A theory of fine structure image models with an application to detection and classification of dementia.

PubMed

O'Neill, William; Penn, Richard; Werner, Michael; Thomas, Justin

2015-06-01

Estimation of stochastic process models from data is a common application of time series analysis methods. Such system identification processes are often cast as hypothesis testing exercises whose intent is to estimate model parameters and test them for statistical significance. Ordinary least squares (OLS) regression and the Levenberg-Marquardt algorithm (LMA) have proven invaluable computational tools for models being described by non-homogeneous, linear, stationary, ordinary differential equations. In this paper we extend stochastic model identification to linear, stationary, partial differential equations in two independent variables (2D) and show that OLS and LMA apply equally well to these systems. The method employs an original nonparametric statistic as a test for the significance of estimated parameters. We show gray scale and color images are special cases of 2D systems satisfying a particular autoregressive partial difference equation which estimates an analogous partial differential equation. Several applications to medical image modeling and classification illustrate the method by correctly classifying demented and normal OLS models of axial magnetic resonance brain scans according to subject Mini Mental State Exam (MMSE) scores. Comparison with 13 image classifiers from the literature indicates our classifier is at least 14 times faster than any of them and has a classification accuracy better than all but one. Our modeling method applies to any linear, stationary, partial differential equation and the method is readily extended to 3D whole-organ systems. Further, in addition to being a robust image classifier, estimated image models offer insights into which parameters carry the most diagnostic image information and thereby suggest finer divisions could be made within a class. Image models can be estimated in milliseconds which translate to whole-organ models in seconds; such runtimes could make real-time medicine and surgery modeling possible.

Parallels between control PDE's (Partial Differential Equations) and systems of ODE's (Ordinary Differential Equations)

NASA Technical Reports Server (NTRS)

Hunt, L. R.; Villarreal, Ramiro

1987-01-01

System theorists understand that the same mathematical objects which determine controllability for nonlinear control systems of ordinary differential equations (ODEs) also determine hypoellipticity for linear partial differentail equations (PDEs). Moreover, almost any study of ODE systems begins with linear systems. It is remarkable that Hormander's paper on hypoellipticity of second order linear p.d.e.'s starts with equations due to Kolmogorov, which are shown to be analogous to the linear PDEs. Eigenvalue placement by state feedback for a controllable linear system can be paralleled for a Kolmogorov equation if an appropriate type of feedback is introduced. Results concerning transformations of nonlinear systems to linear systems are similar to results for transforming a linear PDE to a Kolmogorov equation.

Constructing general partial differential equations using polynomial and neural networks.

PubMed

Zjavka, Ladislav; Pedrycz, Witold

2016-01-01

Sum fraction terms can approximate multi-variable functions on the basis of discrete observations, replacing a partial differential equation definition with polynomial elementary data relation descriptions. Artificial neural networks commonly transform the weighted sum of inputs to describe overall similarity relationships of trained and new testing input patterns. Differential polynomial neural networks form a new class of neural networks, which construct and solve an unknown general partial differential equation of a function of interest with selected substitution relative terms using non-linear multi-variable composite polynomials. The layers of the network generate simple and composite relative substitution terms whose convergent series combinations can describe partial dependent derivative changes of the input variables. This regression is based on trained generalized partial derivative data relations, decomposed into a multi-layer polynomial network structure. The sigmoidal function, commonly used as a nonlinear activation of artificial neurons, may transform some polynomial items together with the parameters with the aim to improve the polynomial derivative term series ability to approximate complicated periodic functions, as simple low order polynomials are not able to fully make up for the complete cycles. The similarity analysis facilitates substitutions for differential equations or can form dimensional units from data samples to describe real-world problems. Copyright © 2015 Elsevier Ltd. All rights reserved.

Numerical analysis of MHD Carreau fluid flow over a stretching cylinder with homogenous-heterogeneous reactions

NASA Astrophysics Data System (ADS)

Khan, Imad; Ullah, Shafquat; Malik, M. Y.; Hussain, Arif

2018-06-01

The current analysis concentrates on the numerical solution of MHD Carreau fluid flow over a stretching cylinder under the influences of homogeneous-heterogeneous reactions. Modelled non-linear partial differential equations are converted into ordinary differential equations by using suitable transformations. The resulting system of equations is solved with the aid of shooting algorithm supported by fifth order Runge-Kutta integration scheme. The impact of non-dimensional governing parameters on the velocity, temperature, skin friction coefficient and local Nusselt number are comprehensively delineated with the help of graphs and tables.

Optimal moving grids for time-dependent partial differential equations

NASA Technical Reports Server (NTRS)

Wathen, A. J.

1992-01-01

Various adaptive moving grid techniques for the numerical solution of time-dependent partial differential equations were proposed. The precise criterion for grid motion varies, but most techniques will attempt to give grids on which the solution of the partial differential equation can be well represented. Moving grids are investigated on which the solutions of the linear heat conduction and viscous Burgers' equation in one space dimension are optimally approximated. Precisely, the results of numerical calculations of optimal moving grids for piecewise linear finite element approximation of PDE solutions in the least-squares norm are reported.

Unsteady Solution of Non-Linear Differential Equations Using Walsh Function Series

NASA Technical Reports Server (NTRS)

Gnoffo, Peter A.

2015-01-01

Walsh functions form an orthonormal basis set consisting of square waves. The discontinuous nature of square waves make the system well suited for representing functions with discontinuities. The product of any two Walsh functions is another Walsh function - a feature that can radically change an algorithm for solving non-linear partial differential equations (PDEs). The solution algorithm of non-linear differential equations using Walsh function series is unique in that integrals and derivatives may be computed using simple matrix multiplication of series representations of functions. Solutions to PDEs are derived as functions of wave component amplitude. Three sample problems are presented to illustrate the Walsh function series approach to solving unsteady PDEs. These include an advection equation, a Burgers equation, and a Riemann problem. The sample problems demonstrate the use of the Walsh function solution algorithms, exploiting Fast Walsh Transforms in multi-dimensions (O(Nlog(N))). Details of a Fast Walsh Reciprocal, defined here for the first time, enable inversion of aWalsh Symmetric Matrix in O(Nlog(N)) operations. Walsh functions have been derived using a fractal recursion algorithm and these fractal patterns are observed in the progression of pairs of wave number amplitudes in the solutions. These patterns are most easily observed in a remapping defined as a fractal fingerprint (FFP). A prolongation of existing solutions to the next highest order exploits these patterns. The algorithms presented here are considered a work in progress that provide new alternatives and new insights into the solution of non-linear PDEs.

Axisymmetric Powell-Eyring fluid flow over a stretching sheet with a convective boundary condition and suction effects

NASA Astrophysics Data System (ADS)

Nasir, Nor Ain Azeany Mohd; Ishak, Anuar; Pop, Ioan

2018-04-01

In this paper, the heat and mass transfer of an axisymmetric Powell-Eyring fluid flow over a stretching sheet with a convective boundary condition and suction effects are investigated. An appropriate similarity transformation is used to reduce the highly non-linear partial differential equation into second and third order non-linear ordinary differential equations. Numerical solutions of the reduced governing equations are computed numerically by utilizing the MATLAB's built-in boundary value problem solver, bvp4c. The physical significance of various parameters such as Biot number, fluid parameters and Prandtl number on the velocity and temperature evolution profiles are illustrated graphically. The effects of these governing parameters on the skin friction coefficient and the local Nusselt number are also displayed graphically. It is noticed that the Powell-Eyring fluid parameter gives significant influence on the rates of heat and mass transfer of the fluid.

Internal friction between fluid particles of MHD tangent hyperbolic fluid with heat generation: Using coefficients improved by Cash and Karp

NASA Astrophysics Data System (ADS)

Salahuddin, T.; Khan, Imad; Malik, M. Y.; Khan, Mair; Hussain, Arif; Awais, Muhammad

2017-05-01

The present work examines the internal resistance between fluid particles of tangent hyperbolic fluid flow due to a non-linear stretching sheet with heat generation. Using similarity transformations, the governing system of partial differential equations is transformed into a coupled non-linear ordinary differential system with variable coefficients. Unlike the current analytical works on the flow problems in the literature, the main concern here is to numerically work out and find the solution by using Runge-Kutta-Fehlberg coefficients improved by Cash and Karp (Naseer et al., Alexandria Eng. J. 53, 747 (2014)). To determine the relevant physical features of numerous mechanisms acting on the deliberated problem, it is sufficient to have the velocity profile and temperature field and also the drag force and heat transfer rate all as given in the current paper.

Numerical study of steady dissipative mixed convection optically-thick micropolar flow with thermal radiation effects

NASA Astrophysics Data System (ADS)

Gupta, Diksha; Kumar, Lokendra; Bég, O. Anwar; Singh, Bani

2017-10-01

The objective of this paper is to study theoretically and numerically the effect of thermal radiation on mixed convection boundary layer flow of a dissipative micropolar non-Newtonian fluid from a continuously moving vertical porous sheet. The governing partial differential equations are transformed into a set of non-linear differential equations by using similarity transformations. These equations are solved iteratively with the Bellman-Kalaba quasi-linearization algorithm. This method converges quadratically and the solution is valid for a large range of parameters. The effects of transpiration (suction or injection) parameter, buoyancy parameter, radiation parameter and Eckert number on velocity, microrotation and temperature functions have been studied. Under a special case comparison of the present numerical results is made with the results available in the literature and an excellent agreement is found. Additionally skin friction and rate of heat transfer have also been computed. The study has applications in polymer processing.

On new classes of solutions of nonlinear partial differential equations in the form of convergent special series

NASA Astrophysics Data System (ADS)

Filimonov, M. Yu.

2017-12-01

The method of special series with recursively calculated coefficients is used to solve nonlinear partial differential equations. The recurrence of finding the coefficients of the series is achieved due to a special choice of functions, in powers of which the solution is expanded in a series. We obtain a sequence of linear partial differential equations to find the coefficients of the series constructed. In many cases, one can deal with a sequence of linear ordinary differential equations. We construct classes of solutions in the form of convergent series for a certain class of nonlinear evolution equations. A new class of solutions of generalized Boussinesque equation with an arbitrary function in the form of a convergent series is constructed.

MHD boundary layer slip flow and heat transfer of ferrofluid along a stretching cylinder with prescribed heat flux.

PubMed

Qasim, Muhammad; Khan, Zafar Hayat; Khan, Waqar Ahmad; Ali Shah, Inayat

2014-01-01

This study investigates the magnetohydrodynamic (MHD) flow of ferrofluid along a stretching cylinder. The velocity slip and prescribed surface heat flux boundary conditions are employed on the cylinder surface. Water as conventional base fluid containing nanoparticles of magnetite (Fe3O4) is used. Comparison between magnetic (Fe3O4) and non-magnetic (Al2O3) nanoparticles is also made. The governing non-linear partial differential equations are reduced to non-linear ordinary differential equations and then solved numerically using shooting method. Present results are compared with the available data in the limiting cases. The present results are found to be in an excellent agreement. It is observed that with an increase in the magnetic field strength, the percent difference in the heat transfer rate of magnetic nanoparticles with Al2O3 decreases. Surface shear stress and the heat transfer rate at the surface increase as the curvature parameter increases, i.e curvature helps to enhance the heat transfer.

On Partial Fraction Decompositions by Repeated Polynomial Divisions

ERIC Educational Resources Information Center

Man, Yiu-Kwong

2017-01-01

We present a method for finding partial fraction decompositions of rational functions with linear or quadratic factors in the denominators by means of repeated polynomial divisions. This method does not involve differentiation or solving linear equations for obtaining the unknown partial fraction coefficients, which is very suitable for either…

A theory of fine structure image models with an application to detection and classification of dementia

PubMed Central

Penn, Richard; Werner, Michael; Thomas, Justin

2015-01-01

Background Estimation of stochastic process models from data is a common application of time series analysis methods. Such system identification processes are often cast as hypothesis testing exercises whose intent is to estimate model parameters and test them for statistical significance. Ordinary least squares (OLS) regression and the Levenberg-Marquardt algorithm (LMA) have proven invaluable computational tools for models being described by non-homogeneous, linear, stationary, ordinary differential equations. Methods In this paper we extend stochastic model identification to linear, stationary, partial differential equations in two independent variables (2D) and show that OLS and LMA apply equally well to these systems. The method employs an original nonparametric statistic as a test for the significance of estimated parameters. Results We show gray scale and color images are special cases of 2D systems satisfying a particular autoregressive partial difference equation which estimates an analogous partial differential equation. Several applications to medical image modeling and classification illustrate the method by correctly classifying demented and normal OLS models of axial magnetic resonance brain scans according to subject Mini Mental State Exam (MMSE) scores. Comparison with 13 image classifiers from the literature indicates our classifier is at least 14 times faster than any of them and has a classification accuracy better than all but one. Conclusions Our modeling method applies to any linear, stationary, partial differential equation and the method is readily extended to 3D whole-organ systems. Further, in addition to being a robust image classifier, estimated image models offer insights into which parameters carry the most diagnostic image information and thereby suggest finer divisions could be made within a class. Image models can be estimated in milliseconds which translate to whole-organ models in seconds; such runtimes could make real-time medicine and surgery modeling possible. PMID:26029638

Time Parallel Solution of Linear Partial Differential Equations on the Intel Touchstone Delta Supercomputer

NASA Technical Reports Server (NTRS)

Toomarian, N.; Fijany, A.; Barhen, J.

1993-01-01

Evolutionary partial differential equations are usually solved by decretization in time and space, and by applying a marching in time procedure to data and algorithms potentially parallelized in the spatial domain.

Operational method of solution of linear non-integer ordinary and partial differential equations.

PubMed

Zhukovsky, K V

2016-01-01

We propose operational method with recourse to generalized forms of orthogonal polynomials for solution of a variety of differential equations of mathematical physics. Operational definitions of generalized families of orthogonal polynomials are used in this context. Integral transforms and the operational exponent together with some special functions are also employed in the solutions. The examples of solution of physical problems, related to such problems as the heat propagation in various models, evolutional processes, Black-Scholes-like equations etc. are demonstrated by the operational technique.

A stopping criterion for the iterative solution of partial differential equations

NASA Astrophysics Data System (ADS)

Rao, Kaustubh; Malan, Paul; Perot, J. Blair

2018-01-01

A stopping criterion for iterative solution methods is presented that accurately estimates the solution error using low computational overhead. The proposed criterion uses information from prior solution changes to estimate the error. When the solution changes are noisy or stagnating it reverts to a less accurate but more robust, low-cost singular value estimate to approximate the error given the residual. This estimator can also be applied to iterative linear matrix solvers such as Krylov subspace or multigrid methods. Examples of the stopping criterion's ability to accurately estimate the non-linear and linear solution error are provided for a number of different test cases in incompressible fluid dynamics.

Pseudo almost periodic solutions to some systems of nonlinear hyperbolic second-order partial differential equations

NASA Astrophysics Data System (ADS)

Al-Islam, Najja Shakir

In this Dissertation, the existence of pseudo almost periodic solutions to some systems of nonlinear hyperbolic second-order partial differential equations is established. For that, (Al-Islam [4]) is first studied and then obtained under some suitable assumptions. That is, the existence of pseudo almost periodic solutions to a hyperbolic second-order partial differential equation with delay. The second-order partial differential equation (1) represents a mathematical model for the dynamics of gas absorption, given by uxt+a x,tux=Cx,t,u x,t , u0,t=4 t, 1 where a : [0, L] x RR , C : [0, L] x R x RR , and ϕ : RR are (jointly) continuous functions ( t being the greatest integer function) and L > 0. The results in this Dissertation generalize those of Poorkarimi and Wiener [22]. Secondly, a generalization of the above-mentioned system consisting of the non-linear hyperbolic second-order partial differential equation uxt+a x,tux+bx,t ut+cx,tu=f x,t,u, x∈ 0,L,t∈ R, 2 equipped with the boundary conditions ux,0 =40x, u0,t=u 0t, uxx,0=y 0x, x∈0,L, t∈R, 3 where a, b, c : [0, L ] x RR and f : [0, L] x R x RR are (jointly) continuous functions is studied. Under some suitable assumptions, the existence and uniqueness of pseudo almost periodic solutions to particular cases, as well as the general case of the second-order hyperbolic partial differential equation (2) are studied. The results of all studies contained within this text extend those obtained by Aziz and Meyers [6] in the periodic setting.

A complete and partial integrability technique of the Lorenz system

NASA Astrophysics Data System (ADS)

Bougoffa, Lazhar; Al-Awfi, Saud; Bougouffa, Smail

2018-06-01

In this paper we deal with the well-known nonlinear Lorenz system that describes the deterministic chaos phenomenon. We consider an interesting problem with time-varying phenomena in quantum optics. Then we establish from the motion equations the passage to the Lorenz system. Furthermore, we show that the reduction to the third order non linear equation can be performed. Therefore, the obtained differential equation can be analytically solved in some special cases and transformed to Abel, Dufing, Painlevé and generalized Emden-Fowler equations. So, a motivating technique that permitted a complete and partial integrability of the Lorenz system is presented.

Linear and nonlinear stability of the Blasius boundary layer

NASA Technical Reports Server (NTRS)

Bertolotti, F. P.; Herbert, TH.; Spalart, P. R.

1992-01-01

Two new techniques for the study of the linear and nonlinear instability in growing boundary layers are presented. The first technique employs partial differential equations of parabolic type exploiting the slow change of the mean flow, disturbance velocity profiles, wavelengths, and growth rates in the streamwise direction. The second technique solves the Navier-Stokes equation for spatially evolving disturbances using buffer zones adjacent to the inflow and outflow boundaries. Results of both techniques are in excellent agreement. The linear and nonlinear development of Tollmien-Schlichting (TS) waves in the Blasius boundary layer is investigated with both techniques and with a local procedure based on a system of ordinary differential equations. The results are compared with previous work and the effects of non-parallelism and nonlinearity are clarified. The effect of nonparallelism is confirmed to be weak and, consequently, not responsible for the discrepancies between measurements and theoretical results for parallel flow.

Adaptive moving mesh methods for simulating one-dimensional groundwater problems with sharp moving fronts

USGS Publications Warehouse

Huang, W.; Zheng, Lingyun; Zhan, X.

2002-01-01

Accurate modelling of groundwater flow and transport with sharp moving fronts often involves high computational cost, when a fixed/uniform mesh is used. In this paper, we investigate the modelling of groundwater problems using a particular adaptive mesh method called the moving mesh partial differential equation approach. With this approach, the mesh is dynamically relocated through a partial differential equation to capture the evolving sharp fronts with a relatively small number of grid points. The mesh movement and physical system modelling are realized by solving the mesh movement and physical partial differential equations alternately. The method is applied to the modelling of a range of groundwater problems, including advection dominated chemical transport and reaction, non-linear infiltration in soil, and the coupling of density dependent flow and transport. Numerical results demonstrate that sharp moving fronts can be accurately and efficiently captured by the moving mesh approach. Also addressed are important implementation strategies, e.g. the construction of the monitor function based on the interpolation error, control of mesh concentration, and two-layer mesh movement. Copyright ?? 2002 John Wiley and Sons, Ltd.

Algorithm refinement for stochastic partial differential equations: II. Correlated systems

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

Alexander, Francis J.; Garcia, Alejandro L.; Tartakovsky, Daniel M.

2005-08-10

We analyze a hybrid particle/continuum algorithm for a hydrodynamic system with long ranged correlations. Specifically, we consider the so-called train model for viscous transport in gases, which is based on a generalization of the random walk process for the diffusion of momentum. This discrete model is coupled with its continuous counterpart, given by a pair of stochastic partial differential equations. At the interface between the particle and continuum computations the coupling is by flux matching, giving exact mass and momentum conservation. This methodology is an extension of our stochastic Algorithm Refinement (AR) hybrid for simple diffusion [F. Alexander, A. Garcia,more » D. Tartakovsky, Algorithm refinement for stochastic partial differential equations: I. Linear diffusion, J. Comput. Phys. 182 (2002) 47-66]. Results from a variety of numerical experiments are presented for steady-state scenarios. In all cases the mean and variance of density and velocity are captured correctly by the stochastic hybrid algorithm. For a non-stochastic version (i.e., using only deterministic continuum fluxes) the long-range correlations of velocity fluctuations are qualitatively preserved but at reduced magnitude.« less

Influence of two-stream relativistic electron beam parameters on the space-charge wave with broad frequency spectrum formation

NASA Astrophysics Data System (ADS)

Alexander, LYSENKO; Iurii, VOLK

2018-03-01

We developed a cubic non-linear theory describing the dynamics of the multiharmonic space-charge wave (SCW), with harmonics frequencies smaller than the two-stream instability critical frequency, with different relativistic electron beam (REB) parameters. The self-consistent differential equation system for multiharmonic SCW harmonic amplitudes was elaborated in a cubic non-linear approximation. This system considers plural three-wave parametric resonant interactions between wave harmonics and the two-stream instability effect. Different REB parameters such as the input angle with respect to focusing magnetic field, the average relativistic factor value, difference of partial relativistic factors, and plasma frequency of partial beams were investigated regarding their influence on the frequency spectrum width and multiharmonic SCW saturation levels. We suggested ways in which the multiharmonic SCW frequency spectrum widths could be increased in order to use them in multiharmonic two-stream superheterodyne free-electron lasers, with the main purpose of forming a powerful multiharmonic electromagnetic wave.

Theory of Metastable State Relaxation for Non-Critical Binary Systems with Non-Conserved Order Parameter

NASA Technical Reports Server (NTRS)

Izmailov, Alexander; Myerson, Allan S.

1993-01-01

A new mathematical ansatz for a solution of the time-dependent Ginzburg-Landau non-linear partial differential equation is developed for non-critical systems such as non-critical binary solutions (solute + solvent) described by the non-conserved scalar order parameter. It is demonstrated that in such systems metastability initiates heterogeneous solute redistribution which results in formation of the non-equilibrium singly-periodic spatial solute structure. It is found how the time-dependent period of this structure evolves in time. In addition, the critical radius r(sub c) for solute embryo of the new solute rich phase together with the metastable state lifetime t(sub c) are determined analytically and analyzed.

Electron Interactions with Non-Linear Polyatomic Molecules and Their Radicals

DTIC Science & Technology

1993-12-01

developed which generates SCE quantities from molecular wave functions. This progress was realized in terms of some actual calculations on some molecules...section 4.A describes the basics of the Partial Differential Equation Theory; section 4.B describes the generalization to a finite element...Information Service (NTIS). At NTIS, it will be available to the general public, including foreign nations. This technical report has been reviewed and

Non-symmetric forms of non-linear vibrations of flexible cylindrical panels and plates under longitudinal load and additive white noise

NASA Astrophysics Data System (ADS)

Krysko, V. A.; Awrejcewicz, J.; Krylova, E. Yu; Papkova, I. V.; Krysko, A. V.

2018-06-01

Parametric non-linear vibrations of flexible cylindrical panels subjected to additive white noise are studied. The governing Marguerre equations are investigated using the finite difference method (FDM) of the second-order accuracy and the Runge-Kutta method. The considered mechanical structural member is treated as a system of many/infinite number of degrees of freedom (DoF). The dependence of chaotic vibrations on the number of DoFs is investigated. Reliability of results is guaranteed by comparing the results obtained using two qualitatively different methods to reduce the problem of PDEs (partial differential equations) to ODEs (ordinary differential equations), i.e. the Faedo-Galerkin method in higher approximations and the 4th and 6th order FDM. The Cauchy problem obtained by the FDM is eventually solved using the 4th-order Runge-Kutta methods. The numerical experiment yielded, for a certain set of parameters, the non-symmetric vibration modes/forms with and without white noise. In particular, it has been illustrated and discussed that action of white noise on chaotic vibrations implies quasi-periodicity, whereas the previously non-symmetric vibration modes are closer to symmetric ones.

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.

On the Monge-Ampere equivalent of the sine-Gordon equation

NASA Astrophysics Data System (ADS)

Ferapontov, E. V.; Nutku, Y.

1994-12-01

Surfaces of constant negative curvature in Euclidean space can be described by either the sine-Gordon equation for the angle between asymptotic directions, or a Monge-Ampere equation for the graph of the surface. We present the explicit form of the correspondence between these two integrable non-linear partial differential equations using their well-known properties in differential geometry. We find that the cotangent of the angle between asymptotic directions is directly related to the mean curvature of the surface. This is a Backlund-type transformation between the sine-Gordon and Monge-Ampere equations.

