Copyright © 2016 Elsevier B.V. All rights reserved.

Nonlinear model identification and spectral submanifolds for multi-degree-of-freedom mechanical vibrations

NASA Astrophysics Data System (ADS)

Szalai, Robert; Ehrhardt, David; Haller, George

2017-06-01

In a nonlinear oscillatory system, spectral submanifolds (SSMs) are the smoothest invariant manifolds tangent to linear modal subspaces of an equilibrium. Amplitude-frequency plots of the dynamics on SSMs provide the classic backbone curves sought in experimental nonlinear model identification. We develop here, a methodology to compute analytically both the shape of SSMs and their corresponding backbone curves from a data-assimilating model fitted to experimental vibration signals. This model identification utilizes Taken's delay-embedding theorem, as well as a least square fit to the Taylor expansion of the sampling map associated with that embedding. The SSMs are then constructed for the sampling map using the parametrization method for invariant manifolds, which assumes that the manifold is an embedding of, rather than a graph over, a spectral subspace. Using examples of both synthetic and real experimental data, we demonstrate that this approach reproduces backbone curves with high accuracy.

Special class of nonlinear damping models in flexible space structures

NASA Technical Reports Server (NTRS)

Hu, Anren; Singh, Ramendra P.; Taylor, Lawrence W.

1991-01-01

A special class of nonlinear damping models is investigated in which the damping force is proportional to the product of positive integer or the fractional power of the absolute values of displacement and velocity. For a one-degree-of-freedom system, the classical Krylov-Bogoliubov 'averaging' method is used, whereas for a distributed system, both an ad hoc perturbation technique and the finite difference method are employed to study the effects of nonlinear damping. The results are compared with linear viscous damping models. The amplitude decrement of free vibration for a single mode system with nonlinear models depends not only on the damping ratio but also on the initial amplitude, the time to measure the response, the frequency of the system, and the powers of displacement and velocity. For the distributed system, the action of nonlinear damping is found to reduce the energy of the system and to pass energy to lower modes.