Non-Linearity in Wide Dynamic Range CMOS Image Sensors Utilizing a Partial Charge Transfer Technique.

PubMed

Shafie, Suhaidi; Kawahito, Shoji; Halin, Izhal Abdul; Hasan, Wan Zuha Wan

2009-01-01

The partial charge transfer technique can expand the dynamic range of a CMOS image sensor by synthesizing two types of signal, namely the long and short accumulation time signals. However the short accumulation time signal obtained from partial transfer operation suffers of non-linearity with respect to the incident light. In this paper, an analysis of the non-linearity in partial charge transfer technique has been carried, and the relationship between dynamic range and the non-linearity is studied. The results show that the non-linearity is caused by two factors, namely the current diffusion, which has an exponential relation with the potential barrier, and the initial condition of photodiodes in which it shows that the error in the high illumination region increases as the ratio of the long to the short accumulation time raises. Moreover, the increment of the saturation level of photodiodes also increases the error in the high illumination region.

A differential equation for the Generalized Born radii.

PubMed

Fogolari, Federico; Corazza, Alessandra; Esposito, Gennaro

2013-06-28

The Generalized Born (GB) model offers a convenient way of representing electrostatics in complex macromolecules like proteins or nucleic acids. The computation of atomic GB radii is currently performed by different non-local approaches involving volume or surface integrals. Here we obtain a non-linear second-order partial differential equation for the Generalized Born radius, which may be solved using local iterative algorithms. The equation is derived under the assumption that the usual GB approximation to the reaction field obeys Laplace's equation. The equation admits as particular solutions the correct GB radii for the sphere and the plane. The tests performed on a set of 55 different proteins show an overall agreement with other reference GB models and "perfect" Poisson-Boltzmann based values.

Non-linear duality invariant partially massless models?

DOE PAGES

Cherney, D.; Deser, S.; Waldron, A.; ...

2015-12-15

We present manifestly duality invariant, non-linear, equations of motion for maximal depth, partially massless higher spins. These are based on a first order, Maxwell-like formulation of the known partially massless systems. Lastly, our models mimic Dirac–Born–Infeld theory but it is unclear whether they are Lagrangian.

Canonical coordinates for partial differential equations

NASA Technical Reports Server (NTRS)

Hunt, L. R.; Villarreal, Ramiro

1988-01-01

Necessary and sufficient conditions are found under which operators of the form Sigma (m, j=1) x (2) sub j + X sub O can be made constant coefficient. In addition, necessary and sufficient conditions are derived which classify those linear partial differential operators that can be moved to the Kolmogorov type.

Canonical coordinates for partial differential equations

NASA Technical Reports Server (NTRS)

Hunt, L. R.; Villarreal, Ramiro

1987-01-01

Necessary and sufficient conditions are found under which operators of the form Sigma(m, j=1) X(2)sub j + X sub 0 can be made constant coefficient. In addition, necessary and sufficient conditions are derived which classify those linear partial differential operators that can be moved to the Kolmogorov type.

Evaluating Feynman integrals by the hypergeometry

NASA Astrophysics Data System (ADS)

Feng, Tai-Fu; Chang, Chao-Hsi; Chen, Jian-Bin; Gu, Zhi-Hua; Zhang, Hai-Bin

2018-02-01

The hypergeometric function method naturally provides the analytic expressions of scalar integrals from concerned Feynman diagrams in some connected regions of independent kinematic variables, also presents the systems of homogeneous linear partial differential equations satisfied by the corresponding scalar integrals. Taking examples of the one-loop B0 and massless C0 functions, as well as the scalar integrals of two-loop vacuum and sunset diagrams, we verify our expressions coinciding with the well-known results of literatures. Based on the multiple hypergeometric functions of independent kinematic variables, the systems of homogeneous linear partial differential equations satisfied by the mentioned scalar integrals are established. Using the calculus of variations, one recognizes the system of linear partial differential equations as stationary conditions of a functional under some given restrictions, which is the cornerstone to perform the continuation of the scalar integrals to whole kinematic domains numerically with the finite element methods. In principle this method can be used to evaluate the scalar integrals of any Feynman diagrams.

Group invariant solution for a pre-existing fracture driven by a power-law fluid in impermeable rock

NASA Astrophysics Data System (ADS)

Fareo, A. G.; Mason, D. P.

2013-12-01

The effect of power-law rheology on hydraulic fracturing is investigated. The evolution of a two-dimensional fracture with non-zero initial length and driven by a power-law fluid is analyzed. Only fluid injection into the fracture is considered. The surrounding rock mass is impermeable. With the aid of lubrication theory and the PKN approximation a partial differential equation for the fracture half-width is derived. Using a linear combination of the Lie-point symmetry generators of the partial differential equation, the group invariant solution is obtained and the problem is reduced to a boundary value problem for an ordinary differential equation. Exact analytical solutions are derived for hydraulic fractures with constant volume and with constant propagation speed. The asymptotic solution near the fracture tip is found. The numerical solution for general working conditions is obtained by transforming the boundary value problem to a pair of initial value problems. Throughout the paper, hydraulic fracturing with shear thinning, Newtonian and shear thickening fluids are compared.

Optimal linear-quadratic control of coupled parabolic-hyperbolic PDEs

NASA Astrophysics Data System (ADS)

Aksikas, I.; Moghadam, A. Alizadeh; Forbes, J. F.

2017-10-01

This paper focuses on the optimal control design for a system of coupled parabolic-hypebolic partial differential equations by using the infinite-dimensional state-space description and the corresponding operator Riccati equation. Some dynamical properties of the coupled system of interest are analysed to guarantee the existence and uniqueness of the solution of the linear-quadratic (LQ)-optimal control problem. A state LQ-feedback operator is computed by solving the operator Riccati equation, which is converted into a set of algebraic and differential Riccati equations, thanks to the eigenvalues and the eigenvectors of the parabolic operator. The results are applied to a non-isothermal packed-bed catalytic reactor. The LQ-optimal controller designed in the early portion of the paper is implemented for the original nonlinear model. Numerical simulations are performed to show the controller performances.

Conservation laws and conserved quantities for (1+1)D linearized Boussinesq equations

NASA Astrophysics Data System (ADS)

Carvalho, Cindy; Harley, Charis

2017-05-01

Conservation laws and physical conserved quantities for the (1+1)D linearized Boussinesq equations at a constant water depth are presented. These equations describe incompressible, inviscid, irrotational fluid flow in the form of a non steady solitary wave. A systematic multiplier approach is used to obtain the conservation laws of the system of third order partial differential equations (PDEs) in dimensional form. Physical conserved quantities are derived by integrating the conservation laws in the direction of wave propagation and imposing decaying boundary conditions in the horizontal direction. One of these is a newly discovered conserved quantity which relates to an energy flux density.

An exploration of viscosity models in the realm of kinetic theory of liquids originated fluids

NASA Astrophysics Data System (ADS)

Hussain, Azad; Ghafoor, Saadia; Malik, M. Y.; Jamal, Sarmad

The preeminent perspective of this article is to study flow of an Eyring Powell fluid model past a penetrable plate. To find the effects of variable viscosity on fluid model, continuity, momentum and energy equations are elaborated. Here, viscosity is taken as function of temperature. To understand the phenomenon, Reynold and Vogel models of variable viscosity are incorporated. The highly non-linear partial differential equations are transfigured into ordinary differential equations with the help of suitable similarity transformations. The numerical solution of the problem is presented. Graphs are plotted to visualize the behavior of pertinent parameters on the velocity and temperature profiles.

Mathematics for Physics

NASA Astrophysics Data System (ADS)

Stone, Michael; Goldbart, Paul

2009-07-01

Preface; 1. Calculus of variations; 2. Function spaces; 3. Linear ordinary differential equations; 4. Linear differential operators; 5. Green functions; 6. Partial differential equations; 7. The mathematics of real waves; 8. Special functions; 9. Integral equations; 10. Vectors and tensors; 11. Differential calculus on manifolds; 12. Integration on manifolds; 13. An introduction to differential topology; 14. Group and group representations; 15. Lie groups; 16. The geometry of fibre bundles; 17. Complex analysis I; 18. Applications of complex variables; 19. Special functions and complex variables; Appendixes; Reference; Index.

Convection Heat and Mass Transfer in a Power Law Fluid with Non Constant Relaxation Time Past a Vertical Porous Plate in the Presence of Thermo and Thermal Diffusion

NASA Astrophysics Data System (ADS)

Olajuwon, B. I.; Oyelakin, I. S.

2012-12-01

The paper investigates convection heat and mass transfer in power law fluid flow with non relaxation time past a vertical porous plate in presence of a chemical reaction, heat generation, thermo diffu- sion and thermal diffusion. The non - linear partial differential equations governing the flow are transformed into ordinary differential equations using the usual similarity method. The resulting similarity equations are solved numerically using Runge-Kutta shooting method. The results are presented as velocity, temperature and concentration profiles for pseudo plastic fluids and for different values of parameters governing the prob- lem. The skin friction, heat transfer and mass transfer rates are presented numerically in tabular form. The results show that these parameters have significant effects on the flow, heat transfer and mass transfer.

Reduced-order modelling of parameter-dependent, linear and nonlinear dynamic partial differential equation models.

PubMed

Shah, A A; Xing, W W; Triantafyllidis, V

2017-04-01

In this paper, we develop reduced-order models for dynamic, parameter-dependent, linear and nonlinear partial differential equations using proper orthogonal decomposition (POD). The main challenges are to accurately and efficiently approximate the POD bases for new parameter values and, in the case of nonlinear problems, to efficiently handle the nonlinear terms. We use a Bayesian nonlinear regression approach to learn the snapshots of the solutions and the nonlinearities for new parameter values. Computational efficiency is ensured by using manifold learning to perform the emulation in a low-dimensional space. The accuracy of the method is demonstrated on a linear and a nonlinear example, with comparisons with a global basis approach.

Reduced-order modelling of parameter-dependent, linear and nonlinear dynamic partial differential equation models

PubMed Central

Xing, W. W.; Triantafyllidis, V.

2017-01-01

In this paper, we develop reduced-order models for dynamic, parameter-dependent, linear and nonlinear partial differential equations using proper orthogonal decomposition (POD). The main challenges are to accurately and efficiently approximate the POD bases for new parameter values and, in the case of nonlinear problems, to efficiently handle the nonlinear terms. We use a Bayesian nonlinear regression approach to learn the snapshots of the solutions and the nonlinearities for new parameter values. Computational efficiency is ensured by using manifold learning to perform the emulation in a low-dimensional space. The accuracy of the method is demonstrated on a linear and a nonlinear example, with comparisons with a global basis approach. PMID:28484327

Analysis of ammonia separation from purge gases in microporous hollow fiber membrane contactors.

PubMed

Karami, M R; Keshavarz, P; Khorram, M; Mehdipour, M

2013-09-15

In this study, a mathematical model was developed to analyze the separation of ammonia from the purge gas of ammonia plants using microporous hollow fiber membrane contactors. A numerical procedure was proposed to solve the simultaneous linear and non linear partial differential equations in the liquid, membrane and gas phases for non-wetted or partially wetted conditions. An equation of state was applied in the model instead of Henry's law because of high solubility of ammonia in water. The experimental data of CO₂-water system in the literature was used to validate the model due to the lack of data for ammonia-water system. The model showed that the membrane contactor can separate ammonia very effectively and with recoveries higher than 99%. SEM images demonstrated that ammonia caused some micro-cracks on the surfaces of polypropylene fibers, which could be an indication of partial wetting of membrane in long term applications. However, the model results revealed that the membrane wetting did not have significant effect on the absorption of ammonia because of very high solubility of ammonia in water. It was also found that the effect of gas velocity on the absorption flux was much more than the effect of liquid velocity. Copyright © 2013 Elsevier B.V. All rights reserved.

The Programming Language Python In Earth System Simulations

NASA Astrophysics Data System (ADS)

Gross, L.; Imranullah, A.; Mora, P.; Saez, E.; Smillie, J.; Wang, C.

2004-12-01

Mathematical models in earth sciences base on the solution of systems of coupled, non-linear, time-dependent partial differential equations (PDEs). The spatial and time-scale vary from a planetary scale and million years for convection problems to 100km and 10 years for fault systems simulations. Various techniques are in use to deal with the time dependency (e.g. Crank-Nicholson), with the non-linearity (e.g. Newton-Raphson) and weakly coupled equations (e.g. non-linear Gauss-Seidel). Besides these high-level solution algorithms discretization methods (e.g. finite element method (FEM), boundary element method (BEM)) are used to deal with spatial derivatives. Typically, large-scale, three dimensional meshes are required to resolve geometrical complexity (e.g. in the case of fault systems) or features in the solution (e.g. in mantel convection simulations). The modelling environment escript allows the rapid implementation of new physics as required for the development of simulation codes in earth sciences. Its main object is to provide a programming language, where the user can define new models and rapidly develop high-level solution algorithms. The current implementation is linked with the finite element package finley as a PDE solver. However, the design is open and other discretization technologies such as finite differences and boundary element methods could be included. escript is implemented as an extension of the interactive programming environment python (see www.python.org). Key concepts introduced are Data objects, which are holding values on nodes or elements of the finite element mesh, and linearPDE objects, which are defining linear partial differential equations to be solved by the underlying discretization technology. In this paper we will show the basic concepts of escript and will show how escript is used to implement a simulation code for interacting fault systems. We will show some results of large-scale, parallel simulations on an SGI Altix system. Acknowledgements: Project work is supported by Australian Commonwealth Government through the Australian Computational Earth Systems Simulator Major National Research Facility, Queensland State Government Smart State Research Facility Fund, The University of Queensland and SGI.

A fast direct method for block triangular Toeplitz-like with tri-diagonal block systems from time-fractional partial differential equations

NASA Astrophysics Data System (ADS)

Ke, Rihuan; Ng, Michael K.; Sun, Hai-Wei

2015-12-01

In this paper, we study the block lower triangular Toeplitz-like with tri-diagonal blocks system which arises from the time-fractional partial differential equation. Existing fast numerical solver (e.g., fast approximate inversion method) cannot handle such linear system as the main diagonal blocks are different. The main contribution of this paper is to propose a fast direct method for solving this linear system, and to illustrate that the proposed method is much faster than the classical block forward substitution method for solving this linear system. Our idea is based on the divide-and-conquer strategy and together with the fast Fourier transforms for calculating Toeplitz matrix-vector multiplication. The complexity needs O (MNlog2 ⁡ M) arithmetic operations, where M is the number of blocks (the number of time steps) in the system and N is the size (number of spatial grid points) of each block. Numerical examples from the finite difference discretization of time-fractional partial differential equations are also given to demonstrate the efficiency of the proposed method.

Detection of Ozone and Nitric Oxide in Decomposition Products of Air-Insulated Switchgear Using Ultraviolet Differential Optical Absorption Spectroscopy (UV-DOAS).

PubMed

Li, Yalong; Zhang, Xiaoxing; Li, Xin; Cui, Zhaolun; Xiao, Hai

2018-01-01

Air-insulated switchgear cabinets play a role in the protection and control of the modern power grid, and partial discharge (PD) switchgear is a long-term process in the non-normal operation of one of the situations; thus, condition monitoring of the switchgear is important. The air-insulated switchgear during PD enables the decomposition of air components, namely, O 3 and NO. A set of experimental platforms was designed on the basis of the principle of ultraviolet differential optical absorption spectroscopy (UV-DOAS) to detect O 3 and NO concentrations in air-insulated switchgear. Differential absorption algorithm and wavelet transform were used to extract effective absorption spectra; a linear relationship between O 3 and NO concentrations and absorption spectrum data were established. O 3 detection linearity was up to 0.9992 and the detection limit was at 3.76 ppm. NO detection linearity was up to 0.9990 and the detection limit was at 0.64 ppm. Results indicate that detection platform is suitable for detecting trace O 3 and NO gases produced by PD of the air-insulated switchgear.

A preconditioner for the finite element computation of incompressible, nonlinear elastic deformations

NASA Astrophysics Data System (ADS)

Whiteley, J. P.

2017-10-01

Large, incompressible elastic deformations are governed by a system of nonlinear partial differential equations. The finite element discretisation of these partial differential equations yields a system of nonlinear algebraic equations that are usually solved using Newton's method. On each iteration of Newton's method, a linear system must be solved. We exploit the structure of the Jacobian matrix to propose a preconditioner, comprising two steps. The first step is the solution of a relatively small, symmetric, positive definite linear system using the preconditioned conjugate gradient method. This is followed by a small number of multigrid V-cycles for a larger linear system. Through the use of exemplar elastic deformations, the preconditioner is demonstrated to facilitate the iterative solution of the linear systems arising. The number of GMRES iterations required has only a very weak dependence on the number of degrees of freedom of the linear systems.

Stability Analysis of Finite Difference Schemes for Hyperbolic Systems, and Problems in Applied and Computational Linear Algebra.

DTIC Science & Technology

FINITE DIFFERENCE THEORY, * LINEAR ALGEBRA , APPLIED MATHEMATICS, APPROXIMATION(MATHEMATICS), BOUNDARY VALUE PROBLEMS, COMPUTATIONS, HYPERBOLAS, MATHEMATICAL MODELS, NUMERICAL ANALYSIS, PARTIAL DIFFERENTIAL EQUATIONS, STABILITY.

Symmetry groups of integro-differential equations for linear thermoviscoelastic materials with memory

NASA Astrophysics Data System (ADS)

Zhou, L.-Q.; Meleshko, S. V.

2017-07-01

The group analysis method is applied to a system of integro-differential equations corresponding to a linear thermoviscoelastic model. A recently developed approach for calculating the symmetry groups of such equations is used. The general solution of the determining equations for the system is obtained. Using subalgebras of the admitted Lie algebra, two classes of partially invariant solutions of the considered system of integro-differential equations are studied.

FAST TRACK COMMUNICATION Quasi self-adjoint nonlinear wave equations

NASA Astrophysics Data System (ADS)

Ibragimov, N. H.; Torrisi, M.; Tracinà, R.

2010-11-01

In this paper we generalize the classification of self-adjoint second-order linear partial differential equation to a family of nonlinear wave equations with two independent variables. We find a class of quasi self-adjoint nonlinear equations which includes the self-adjoint linear equations as a particular case. The property of a differential equation to be quasi self-adjoint is important, e.g. for constructing conservation laws associated with symmetries of the differential equation.

[Correlation between gaseous exchange rate, body temperature, and mitochondrial protein content in the liver of mice].

PubMed

Muradian, Kh K; Utko, N O; Mozzhukhina, T H; Pishel', I M; Litoshenko, O Ia; Bezrukov, V V; Fraĭfel'd, V E

2002-01-01

Correlative and regressive relations between the gaseous exchange, thermoregulation and mitochondrial protein content were analyzed by two- and three-dimensional statistics in mice. It has been shown that the pair wise linear methods of analysis did not reveal any significant correlation between the parameters under exploration. However, it became evident at three-dimensional and non-linear plotting for which the coefficients of multivariable correlation reached and even exceeded 0.7-0.8. The calculations based on partial differentiation of the multivariable regression equations allow to conclude that at certain values of VO2, VCO2 and body temperature negative relations between the systems of gaseous exchange and thermoregulation become dominating.

Effect of thermal radiation on laminar boundary layer flow over a permeable flat plate with Newtonian heating

NASA Astrophysics Data System (ADS)

Khairul Anuar Mohamed, Muhammad; Zuki Salleh, Mohd; Noar, Nor Aida Zuraimi Md; Ishak, Anuar

2017-09-01

The laminar boundary layer flow over a permeable flat plat with the presence of thermal radiation and Newtonian heating is numerically studied. The non linear partial differential equations that governed the model are transformed to ordinary differential equations before being solved numerically by Runge-Kutta-Fehlberg (RKF) method using Maple software. The influenced and characteristic of pertinent parameters which are the Prandtl number, the suction/blowing parameter, the thermal radiation parameter and the conjugate parameter are analyzed and discussed. It is found that the presence of thermal radiation and blowing parameter has increased the value of wall temperature. Meanwhile, the trend is contrary with the suction effect.

Gröbner Bases and Generation of Difference Schemes for Partial Differential Equations

NASA Astrophysics Data System (ADS)

Gerdt, Vladimir P.; Blinkov, Yuri A.; Mozzhilkin, Vladimir V.

2006-05-01

In this paper we present an algorithmic approach to the generation of fully conservative difference schemes for linear partial differential equations. The approach is based on enlargement of the equations in their integral conservation law form by extra integral relations between unknown functions and their derivatives, and on discretization of the obtained system. The structure of the discrete system depends on numerical approximation methods for the integrals occurring in the enlarged system. As a result of the discretization, a system of linear polynomial difference equations is derived for the unknown functions and their partial derivatives. A difference scheme is constructed by elimination of all the partial derivatives. The elimination can be achieved by selecting a proper elimination ranking and by computing a Gröbner basis of the linear difference ideal generated by the polynomials in the discrete system. For these purposes we use the difference form of Janet-like Gröbner bases and their implementation in Maple. As illustration of the described methods and algorithms, we construct a number of difference schemes for Burgers and Falkowich-Karman equations and discuss their numerical properties.

Flow and Heat Transfer in Sisko Fluid with Convective Boundary Condition

PubMed Central

Malik, Rabia; Khan, Masood; Munir, Asif; Khan, Waqar Azeem

2014-01-01

In this article, we have studied the flow and heat transfer in Sisko fluid with convective boundary condition over a non-isothermal stretching sheet. The flow is influenced by non-linearly stretching sheet in the presence of a uniform transverse magnetic field. The partial differential equations governing the problem have been reduced by similarity transformations into the ordinary differential equations. The transformed coupled ordinary differential equations are then solved analytically by using the homotopy analysis method (HAM) and numerically by the shooting method. Effects of different parameters like power-law index , magnetic parameter , stretching parameter , generalized Prandtl number Pr and generalized Biot number are presented graphically. It is found that temperature profile increases with the increasing value of and whereas it decreases for . Numerical values of the skin-friction coefficient and local Nusselt number are tabulated at various physical situations. In addition, a comparison between the HAM and exact solutions is also made as a special case and excellent agreement between results enhance a confidence in the HAM results. PMID:25285822

Linearized Model of an Actively Controlled Cable for a Carlina Diluted Telescope

NASA Astrophysics Data System (ADS)

Andersen, T.; Le Coroller, H.; Owner-Petersen, M.; Dejonghe, J.

2014-04-01

The Carlina thinned pupil telescope has a focal unit (``gondola'') suspended by cables over the primary mirror. To predict the structural behavior of the gondola system, a simulation building block of a single cable is needed. A preloaded cable is a strongly non-linear system and can be modeled either with partial differential equations or non-linear finite elements. Using the latter, we set up an iteration procedure for determination of the static cable form and we formulate the necessary second-order differential equations for such a model. We convert them to a set of first-order differential equations (an ``ABCD''-model). Symmetrical in-plane eigenmodes and ``axial'' eigenmodes are the only eigenmodes that play a role in practice for a taut cable. Using the model and a generic suspension, a parameter study is made to find the influence of various design parameters. We conclude that the cable should be as stiff and thick as practically possible with a fairly high preload. Steel or Aramid are suitable materials. Further, placing the cable winches on the gondola and not on the ground does not provide significant advantages. Finally, it seems that use of reaction-wheels and/or reaction-masses will make the way for more accurate control of the gondola position under wind load. An adaptive stage with tip/tilt/piston correction for subapertures together with a focus and guiding system for freezing the fringes must also be studied.

Computer simulation of two-dimensional unsteady flows in estuaries and embayments by the method of characteristics : basic theory and the formulation of the numerical method

USGS Publications Warehouse

Lai, Chintu

1977-01-01

Two-dimensional unsteady flows of homogeneous density in estuaries and embayments can be described by hyperbolic, quasi-linear partial differential equations involving three dependent and three independent variables. A linear combination of these equations leads to a parametric equation of characteristic form, which consists of two parts: total differentiation along the bicharacteristics and partial differentiation in space. For its numerical solution, the specified-time-interval scheme has been used. The unknown, partial space-derivative terms can be eliminated first by suitable combinations of difference equations, converted from the corresponding differential forms and written along four selected bicharacteristics and a streamline. Other unknowns are thus made solvable from the known variables on the current time plane. The computation is carried to the second-order accuracy by using trapezoidal rule of integration. Means to handle complex boundary conditions are developed for practical application. Computer programs have been written and a mathematical model has been constructed for flow simulation. The favorable computer outputs suggest further exploration and development of model worthwhile. (Woodard-USGS)

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

DTIC Science & Technology

1971-06-01

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

An Improved Heaviside Approach to Partial Fraction Expansion and Its Applications

ERIC Educational Resources Information Center

Man, Yiu-Kwong

2009-01-01

In this note, we present an improved Heaviside approach to compute the partial fraction expansions of proper rational functions. This method uses synthetic divisions to determine the unknown partial fraction coefficients successively, without the need to use differentiation or to solve a system of linear equations. Examples of its applications in…

Second-order numerical methods for multi-term fractional differential equations: Smooth and non-smooth solutions

NASA Astrophysics Data System (ADS)

Zeng, Fanhai; Zhang, Zhongqiang; Karniadakis, George Em

2017-12-01

Starting with the asymptotic expansion of the error equation of the shifted Gr\\"{u}nwald--Letnikov formula, we derive a new modified weighted shifted Gr\\"{u}nwald--Letnikov (WSGL) formula by introducing appropriate correction terms. We then apply one special case of the modified WSGL formula to solve multi-term fractional ordinary and partial differential equations, and we prove the linear stability and second-order convergence for both smooth and non-smooth solutions. We show theoretically and numerically that numerical solutions up to certain accuracy can be obtained with only a few correction terms. Moreover, the correction terms can be tuned according to the fractional derivative orders without explicitly knowing the analytical solutions. Numerical simulations verify the theoretical results and demonstrate that the new formula leads to better performance compared to other known numerical approximations with similar resolution.

Non-linear quenching of current fluctuations in a self-exciting homopolar dynamo, proved by feedback system theory

NASA Astrophysics Data System (ADS)

de Paor, A. M.

Hide (Nonlinear Processes in Geophysics, 1998) has produced a new mathematical model of a self-exciting homopolar dynamo driving a series- wound motor, as a continuing contribution to the theory of the geomagnetic field. By a process of exact perturbation analysis, followed by combination and partial solution of differential equations, the complete nonlinear quenching of current fluctuations reported by Hide in the case that a parameter ɛ has the value 1 is proved via the Popov theorem from feedback system stability theory.

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

NASA Technical Reports Server (NTRS)

Banks, H. T.; Kunisch, K.

1982-01-01

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

Numerical simulation for flow and heat transfer to Carreau fluid with magnetic field effect: Dual nature study

NASA Astrophysics Data System (ADS)

Hashim; Khan, Masood; Alshomrani, Ali Saleh

2017-12-01

This article considers a realistic approach to examine the magnetohydrodynamics (MHD) flow of Carreau fluid induced by the shrinking sheet subject to the stagnation-point. This study also explores the impacts of non-linear thermal radiation on the heat transfer process. The governing equations of physical model are expressed as a system of partial differential equations and are transformed into non-linear ordinary differential equations by introducing local similarity variables. The economized equations of the problem are numerically integrated using the Runge-Kutta Fehlberg integration scheme. In this study, we explore the condition of existence, non-existence, uniqueness and dual nature for obtaining numerical solutions. It is found that the solutions may possess multiple natures, upper and lower branch, for a specific range of shrinking parameter. Results indicate that due to an increment in the magnetic parameter, range of shrinking parameter where a dual solution exists, increases. Further, strong magnetic field enhances the thickness of the momentum boundary layer in case of the second solution while for first solution it reduces. We further note that the fluid suction diminishes the fluid velocity and therefore the thickness of the hydrodynamic boundary layer decreases as well. A critical analysis with existing works is performed which shows that outcome are benchmarks with these works.

On multiple solutions of non-Newtonian Carreau fluid flow over an inclined shrinking sheet

NASA Astrophysics Data System (ADS)

Khan, Masood; Sardar, Humara; Gulzar, M. Mudassar; Alshomrani, Ali Saleh

2018-03-01

This paper presents the multiple solutions of a non-Newtonian Carreau fluid flow over a nonlinear inclined shrinking surface in presence of infinite shear rate viscosity. The governing boundary layer equations are derived for the Carreau fluid with infinite shear rate viscosity. The suitable transformations are employed to alter the leading partial differential equations to a set of ordinary differential equations. The consequential non-linear ODEs are solved numerically by an active numerical approach namely Runge-Kutta Fehlberg fourth-fifth order method accompanied by shooting technique. Multiple solutions are presented graphically and results are shown for various physical parameters. It is important to state that the velocity and momentum boundary layer thickness reduce with increasing viscosity ratio parameter in shear thickening fluid while opposite trend is observed for shear thinning fluid. Another important observation is that the wall shear stress is significantly decreased by the viscosity ratio parameter β∗ for the first solution and opposite trend is observed for the second solution.

A Unified Introduction to Ordinary Differential Equations

ERIC Educational Resources Information Center

Lutzer, Carl V.

2006-01-01

This article describes how a presentation from the point of view of differential operators can be used to (partially) unify the myriad techniques in an introductory course in ordinary differential equations by providing students with a powerful, flexible paradigm that extends into (or from) linear algebra. (Contains 1 footnote.)

Analytical study on the thermal performance of a partially wet constructal T-shaped fin

NASA Astrophysics Data System (ADS)

Hazarika, Saheera Azmi; Zeeshan, Mohd; Bhanja, Dipankar; Nath, Sujit

2017-07-01

The present paper addresses the thermal analysis of a T-shaped fin under partially wet condition by adopting a cubic variation of the humidity ratio of saturated air with the corresponding fin surface temperature. The point separating the dry and wet parts may lie either in the flange or stem part of the fin and so, two different cases having different governing equations and boundary conditions are analyzed in this paper. Since the governing equations are highly non-linear, they are solved by using an analytical technique called the Differential Transform Method and subsequently, the dry fin length, temperature distribution and fin performances are evaluated and analyzed for a wide range of the various psychometric, geometric and thermo-physical parameters. Finally, it can be highlighted that relative humidity has a pronounced effect on the performance parameters when the fin surface is partially wet whereas this effect is marginally small for fully wet surface.

Scattering on two Aharonov-Bohm vortices

NASA Astrophysics Data System (ADS)

Bogomolny, E.

2016-12-01

The problem of two Aharonov-Bohm (AB) vortices for the Helmholtz equation is examined in detail. It is demonstrated that the method proposed by Myers (1963 J. Math. Phys. 6 1839) for slit diffraction can be generalised to obtain an explicit solution for AB vortices. Due to the singular nature of AB interaction the Green function and scattering amplitude for two AB vortices obey a series of partial differential equations. Coefficients entering these equations, fulfil ordinary non-linear differential equations whose solutions can be obtained by solving the Painlevé III equation. The asymptotics of necessary functions for very large and very small vortex separations are calculated explicitly. Taken together, this means that the problem of two AB vortices is exactly solvable.

Effects of Heat Source/Sink and Chemical Reaction on MHD Maxwell Nanofluid Flow Over a Convectively Heated Exponentially Stretching Sheet Using Homotopy Analysis Method

NASA Astrophysics Data System (ADS)

Sravanthi, C. S.; Gorla, R. S. R.

2018-02-01

The aim of this paper is to study the effects of chemical reaction and heat source/sink on a steady MHD (magnetohydrodynamic) two-dimensional mixed convective boundary layer flow of a Maxwell nanofluid over a porous exponentially stretching sheet in the presence of suction/blowing. Convective boundary conditions of temperature and nanoparticle concentration are employed in the formulation. Similarity transformations are used to convert the governing partial differential equations into non-linear ordinary differential equations. The resulting non-linear system has been solved analytically using an efficient technique, namely: the homotopy analysis method (HAM). Expressions for velocity, temperature and nanoparticle concentration fields are developed in series form. Convergence of the constructed solution is verified. A comparison is made with the available results in the literature and our results are in very good agreement with the known results. The obtained results are presented through graphs for several sets of values of the parameters and salient features of the solutions are analyzed. Numerical values of the local skin-friction, Nusselt number and nanoparticle Sherwood number are computed and analyzed.

Cattaneo-Christov based study of {TiO}_2 -CuO/EG Casson hybrid nanofluid flow over a stretching surface with entropy generation

NASA Astrophysics Data System (ADS)

Jamshed, Wasim; Aziz, Asim

2018-06-01

In the present research, a simplified mathematical model is presented to study the heat transfer and entropy generation analysis of thermal system containing hybrid nanofluid. Nanofluid occupies the space over an infinite horizontal surface and the flow is induced by the non-linear stretching of surface. A uniform transverse magnetic field, Cattaneo-Christov heat flux model and thermal radiation effects are also included in the present study. The similarity technique is employed to reduce the governing non-linear partial differential equations to a set of ordinary differential equation. Keller Box numerical scheme is then used to approximate the solutions for the thermal analysis. Results are presented for conventional copper oxide-ethylene glycol (CuO-EG) and hybrid titanium-copper oxide/ethylene glycol ({TiO}_2 -CuO/EG) nanofluids. The spherical, hexahedron, tetrahedron, cylindrical, and lamina-shaped nanoparticles are considered in the present analysis. The significant findings of the study is the enhanced heat transfer capability of hybrid nanofluids over the conventional nanofluids, greatest heat transfer rate for the smallest value of the shape factor parameter and the increase in Reynolds number and Brinkman number increases the overall entropy of the system.

Introducing the Improved Heaviside Approach to Partial Fraction Decomposition to Undergraduate Students: Results and Implications from a Pilot Study

ERIC Educational Resources Information Center

Man, Yiu-Kwong

2012-01-01

Partial fraction decomposition is a useful technique often taught at senior secondary or undergraduate levels to handle integrations, inverse Laplace transforms or linear ordinary differential equations, etc. In recent years, an improved Heaviside's approach to partial fraction decomposition was introduced and developed by the author. An important…

Observability of discretized partial differential equations

NASA Technical Reports Server (NTRS)

Cohn, Stephen E.; Dee, Dick P.

1988-01-01

It is shown that complete observability of the discrete model used to assimilate data from a linear partial differential equation (PDE) system is necessary and sufficient for asymptotic stability of the data assimilation process. The observability theory for discrete systems is reviewed and applied to obtain simple observability tests for discretized constant-coefficient PDEs. Examples are used to show how numerical dispersion can result in discrete dynamics with multiple eigenvalues, thereby detracting from observability.

A Textbook for a First Course in Computational Fluid Dynamics

NASA Technical Reports Server (NTRS)

Zingg, D. W.; Pulliam, T. H.; Nixon, David (Technical Monitor)

1999-01-01

This paper describes and discusses the textbook, Fundamentals of Computational Fluid Dynamics by Lomax, Pulliam, and Zingg, which is intended for a graduate level first course in computational fluid dynamics. This textbook emphasizes fundamental concepts in developing, analyzing, and understanding numerical methods for the partial differential equations governing the physics of fluid flow. Its underlying philosophy is that the theory of linear algebra and the attendant eigenanalysis of linear systems provides a mathematical framework to describe and unify most numerical methods in common use in the field of fluid dynamics. Two linear model equations, the linear convection and diffusion equations, are used to illustrate concepts throughout. Emphasis is on the semi-discrete approach, in which the governing partial differential equations (PDE's) are reduced to systems of ordinary differential equations (ODE's) through a discretization of the spatial derivatives. The ordinary differential equations are then reduced to ordinary difference equations (O(Delta)E's) using a time-marching method. This methodology, using the progression from PDE through ODE's to O(Delta)E's, together with the use of the eigensystems of tridiagonal matrices and the theory of O(Delta)E's, gives the book its distinctiveness and provides a sound basis for a deep understanding of fundamental concepts in computational fluid dynamics.

Chemical networks with inflows and outflows: a positive linear differential inclusions approach.

PubMed

Angeli, David; De Leenheer, Patrick; Sontag, Eduardo D

2009-01-01

Certain mass-action kinetics models of biochemical reaction networks, although described by nonlinear differential equations, may be partially viewed as state-dependent linear time-varying systems, which in turn may be modeled by convex compact valued positive linear differential inclusions. A result is provided on asymptotic stability of such inclusions, and applied to a ubiquitous biochemical reaction network with inflows and outflows, known as the futile cycle. We also provide a characterization of exponential stability of general homogeneous switched systems which is not only of interest in itself, but also plays a role in the analysis of the futile cycle. 2009 American Institute of Chemical Engineers

Spherical means of solutions of partial differential equations in a conical region

NASA Technical Reports Server (NTRS)

Ting, L.

1974-01-01

The spherical means of the solutions of a linear partial differential equation Lu = f in a conical region are studied. The conical region is bounded by a surface generated by curvilinear ti surfaces. The spherical mean is the average of u over a constant ti surface. The conditions on the linear differential operator, L, and on the orthogonal coordinates (ti, eta, zeta) are established so that the spherical mean of the solution subjected to the appropriate boundary and initial conditions can be determined directly as a problem with only space variable. Conditions are then established so that the spherical mean of the solution in one concial region will be proportional to that of a known solution in another conical region. Applications to various problems of mathematical physics and their physical interpretations are presented.

Partial Fractions via Calculus

ERIC Educational Resources Information Center

Bauldry, William C.

2018-01-01

The standard technique taught in calculus courses for partial fraction expansions uses undetermined coefficients to generate a system of linear equations; we present a derivative-based technique that calculus and differential equations instructors can use to reinforce connections to calculus. Simple algebra shows that we can use the derivative to…

Topics in spectral methods

NASA Technical Reports Server (NTRS)

Gottlieb, D.; Turkel, E.

1985-01-01

After detailing the construction of spectral approximations to time-dependent mixed initial boundary value problems, a study is conducted of differential equations of the form 'partial derivative of u/partial derivative of t = Lu + f', where for each t, u(t) belongs to a Hilbert space such that u satisfies homogeneous boundary conditions. For the sake of simplicity, it is assumed that L is an unbounded, time-independent linear operator. Attention is given to Fourier methods of both Galerkin and pseudospectral method types, the Galerkin method, the pseudospectral Chebyshev and Legendre methods, the error equation, hyperbolic partial differentiation equations, and time discretization and iterative methods.

Bifurcations in two-image photometric stereo for orthogonal illuminations

NASA Astrophysics Data System (ADS)

Kozera, R.; Prokopenya, A.; Noakes, L.; Śluzek, A.

2017-07-01

This paper discusses the ambiguous shape recovery in two-image photometric stereo for a Lambertian surface. The current uniqueness analysis refers to linearly independent light-source directions p = (0, 0, -1) and q arbitrary. For this case necessary and sufficient condition determining ambiguous reconstruction is governed by a second-order linear partial differential equation with constant coefficients. In contrast, a general position of both non-colinear illumination directions p and q leads to a highly non-linear PDE which raises a number of technical difficulties. As recently shown, the latter can also be handled for another family of orthogonal illuminations parallel to the OXZ-plane. For the special case of p = (0, 0, -1) a potential ambiguity stems also from the possible bifurcations of sub-local solutions glued together along a curve defined by an algebraic equation in terms of the data. This paper discusses the occurrence of similar bifurcations for such configurations of orthogonal light-source directions. The discussion to follow is supplemented with examples based on continuous reflectance map model and generated synthetic images.

Transformation matrices between non-linear and linear differential equations

NASA Technical Reports Server (NTRS)

Sartain, R. L.

1983-01-01

In the linearization of systems of non-linear differential equations, those systems which can be exactly transformed into the second order linear differential equation Y"-AY'-BY=0 where Y, Y', and Y" are n x 1 vectors and A and B are constant n x n matrices of real numbers were considered. The 2n x 2n matrix was used to transform the above matrix equation into the first order matrix equation X' = MX. Specially the matrix M and the conditions which will diagonalize or triangularize M were studied. Transformation matrices P and P sub -1 were used to accomplish this diagonalization or triangularization to return to the solution of the second order matrix differential equation system from the first order system.

Numerical method for solution of systems of non-stationary spatially one-dimensional nonlinear differential equations

NASA Technical Reports Server (NTRS)

Morozov, S. K.; Krasitskiy, O. P.

1978-01-01

A computational scheme and a standard program is proposed for solving systems of nonstationary spatially one-dimensional nonlinear differential equations using Newton's method. The proposed scheme is universal in its applicability and its reduces to a minimum the work of programming. The program is written in the FORTRAN language and can be used without change on electronic computers of type YeS and BESM-6. The standard program described permits the identification of nonstationary (or stationary) solutions to systems of spatially one-dimensional nonlinear (or linear) partial differential equations. The proposed method may be used to solve a series of geophysical problems which take chemical reactions, diffusion, and heat conductivity into account, to evaluate nonstationary thermal fields in two-dimensional structures when in one of the geometrical directions it can take a small number of discrete levels, and to solve problems in nonstationary gas dynamics.

On radiative heat transfer in stagnation point flow of MHD Carreau fluid over a stretched surface

NASA Astrophysics Data System (ADS)

Khan, Masood; Sardar, Humara; Mudassar Gulzar, M.

2018-03-01

This paper investigates the behavior of MHD stagnation point flow of Carreau fluid in the presence of infinite shear rate viscosity. Additionally heat transfer analysis in the existence of non-linear radiation with convective boundary condition is performed. Moreover effects of Joule heating is observed and mathematical analysis is presented in the presence of viscous dissipation. The suitable transformations are employed to alter the leading partial differential equations to a set of ordinary differential equations. The subsequent non-straight common ordinary differential equations are solved numerically by an effective numerical approach specifically Runge-Kutta Fehlberg method alongside shooting technique. It is found that the higher values of Hartmann number (M) correspond to thickening of the thermal and thinning of momentum boundary layer thickness. The analysis further reveals that the fluid velocity is diminished by increasing the viscosity ratio parameter (β∗) and opposite trend is observed for temperature profile for both hydrodynamic and hydromagnetic flows. In addition the momentum boundary layer thickness is increased with velocity ratio parameter (α) and opposite is true for thermal boundary layer thickness.

Spherical means of solutions of partial differential equations in a conical region

NASA Technical Reports Server (NTRS)

Ting, L.

1975-01-01

The spherical means of the solutions of a linear partial differential equation Lu = f in a conical region are studied. The conical region is bounded by a surface generated by curvilinear xi lines and by two truncating xi surfaces. The spherical mean is the average of u over a constant xi surface. Conditions on the linear differential operator, L, and on the orthogonal coordinates xi, eta, and zeta are established so that the problem for the determination of the spherical mean of the solution subjected to the appropriate boundary and initial conditions can be reduced to a problem with only one space variable. Conditions are then established so that the spherical mean of the solution in one conical region will be proportional to that of a known solution in another conical region. Applications to various problems of mathematical physics and their physical interpretations are presented.

Double slip effects of Magnetohydrodynamic (MHD) boundary layer flow over an exponentially stretching sheet with radiation, heat source and chemical reaction

NASA Astrophysics Data System (ADS)

Shaharuz Zaman, Azmanira; Aziz, Ahmad Sukri Abd; Ali, Zaileha Md

2017-09-01

The double slips effect on the magnetohydrodynamic boundary layer flow over an exponentially stretching sheet with suction/blowing, radiation, chemical reaction and heat source is presented in this analysis. By using the similarity transformation, the governing partial differential equations of momentum, energy and concentration are transformed into the non-linear ordinary equations. These equations are solved using Runge-Kutta-Fehlberg method with shooting technique in MAPLE software environment. The effects of the various parameter on the velocity, temperature and concentration profiles are graphically presented and discussed.

Reprint of Solution of Ambrosio-Tortorelli model for image segmentation by generalized relaxation method

NASA Astrophysics Data System (ADS)

D'Ambra, Pasqua; Tartaglione, Gaetano

2015-04-01

Image segmentation addresses the problem to partition a given image into its constituent objects and then to identify the boundaries of the objects. This problem can be formulated in terms of a variational model aimed to find optimal approximations of a bounded function by piecewise-smooth functions, minimizing a given functional. The corresponding Euler-Lagrange equations are a set of two coupled elliptic partial differential equations with varying coefficients. Numerical solution of the above system often relies on alternating minimization techniques involving descent methods coupled with explicit or semi-implicit finite-difference discretization schemes, which are slowly convergent and poorly scalable with respect to image size. In this work we focus on generalized relaxation methods also coupled with multigrid linear solvers, when a finite-difference discretization is applied to the Euler-Lagrange equations of Ambrosio-Tortorelli model. We show that non-linear Gauss-Seidel, accelerated by inner linear iterations, is an effective method for large-scale image analysis as those arising from high-throughput screening platforms for stem cells targeted differentiation, where one of the main goal is segmentation of thousand of images to analyze cell colonies morphology.

Solution of Ambrosio-Tortorelli model for image segmentation by generalized relaxation method

NASA Astrophysics Data System (ADS)

D'Ambra, Pasqua; Tartaglione, Gaetano

2015-03-01

Image segmentation addresses the problem to partition a given image into its constituent objects and then to identify the boundaries of the objects. This problem can be formulated in terms of a variational model aimed to find optimal approximations of a bounded function by piecewise-smooth functions, minimizing a given functional. The corresponding Euler-Lagrange equations are a set of two coupled elliptic partial differential equations with varying coefficients. Numerical solution of the above system often relies on alternating minimization techniques involving descent methods coupled with explicit or semi-implicit finite-difference discretization schemes, which are slowly convergent and poorly scalable with respect to image size. In this work we focus on generalized relaxation methods also coupled with multigrid linear solvers, when a finite-difference discretization is applied to the Euler-Lagrange equations of Ambrosio-Tortorelli model. We show that non-linear Gauss-Seidel, accelerated by inner linear iterations, is an effective method for large-scale image analysis as those arising from high-throughput screening platforms for stem cells targeted differentiation, where one of the main goal is segmentation of thousand of images to analyze cell colonies morphology.

Electric current-producing device having sulfone-based electrolyte

DOEpatents

Angell, Charles Austen; Sun, Xiao-Guang

2010-11-16

Electrolytic solvents and applications of such solvents including electric current-producing devices. For example, a solvent can include a sulfone compound of R1--SO2--R2, with R1 being an alkyl group and R2 a partially oxygenated alkyl group, to exhibit high chemical and thermal stability and high oxidation resistance. For another example, a battery can include, between an anode and a cathode, an electrolyte which includes ionic electrolyte salts and a non-aqueous electrolyte solvent which includes a non-symmetrical, non-cyclic sulfone. The sulfone has a formula of R1--SO2--R2, wherein R1 is a linear or branched alkyl or partially or fully fluorinated linear or branched alkyl group having 1 to 7 carbon atoms, and R2 is a linear or branched or partially or fully fluorinated linear or branched oxygen containing alkyl group having 1 to 7 carbon atoms. The electrolyte can include an electrolyte co-solvent and an electrolyte additive for protective layer formation.

A computational analysis subject to thermophysical aspects of Sisko fluid flow over a cylindrical surface

NASA Astrophysics Data System (ADS)

Awais, M.; Khalil-Ur-Rehman; Malik, M. Y.; Hussain, Arif; Salahuddin, T.

2017-09-01

The present analysis is devoted to probing the salient features of the mixed convection and non-linear thermal radiation effects on non-Newtonian Sisko fluid flow over a linearly stretching cylindrical surface. Properties of heat transfer are outlined via variable thermal conductivity and convective boundary conditions. The boundary layer approach is implemented to construct the mathematical model in the form of partial differential equations. Then, the requisite PDEs are transmuted into a complex ordinary differential system by invoking appropriate dimensionless variables. Solution of subsequent ODEs is obtained by utilizing the Runge-Kutta algorithm (fifth order) along with the shooting scheme. The graphical illustrations are presented to interpret the features of the involved pertinent flow parameters on concerning profiles. For a better description of the fluid flow, numerical variations in local skin friction coefficient and local Nusselt number are scrutinized in tables. From thorough analysis, it is inferred that the mixed convection parameter and the curvature parameter increase the velocity while temperature shows a different behavior. Additionally, both momentum and thermal distribution of fluid flow decrease with increasing values of the non-linearity index. Furthermore, variable thermal parameter and heat generation/absorption parameter amplify the temperature significantly. The skin friction is an increasing function of all momentum controlling parameters. The local Nusselt number also shows a similar behavior against heat radiation parameter and variable thermal conductivity parameter while it shows a dual nature for the heat generation/absorption parameter. Finally, the obtained results are validated by comparison with the existing literature and hence the correctness of the analysis is proved.

Nonlinear grid error effects on numerical solution of partial differential equations

NASA Technical Reports Server (NTRS)

Dey, S. K.

1980-01-01

Finite difference solutions of nonlinear partial differential equations require discretizations and consequently grid errors are generated. These errors strongly affect stability and convergence properties of difference models. Previously such errors were analyzed by linearizing the difference equations for solutions. Properties of mappings of decadence were used to analyze nonlinear instabilities. Such an analysis is directly affected by initial/boundary conditions. An algorithm was developed, applied to nonlinear Burgers equations, and verified computationally. A preliminary test shows that Navier-Stokes equations may be treated similarly.

Thermal radiation and mass transfer effects on unsteady MHD free convection flow past a vertical oscillating plate

NASA Astrophysics Data System (ADS)

Rana, B. M. Jewel; Ahmed, Rubel; Ahmmed, S. F.

2017-06-01

Unsteady MHD free convection flow past a vertical porous plate in porous medium with radiation, diffusion thermo, thermal diffusion and heat source are analyzed. The governing non-linear, partial differential equations are transformed into dimensionless by using non-dimensional quantities. Then the resultant dimensionless equations are solved numerically by applying an efficient, accurate and conditionally stable finite difference scheme of explicit type with the help of a computer programming language Compaq Visual Fortran. The stability and convergence analysis has been carried out to establish the effect of velocity, temperature, concentration, skin friction, Nusselt number, Sherwood number, stream lines and isotherms line. Finally, the effects of various parameters are presented graphically and discussed qualitatively.

On the classification of scalar evolution equations with non-constant separant

NASA Astrophysics Data System (ADS)

Hümeyra Bilge, Ayşe; Mizrahi, Eti

2017-01-01

The ‘separant’ of the evolution equation u t   =  F, where F is some differentiable function of the derivatives of u up to order m, is the partial derivative \\partial F/\\partial {{u}m}, where {{u}m}={{\\partial}m}u/\\partial {{x}m} . As an integrability test, we use the formal symmetry method of Mikhailov-Shabat-Sokolov, which is based on the existence of a recursion operator as a formal series. The solvability of its coefficients in the class of local functions gives a sequence of conservation laws, called the ‘conserved densities’ {ρ(i)}, i=-1,1,2,3,\\ldots . We apply this method to the classification of scalar evolution equations of orders 3≤slant m≤slant 15 , for which {ρ(-1)}={≤ft[\\partial F/\\partial {{u}m}\\right]}-1/m} and {{ρ(1)} are non-trivial, i.e. they are not total derivatives and {ρ(-1)} is not linear in its highest order derivative. We obtain the ‘top level’ parts of these equations and their ‘top dependencies’ with respect to the ‘level grading’, that we defined in a previous paper, as a grading on the algebra of polynomials generated by the derivatives u b+i , over the ring of {{C}∞} functions of u,{{u}1},\\ldots,{{u}b} . In this setting b and i are called ‘base’ and ‘level’, respectively. We solve the conserved density conditions to show that if {ρ(-1)} depends on u,{{u}1},\\ldots,{{u}b}, then, these equations are level homogeneous polynomials in {{u}b+i},\\ldots,{{u}m} , i≥slant 1 . Furthermore, we prove that if {ρ(3)} is non-trivial, then {ρ(-1)}={≤ft(α ub2+β {{u}b}+γ \\right)}1/2} , with b≤slant 3 while if {{ρ(3)} is trivial, then {ρ(-1)}={≤ft(λ {{u}b}+μ \\right)}1/3} , where b≤slant 5 and α, β, γ, λ and μ are functions of u,\\ldots,{{u}b-1} . We show that the equations that we obtain form commuting flows and we construct their recursion operators that are respectively of orders 2 and 6 for non-trivial and trivial {{ρ(3)} respectively. Omitting lower order dependencies, we show that equations with non-trivial {ρ(3)} and b  =  3 are symmetries of the ‘essentially non-linear third order equation’ for trivial {ρ(3)} , the equations with b  =  5 are symmetries of a non-quasilinear fifth order equation obtained in previous work, while for b  =  3, 4 they are symmetries of quasilinear fifth order equations.

A simple method for identifying parameter correlations in partially observed linear dynamic models.

PubMed

Li, Pu; Vu, Quoc Dong

2015-12-14

Parameter estimation represents one of the most significant challenges in systems biology. This is because biological models commonly contain a large number of parameters among which there may be functional interrelationships, thus leading to the problem of non-identifiability. Although identifiability analysis has been extensively studied by analytical as well as numerical approaches, systematic methods for remedying practically non-identifiable models have rarely been investigated. We propose a simple method for identifying pairwise correlations and higher order interrelationships of parameters in partially observed linear dynamic models. This is made by derivation of the output sensitivity matrix and analysis of the linear dependencies of its columns. Consequently, analytical relations between the identifiability of the model parameters and the initial conditions as well as the input functions can be achieved. In the case of structural non-identifiability, identifiable combinations can be obtained by solving the resulting homogenous linear equations. In the case of practical non-identifiability, experiment conditions (i.e. initial condition and constant control signals) can be provided which are necessary for remedying the non-identifiability and unique parameter estimation. It is noted that the approach does not consider noisy data. In this way, the practical non-identifiability issue, which is popular for linear biological models, can be remedied. Several linear compartment models including an insulin receptor dynamics model are taken to illustrate the application of the proposed approach. Both structural and practical identifiability of partially observed linear dynamic models can be clarified by the proposed method. The result of this method provides important information for experimental design to remedy the practical non-identifiability if applicable. The derivation of the method is straightforward and thus the algorithm can be easily implemented into a software packet.

Non-linear feedback control of the p53 protein-mdm2 inhibitor system using the derivative-free non-linear Kalman filter.

PubMed

Rigatos, Gerasimos G

2016-06-01

It is proven that the model of the p53-mdm2 protein synthesis loop is a differentially flat one and using a diffeomorphism (change of state variables) that is proposed by differential flatness theory it is shown that the protein synthesis model can be transformed into the canonical (Brunovsky) form. This enables the design of a feedback control law that maintains the concentration of the p53 protein at the desirable levels. To estimate the non-measurable elements of the state vector describing the p53-mdm2 system dynamics, the derivative-free non-linear Kalman filter is used. Moreover, to compensate for modelling uncertainties and external disturbances that affect the p53-mdm2 system, the derivative-free non-linear Kalman filter is re-designed as a disturbance observer. The derivative-free non-linear Kalman filter consists of the Kalman filter recursion applied on the linearised equivalent of the protein synthesis model together with an inverse transformation based on differential flatness theory that enables to retrieve estimates for the state variables of the initial non-linear model. The proposed non-linear feedback control and perturbations compensation method for the p53-mdm2 system can result in more efficient chemotherapy schemes where the infusion of medication will be better administered.

Group invariant solution for a pre-existing fluid-driven fracture in impermeable rock

NASA Astrophysics Data System (ADS)

Fitt, A. D.; Mason, D. P.; Moss, E. A.

2007-11-01

The propagation of a two-dimensional fluid-driven fracture in impermeable rock is considered. The fluid flow in the fracture is laminar. By applying lubrication theory a partial differential equation relating the half-width of the fracture to the fluid pressure is derived. To close the model the PKN formulation is adopted in which the fluid pressure is proportional to the half-width of the fracture. By considering a linear combination of the Lie point symmetries of the resulting non-linear diffusion equation the boundary value problem is expressed in a form appropriate for a similarity solution. The boundary value problem is reformulated as two initial value problems which are readily solved numerically. The similarity solution describes a preexisting fracture since both the total volume and length of the fracture are initially finite and non-zero. Applications in which the rate of fluid injection into the fracture and the pressure at the fracture entry are independent of time are considered.

An automatic multigrid method for the solution of sparse linear systems

NASA Technical Reports Server (NTRS)

Shapira, Yair; Israeli, Moshe; Sidi, Avram

1993-01-01

An automatic version of the multigrid method for the solution of linear systems arising from the discretization of elliptic PDE's is presented. This version is based on the structure of the algebraic system solely, and does not use the original partial differential operator. Numerical experiments show that for the Poisson equation the rate of convergence of our method is equal to that of classical multigrid methods. Moreover, the method is robust in the sense that its high rate of convergence is conserved for other classes of problems: non-symmetric, hyperbolic (even with closed characteristics) and problems on non-uniform grids. No double discretization or special treatment of sub-domains (e.g. boundaries) is needed. When supplemented with a vector extrapolation method, high rates of convergence are achieved also for anisotropic and discontinuous problems and also for indefinite Helmholtz equations. A new double discretization strategy is proposed for finite and spectral element schemes and is found better than known strategies.

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

NASA Astrophysics Data System (ADS)

Cresson, Jacky; Pierret, Frédéric

2016-05-01

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

Time domain convergence properties of Lyapunov stable penalty methods

NASA Technical Reports Server (NTRS)

Kurdila, A. J.; Sunkel, John

1991-01-01

Linear hyperbolic partial differential equations are analyzed using standard techniques to show that a sequence of solutions generated by the Liapunov stable penalty equations approaches the solution of the differential-algebraic equations governing the dynamics of multibody problems arising in linear vibrations. The analysis does not require that the system be conservative and does not impose any specific integration scheme. Variational statements are derived which bound the error in approximation by the norm of the constraint violation obtained in the approximate solutions.

A Solution Space for a System of Null-State Partial Differential Equations: Part 3

NASA Astrophysics Data System (ADS)

Flores, Steven M.; Kleban, Peter

2015-01-01

This article is the third of four that completely and rigorously characterize a solution space for a homogeneous system of 2 N + 3 linear partial differential equations (PDEs) in 2 N variables that arises in conformal field theory (CFT) and multiple Schramm-Löwner evolution (SLE κ ). The system comprises 2 N null-state equations and three conformal Ward identities that govern CFT correlation functions of 2 N one-leg boundary operators. In the first two articles (Flores and Kleban, in Commun Math Phys, arXiv:1212.2301, 2012; Commun Math Phys, arXiv:1404.0035, 2014), we use methods of analysis and linear algebra to prove that dim , with C N the Nth Catalan number. Extending these results, we prove in this article that dim and entirely consists of (real-valued) solutions constructed with the CFT Coulomb gas (contour integral) formalism. In order to prove this claim, we show that a certain set of C N such solutions is linearly independent. Because the formulas for these solutions are complicated, we prove linear independence indirectly. We use the linear injective map of Lemma 15 in Flores and Kleban (Commun Math Phys, arXiv:1212.2301, 2012) to send each solution of the mentioned set to a vector in , whose components we find as inner products of elements in a Temperley-Lieb algebra. We gather these vectors together as columns of a symmetric matrix, with the form of a meander matrix. If the determinant of this matrix does not vanish, then the set of C N Coulomb gas solutions is linearly independent. And if this determinant does vanish, then we construct an alternative set of C N Coulomb gas solutions and follow a similar procedure to show that this set is linearly independent. The latter situation is closely related to CFT minimal models. We emphasize that, although the system of PDEs arises in CFT in away that is typically non-rigorous, our treatment of this system here and in Flores and Kleban (Commun Math Phys, arXiv:1212.2301, 2012; Commun Math Phys, arXiv:1404.0035, 2014; Commun Math Phys, arXiv:1405.2747, 2014) is completely rigorous.

Non-linear analysis of wave progagation using transform methods and plates and shells using integral equations

NASA Astrophysics Data System (ADS)

Pipkins, Daniel Scott

Two diverse topics of relevance in modern computational mechanics are treated. The first involves the modeling of linear and non-linear wave propagation in flexible, lattice structures. The technique used combines the Laplace Transform with the Finite Element Method (FEM). The procedure is to transform the governing differential equations and boundary conditions into the transform domain where the FEM formulation is carried out. For linear problems, the transformed differential equations can be solved exactly, hence the method is exact. As a result, each member of the lattice structure is modeled using only one element. In the non-linear problem, the method is no longer exact. The approximation introduced is a spatial discretization of the transformed non-linear terms. The non-linear terms are represented in the transform domain by making use of the complex convolution theorem. A weak formulation of the resulting transformed non-linear equations yields a set of element level matrix equations. The trial and test functions used in the weak formulation correspond to the exact solution of the linear part of the transformed governing differential equation. Numerical results are presented for both linear and non-linear systems. The linear systems modeled are longitudinal and torsional rods and Bernoulli-Euler and Timoshenko beams. For non-linear systems, a viscoelastic rod and Von Karman type beam are modeled. The second topic is the analysis of plates and shallow shells under-going finite deflections by the Field/Boundary Element Method. Numerical results are presented for two plate problems. The first is the bifurcation problem associated with a square plate having free boundaries which is loaded by four, self equilibrating corner forces. The results are compared to two existing numerical solutions of the problem which differ substantially.

Minimum time search in uncertain dynamic domains with complex sensorial platforms.

PubMed

Lanillos, Pablo; Besada-Portas, Eva; Lopez-Orozco, Jose Antonio; de la Cruz, Jesus Manuel

2014-08-04

The minimum time search in uncertain domains is a searching task, which appears in real world problems such as natural disasters and sea rescue operations, where a target has to be found, as soon as possible, by a set of sensor-equipped searchers. The automation of this task, where the time to detect the target is critical, can be achieved by new probabilistic techniques that directly minimize the Expected Time (ET) to detect a dynamic target using the observation probability models and actual observations collected by the sensors on board the searchers. The selected technique, described in algorithmic form in this paper for completeness, has only been previously partially tested with an ideal binary detection model, in spite of being designed to deal with complex non-linear/non-differential sensorial models. This paper covers the gap, testing its performance and applicability over different searching tasks with searchers equipped with different complex sensors. The sensorial models under test vary from stepped detection probabilities to continuous/discontinuous differentiable/non-differentiable detection probabilities dependent on distance, orientation, and structured maps. The analysis of the simulated results of several static and dynamic scenarios performed in this paper validates the applicability of the technique with different types of sensor models.

Minimum Time Search in Uncertain Dynamic Domains with Complex Sensorial Platforms

PubMed Central

Lanillos, Pablo; Besada-Portas, Eva; Lopez-Orozco, Jose Antonio; de la Cruz, Jesus Manuel

2014-01-01

The minimum time search in uncertain domains is a searching task, which appears in real world problems such as natural disasters and sea rescue operations, where a target has to be found, as soon as possible, by a set of sensor-equipped searchers. The automation of this task, where the time to detect the target is critical, can be achieved by new probabilistic techniques that directly minimize the Expected Time (ET) to detect a dynamic target using the observation probability models and actual observations collected by the sensors on board the searchers. The selected technique, described in algorithmic form in this paper for completeness, has only been previously partially tested with an ideal binary detection model, in spite of being designed to deal with complex non-linear/non-differential sensorial models. This paper covers the gap, testing its performance and applicability over different searching tasks with searchers equipped with different complex sensors. The sensorial models under test vary from stepped detection probabilities to continuous/discontinuous differentiable/non-differentiable detection probabilities dependent on distance, orientation, and structured maps. The analysis of the simulated results of several static and dynamic scenarios performed in this paper validates the applicability of the technique with different types of sensor models. PMID:25093345

Non-linear dynamics of compound sawteeth in tokamaks

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

Ahn, J.-H., E-mail: jae-heon.ahn@polytechnique.edu; Garbet, X.; Sabot, R.

2016-05-15

Compound sawteeth is studied with the XTOR-2F code. Non-linear full 3D magnetohydrodynamic simulations show that the plasma hot core is radially displaced and rotates during the partial crash, but is not fully expelled out of the q = 1 surface. Partial crashes occur when the radius of the q = 1 surface exceeds a critical value, at fixed poloidal beta. This critical value depends on the plasma elongation. The partial crash time is larger than the collapse time of an ordinary sawtooth, likely due to a weaker diamagnetic stabilization. This suggests that partial crashes result from a competition between destabilizing effects such as themore » q = 1 radius and diamagnetic stabilization.« less

Computed tear film and osmolarity dynamics on an eye-shaped domain

PubMed Central

Li, Longfei; Braun, Richard J.; Driscoll, Tobin A.; Henshaw, William D.; Banks, Jeffrey W.; King-Smith, P. Ewen

2016-01-01

The concentration of ions, or osmolarity, in the tear film is a key variable in understanding dry eye symptoms and disease. In this manuscript, we derive a mathematical model that couples osmolarity (treated as a single solute) and fluid dynamics within the tear film on a 2D eye-shaped domain. The model includes the physical effects of evaporation, surface tension, viscosity, ocular surface wettability, osmolarity, osmosis and tear fluid supply and drainage. The governing system of coupled non-linear partial differential equations is solved using the Overture computational framework, together with a hybrid time-stepping scheme, using a variable step backward differentiation formula and a Runge–Kutta–Chebyshev method that were added to the framework. The results of our numerical simulations provide new insight into the osmolarity distribution over the ocular surface during the interblink. PMID:25883248

Hydromagnetic couple-stress nanofluid flow over a moving convective wall: OHAM analysis

NASA Astrophysics Data System (ADS)

Awais, M.; Saleem, S.; Hayat, T.; Irum, S.

2016-12-01

This communication presents the magnetohydrodynamics (MHD) flow of a couple-stress nanofluid over a convective moving wall. The flow dynamics are analyzed in the boundary layer region. Convective cooling phenomenon combined with thermophoresis and Brownian motion effects has been discussed. Similarity transforms are utilized to convert the system of partial differential equations into coupled non-linear ordinary differential equation. Optimal homotopy analysis method (OHAM) is utilized and the concept of minimization is employed by defining the average squared residual errors. Effects of couple-stress parameter, convective cooling process parameter and energy enhancement parameters are displayed via graphs and discussed in detail. Various tables are also constructed to present the error analysis and a comparison of obtained results with the already published data. Stream lines are plotted showing a difference of Newtonian fluid model and couplestress fluid model.

Prolongation structures of nonlinear evolution equations

NASA Technical Reports Server (NTRS)

Wahlquist, H. D.; Estabrook, F. B.

1975-01-01

A technique is developed for systematically deriving a 'prolongation structure' - a set of interrelated potentials and pseudopotentials - for nonlinear partial differential equations in two independent variables. When this is applied to the Korteweg-de Vries equation, a new infinite set of conserved quantities is obtained. Known solution techniques are shown to result from the discovery of such a structure: related partial differential equations for the potential functions, linear 'inverse scattering' equations for auxiliary functions, Backlund transformations. Generalizations of these techniques will result from the use of irreducible matrix representations of the prolongation structure.

Thermodynamic aspect in using modified Boltzmann model as an acoustic probe for URu2Si2

NASA Astrophysics Data System (ADS)

Kwang-Hua, Chu Rainer

2018-05-01

The approximate system of equations describing ultrasonic attenuation propagating in many electrons of the heavy-fermion materials URu2Si2 under high magnetic fields were firstly derived and then calculated based on the modified Boltzmann model considering the microscopic contributions due to electronic fluids. A system of nonlinear partial differential coupled with integral equations were linearized firstly and approximately solved considering the perturbed thermodynamic equilibrium states. Our numerical data were compared with previous measurements using non-dimensional or normalized physical values. The rather good fit of our numerical calculations with experimental measurements confirms our present approach.

Lump solutions to nonlinear partial differential equations via Hirota bilinear forms

NASA Astrophysics Data System (ADS)

Ma, Wen-Xiu; Zhou, Yuan

2018-02-01

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

Note: Nonpolar solute partial molar volume response to attractive interactions with water.

PubMed

Williams, Steven M; Ashbaugh, Henry S

2014-01-07

The impact of attractive interactions on the partial molar volumes of methane-like solutes in water is characterized using molecular simulations. Attractions account for a significant 20% volume drop between a repulsive Weeks-Chandler-Andersen and full Lennard-Jones description of methane interactions. The response of the volume to interaction perturbations is characterized by linear fits to our simulations and a rigorous statistical thermodynamic expression for the derivative of the volume to increasing attractions. While a weak non-linear response is observed, an average effective slope accurately captures the volume decrease. This response, however, is anticipated to become more non-linear with increasing solute size.

Note: Nonpolar solute partial molar volume response to attractive interactions with water

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

Williams, Steven M.; Ashbaugh, Henry S., E-mail: hanka@tulane.edu

2014-01-07

The impact of attractive interactions on the partial molar volumes of methane-like solutes in water is characterized using molecular simulations. Attractions account for a significant 20% volume drop between a repulsive Weeks-Chandler-Andersen and full Lennard-Jones description of methane interactions. The response of the volume to interaction perturbations is characterized by linear fits to our simulations and a rigorous statistical thermodynamic expression for the derivative of the volume to increasing attractions. While a weak non-linear response is observed, an average effective slope accurately captures the volume decrease. This response, however, is anticipated to become more non-linear with increasing solute size.

A macroscopic plasma Lagrangian and its application to wave interactions and resonances

NASA Technical Reports Server (NTRS)

Peng, Y. K. M.

1974-01-01

The derivation of a macroscopic plasma Lagrangian is considered, along with its application to the description of nonlinear three-wave interaction in a homogeneous plasma and linear resonance oscillations in a inhomogeneous plasma. One approach to obtain the Lagrangian is via the inverse problem of the calculus of variations for arbitrary first and second order quasilinear partial differential systems. Necessary and sufficient conditions for the given equations to be Euler-Lagrange equations of a Lagrangian are obtained. These conditions are then used to determine the transformations that convert some classes of non-Euler-Lagrange equations to Euler-Lagrange equation form. The Lagrangians for a linear resistive transmission line and a linear warm collisional plasma are derived as examples. Using energy considerations, the correct macroscopic plasma Lagrangian is shown to differ from the velocity-integrated low Lagrangian by a macroscopic potential energy that equals twice the particle thermal kinetic energy plus the energy lost by heat conduction.

Legendre-tau approximations for functional differential equations

NASA Technical Reports Server (NTRS)

Ito, K.; Teglas, R.

1986-01-01

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

Legendre-Tau approximations for functional differential equations

NASA Technical Reports Server (NTRS)

Ito, K.; Teglas, R.

1983-01-01

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

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

Thompson, S.

This report describes the use of several subroutines from the CORLIB core mathematical subroutine library for the solution of a model fluid flow problem. The model consists of the Euler partial differential equations. The equations are spatially discretized using the method of pseudo-characteristics. The resulting system of ordinary differential equations is then integrated using the method of lines. The stiff ordinary differential equation solver LSODE (2) from CORLIB is used to perform the time integration. The non-stiff solver ODE (4) is used to perform a related integration. The linear equation solver subroutines DECOMP and SOLVE are used to solve linearmore » systems whose solutions are required in the calculation of the time derivatives. The monotone cubic spline interpolation subroutines PCHIM and PCHFE are used to approximate water properties. The report describes the use of each of these subroutines in detail. It illustrates the manner in which modules from a standard mathematical software library such as CORLIB can be used as building blocks in the solution of complex problems of practical interest. 9 refs., 2 figs., 4 tabs.« less

Efficient numerical method of freeform lens design for arbitrary irradiance shaping

NASA Astrophysics Data System (ADS)

Wojtanowski, Jacek

2018-05-01

A computational method to design a lens with a flat entrance surface and a freeform exit surface that can transform a collimated, generally non-uniform input beam into a beam with a desired irradiance distribution of arbitrary shape is presented. The methodology is based on non-linear elliptic partial differential equations, known as Monge-Ampère PDEs. This paper describes an original numerical algorithm to solve this problem by applying the Gauss-Seidel method with simplified boundary conditions. A joint MATLAB-ZEMAX environment is used to implement and verify the method. To prove the efficiency of the proposed approach, an exemplary study where the designed lens is faced with the challenging illumination task is shown. An analysis of solution stability, iteration-to-iteration ray mapping evolution (attached in video format), depth of focus and non-zero étendue efficiency is performed.

Analytical exploration of a TiO2 nanofluid along a rotating disk with homogeneous-heterogeneous chemical reactions and non-uniform heat source/sink

NASA Astrophysics Data System (ADS)

Das, Kalidas; Chakraborty, Tanmoy; Kumar Kundu, Prabir

2017-12-01

Comparative flow features of two different nanofluids containing TiO2 nanoparticles along a rotating disk near a stagnation point are theoretically addressed here. The primary fluids are presumed as ethylene glycol and water. The influences of non-uniform heat absorption/generation with homogeneous and heterogeneous chemical reactions have been integrated to modify the energy and concentration profiles. By virtue of similarity conversions, the leading partial differential system has been standardized into non-linear ODEs and then cracked analytically by NDM and numerically by RK-4 based shooting practice. Impressions of emerging parameters on the flow regime have been reported by tables and graphs coupled with required discussions. One of our results predicts that, with the augmentation of TiO2 nanoparticles concentration, the rate of heat transport for ethylene glycol nanofluid becomes 30-36% higher compared to that of a water nanofluid.

New numerical approximation of fractional derivative with non-local and non-singular kernel: Application to chaotic models

NASA Astrophysics Data System (ADS)

Toufik, Mekkaoui; Atangana, Abdon

2017-10-01

Recently a new concept of fractional differentiation with non-local and non-singular kernel was introduced in order to extend the limitations of the conventional Riemann-Liouville and Caputo fractional derivatives. A new numerical scheme has been developed, in this paper, for the newly established fractional differentiation. We present in general the error analysis. The new numerical scheme was applied to solve linear and non-linear fractional differential equations. We do not need a predictor-corrector to have an efficient algorithm, in this method. The comparison of approximate and exact solutions leaves no doubt believing that, the new numerical scheme is very efficient and converges toward exact solution very rapidly.

Direct Shear Failure in Reinforced Concrete Beams under Impulsive Loading

DTIC Science & Technology

1983-09-01

115 References ............... ............................. 119 Tables . ............................. 124 Figures ............ 1..............30...8217. : = differentiable functions of time 1 = elastic modulus enhancement function 4) 41’ = constants for a given mode W’, = frequency w tfirst thickness-shear...are defined by linear partial differential equations. The analytic results are compared to data gathered on one-way slabs loaded with impulsive blast

Finite-horizon differential games for missile-target interception system using adaptive dynamic programming with input constraints

NASA Astrophysics Data System (ADS)

Sun, Jingliang; Liu, Chunsheng

2018-01-01

In this paper, the problem of intercepting a manoeuvring target within a fixed final time is posed in a non-linear constrained zero-sum differential game framework. The Nash equilibrium solution is found by solving the finite-horizon constrained differential game problem via adaptive dynamic programming technique. Besides, a suitable non-quadratic functional is utilised to encode the control constraints into a differential game problem. The single critic network with constant weights and time-varying activation functions is constructed to approximate the solution of associated time-varying Hamilton-Jacobi-Isaacs equation online. To properly satisfy the terminal constraint, an additional error term is incorporated in a novel weight-updating law such that the terminal constraint error is also minimised over time. By utilising Lyapunov's direct method, the closed-loop differential game system and the estimation weight error of the critic network are proved to be uniformly ultimately bounded. Finally, the effectiveness of the proposed method is demonstrated by using a simple non-linear system and a non-linear missile-target interception system, assuming first-order dynamics for the interceptor and target.

Runge-Kutta Methods for Linear Ordinary Differential Equations

NASA Technical Reports Server (NTRS)

Zingg, David W.; Chisholm, Todd T.

1997-01-01

Three new Runge-Kutta methods are presented for numerical integration of systems of linear inhomogeneous ordinary differential equations (ODES) with constant coefficients. Such ODEs arise in the numerical solution of the partial differential equations governing linear wave phenomena. The restriction to linear ODEs with constant coefficients reduces the number of conditions which the coefficients of the Runge-Kutta method must satisfy. This freedom is used to develop methods which are more efficient than conventional Runge-Kutta methods. A fourth-order method is presented which uses only two memory locations per dependent variable, while the classical fourth-order Runge-Kutta method uses three. This method is an excellent choice for simulations of linear wave phenomena if memory is a primary concern. In addition, fifth- and sixth-order methods are presented which require five and six stages, respectively, one fewer than their conventional counterparts, and are therefore more efficient. These methods are an excellent option for use with high-order spatial discretizations.

Partial differential equations constrained combinatorial optimization on an adiabatic quantum computer

NASA Astrophysics Data System (ADS)

Chandra, Rishabh

Partial differential equation-constrained combinatorial optimization (PDECCO) problems are a mixture of continuous and discrete optimization problems. PDECCO problems have discrete controls, but since the partial differential equations (PDE) are continuous, the optimization space is continuous as well. Such problems have several applications, such as gas/water network optimization, traffic optimization, micro-chip cooling optimization, etc. Currently, no efficient classical algorithm which guarantees a global minimum for PDECCO problems exists. A new mapping has been developed that transforms PDECCO problem, which only have linear PDEs as constraints, into quadratic unconstrained binary optimization (QUBO) problems that can be solved using an adiabatic quantum optimizer (AQO). The mapping is efficient, it scales polynomially with the size of the PDECCO problem, requires only one PDE solve to form the QUBO problem, and if the QUBO problem is solved correctly and efficiently on an AQO, guarantees a global optimal solution for the original PDECCO problem.

Fast secant methods for the iterative solution of large nonsymmetric linear systems

NASA Technical Reports Server (NTRS)

Deuflhard, Peter; Freund, Roland; Walter, Artur

1990-01-01

A family of secant methods based on general rank-1 updates was revisited in view of the construction of iterative solvers for large non-Hermitian linear systems. As it turns out, both Broyden's good and bad update techniques play a special role, but should be associated with two different line search principles. For Broyden's bad update technique, a minimum residual principle is natural, thus making it theoretically comparable with a series of well known algorithms like GMRES. Broyden's good update technique, however, is shown to be naturally linked with a minimum next correction principle, which asymptotically mimics a minimum error principle. The two minimization principles differ significantly for sufficiently large system dimension. Numerical experiments on discretized partial differential equations of convection diffusion type in 2-D with integral layers give a first impression of the possible power of the derived good Broyden variant.

Conformational statistics of stiff macromolecules as solutions to partial differential equations on the rotation and motion groups

PubMed

Chirikjian; Wang

2000-07-01

Partial differential equations (PDE's) for the probability density function (PDF) of the position and orientation of the distal end of a stiff macromolecule relative to its proximal end are derived and solved. The Kratky-Porod wormlike chain, the Yamakawa helical wormlike chain, and the original and revised Marko-Siggia models are examples of stiffness models to which the present formulation is applied. The solution technique uses harmonic analysis on the rotation and motion groups to convert PDE's governing the PDF's of interest into linear algebraic equations which have mathematically elegant solutions.

Non-Asymptotic Oracle Inequalities for the High-Dimensional Cox Regression via Lasso.

PubMed

Kong, Shengchun; Nan, Bin

2014-01-01

We consider finite sample properties of the regularized high-dimensional Cox regression via lasso. Existing literature focuses on linear models or generalized linear models with Lipschitz loss functions, where the empirical risk functions are the summations of independent and identically distributed (iid) losses. The summands in the negative log partial likelihood function for censored survival data, however, are neither iid nor Lipschitz.We first approximate the negative log partial likelihood function by a sum of iid non-Lipschitz terms, then derive the non-asymptotic oracle inequalities for the lasso penalized Cox regression using pointwise arguments to tackle the difficulties caused by lacking iid Lipschitz losses.

Non-Asymptotic Oracle Inequalities for the High-Dimensional Cox Regression via Lasso

PubMed Central

Kong, Shengchun; Nan, Bin

2013-01-01

We consider finite sample properties of the regularized high-dimensional Cox regression via lasso. Existing literature focuses on linear models or generalized linear models with Lipschitz loss functions, where the empirical risk functions are the summations of independent and identically distributed (iid) losses. The summands in the negative log partial likelihood function for censored survival data, however, are neither iid nor Lipschitz.We first approximate the negative log partial likelihood function by a sum of iid non-Lipschitz terms, then derive the non-asymptotic oracle inequalities for the lasso penalized Cox regression using pointwise arguments to tackle the difficulties caused by lacking iid Lipschitz losses. PMID:24516328

Scheduled Relaxation Jacobi method: Improvements and applications

NASA Astrophysics Data System (ADS)

Adsuara, J. E.; Cordero-Carrión, I.; Cerdá-Durán, P.; Aloy, M. A.

2016-09-01

Elliptic partial differential equations (ePDEs) appear in a wide variety of areas of mathematics, physics and engineering. Typically, ePDEs must be solved numerically, which sets an ever growing demand for efficient and highly parallel algorithms to tackle their computational solution. The Scheduled Relaxation Jacobi (SRJ) is a promising class of methods, atypical for combining simplicity and efficiency, that has been recently introduced for solving linear Poisson-like ePDEs. The SRJ methodology relies on computing the appropriate parameters of a multilevel approach with the goal of minimizing the number of iterations needed to cut down the residuals below specified tolerances. The efficiency in the reduction of the residual increases with the number of levels employed in the algorithm. Applying the original methodology to compute the algorithm parameters with more than 5 levels notably hinders obtaining optimal SRJ schemes, as the mixed (non-linear) algebraic-differential system of equations from which they result becomes notably stiff. Here we present a new methodology for obtaining the parameters of SRJ schemes that overcomes the limitations of the original algorithm and provide parameters for SRJ schemes with up to 15 levels and resolutions of up to 215 points per dimension, allowing for acceleration factors larger than several hundreds with respect to the Jacobi method for typical resolutions and, in some high resolution cases, close to 1000. Most of the success in finding SRJ optimal schemes with more than 10 levels is based on an analytic reduction of the complexity of the previously mentioned system of equations. Furthermore, we extend the original algorithm to apply it to certain systems of non-linear ePDEs.

Oblique transport of gyrotactic microorganisms and bioconvection nanoparticles with convective mass flux

NASA Astrophysics Data System (ADS)

Iqbal, Z.; Mehmood, Zaffar; Maraj, E. N.

2017-04-01

The present study deals with examination of steady two dimensional nanofluid containing both nanoparticles and gyrotactic microorganisms. Moreover the study comprises stagnation point flow of an obliquely striking nanofluid. The governing partial differential equations are complex and highly non-linear in nature. These are converted into system of ordinary differential equations using suitable transformations. The system is then solved numerically using shooting technique with Runge - Kutta Fehlberg method of order 5. Further, effect of different physical parameters on velocity f ‧ (η) , temperature θ (η) , density of motile microorganisms w (η) and concentration ϕ (η) along with skin friction coefficient Cf, local Nusselt Nux, Sherwood Shx and density of motile microorganism Nnx numbers have been discussed through graphs and tables. Results depict that temperature, concentration, density of motile microorganisms and local Nusselt number are increasing functions of thermophoresis parameter Nt. Whereas Nt contributes in lessening Sherwood and local density numbers.

A computational study of entropy generation in magnetohydrodynamic flow and heat transfer over an unsteady stretching permeable sheet

NASA Astrophysics Data System (ADS)

Saeed Butt, Adnan; Ali, Asif

2014-01-01

The present article aims to investigate the entropy effects in magnetohydrodynamic flow and heat transfer over an unsteady permeable stretching surface. The time-dependent partial differential equations are converted into non-linear ordinary differential equations by suitable similarity transformations. The solutions of these equations are computed analytically by the Homotopy Analysis Method (HAM) then solved numerically by the MATLAB built-in routine. Comparison of the obtained results is made with the existing literature under limiting cases to validate our study. The effects of unsteadiness parameter, magnetic field parameter, suction/injection parameter, Prandtl number, group parameter and Reynolds number on flow and heat transfer characteristics are checked and analysed with the aid of graphs and tables. Moreover, the effects of these parameters on entropy generation number and Bejan number are also shown graphically. It is examined that the unsteadiness and presence of magnetic field augments the entropy production.

Optogenetic stimulation of a meso-scale human cortical model

NASA Astrophysics Data System (ADS)

Selvaraj, Prashanth; Szeri, Andrew; Sleigh, Jamie; Kirsch, Heidi

2015-03-01

Neurological phenomena like sleep and seizures depend not only on the activity of individual neurons, but on the dynamics of neuron populations as well. Meso-scale models of cortical activity provide a means to study neural dynamics at the level of neuron populations. Additionally, they offer a safe and economical way to test the effects and efficacy of stimulation techniques on the dynamics of the cortex. Here, we use a physiologically relevant meso-scale model of the cortex to study the hypersynchronous activity of neuron populations during epileptic seizures. The model consists of a set of stochastic, highly non-linear partial differential equations. Next, we use optogenetic stimulation to control seizures in a hyperexcited cortex, and to induce seizures in a normally functioning cortex. The high spatial and temporal resolution this method offers makes a strong case for the use of optogenetics in treating meso scale cortical disorders such as epileptic seizures. We use bifurcation analysis to investigate the effect of optogenetic stimulation in the meso scale model, and its efficacy in suppressing the non-linear dynamics of seizures.

Assessment of the non-Gaussianity and non-linearity levels of simulated sEMG signals on stationary segments.

PubMed

Messaoudi, Noureddine; Bekka, Raïs El'hadi; Ravier, Philippe; Harba, Rachid

2017-02-01

The purpose of this paper was to evaluate the effects of the longitudinal single differential (LSD), the longitudinal double differential (LDD) and the normal double differential (NDD) spatial filters, the electrode shape, the inter-electrode distance (IED) on non-Gaussianity and non-linearity levels of simulated surface EMG (sEMG) signals when the maximum voluntary contraction (MVC) varied from 10% to 100% by a step of 10%. The effects of recruitment range thresholds (RR), the firing rate (FR) strategy and the peak firing rate (PFR) of motor units were also considered. A cylindrical multilayer model of the volume conductor and a model of motor unit (MU) recruitment and firing rate were used to simulate sEMG signals in a pool of 120 MUs for 5s. Firstly, the stationarity of sEMG signals was tested by the runs, the reverse arrangements (RA) and the modified reverse arrangements (MRA) tests. Then the non-Gaussianity was characterised with bicoherence and kurtosis, and non-linearity levels was evaluated with linearity test. The kurtosis analysis showed that the sEMG signals detected by the LSD filter were the most Gaussian and those detected by the NDD filter were the least Gaussian. In addition, the sEMG signals detected by the LSD filter were the most linear. For a given filter, the sEMG signals detected by using rectangular electrodes were more Gaussian and more linear than that detected with circular electrodes. Moreover, the sEMG signals are less non-Gaussian and more linear with reverse onion-skin firing rate strategy than those with onion-skin strategy. The levels of sEMG signal Gaussianity and linearity increased with the increase of the IED, RR and PFR. Copyright © 2016 Elsevier Ltd. All rights reserved.

Portent of Heine's Reciprocal Square Root Identity

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

Cohl, H W

Precise efforts in theoretical astrophysics are needed to fully understand the mechanisms that govern the structure, stability, dynamics, formation, and evolution of differentially rotating stars. Direct computation of the physical attributes of a star can be facilitated by the use of highly compact azimuthal and separation angle Fourier formulations of the Green's functions for the linear partial differential equations of mathematical physics.

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

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

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

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

Non-planar vibrations of slightly curved pipes conveying fluid in simple and combination parametric resonances

NASA Astrophysics Data System (ADS)

Czerwiński, Andrzej; Łuczko, Jan

2018-01-01

The paper summarises the experimental investigations and numerical simulations of non-planar parametric vibrations of a statically deformed pipe. Underpinning the theoretical analysis is a 3D dynamic model of curved pipe. The pipe motion is governed by four non-linear partial differential equations with periodically varying coefficients. The Galerkin method was applied, the shape function being that governing the beam's natural vibrations. Experiments were conducted in the range of simple and combination parametric resonances, evidencing the possibility of in-plane and out-of-plane vibrations as well as fully non-planar vibrations in the combination resonance range. It is demonstrated that sub-harmonic and quasi-periodic vibrations are likely to be excited. The method suggested allows the spatial modes to be determined basing on results registered at selected points in the pipe. Results are summarised in the form of time histories, phase trajectory plots and spectral diagrams. Dedicated video materials give us a better insight into the investigated phenomena.

Calibration of Lévy Processes with American Options

NASA Astrophysics Data System (ADS)

Achdou, Yves

We study options on financial assets whose discounted prices are exponential of Lévy processes. The price of an American vanilla option as a function of the maturity and the strike satisfies a linear complementarity problem involving a non-local partial integro-differential operator. It leads to a variational inequality in a suitable weighted Sobolev space. Calibrating the Lévy process may be done by solving an inverse least square problem where the state variable satisfies the previously mentioned variational inequality. We first assume that the volatility is positive: after carefully studying the direct problem, we propose necessary optimality conditions for the least square inverse problem. We also consider the direct problem when the volatility is zero.

Hidden physics models: Machine learning of nonlinear partial differential equations

NASA Astrophysics Data System (ADS)

Raissi, Maziar; Karniadakis, George Em

2018-03-01

While there is currently a lot of enthusiasm about "big data", useful data is usually "small" and expensive to acquire. In this paper, we present a new paradigm of learning partial differential equations from small data. In particular, we introduce hidden physics models, which are essentially data-efficient learning machines capable of leveraging the underlying laws of physics, expressed by time dependent and nonlinear partial differential equations, to extract patterns from high-dimensional data generated from experiments. The proposed methodology may be applied to the problem of learning, system identification, or data-driven discovery of partial differential equations. Our framework relies on Gaussian processes, a powerful tool for probabilistic inference over functions, that enables us to strike a balance between model complexity and data fitting. The effectiveness of the proposed approach is demonstrated through a variety of canonical problems, spanning a number of scientific domains, including the Navier-Stokes, Schrödinger, Kuramoto-Sivashinsky, and time dependent linear fractional equations. The methodology provides a promising new direction for harnessing the long-standing developments of classical methods in applied mathematics and mathematical physics to design learning machines with the ability to operate in complex domains without requiring large quantities of data.

Local classification: Locally weighted-partial least squares-discriminant analysis (LW-PLS-DA).

PubMed

Bevilacqua, Marta; Marini, Federico

2014-08-01

The possibility of devising a simple, flexible and accurate non-linear classification method, by extending the locally weighted partial least squares (LW-PLS) approach to the cases where the algorithm is used in a discriminant way (partial least squares discriminant analysis, PLS-DA), is presented. In particular, to assess which category an unknown sample belongs to, the proposed algorithm operates by identifying which training objects are most similar to the one to be predicted and building a PLS-DA model using these calibration samples only. Moreover, the influence of the selected training samples on the local model can be further modulated by adopting a not uniform distance-based weighting scheme which allows the farthest calibration objects to have less impact than the closest ones. The performances of the proposed locally weighted-partial least squares-discriminant analysis (LW-PLS-DA) algorithm have been tested on three simulated data sets characterized by a varying degree of non-linearity: in all cases, a classification accuracy higher than 99% on external validation samples was achieved. Moreover, when also applied to a real data set (classification of rice varieties), characterized by a high extent of non-linearity, the proposed method provided an average correct classification rate of about 93% on the test set. By the preliminary results, showed in this paper, the performances of the proposed LW-PLS-DA approach have proved to be comparable and in some cases better than those obtained by other non-linear methods (k nearest neighbors, kernel-PLS-DA and, in the case of rice, counterpropagation neural networks). Copyright © 2014 Elsevier B.V. All rights reserved.

Iterative algorithms for large sparse linear systems on parallel computers

NASA Technical Reports Server (NTRS)

Adams, L. M.

1982-01-01

Algorithms for assembling in parallel the sparse system of linear equations that result from finite difference or finite element discretizations of elliptic partial differential equations, such as those that arise in structural engineering are developed. Parallel linear stationary iterative algorithms and parallel preconditioned conjugate gradient algorithms are developed for solving these systems. In addition, a model for comparing parallel algorithms on array architectures is developed and results of this model for the algorithms are given.

(N+1)-dimensional fractional reduced differential transform method for fractional order partial differential equations

NASA Astrophysics Data System (ADS)

Arshad, Muhammad; Lu, Dianchen; Wang, Jun

2017-07-01

In this paper, we pursue the general form of the fractional reduced differential transform method (DTM) to (N+1)-dimensional case, so that fractional order partial differential equations (PDEs) can be resolved effectively. The most distinct aspect of this method is that no prescribed assumptions are required, and the huge computational exertion is reduced and round-off errors are also evaded. We utilize the proposed scheme on some initial value problems and approximate numerical solutions of linear and nonlinear time fractional PDEs are obtained, which shows that the method is highly accurate and simple to apply. The proposed technique is thus an influential technique for solving the fractional PDEs and fractional order problems occurring in the field of engineering, physics etc. Numerical results are obtained for verification and demonstration purpose by using Mathematica software.

Fast solution of elliptic partial differential equations using linear combinations of plane waves.

PubMed

Pérez-Jordá, José M

2016-02-01

Given an arbitrary elliptic partial differential equation (PDE), a procedure for obtaining its solution is proposed based on the method of Ritz: the solution is written as a linear combination of plane waves and the coefficients are obtained by variational minimization. The PDE to be solved is cast as a system of linear equations Ax=b, where the matrix A is not sparse, which prevents the straightforward application of standard iterative methods in order to solve it. This sparseness problem can be circumvented by means of a recursive bisection approach based on the fast Fourier transform, which makes it possible to implement fast versions of some stationary iterative methods (such as Gauss-Seidel) consuming O(NlogN) memory and executing an iteration in O(Nlog(2)N) time, N being the number of plane waves used. In a similar way, fast versions of Krylov subspace methods and multigrid methods can also be implemented. These procedures are tested on Poisson's equation expressed in adaptive coordinates. It is found that the best results are obtained with the GMRES method using a multigrid preconditioner with Gauss-Seidel relaxation steps.

Stability analysis on the flow and heat transfer of nanofluid past a stretching/shrinking cylinder with suction effect

NASA Astrophysics Data System (ADS)

Bakar, Nor Ashikin Abu; Bachok, Norfifah; Arifin, Norihan Md.; Pop, Ioan

2018-06-01

The steady boundary layer flow over a stretching/shrinking cylinder with suction effect is numerically studied. Using a similarity transformations, the governing partial differential equations are transformed into a set of nonlinear differential equations and have been solved numerically using a bvp4c code in Matlab software. The nanofluid model used is taking into account the effects of Brownian motion and thermophoresis. The influences of the governing parameters namely the curvature parameter γ, mass suction parameter S, Brownian motion parameter Nb and thermophoresis parameter Nt on the flow, heat and mass transfers characteristics are presented graphically. The numerical results obtained for the skin friction coefficient, local Nusselt number and local Sherwood number are thoroughly determined and presented graphically for several values of the governing parameters. From our investigation, it is found that the non-unique (dual) solutions exist for a certain range of mass suction parameter. It is observed that as curvature parameter increases, the skin friction coefficient and heat transfer rate decrease, meanwhile the mass transfer rates increase. Moreover, the stability analysis showed that the first solution is linearly stable, while the second solution is linearly unstable.

A DGTD method for the numerical modeling of the interaction of light with nanometer scale metallic structures taking into account non-local dispersion effects

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

Schmitt, Nikolai; Technische Universitaet Darmstadt, Institut fuer Theorie Elektromagnetischer Felder; Scheid, Claire

2016-07-01

The interaction of light with metallic nanostructures is increasingly attracting interest because of numerous potential applications. Sub-wavelength metallic structures, when illuminated with a frequency close to the plasma frequency of the metal, present resonances that cause extreme local field enhancements. Exploiting the latter in applications of interest requires a detailed knowledge about the occurring fields which can actually not be obtained analytically. For the latter mentioned reason, numerical tools are thus an absolute necessity. The insight they provide is very often the only way to get a deep enough understanding of the very rich physics at play. For the numericalmore » modeling of light-structure interaction on the nanoscale, the choice of an appropriate material model is a crucial point. Approaches that are adopted in a first instance are based on local (i.e. with no interaction between electrons) dispersive models, e.g. Drude or Drude–Lorentz models. From the mathematical point of view, when a time-domain modeling is considered, these models lead to an additional system of ordinary differential equations coupled to Maxwell's equations. However, recent experiments have shown that the repulsive interaction between electrons inside the metal makes the response of metals intrinsically non-local and that this effect cannot generally be overlooked. Technological achievements have enabled the consideration of metallic structures in a regime where such non-localities have a significant influence on the structures' optical response. This leads to an additional, in general non-linear, system of partial differential equations which is, when coupled to Maxwell's equations, significantly more difficult to treat. Nevertheless, dealing with a linearized non-local dispersion model already opens the route to numerous practical applications of plasmonics. In this work, we present a Discontinuous Galerkin Time-Domain (DGTD) method able to solve the system of Maxwell's equations coupled to a linearized non-local dispersion model relevant to plasmonics. While the method is presented in the general 3D case, numerical results are given for 2D simulation settings.« less

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

NASA Astrophysics Data System (ADS)

Waubke, Holger; Kasess, Christian H.

2016-11-01

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

A Maple package for computing Gröbner bases for linear recurrence relations

NASA Astrophysics Data System (ADS)

Gerdt, Vladimir P.; Robertz, Daniel

2006-04-01

A Maple package for computing Gröbner bases of linear difference ideals is described. The underlying algorithm is based on Janet and Janet-like monomial divisions associated with finite difference operators. The package can be used, for example, for automatic generation of difference schemes for linear partial differential equations and for reduction of multiloop Feynman integrals. These two possible applications are illustrated by simple examples of the Laplace equation and a one-loop scalar integral of propagator type.

Role of Alternative Polyadenylation during Adipogenic Differentiation: An In Silico Approach

PubMed Central

Spangenberg, Lucía; Correa, Alejandro; Dallagiovanna, Bruno; Naya, Hugo

2013-01-01

Post-transcriptional regulation of stem cell differentiation is far from being completely understood. Changes in protein levels are not fully correlated with corresponding changes in mRNAs; the observed differences might be partially explained by post-transcriptional regulation mechanisms, such as alternative polyadenylation. This would involve changes in protein binding, transcript usage, miRNAs and other non-coding RNAs. In the present work we analyzed the distribution of alternative transcripts during adipogenic differentiation and the potential role of miRNAs in post-transcriptional regulation. Our in silico analysis suggests a modest, consistent, bias in 3′UTR lengths during differentiation enabling a fine-tuned transcript regulation via small non-coding RNAs. Including these effects in the analyses partially accounts for the observed discrepancies in relative abundance of protein and mRNA. PMID:24143171

Conference on Non-linear Phenomena in Mathematical Physics: Dedicated to Cathleen Synge Morawetz on her 85th Birthday. The Fields Institute, Toronto, Canada September 18-20, 2008. Sponsors: Association for Women in Mathematics, Inc. and The Fields Institute

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

Lewis, Jennifer

2012-10-15

This scientific meeting focused on the legacy of Cathleen S. Morawetz and the impact that her scientific work on transonic flow and the non-linear wave equation has had in recent progress on different aspects of analysis for non-linear wave, kinetic and quantum transport problems associated to mathematical physics. These are areas where the elements of continuum, statistical and stochastic mechanics, and their interplay, have counterparts in the theory of existence, uniqueness and stability of the associated systems of equations and geometric constraints. It was a central event for the applied and computational analysis community focusing on Partial Differential Equations. Themore » goal of the proposal was to honor Cathleen Morawetz, a highly successful woman in mathematics, while encouraging beginning researchers. The conference was successful in show casing the work of successful women, enhancing the visibility of women in the profession and providing role models for those just beginning their careers. The two-day conference included seven 45-minute lectures and one day of six 45-minute lectures, and a poster session for junior participants. The conference program included 19 distinguished speakers, 10 poster presentations, about 70 junior and senior participants and, of course, the participation of Cathleen Synge Morawetz. The conference celebrated Morawetz's paramount contributions to the theory of non-linear equations in gas dynamics and their impact in the current trends of nonlinear phenomena in mathematical physics, but also served as an awareness session of current women's contribution to mathematics.« less

On the Importance of the Dynamics of Discretizations

NASA Technical Reports Server (NTRS)

Sweby, Peter K.; Yee, H. C.; Rai, ManMohan (Technical Monitor)

1995-01-01

It has been realized recently that the discrete maps resulting from numerical discretizations of differential equations can possess asymptotic dynamical behavior quite different from that of the original systems. This is the case not only for systems of Ordinary Differential Equations (ODEs) but in a more complicated manner for Partial Differential Equations (PDEs) used to model complex physics. The impact of the modified dynamics may be mild and even not observed for some numerical methods. For other classes of discretizations the impact may be pronounced, but not always obvious depending on the nonlinear model equations, the time steps, the grid spacings and the initial conditions. Non-convergence or convergence to periodic solutions might be easily recognizable but convergence to incorrect but plausible solutions may not be so obvious - even for discretized parameters within the linearized stability constraint. Based on our past four years of research, we will illustrate some of the pathology of the dynamics of discretizations, its possible impact and the usage of these schemes for model nonlinear ODEs, convection-diffusion equations and grid adaptations.

On asymptotic behavior and energy distribution for some one-dimensional non-parabolic diffusion problems

NASA Astrophysics Data System (ADS)

Kim, Seonghak; Yan, Baisheng

2018-06-01

We study some non-parabolic diffusion problems in one space dimension, where the diffusion flux exhibits forward and backward nature of the Perona–Malik, Höllig or non-Fourier type. Classical weak solutions to such problems are constructed in a way to capture some expected and unexpected properties, including anomalous asymptotic behaviors and energy dissipation or allocation. Specific properties of solutions will depend on the type of the diffusion flux, but the primary method of our study relies on reformulating diffusion equations involved as an inhomogeneous partial differential inclusion and on constructing solutions from the differential inclusion by a combination of the convex integration and Baire’s category methods. In doing so, we introduce the appropriate notion of subsolutions of the partial differential inclusion and their transition gauge, which plays a pivotal role in dealing with some specific features of the constructed weak solutions.

Experimental and Numerical Investigation of Adsorption/Desorption in Packed Sorption Beds Under Ideal and Non-Ideal Flows

NASA Technical Reports Server (NTRS)

Mohamadinejad, H.; Knox, J. C.; Smith, James E.

1999-01-01

The importance of the wall effect on packed beds in the adsorption and desorption of carbon dioxide, nitrogen, and water on molecular sieve 5A of 0.127 cm in radius is examined experimentally and with one-dimensional computer simulations. Experimental results are presented for a 22.5-cm long by 4.5-cm diameter cylindrical column with concentration measurements taken at various radial locations. The set of partial differential equations are solved using finite differences and Newman's method. Comparison of test data with the axial-dispersed, non-isothermal, linear driving force model suggests that a two-dimensional model (submitted to Separation Science and Technology) is required for accurate simulation of the average column breakthrough concentration. Additional comparisons of test data with the model provided information on the interactive effects of carrier gas coadsorption with CO2, as well as CO2-H2O interactions.

Optimal Control of Stochastic Systems Driven by Fractional Brownian Motions

DTIC Science & Technology

2014-10-09

problems for stochastic partial differential equations driven by fractional Brownian motions are explicitly solved. For the control of a continuous time...linear systems with Brownian motion or a discrete time linear system with a white Gaussian noise and costs 1. REPORT DATE (DD-MM-YYYY) 4. TITLE AND...Army Research Office P.O. Box 12211 Research Triangle Park, NC 27709-2211 stochastic optimal control, fractional Brownian motion , stochastic

The Shock and Vibration Digest. Volume 16, Number 11

DTIC Science & Technology

1984-11-01

wave [19], a secular equation for Rayleigh waves on ing, seismic risk, and related problems are discussed. the surface of an anisotropic half-space...waves in an !so- tive equation of an elastic-plastic rack medium was....... tropic linear elastic half-space with plane material used; the coefficient...pair of semi-linear hyperbolic partial differential -- " Conditions under which the equations of motion equations governing slow variations in amplitude

Biomagnetic fluid flow in an aneurysm using ferrohydrodynamics principles

NASA Astrophysics Data System (ADS)

Tzirtzilakis, E. E.

2015-06-01

In this study, the fundamental problem of biomagnetic fluid flow in an aneurysmal geometry under the influence of a steady localized magnetic field is numerically investigated. The mathematical model used to formulate the problem is consistent with the principles of ferrohydrodynamics. Blood is considered to be an electrically non-conducting, homogeneous, non-isothermal Newtonian magnetic fluid. For the numerical solution of the problem, which is described by a coupled, non-linear system of Partial Differential Equations (PDEs), with appropriate boundary conditions, the stream function-vorticity formulation is adopted. The solution is obtained by applying an efficient pseudotransient numerical methodology using finite differences. This methodology is based on the application of a semi-implicit numerical technique, transformations, stretching of the grid, and construction of the boundary conditions for the vorticity. The results regarding the velocity and temperature field, skin friction, and rate of heat transfer indicate that the presence of a magnetic field considerably influences the flow field, particularly in the region of the aneurysm.

Fluid Flow and Heat Transfer Analysis of a Nanofluid Containing Motile Gyrotactic Micro-Organisms Passing a Nonlinear Stretching Vertical Sheet in the Presence of a Non-Uniform Magnetic Field; Numerical Approach

PubMed Central

M. Mehryan, S. A.; Moradi Kashkooli, Farshad; Soltani, M.; Raahemifar, Kaamran

2016-01-01

The behavior of a water-based nanofluid containing motile gyrotactic micro-organisms passing an isothermal nonlinear stretching sheet in the presence of a non-uniform magnetic field is studied numerically. The governing partial differential equations including continuity, momentums, energy, concentration of the nanoparticles, and density of motile micro-organisms are converted into a system of the ordinary differential equations via a set of similarity transformations. New set of equations are discretized using the finite difference method and have been linearized by employing the Newton’s linearization technique. The tri-diagonal system of algebraic equations from discretization is solved using the well-known Thomas algorithm. The numerical results for profiles of velocity, temperature, nanoparticles concentration and density of motile micro-organisms as well as the local skin friction coefficient Cfx, the local Nusselt number Nux, the local Sherwood number Shx and the local density number of the motile microorganism Nnx are expressed graphically and described in detail. This investigation shows the density number of the motile micro-organisms enhances with rise of M, Gr/Re2, Pe and Ω but it decreases with augment of Rb and n. Also, Sherwood number augments with an increase of M and Gr/Re2, while decreases with n, Rb, Nb and Nr. To show the validity of the current results, a comparison between the present results and the existing literature has been carried out. PMID:27322536

On the solution of the complex eikonal equation in acoustic VTI media: A perturbation plus optimization scheme

NASA Astrophysics Data System (ADS)

Huang, Xingguo; Sun, Jianguo; Greenhalgh, Stewart

2018-04-01

We present methods for obtaining numerical and analytic solutions of the complex eikonal equation in inhomogeneous acoustic VTI media (transversely isotropic media with a vertical symmetry axis). The key and novel point of the method for obtaining numerical solutions is to transform the problem of solving the highly nonlinear acoustic VTI eikonal equation into one of solving the relatively simple eikonal equation for the background (isotropic) medium and a system of linear partial differential equations. Specifically, to obtain the real and imaginary parts of the complex traveltime in inhomogeneous acoustic VTI media, we generalize a perturbation theory, which was developed earlier for solving the conventional real eikonal equation in inhomogeneous anisotropic media, to the complex eikonal equation in such media. After the perturbation analysis, we obtain two types of equations. One is the complex eikonal equation for the background medium and the other is a system of linearized partial differential equations for the coefficients of the corresponding complex traveltime formulas. To solve the complex eikonal equation for the background medium, we employ an optimization scheme that we developed for solving the complex eikonal equation in isotropic media. Then, to solve the system of linearized partial differential equations for the coefficients of the complex traveltime formulas, we use the finite difference method based on the fast marching strategy. Furthermore, by applying the complex source point method and the paraxial approximation, we develop the analytic solutions of the complex eikonal equation in acoustic VTI media, both for the isotropic and elliptical anisotropic background medium. Our numerical results demonstrate the effectiveness of our derivations and illustrate the influence of the beam widths and the anisotropic parameters on the complex traveltimes.

Analytical modeling of large amplitude free vibration of non-uniform beams carrying a both transversely and axially eccentric tip mass

NASA Astrophysics Data System (ADS)

Malaeke, Hasan; Moeenfard, Hamid

2016-03-01

The objective of this paper is to study large amplitude flexural-extensional free vibration of non-uniform cantilever beams carrying a both transversely and axially eccentric tip mass. The effects of variable axial force is also taken into account. Hamilton's principle is utilized to obtain the partial differential equations governing the nonlinear vibration of the system as well as the corresponding boundary conditions. A numerical finite difference scheme is proposed to find the natural frequencies and mode shapes of the system which is validated specifically for a beam with linearly varying cross section. Using a single mode approximation in conjunction with the Lagrange method, the governing equations are reduced to a set of two nonlinear ordinary differential equations in terms of end displacement components of the beam which are coupled due to the presence of the transverse eccentricity. These temporal coupled equations are then solved analytically using the multiple time scales perturbation technique. The obtained analytical results are compared with the numerical ones and excellent agreement is observed. The qualitative and quantitative knowledge resulting from this research is expected to enable the study of the effects of eccentric tip mass and non-uniformity on the large amplitude flexural-extensional vibration of beams for improved dynamic performance.

Numerical Study of Pressure Field in Laterally Closed Industrial Buildings with Curved Metallic Roofs due to the Wind Effect by FEM and European Rule Comparison

NASA Astrophysics Data System (ADS)

Nieto, P. J. García; del Coz Díaz, J. J.; Vilán, J. A. Vilán; Placer, C. Casqueiro

2009-08-01

In this paper, an evaluation of distribution of the air pressure is determined throughout the laterally closed industrial buildings with curved metallic roofs due to the wind effect by the finite element method (FEM). The non-linearity is due to Reynolds-averaged Navier-Stokes (RANS) equations that govern the turbulent flow. The Navier-Stokes equations are non-linear partial differential equations and this non-linearity makes most problems difficult to solve and is part of the cause of turbulence. The RANS equations are time-averaged equations of motion for fluid flow. They are primarily used while dealing with turbulent flows. Turbulence is a highly complex physical phenomenon that is pervasive in flow problems of scientific and engineering concern like this one. In order to solve the RANS equations a two-equation model is used: the standard k-ɛ model. The calculation has been carried out keeping in mind the following assumptions: turbulent flow, an exponential-like wind speed profile with a maximum velocity of 40 m/s at 10 m reference height, and different heights of the building ranging from 6 to 10 meters. Finally, the forces and moments are determined on the cover, as well as the distribution of pressures on the same one, comparing the numerical results obtained with the Spanish CTE DB SE-AE, Spanish NBE AE-88 and European standard rules, giving place to the conclusions that are exposed in the study.

Time-periodic solutions of the Benjamin-Ono equation

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

Ambrose , D.M.; Wilkening, Jon

2008-04-01

We present a spectrally accurate numerical method for finding non-trivial time-periodic solutions of non-linear partial differential equations. The method is based on minimizing a functional (of the initial condition and the period) that is positive unless the solution is periodic, in which case it is zero. We solve an adjoint PDE to compute the gradient of this functional with respect to the initial condition. We include additional terms in the functional to specify the free parameters, which, in the case of the Benjamin-Ono equation, are the mean, a spatial phase, a temporal phase and the real part of one ofmore » the Fourier modes at t = 0. We use our method to study global paths of non-trivial time-periodic solutions connecting stationary and traveling waves of the Benjamin-Ono equation. As a starting guess for each path, we compute periodic solutions of the linearized problem by solving an infinite dimensional eigenvalue problem in closed form. We then use our numerical method to continue these solutions beyond the realm of linear theory until another traveling wave is reached (or until the solution blows up). By experimentation with data fitting, we identify the analytical form of the solutions on the path connecting the one-hump stationary solution to the two-hump traveling wave. We then derive exact formulas for these solutions by explicitly solving the system of ODE's governing the evolution of solitons using the ansatz suggested by the numerical simulations.« less

Invariant algebraic surfaces for a virus dynamics

NASA Astrophysics Data System (ADS)

Valls, Claudia

2015-08-01

In this paper, we provide a complete classification of the invariant algebraic surfaces and of the rational first integrals for a well-known virus system. In the proofs, we use the weight-homogeneous polynomials and the method of characteristic curves for solving linear partial differential equations.

Fast Time and Space Parallel Algorithms for Solution of Parabolic Partial Differential Equations

NASA Technical Reports Server (NTRS)

Fijany, Amir

1993-01-01

In this paper, fast time- and Space -Parallel agorithms for solution of linear parabolic PDEs are developed. It is shown that the seemingly strictly serial iterations of the time-stepping procedure for solution of the problem can be completed decoupled.

Optimal Control for Stochastic Delay Evolution Equations

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

Meng, Qingxin, E-mail: mqx@hutc.zj.cn; Shen, Yang, E-mail: skyshen87@gmail.com

2016-08-15

In this paper, we investigate a class of infinite-dimensional optimal control problems, where the state equation is given by a stochastic delay evolution equation with random coefficients, and the corresponding adjoint equation is given by an anticipated backward stochastic evolution equation. We first prove the continuous dependence theorems for stochastic delay evolution equations and anticipated backward stochastic evolution equations, and show the existence and uniqueness of solutions to anticipated backward stochastic evolution equations. Then we establish necessary and sufficient conditions for optimality of the control problem in the form of Pontryagin’s maximum principles. To illustrate the theoretical results, we applymore » stochastic maximum principles to study two examples, an infinite-dimensional linear-quadratic control problem with delay and an optimal control of a Dirichlet problem for a stochastic partial differential equation with delay. Further applications of the two examples to a Cauchy problem for a controlled linear stochastic partial differential equation and an optimal harvesting problem are also considered.« less

Nebo: An efficient, parallel, and portable domain-specific language for numerically solving partial differential equations

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

Earl, Christopher; Might, Matthew; Bagusetty, Abhishek

This study presents Nebo, a declarative domain-specific language embedded in C++ for discretizing partial differential equations for transport phenomena on multiple architectures. Application programmers use Nebo to write code that appears sequential but can be run in parallel, without editing the code. Currently Nebo supports single-thread execution, multi-thread execution, and many-core (GPU-based) execution. With single-thread execution, Nebo performs on par with code written by domain experts. With multi-thread execution, Nebo can linearly scale (with roughly 90% efficiency) up to 12 cores, compared to its single-thread execution. Moreover, Nebo’s many-core execution can be over 140x faster than its single-thread execution.

Nebo: An efficient, parallel, and portable domain-specific language for numerically solving partial differential equations

DOE PAGES

Earl, Christopher; Might, Matthew; Bagusetty, Abhishek; ...

2016-01-26

This study presents Nebo, a declarative domain-specific language embedded in C++ for discretizing partial differential equations for transport phenomena on multiple architectures. Application programmers use Nebo to write code that appears sequential but can be run in parallel, without editing the code. Currently Nebo supports single-thread execution, multi-thread execution, and many-core (GPU-based) execution. With single-thread execution, Nebo performs on par with code written by domain experts. With multi-thread execution, Nebo can linearly scale (with roughly 90% efficiency) up to 12 cores, compared to its single-thread execution. Moreover, Nebo’s many-core execution can be over 140x faster than its single-thread execution.

A note on the accuracy of spectral method applied to nonlinear conservation laws

NASA Technical Reports Server (NTRS)

Shu, Chi-Wang; Wong, Peter S.

1994-01-01

Fourier spectral method can achieve exponential accuracy both on the approximation level and for solving partial differential equations if the solutions are analytic. For a linear partial differential equation with a discontinuous solution, Fourier spectral method produces poor point-wise accuracy without post-processing, but still maintains exponential accuracy for all moments against analytic functions. In this note we assess the accuracy of Fourier spectral method applied to nonlinear conservation laws through a numerical case study. We find that the moments with respect to analytic functions are no longer very accurate. However the numerical solution does contain accurate information which can be extracted by a post-processing based on Gegenbauer polynomials.

Population response to climate change: linear vs. non-linear modeling approaches.

PubMed

Ellis, Alicia M; Post, Eric

2004-03-31

Research on the ecological consequences of global climate change has elicited a growing interest in the use of time series analysis to investigate population dynamics in a changing climate. Here, we compare linear and non-linear models describing the contribution of climate to the density fluctuations of the population of wolves on Isle Royale, Michigan from 1959 to 1999. The non-linear self excitatory threshold autoregressive (SETAR) model revealed that, due to differences in the strength and nature of density dependence, relatively small and large populations may be differentially affected by future changes in climate. Both linear and non-linear models predict a decrease in the population of wolves with predicted changes in climate. Because specific predictions differed between linear and non-linear models, our study highlights the importance of using non-linear methods that allow the detection of non-linearity in the strength and nature of density dependence. Failure to adopt a non-linear approach to modelling population response to climate change, either exclusively or in addition to linear approaches, may compromise efforts to quantify ecological consequences of future warming.

Aspects of decision support in water management--example Berlin and Potsdam (Germany) I--spatially differentiated evaluation.

PubMed

Simon, Ute; Brüggemann, Rainer; Pudenz, Stefan

2004-04-01

Decisions about sustainable development demand spatially differentiated evaluations. As an example, we demonstrate the evaluation of water management strategies in the cities of Berlin and Potsdam (Germany) with respect to their ecological effects in 14 sections of the surface water system. Two decision support systems were compared, namely PROMETHEE, which is designed to obtain a clear decision (linear ranking), and Hasse Diagram Technique (HDT), normally providing more than one favourable solution (partial order). By PROMETHEE, the spatial differentiation had unwanted effects on the result, negating the stakeholders determined weighting of indicators. Therefore, the stakeholder can barely benefit from the convenience of obtaining a clear decision (linear ranking). In contrast, the result obtained by HDT was not influenced by spatial differentiation. Furthermore, HDT provided helpful tools to analyse the evaluation result, such as the concept of antagonistic indicators to discover conflicts in the evaluation process.

Analysis of Instabilities in Non-Axisymmetric Hypersonic Boundary Layers Over Cones

NASA Technical Reports Server (NTRS)

Li, Fei; Choudhari, Meelan M.; Chang, Chau-Lyan; White, Jeffery A.

2010-01-01

Hypersonic flows over circular cones constitute one of the most important generic configurations for fundamental aerodynamic and aerothermodynamic studies. In this paper, numerical computations are carried out for Mach 6 flows over a 7-degree half-angle cone with two different flow incidence angles and a compression cone with a large concave curvature. Instability wave and transition-related flow physics are investigated using a series of advanced stability methods ranging from conventional linear stability theory (LST) and a higher-fidelity linear and nonlinear parabolized stability equations (PSE), to the 2D eigenvalue analysis based on partial differential equations. Computed N factor distribution pertinent to various instability mechanisms over the cone surface provides initial assessments of possible transition fronts and a guide to corresponding disturbance characteristics such as frequency and azimuthal wave numbers. It is also shown that strong secondary instability that eventually leads to transition to turbulence can be simulated very efficiently using a combination of advanced stability methods described above.

Computational manipulation of a radiative MHD flow with Hall current and chemical reaction in the presence of rotating fluid

NASA Astrophysics Data System (ADS)

Alias Suba, Subbu; Muthucumaraswamy, R.

2018-04-01

A numerical analysis of transient radiative MHD(MagnetoHydroDynamic) natural convective flow of a viscous, incompressible, electrically conducting and rotating fluid along a semi-infinite isothermal vertical plate is carried out taking into consideration Hall current, rotation and first order chemical reaction.The coupled non-linear partial differential equations are expressed in difference form using implicit finite difference scheme. The difference equations are then reduced to a system of linear algebraic equations with a tri-diagonal structure which is solved by Thomas Algorithm. The primary and secondary velocity profiles, temperature profile, concentration profile, skin friction, Nusselt number and Sherwood Number are depicted graphically for a range of values of rotation parameter, Hall parameter,magnetic parameter, chemical reaction parameter, radiation parameter, Prandtl number and Schmidt number.It is recognized that rate of heat transfer and rate of mass transfer decrease with increase in time but they increase with increasing values of radiation parameter and Schmidt number respectively.

A comparison of numerical solutions of partial differential equations with probabilistic and possibilistic parameters for the quantification of uncertainty in subsurface solute transport.

PubMed

Zhang, Kejiang; Achari, Gopal; Li, Hua

2009-11-03

Traditionally, uncertainty in parameters are represented as probabilistic distributions and incorporated into groundwater flow and contaminant transport models. With the advent of newer uncertainty theories, it is now understood that stochastic methods cannot properly represent non random uncertainties. In the groundwater flow and contaminant transport equations, uncertainty in some parameters may be random, whereas those of others may be non random. The objective of this paper is to develop a fuzzy-stochastic partial differential equation (FSPDE) model to simulate conditions where both random and non random uncertainties are involved in groundwater flow and solute transport. Three potential solution techniques namely, (a) transforming a probability distribution to a possibility distribution (Method I) then a FSPDE becomes a fuzzy partial differential equation (FPDE), (b) transforming a possibility distribution to a probability distribution (Method II) and then a FSPDE becomes a stochastic partial differential equation (SPDE), and (c) the combination of Monte Carlo methods and FPDE solution techniques (Method III) are proposed and compared. The effects of these three methods on the predictive results are investigated by using two case studies. The results show that the predictions obtained from Method II is a specific case of that got from Method I. When an exact probabilistic result is needed, Method II is suggested. As the loss or gain of information during a probability-possibility (or vice versa) transformation cannot be quantified, their influences on the predictive results is not known. Thus, Method III should probably be preferred for risk assessments.

Minimal string theories and integrable hierarchies

NASA Astrophysics Data System (ADS)

Iyer, Ramakrishnan

Well-defined, non-perturbative formulations of the physics of string theories in specific minimal or superminimal model backgrounds can be obtained by solving matrix models in the double scaling limit. They provide us with the first examples of completely solvable string theories. Despite being relatively simple compared to higher dimensional critical string theories, they furnish non-perturbative descriptions of interesting physical phenomena such as geometrical transitions between D-branes and fluxes, tachyon condensation and holography. The physics of these theories in the minimal model backgrounds is succinctly encoded in a non-linear differential equation known as the string equation, along with an associated hierarchy of integrable partial differential equations (PDEs). The bosonic string in (2,2m-1) conformal minimal model backgrounds and the type 0A string in (2,4 m) superconformal minimal model backgrounds have the Korteweg-de Vries system, while type 0B in (2,4m) backgrounds has the Zakharov-Shabat system. The integrable PDE hierarchy governs flows between backgrounds with different m. In this thesis, we explore this interesting connection between minimal string theories and integrable hierarchies further. We uncover the remarkable role that an infinite hierarchy of non-linear differential equations plays in organizing and connecting certain minimal string theories non-perturbatively. We are able to embed the type 0A and 0B (A,A) minimal string theories into this single framework. The string theories arise as special limits of a rich system of equations underpinned by an integrable system known as the dispersive water wave hierarchy. We find that there are several other string-like limits of the system, and conjecture that some of them are type IIA and IIB (A,D) minimal string backgrounds. We explain how these and several other string-like special points arise and are connected. In some cases, the framework endows the theories with a non-perturbative definition for the first time. Notably, we discover that the Painleve IV equation plays a key role in organizing the string theory physics, joining its siblings, Painleve I and II, whose roles have previously been identified in this minimal string context. We then present evidence that the conjectured type II theories have smooth non-perturbative solutions, connecting two perturbative asymptotic regimes, in a 't Hooft limit. Our technique also demonstrates evidence for new minimal string theories that are not apparent in a perturbative analysis.

Local uncontrollability for affine control systems with jumps

NASA Astrophysics Data System (ADS)

Treanţă, Savin

2017-09-01

This paper investigates affine control systems with jumps for which the ideal If(g1, …, gm) generated by the drift vector field f in the Lie algebra L(f, g1, …, gm) can be imbedded as a kernel of a linear first-order partial differential equation. It will lead us to uncontrollable affine control systems with jumps for which the corresponding reachable sets are included in explicitly described differentiable manifolds.

Discontinuous Galerkin Methods for NonLinear Differential Systems

NASA Technical Reports Server (NTRS)

Barth, Timothy; Mansour, Nagi (Technical Monitor)

2001-01-01

This talk considers simplified finite element discretization techniques for first-order systems of conservation laws equipped with a convex (entropy) extension. Using newly developed techniques in entropy symmetrization theory, simplified forms of the discontinuous Galerkin (DG) finite element method have been developed and analyzed. The use of symmetrization variables yields numerical schemes which inherit global entropy stability properties of the PDE (partial differential equation) system. Central to the development of the simplified DG methods is the Eigenvalue Scaling Theorem which characterizes right symmetrizers of an arbitrary first-order hyperbolic system in terms of scaled eigenvectors of the corresponding flux Jacobian matrices. A constructive proof is provided for the Eigenvalue Scaling Theorem with detailed consideration given to the Euler equations of gas dynamics and extended conservation law systems derivable as moments of the Boltzmann equation. Using results from kinetic Boltzmann moment closure theory, we then derive and prove energy stability for several approximate DG fluxes which have practical and theoretical merit.

Thermal Marangoni convection in two-phase flow of dusty Casson fluid

NASA Astrophysics Data System (ADS)

Mahanthesh, B.; Gireesha, B. J.

2018-03-01

This paper deals with the thermal Marangoni convection effects in magneto-Casson liquid flow through suspension of dust particles. The transpiration cooling aspect is accounted. The surface tension is assumed to be fluctuating linearly with temperature. The fluid and dust particle's temperature of the interface is chosen as a quadratic function of interface arc length. The governing problem is modelled by conservation laws of mass, momentum and energy for fluid and dust particle phase. Stretching transformation technique is utilized to form ordinary differential equations from the partial differential equations. Later, the numerical solutions based on Runge-Kutta-Fehlberg method are established. The momentum and heat transport distributions are focused on the outcome of distinct governing parameters. The results of Nusselt number is also presented and discussed. It is established that the heat transfer rate is higher in the case of dusty non-Newtonian fluid than dusty Newtonian fluid. The rate of heat transfer can be enhanced by suspending dust particles in a base liquid.

Hybrid finite element method for describing the electrical response of biological cells to applied fields.

PubMed

Ying, Wenjun; Henriquez, Craig S

2007-04-01

A novel hybrid finite element method (FEM) for modeling the response of passive and active biological membranes to external stimuli is presented. The method is based on the differential equations that describe the conservation of electric flux and membrane currents. By introducing the electric flux through the cell membrane as an additional variable, the algorithm decouples the linear partial differential equation part from the nonlinear ordinary differential equation part that defines the membrane dynamics of interest. This conveniently results in two subproblems: a linear interface problem and a nonlinear initial value problem. The linear interface problem is solved with a hybrid FEM. The initial value problem is integrated by a standard ordinary differential equation solver such as the Euler and Runge-Kutta methods. During time integration, these two subproblems are solved alternatively. The algorithm can be used to model the interaction of stimuli with multiple cells of almost arbitrary geometries and complex ion-channel gating at the plasma membrane. Numerical experiments are presented demonstrating the uses of the method for modeling field stimulation and action potential propagation.

Networked dynamical systems with linear coupling: synchronisation patterns, coherence and other behaviours.

PubMed

Judd, Kevin

2013-12-01

Many physical and biochemical systems are well modelled as a network of identical non-linear dynamical elements with linear coupling between them. An important question is how network structure affects chaotic dynamics, for example, by patterns of synchronisation and coherence. It is shown that small networks can be characterised precisely into patterns of exact synchronisation and large networks characterised by partial synchronisation at the local and global scale. Exact synchronisation modes are explained using tools of symmetry groups and invariance, and partial synchronisation is explained by finite-time shadowing of exact synchronisation modes.

The Artificial Hamiltonian, First Integrals, and Closed-Form Solutions of Dynamical Systems for Epidemics

NASA Astrophysics Data System (ADS)

Naz, Rehana; Naeem, Imran

2018-03-01

The non-standard Hamiltonian system, also referred to as a partial Hamiltonian system in the literature, of the form {\\dot q^i} = {partial H}/{partial {p_i}},\\dot p^i = - {partial H}/{partial {q_i}} + {Γ ^i}(t,{q^i},{p_i}) appears widely in economics, physics, mechanics, and other fields. The non-standard (partial) Hamiltonian systems arise from physical Hamiltonian structures as well as from artificial Hamiltonian structures. We introduce the term `artificial Hamiltonian' for the Hamiltonian of a model having no physical structure. We provide here explicitly the notion of an artificial Hamiltonian for dynamical systems of ordinary differential equations (ODEs). Also, we show that every system of second-order ODEs can be expressed as a non-standard (partial) Hamiltonian system of first-order ODEs by introducing an artificial Hamiltonian. This notion of an artificial Hamiltonian gives a new way to solve dynamical systems of first-order ODEs and systems of second-order ODEs that can be expressed as a non-standard (partial) Hamiltonian system by using the known techniques applicable to the non-standard Hamiltonian systems. We employ the proposed notion to solve dynamical systems of first-order ODEs arising in epidemics.

The Effects of Topographical Patterns and Sizes on Neural Stem Cell Behavior

PubMed Central

Qi, Lin; Li, Ning; Huang, Rong; Song, Qin; Wang, Long; Zhang, Qi; Su, Ruigong; Kong, Tao; Tang, Mingliang; Cheng, Guosheng

2013-01-01

Engineered topographical manipulation, a paralleling approach with conventional biochemical cues, has recently attracted the growing interests in utilizations to control stem cell fate. In this study, effects of topological parameters, pattern and size are emphasized on the proliferation and differentiation of adult neural stem cells (ANSCs). We fabricate micro-scale topographical Si wafers with two different feature sizes. These topographical patterns present linear micro-pattern (LMP), circular micro-pattern (CMP) and dot micro-pattern (DMP). The results show that the three topography substrates are suitable for ANSC growth, while they all depress ANSC proliferation when compared to non-patterned substrates (control). Meanwhile, LMP and CMP with two feature sizes can both significantly enhance ANSC differentiation to neurons compared to control. The smaller the feature size is, the better upregulation applies to ANSC for the differentiated neurons. The underlying mechanisms of topography-enhanced neuronal differentiation are further revealed by directing suppression of mitogen-activated protein kinase/extracellular signaling-regulated kinase (MAPK/Erk) signaling pathway in ANSC using U0126, known to inhibit the activation of Erk. The statistical results suggest MAPK/Erk pathway is partially involved in topography-induced differentiation. These observations provide a better understanding on the different roles of topographical cues on stem cell behavior, especially on the selective differentiation, and facilitate to advance the field of stem cell therapy. PMID:23527077

Reference Models for Multi-Layer Tissue Structures

DTIC Science & Technology

2016-09-01

simulation,  finite   element  analysis 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT 18. NUMBER OF PAGES 19a. NAME OF RESPONSIBLE PERSON USAMRMC...Physiologically realistic, fully specimen-specific, nonlinear reference models. Tasks. Finite element analysis of non-linear mechanics of cadaver...models. Tasks. Finite element analysis of non-linear mechanics of multi-layer tissue regions of human subjects. Deliverables. Partially subject- and

Assessing non-uniqueness: An algebraic approach

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

Vasco, Don W.

Geophysical inverse problems are endowed with a rich mathematical structure. When discretized, most differential and integral equations of interest are algebraic (polynomial) in form. Techniques from algebraic geometry and computational algebra provide a means to address questions of existence and uniqueness for both linear and non-linear inverse problem. In a sense, the methods extend ideas which have proven fruitful in treating linear inverse problems.

General linear methods and friends: Toward efficient solutions of multiphysics problems

NASA Astrophysics Data System (ADS)

Sandu, Adrian

2017-07-01

Time dependent multiphysics partial differential equations are of great practical importance as they model diverse phenomena that appear in mechanical and chemical engineering, aeronautics, astrophysics, meteorology and oceanography, financial modeling, environmental sciences, etc. There is no single best time discretization for the complex multiphysics systems of practical interest. We discuss "multimethod" approaches that combine different time steps and discretizations using the rigourous frameworks provided by Partitioned General Linear Methods and Generalize-structure Additive Runge Kutta Methods..

Women's Endorsement of Models of Sexual Response: Correlates and Predictors.

PubMed

Nowosielski, Krzysztof; Wróbel, Beata; Kowalczyk, Robert

2016-02-01

Few studies have investigated endorsement of female sexual response models, and no single model has been accepted as a normative description of women's sexual response. The aim of the study was to establish how women from a population-based sample endorse current theoretical models of the female sexual response--the linear models and circular model (partial and composite Basson models)--as well as predictors of endorsement. Accordingly, 174 heterosexual women aged 18-55 years were included in a cross-sectional study: 74 women diagnosed with female sexual dysfunction (FSD) based on DSM-5 criteria and 100 non-dysfunctional women. The description of sexual response models was used to divide subjects into four subgroups: linear (Masters-Johnson and Kaplan models), circular (partial Basson model), mixed (linear and circular models in similar proportions, reflective of the composite Basson model), and a different model. Women were asked to choose which of the models best described their pattern of sexual response and how frequently they engaged in each model. Results showed that 28.7% of women endorsed the linear models, 19.5% the partial Basson model, 40.8% the composite Basson model, and 10.9% a different model. Women with FSD endorsed the partial Basson model and a different model more frequently than did non-dysfunctional controls. Individuals who were dissatisfied with a partner as a lover were more likely to endorse a different model. Based on the results, we concluded that the majority of women endorsed a mixed model combining the circular response with the possibility of an innate desire triggering a linear response. Further, relationship difficulties, not FSD, predicted model endorsement.

The Riemann-Lanczos equations in general relativity and their integrability

NASA Astrophysics Data System (ADS)

Dolan, P.; Gerber, A.

2008-06-01

The aim of this paper is to examine the Riemann-Lanczos equations and how they can be made integrable. They consist of a system of linear first-order partial differential equations that arise in general relativity, whereby the Riemann curvature tensor is generated by an unknown third-order tensor potential field called the Lanczos tensor. Our approach is based on the theory of jet bundles, where all field variables and all their partial derivatives of all relevant orders are treated as independent variables alongside the local manifold coordinates (xa) on the given space-time manifold M. This approach is adopted in (a) Cartan's method of exterior differential systems, (b) Vessiot's dual method using vector field systems, and (c) the Janet-Riquier theory of systems of partial differential equations. All three methods allow for the most general situations under which integrability conditions can be found. They give equivalent results, namely, that involutivity is always achieved at all generic points of the jet manifold M after a finite number of prolongations. Two alternative methods that appear in the general relativity literature to find integrability conditions for the Riemann-Lanczos equations generate new partial differential equations for the Lanczos potential that introduce a source term, which is nonlinear in the components of the Riemann tensor. We show that such sources do not occur when either of method (a), (b), or (c) are used.

Local Discontinuous Galerkin Methods for Partial Differential Equations with Higher Order Derivatives

NASA Technical Reports Server (NTRS)

Yan, Jue; Shu, Chi-Wang; Bushnell, Dennis M. (Technical Monitor)

2002-01-01

In this paper we review the existing and develop new continuous Galerkin methods for solving time dependent partial differential equations with higher order derivatives in one and multiple space dimensions. We review local discontinuous Galerkin methods for convection diffusion equations involving second derivatives and for KdV type equations involving third derivatives. We then develop new local discontinuous Galerkin methods for the time dependent bi-harmonic type equations involving fourth derivatives, and partial differential equations involving fifth derivatives. For these new methods we present correct interface numerical fluxes and prove L(exp 2) stability for general nonlinear problems. Preliminary numerical examples are shown to illustrate these methods. Finally, we present new results on a post-processing technique, originally designed for methods with good negative-order error estimates, on the local discontinuous Galerkin methods applied to equations with higher derivatives. Numerical experiments show that this technique works as well for the new higher derivative cases, in effectively doubling the rate of convergence with negligible additional computational cost, for linear as well as some nonlinear problems, with a local uniform mesh.

Reliable Real-Time Solution of Parametrized Partial Differential Equations: Reduced-Basis Output Bound Methods. Appendix 2

NASA Technical Reports Server (NTRS)

Prudhomme, C.; Rovas, D. V.; Veroy, K.; Machiels, L.; Maday, Y.; Patera, A. T.; Turinici, G.; Zang, Thomas A., Jr. (Technical Monitor)

2002-01-01

We present a technique for the rapid and reliable prediction of linear-functional outputs of elliptic (and parabolic) partial differential equations with affine parameter dependence. The essential components are (i) (provably) rapidly convergent global reduced basis approximations, Galerkin projection onto a space W(sub N) spanned by solutions of the governing partial differential equation at N selected points in parameter space; (ii) a posteriori error estimation, relaxations of the error-residual equation that provide inexpensive yet sharp and rigorous bounds for the error in the outputs of interest; and (iii) off-line/on-line computational procedures, methods which decouple the generation and projection stages of the approximation process. The operation count for the on-line stage, in which, given a new parameter value, we calculate the output of interest and associated error bound, depends only on N (typically very small) and the parametric complexity of the problem; the method is thus ideally suited for the repeated and rapid evaluations required in the context of parameter estimation, design, optimization, and real-time control.

A classical Perron method for existence of smooth solutions to boundary value and obstacle problems for degenerate-elliptic operators via holomorphic maps

NASA Astrophysics Data System (ADS)

Feehan, Paul M. N.

2017-09-01

We prove existence of solutions to boundary value problems and obstacle problems for degenerate-elliptic, linear, second-order partial differential operators with partial Dirichlet boundary conditions using a new version of the Perron method. The elliptic operators considered have a degeneracy along a portion of the domain boundary which is similar to the degeneracy of a model linear operator identified by Daskalopoulos and Hamilton [9] in their study of the porous medium equation or the degeneracy of the Heston operator [21] in mathematical finance. Existence of a solution to the partial Dirichlet problem on a half-ball, where the operator becomes degenerate on the flat boundary and a Dirichlet condition is only imposed on the spherical boundary, provides the key additional ingredient required for our Perron method. Surprisingly, proving existence of a solution to this partial Dirichlet problem with ;mixed; boundary conditions on a half-ball is more challenging than one might expect. Due to the difficulty in developing a global Schauder estimate and due to compatibility conditions arising where the ;degenerate; and ;non-degenerate boundaries; touch, one cannot directly apply the continuity or approximate solution methods. However, in dimension two, there is a holomorphic map from the half-disk onto the infinite strip in the complex plane and one can extend this definition to higher dimensions to give a diffeomorphism from the half-ball onto the infinite ;slab;. The solution to the partial Dirichlet problem on the half-ball can thus be converted to a partial Dirichlet problem on the slab, albeit for an operator which now has exponentially growing coefficients. The required Schauder regularity theory and existence of a solution to the partial Dirichlet problem on the slab can nevertheless be obtained using previous work of the author and C. Pop [16]. Our Perron method relies on weak and strong maximum principles for degenerate-elliptic operators, concepts of continuous subsolutions and supersolutions for boundary value and obstacle problems for degenerate-elliptic operators, and maximum and comparison principle estimates previously developed by the author [13].

High-performance image reconstruction in fluorescence tomography on desktop computers and graphics hardware.

PubMed

Freiberger, Manuel; Egger, Herbert; Liebmann, Manfred; Scharfetter, Hermann

2011-11-01

Image reconstruction in fluorescence optical tomography is a three-dimensional nonlinear ill-posed problem governed by a system of partial differential equations. In this paper we demonstrate that a combination of state of the art numerical algorithms and a careful hardware optimized implementation allows to solve this large-scale inverse problem in a few seconds on standard desktop PCs with modern graphics hardware. In particular, we present methods to solve not only the forward but also the non-linear inverse problem by massively parallel programming on graphics processors. A comparison of optimized CPU and GPU implementations shows that the reconstruction can be accelerated by factors of about 15 through the use of the graphics hardware without compromising the accuracy in the reconstructed images.

Unsteady MHD free convection flow of casson fluid over an inclined vertical plate embedded in a porous media

NASA Astrophysics Data System (ADS)

Manideep, P.; Raju, R. Srinivasa; Rao, T. Siva Nageswar; Reddy, G. Jithender

2018-05-01

This paper deals, an unsteady magnetohydrodynamic heat transfer natural convection flow of non-Newtonian Casson fluid over an inclined vertical plate embedded in a porous media with the presence of boundary conditions such as oscillating velocity, constant wall temperature. The governing dimensionless boundary layer partial differential equations are reduced to simultaneous algebraic linear equation for velocity, temperature of Casson fluid through finite element method. Those equations are solved by Thomas algorithm after imposing the boundary conditions through MATLAB for analyzing the behavior of Casson fluid velocity and temperature with various physical parameters. Also analyzed the local skin-friction and rate of heat transfer. Compared the present results with earlier reported studies, the results are comprehensively authenticated and robust FEM.

Activation of TRPV2 negatively regulates the differentiation of mouse brown adipocytes.

PubMed

Sun, Wuping; Uchida, Kunitoshi; Takahashi, Nobuyuki; Iwata, Yuko; Wakabayashi, Shigeo; Goto, Tsuyoshi; Kawada, Teruo; Tominaga, Makoto

2016-09-01

Transient receptor potential vanilloid 2 (TRPV2) acts as a Ca(2+)-permeable non-selective cation channel that has been reported to be sensitive to temperature, mechanical force, and some chemicals. We recently showed that TRPV2 is critical for maintenance of the thermogenic function of brown adipose tissue in mice. However, the involvement of TRPV2 in the differentiation of brown adipocytes remains unexplored. We found that the expression of TRPV2 was dramatically increased during the differentiation of brown adipocytes. Non-selective TRPV2 agonists (2-aminoethoxydiphenyl borate and lysophosphatidylcholine) inhibited the differentiation of brown adipocytes in a dose-dependent manner during the early stage of differentiation of brown adipocytes. The inhibition was rescued by a TRPV2-selective antagonist, SKF96365 (SKF). Mechanical force, which activates TRPV2, also inhibited the differentiation of brown adipocytes in a strength-dependent manner, and the effect was reversed by SKF. In addition, the inhibition of adipocyte differentiation by either TRPV2 ligand or mechanical stimulation was significantly smaller in the cells from TRPV2KO mice. Moreover, calcineurin inhibitors, cyclosporine A and FK506, partially reversed TRPV2 activation-induced inhibition of brown adipocyte differentiation. Thus, we conclude that TRPV2 might be involved in the modulation of brown adipocyte differentiation partially via a calcineurin pathway.

ML 3.0 smoothed aggregation user's guide.

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

Sala, Marzio; Hu, Jonathan Joseph; Tuminaro, Raymond Stephen

2004-05-01

ML is a multigrid preconditioning package intended to solve linear systems of equations Az = b where A is a user supplied n x n sparse matrix, b is a user supplied vector of length n and x is a vector of length n to be computed. ML should be used on large sparse linear systems arising from partial differential equation (PDE) discretizations. While technically any linear system can be considered, ML should be used on linear systems that correspond to things that work well with multigrid methods (e.g. elliptic PDEs). ML can be used as a stand-alone package ormore » to generate preconditioners for a traditional iterative solver package (e.g. Krylov methods). We have supplied support for working with the AZTEC 2.1 and AZTECOO iterative package [15]. However, other solvers can be used by supplying a few functions. This document describes one specific algebraic multigrid approach: smoothed aggregation. This approach is used within several specialized multigrid methods: one for the eddy current formulation for Maxwell's equations, and a multilevel and domain decomposition method for symmetric and non-symmetric systems of equations (like elliptic equations, or compressible and incompressible fluid dynamics problems). Other methods exist within ML but are not described in this document. Examples are given illustrating the problem definition and exercising multigrid options.« less

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

Three dimensional radiative flow of magnetite-nanofluid with homogeneous-heterogeneous reactions

NASA Astrophysics Data System (ADS)

Hayat, Tasawar; Rashid, Madiha; Alsaedi, Ahmed

2018-03-01

Present communication deals with the effects of homogeneous-heterogeneous reactions in flow of nanofluid by non-linear stretching sheet. Water based nanofluid containing magnetite nanoparticles is considered. Non-linear radiation and non-uniform heat sink/source effects are examined. Non-linear differential systems are computed by Optimal homotopy analysis method (OHAM). Convergent solutions of nonlinear systems are established. The optimal data of auxiliary variables is obtained. Impact of several non-dimensional parameters for velocity components, temperature and concentration fields are examined. Graphs are plotted for analysis of surface drag force and heat transfer rate.

Size-dependent geometrically nonlinear free vibration analysis of fractional viscoelastic nanobeams based on the nonlocal elasticity theory

NASA Astrophysics Data System (ADS)

Ansari, R.; Faraji Oskouie, M.; Gholami, R.

2016-01-01

In recent decades, mathematical modeling and engineering applications of fractional-order calculus have been extensively utilized to provide efficient simulation tools in the field of solid mechanics. In this paper, a nonlinear fractional nonlocal Euler-Bernoulli beam model is established using the concept of fractional derivative and nonlocal elasticity theory to investigate the size-dependent geometrically nonlinear free vibration of fractional viscoelastic nanobeams. The non-classical fractional integro-differential Euler-Bernoulli beam model contains the nonlocal parameter, viscoelasticity coefficient and order of the fractional derivative to interpret the size effect, viscoelastic material and fractional behavior in the nanoscale fractional viscoelastic structures, respectively. In the solution procedure, the Galerkin method is employed to reduce the fractional integro-partial differential governing equation to a fractional ordinary differential equation in the time domain. Afterwards, the predictor-corrector method is used to solve the nonlinear fractional time-dependent equation. Finally, the influences of nonlocal parameter, order of fractional derivative and viscoelasticity coefficient on the nonlinear time response of fractional viscoelastic nanobeams are discussed in detail. Moreover, comparisons are made between the time responses of linear and nonlinear models.

The existence of solutions of q-difference-differential equations.

PubMed

Wang, Xin-Li; Wang, Hua; Xu, Hong-Yan

2016-01-01

By using the Nevanlinna theory of value distribution, we investigate the existence of solutions of some types of non-linear q-difference differential equations. In particular, we generalize the Rellich-Wittich-type theorem and Malmquist-type theorem about differential equations to the case of q-difference differential equations (system).

Response of a tethered aerostat to simulated turbulence

NASA Astrophysics Data System (ADS)

Stanney, Keith A.; Rahn, Christopher D.

2006-09-01

Aerostats are lighter-than-air vehicles tethered to the ground by a cable and used for broadcasting, communications, surveillance, and drug interdiction. The dynamic response of tethered aerostats subject to extreme atmospheric turbulence often dictates survivability. This paper develops a theoretical model that predicts the planar response of a tethered aerostat subject to atmospheric turbulence and simulates the response to 1000 simulated hurricane scale turbulent time histories. The aerostat dynamic model assumes the aerostat hull to be a rigid body with non-linear fluid loading, instantaneous weathervaning for planar response, and a continuous tether. Galerkin's method discretizes the coupled aerostat and tether partial differential equations to produce a non-linear initial value problem that is integrated numerically given initial conditions and wind inputs. The proper orthogonal decomposition theorem generates, based on Hurricane Georges wind data, turbulent time histories that possess the sequential behavior of actual turbulence, are spectrally accurate, and have non-Gaussian density functions. The generated turbulent time histories are simulated to predict the aerostat response to severe turbulence. The resulting probability distributions for the aerostat position, pitch angle, and confluence point tension predict the aerostat behavior in high gust environments. The dynamic results can be up to twice as large as a static analysis indicating the importance of dynamics in aerostat modeling. The results uncover a worst case wind input consisting of a two-pulse vertical gust.

Semi-automatic sparse preconditioners for high-order finite element methods on non-uniform meshes

NASA Astrophysics Data System (ADS)

Austin, Travis M.; Brezina, Marian; Jamroz, Ben; Jhurani, Chetan; Manteuffel, Thomas A.; Ruge, John

2012-05-01

High-order finite elements often have a higher accuracy per degree of freedom than the classical low-order finite elements. However, in the context of implicit time-stepping methods, high-order finite elements present challenges to the construction of efficient simulations due to the high cost of inverting the denser finite element matrix. There are many cases where simulations are limited by the memory required to store the matrix and/or the algorithmic components of the linear solver. We are particularly interested in preconditioned Krylov methods for linear systems generated by discretization of elliptic partial differential equations with high-order finite elements. Using a preconditioner like Algebraic Multigrid can be costly in terms of memory due to the need to store matrix information at the various levels. We present a novel method for defining a preconditioner for systems generated by high-order finite elements that is based on a much sparser system than the original high-order finite element system. We investigate the performance for non-uniform meshes on a cube and a cubed sphere mesh, showing that the sparser preconditioner is more efficient and uses significantly less memory. Finally, we explore new methods to construct the sparse preconditioner and examine their effectiveness for non-uniform meshes. We compare results to a direct use of Algebraic Multigrid as a preconditioner and to a two-level additive Schwarz method.

Steady MHD free convection heat and mass transfer flow about a vertical porous surface with thermal diffusion and induced magnetic field

NASA Astrophysics Data System (ADS)

Touhid Hossain, M. M.; Afruz-Zaman, Md.; Rahman, Fouzia; Hossain, M. Arif

2013-09-01

In this study the thermal diffusion effect on the steady laminar free convection flow and heat transfer of viscous incompressible MHD electrically conducting fluid above a vertical porous surface is considered under the influence of an induced magnetic field. The governing non-dimensional equations relevant to the problem, containing the partial differential equations, are transformed by usual similarity transformations into a system of coupled non-linear ordinary differential equations and will be solved analytically by using the perturbation technique. On introducing the non-dimensional concept and applying Boussinesq's approximation, the solutions for velocity field, temperature distribution and induced magnetic field to the second order approximations are obtained for large suction with different selected values of the established dimensionless parameters. The influences of these various establish parameters on the velocity and temperature fields and on the induced magnetic fields are exhibited under certain assumptions and are studied graphically in the present analysis. It is observed that the effects of thermal-diffusion and large suction have great importance on the velocity, temperature and induced magnetic fields and mass concentration for several fluids considered, so that their effects should be taken into account with other useful parameters associated. It is also found that the dimensionless Prandtl number, Grashof number, Modified Grashof number and magnetic parameter have an appreciable influence on the concerned independent variables.

Mathematical Methods for Optical Physics and Engineering

NASA Astrophysics Data System (ADS)

Gbur, Gregory J.

2011-01-01

1. Vector algebra; 2. Vector calculus; 3. Vector calculus in curvilinear coordinate systems; 4. Matrices and linear algebra; 5. Advanced matrix techniques and tensors; 6. Distributions; 7. Infinite series; 8. Fourier series; 9. Complex analysis; 10. Advanced complex analysis; 11. Fourier transforms; 12. Other integral transforms; 13. Discrete transforms; 14. Ordinary differential equations; 15. Partial differential equations; 16. Bessel functions; 17. Legendre functions and spherical harmonics; 18. Orthogonal functions; 19. Green's functions; 20. The calculus of variations; 21. Asymptotic techniques; Appendices; References; Index.

Photon induced non-linear quantized double layer charging in quaternary semiconducting quantum dots.

PubMed

Nair, Vishnu; Ananthoju, Balakrishna; Mohapatra, Jeotikanta; Aslam, M

2018-03-15

Room temperature quantized double layer charging was observed in 2 nm Cu 2 ZnSnS 4 (CZTS) quantum dots. In addition to this we observed a distinct non-linearity in the quantized double layer charging arising from UV light modulation of double layer. UV light irradiation resulted in a 26% increase in the integral capacitance at the semiconductor-dielectric (CZTS-oleylamine) interface of the quantum dot without any change in its core size suggesting that the cause be photocapacitive. The increasing charge separation at the semiconductor-dielectric interface due to highly stable and mobile photogenerated carriers cause larger electrostatic forces between the quantum dot and electrolyte leading to an enhanced double layer. This idea was supported by a decrease in the differential capacitance possible due to an enhanced double layer. Furthermore the UV illumination enhanced double layer gives us an AC excitation dependent differential double layer capacitance which confirms that the charging process is non-linear. This ultimately illustrates the utility of a colloidal quantum dot-electrolyte interface as a non-linear photocapacitor. Copyright © 2017 Elsevier Inc. All rights reserved.

Online sequential Monte Carlo smoother for partially observed diffusion processes

NASA Astrophysics Data System (ADS)

Gloaguen, Pierre; Étienne, Marie-Pierre; Le Corff, Sylvain

2018-12-01

This paper introduces a new algorithm to approximate smoothed additive functionals of partially observed diffusion processes. This method relies on a new sequential Monte Carlo method which allows to compute such approximations online, i.e., as the observations are received, and with a computational complexity growing linearly with the number of Monte Carlo samples. The original algorithm cannot be used in the case of partially observed stochastic differential equations since the transition density of the latent data is usually unknown. We prove that it may be extended to partially observed continuous processes by replacing this unknown quantity by an unbiased estimator obtained for instance using general Poisson estimators. This estimator is proved to be consistent and its performance are illustrated using data from two models.

A numerical algorithm for optimal feedback gains in high dimensional linear quadratic regulator problems

NASA Technical Reports Server (NTRS)

Banks, H. T.; Ito, K.

1991-01-01

A hybrid method for computing the feedback gains in linear quadratic regulator problem is proposed. The method, which combines use of a Chandrasekhar type system with an iteration of the Newton-Kleinman form with variable acceleration parameter Smith schemes, is formulated to efficiently compute directly the feedback gains rather than solutions of an associated Riccati equation. The hybrid method is particularly appropriate when used with large dimensional systems such as those arising in approximating infinite-dimensional (distributed parameter) control systems (e.g., those governed by delay-differential and partial differential equations). Computational advantages of the proposed algorithm over the standard eigenvector (Potter, Laub-Schur) based techniques are discussed, and numerical evidence of the efficacy of these ideas is presented.

Numerical study at moderate Reynolds number of peristaltic flow of micropolar fluid through a porous-saturated channel in magnetic field

NASA Astrophysics Data System (ADS)

Ahmed, Bilal; Javed, Tariq; Ali, N.

2018-01-01

This paper analyzes the MHD flow of micropolar fluid induced by peristaltic waves passing through the porous saturated channel at large Reynolds number. The flow model is formulated in the absence of assumptions of lubrication theory which yields the governing equations into a non-linear set of coupled partial differential equations which allows studying the peristaltic mechanism at non-zero Reynolds and wave numbers. The influence of other involved parameters on velocity, stream function and microrotation are discussed through graphs plotted by using Galerkin's finite element method. Besides that, the phenomena of pumping and trapping are also analyzed in the later part of the paper. To ensure the accuracy of the developed code, obtained results are compared with the results available in the literature and found in excellent agreement. It is found that the peristalsis mixing can be enhanced by increasing Hartmann number while it reduces by increasing permeability of the porous medium.

Chosen interval methods for solving linear interval systems with special type of matrix

NASA Astrophysics Data System (ADS)

Szyszka, Barbara

2013-10-01

The paper is devoted to chosen direct interval methods for solving linear interval systems with special type of matrix. This kind of matrix: band matrix with a parameter, from finite difference problem is obtained. Such linear systems occur while solving one dimensional wave equation (Partial Differential Equations of hyperbolic type) by using the central difference interval method of the second order. Interval methods are constructed so as the errors of method are enclosed in obtained results, therefore presented linear interval systems contain elements that determining the errors of difference method. The chosen direct algorithms have been applied for solving linear systems because they have no errors of method. All calculations were performed in floating-point interval arithmetic.

Linear approximations of nonlinear systems

NASA Technical Reports Server (NTRS)

Hunt, L. R.; Su, R.

1983-01-01

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

Sustained modelling ability of artificial neural networks in the analysis of two pharmaceuticals (dextropropoxyphene and dipyrone) present in unequal concentrations.

PubMed

Cámara, María S; Ferroni, Félix M; De Zan, Mercedes; Goicoechea, Héctor C

2003-07-01

An improvement is presented on the simultaneous determination of two active ingredients present in unequal concentrations in injections. The analysis was carried out with spectrophotometric data and non-linear multivariate calibration methods, in particular artificial neural networks (ANNs). The presence of non-linearities caused by the major analyte concentrations which deviate from Beer's law was confirmed by plotting actual vs. predicted concentrations, and observing curvatures in the residuals for the estimated concentrations with linear methods. Mixtures of dextropropoxyphene and dipyrone have been analysed by using linear and non-linear partial least-squares (PLS and NPLSs) and ANNs. Notwithstanding the high degree of spectral overlap and the occurrence of non-linearities, rapid and simultaneous analysis has been achieved, with reasonably good accuracy and precision. A commercial sample was analysed by using the present methodology, and the obtained results show reasonably good agreement with those obtained by using high-performance liquid chromatography (HPLC) and a UV-spectrophotometric comparative methods.

Analysis of Monte Carlo accelerated iterative methods for sparse linear systems: Analysis of Monte Carlo accelerated iterative methods for sparse linear systems

DOE PAGES

Benzi, Michele; Evans, Thomas M.; Hamilton, Steven P.; ...

2017-03-05

Here, we consider hybrid deterministic-stochastic iterative algorithms for the solution of large, sparse linear systems. Starting from a convergent splitting of the coefficient matrix, we analyze various types of Monte Carlo acceleration schemes applied to the original preconditioned Richardson (stationary) iteration. We expect that these methods will have considerable potential for resiliency to faults when implemented on massively parallel machines. We also establish sufficient conditions for the convergence of the hybrid schemes, and we investigate different types of preconditioners including sparse approximate inverses. Numerical experiments on linear systems arising from the discretization of partial differential equations are presented.

Stencil computations for PDE-based applications with examples from DUNE and hypre

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

Engwer, C.; Falgout, R. D.; Yang, U. M.

Here, stencils are commonly used to implement efficient on–the–fly computations of linear operators arising from partial differential equations. At the same time the term “stencil” is not fully defined and can be interpreted differently depending on the application domain and the background of the software developers. Common features in stencil codes are the preservation of the structure given by the discretization of the partial differential equation and the benefit of minimal data storage. We discuss stencil concepts of different complexity, show how they are used in modern software packages like hypre and DUNE, and discuss recent efforts to extend themore » software to enable stencil computations of more complex problems and methods such as inf–sup–stable Stokes discretizations and mixed finite element discretizations.« less

Stencil computations for PDE-based applications with examples from DUNE and hypre

DOE PAGES

Engwer, C.; Falgout, R. D.; Yang, U. M.

2017-02-24

Here, stencils are commonly used to implement efficient on–the–fly computations of linear operators arising from partial differential equations. At the same time the term “stencil” is not fully defined and can be interpreted differently depending on the application domain and the background of the software developers. Common features in stencil codes are the preservation of the structure given by the discretization of the partial differential equation and the benefit of minimal data storage. We discuss stencil concepts of different complexity, show how they are used in modern software packages like hypre and DUNE, and discuss recent efforts to extend themore » software to enable stencil computations of more complex problems and methods such as inf–sup–stable Stokes discretizations and mixed finite element discretizations.« less

Bifurcation of rupture path by linear and cubic damping force

NASA Astrophysics Data System (ADS)

Dennis L. C., C.; Chew X., Y.; Lee Y., C.

2014-06-01

Bifurcation of rupture path is studied for the effect of linear and cubic damping. Momentum equation with Rayleigh factor was transformed into ordinary differential form. Bernoulli differential equation was obtained and solved by the separation of variables. Analytical or exact solutions yielded the bifurcation was visible at imaginary part when the wave was non dispersive. For the dispersive wave, bifurcation of rupture path was invisible.

Existence of entire solutions of some non-linear differential-difference equations.

PubMed

Chen, Minfeng; Gao, Zongsheng; Du, Yunfei

2017-01-01

In this paper, we investigate the admissible entire solutions of finite order of the differential-difference equations [Formula: see text] and [Formula: see text], where [Formula: see text], [Formula: see text] are two non-zero polynomials, [Formula: see text] is a polynomial and [Formula: see text]. In addition, we investigate the non-existence of entire solutions of finite order of the differential-difference equation [Formula: see text], where [Formula: see text], [Formula: see text] are two non-constant polynomials, [Formula: see text], m , n are positive integers and satisfy [Formula: see text] except for [Formula: see text], [Formula: see text].

Non-linear patterns in age-related DNA methylation may reflect CD4+ T cell differentiation

PubMed Central

Johnson, Nicholas D.; Wiener, Howard W.; Smith, Alicia K.; Nishitani, Shota; Absher, Devin M.; Arnett, Donna K.; Aslibekyan, Stella; Conneely, Karen N.

2017-01-01

ABSTRACT DNA methylation (DNAm) is an important epigenetic process involved in the regulation of gene expression. While many studies have identified thousands of loci associated with age, few have differentiated between linear and non-linear DNAm trends with age. Non-linear trends could indicate early- or late-life gene regulatory processes. Using data from the Illumina 450K array on 336 human peripheral blood samples, we identified 21 CpG sites that associated with age (P<1.03E-7) and exhibited changing rates of DNAm change with age (P<1.94E-6). For 2 of these CpG sites (cg07955995 and cg22285878), DNAm increased with age at an increasing rate, indicating that differential DNAm was greatest among elderly individuals. We observed significant replication for both CpG sites (P<5.0E-8) in a second set of peripheral blood samples. In 8 of 9 additional data sets comprising samples of monocytes, T cell subtypes, and brain tissue, we observed a pattern directionally consistent with DNAm increasing with age at an increasing rate, which was nominally significant in the 3 largest data sets (4.3E-15

Time-stable overset grid method for hyperbolic problems using summation-by-parts operators

NASA Astrophysics Data System (ADS)

Sharan, Nek; Pantano, Carlos; Bodony, Daniel J.

2018-05-01

A provably time-stable method for solving hyperbolic partial differential equations arising in fluid dynamics on overset grids is presented in this paper. The method uses interface treatments based on the simultaneous approximation term (SAT) penalty method and derivative approximations that satisfy the summation-by-parts (SBP) property. Time-stability is proven using energy arguments in a norm that naturally relaxes to the standard diagonal norm when the overlap reduces to a traditional multiblock arrangement. The proposed overset interface closures are time-stable for arbitrary overlap arrangements. The information between grids is transferred using Lagrangian interpolation applied to the incoming characteristics, although other interpolation schemes could also be used. The conservation properties of the method are analyzed. Several one-, two-, and three-dimensional, linear and non-linear numerical examples are presented to confirm the stability and accuracy of the method. A performance comparison between the proposed SAT-based interface treatment and the commonly-used approach of injecting the interpolated data onto each grid is performed to highlight the efficacy of the SAT method.

Application of a new multiphase multicomponent volcanic conduit model with magma degassing and crystallization to Stromboli volcano.

NASA Astrophysics Data System (ADS)

La Spina, Giuseppe; Burton, Mike; de'Michieli Vitturi, Mattia

2014-05-01

Volcanoes exhibit a wide range of eruption styles, from relatively slow effusive eruptions, generating lava flows and lava domes, to explosive eruptions, in which very large volumes of fragmented magma and volcanic gas are ejected high into the atmosphere. During an eruption, much information regarding the magma ascent dynamics can be gathered: melt and exsolved gas composition, crystal content, mass flow rate and ballistic velocities, to name just a few. Due to the lack of direct observations of the conduit itself, mathematical models for magma ascent provide invaluable tools for a better comprehension of the system. The complexity of the multiphase multicomponent gas-magma-solid system is reflected in the corresponding mathematical model; a set of non-linear hyperbolic partial differential and constitutive equations, which describe the physical system, has to be formulated and solved. The standard approach to derive governing equations for two-phase flow is based on averaging procedures, which leads to a system of governing equations in the form of mass, momentum and energy balance laws for each phase coupled with algebraic and differential source terms which represent phase interactions. For this work, we used the model presented by de' Michieli Vitturi et al. (EGU General Assembly Conference Abstracts, 2013), where a different approach based on the theory of thermodynamically compatible systems has been adopted to write the governing multiphase equations for two-phase compressible flow (with two velocities and two pressures) in the form of a conservative hyperbolic system of partial differential equations, coupled with non-differential source terms. Here, in order to better describe the multicomponent nature of the system, we extended the model adding several transport equations to the system for different crystal components and different gas species, and implementing appropriate equations of state. The constitutive equations of the model are chosen to reproduce both effusive and explosive eruptive activities at Stromboli volcano. Three different crystal components (olivine, pyroxene and feldspar) and two different gas species (water and carbon dioxide) are taken into account. The equilibrium profiles of crystallization as function of pressure, temperature and water content are modeled using the numerical codes AlphaMELTS and DAKOTA. The equilibrium of dissolved gas content, instead, is obtained using a non-linear fitting of data computed using VolatileCALC. With these data, we simulate numerically the lava effusion that occurred at Stromboli between 27 February and 2 April 2007, and find good agreement with the observed data (vesicularity, exsolved gas composition, crystal content and mass flow rate) at the vent. We find that the model is highly sensitive to input magma temperature, going from effusive to explosive eruption with temperature changes by just 20 °C. We thoroughly investigated through a sensitivity analysis the control of the temperature of magma chamber and of the radius of the conduit on the mass flow rate, obtaining also a set of admissible temperatures and conduit radii that produce results in agreement with the real observations.

Unsteady boundary layer flow and heat transfer of a Casson fluid past an oscillating vertical plate with Newtonian heating.

PubMed

Hussanan, Abid; Zuki Salleh, Mohd; Tahar, Razman Mat; Khan, Ilyas

2014-01-01

In this paper, the heat transfer effect on the unsteady boundary layer flow of a Casson fluid past an infinite oscillating vertical plate with Newtonian heating is investigated. The governing equations are transformed to a systems of linear partial differential equations using appropriate non-dimensional variables. The resulting equations are solved analytically by using the Laplace transform method and the expressions for velocity and temperature are obtained. They satisfy all imposed initial and boundary conditions and reduce to some well-known solutions for Newtonian fluids. Numerical results for velocity, temperature, skin friction and Nusselt number are shown in various graphs and discussed for embedded flow parameters. It is found that velocity decreases as Casson parameters increases and thermal boundary layer thickness increases with increasing Newtonian heating parameter.

Magnetohydrodynamics Carreau nanofluid flow over an inclined convective heated stretching cylinder with Joule heating

NASA Astrophysics Data System (ADS)

Khan, Imad; Shafquatullah; Malik, M. Y.; Hussain, Arif; Khan, Mair

Current work highlights the computational aspects of MHD Carreau nanofluid flow over an inclined stretching cylinder with convective boundary conditions and Joule heating. The mathematical modeling of physical problem yields nonlinear set of partial differential equations. A suitable scaling group of variables is employed on modeled equations to convert them into non-dimensional form. The integration scheme Runge-Kutta-Fehlberg on the behalf of shooting technique is utilized to solve attained set of equations. The interesting aspects of physical problem (linear momentum, energy and nanoparticles concentration) are elaborated under the different parametric conditions through graphical and tabular manners. Additionally, the quantities (local skin friction coefficient, local Nusselt number and local Sherwood number) which are responsible to dig out the physical phenomena in the vicinity of stretched surface are computed and delineated by varying controlling flow parameters.

Two-dimensional mesh embedding for Galerkin B-spline methods

NASA Technical Reports Server (NTRS)

Shariff, Karim; Moser, Robert D.

1995-01-01

A number of advantages result from using B-splines as basis functions in a Galerkin method for solving partial differential equations. Among them are arbitrary order of accuracy and high resolution similar to that of compact schemes but without the aliasing error. This work develops another property, namely, the ability to treat semi-structured embedded or zonal meshes for two-dimensional geometries. This can drastically reduce the number of grid points in many applications. Both integer and non-integer refinement ratios are allowed. The report begins by developing an algorithm for choosing basis functions that yield the desired mesh resolution. These functions are suitable products of one-dimensional B-splines. Finally, test cases for linear scalar equations such as the Poisson and advection equation are presented. The scheme is conservative and has uniformly high order of accuracy throughout the domain.

Convective heat transfer in MHD slip flow over a stretching surface in the presence of carbon nanotubes

NASA Astrophysics Data System (ADS)

Ul Haq, Rizwan; Nadeem, Sohail; Khan, Z. H.; Noor, N. F. M.

2015-01-01

In the present study, thermal conductivity and viscosity of both single-wall and multiple-wall Carbon Nanotubes (CNT) within the base fluids (water, engine oil and ethylene glycol) of similar volume have been investigated when the fluid is flowing over a stretching surface. The magnetohydrodynamic (MHD) and viscous dissipation effects are also incorporated in the present phenomena. Experimental data consists of thermo-physical properties of each base fluid and CNT have been considered. The mathematical model has been constructed and by employing similarity transformation, system of partial differential equations is rehabilitated into the system of non-linear ordinary differential equations. The results of local skin friction and local Nusselt number are plotted for each base fluid by considering both Single Wall Carbon Nanotube (SWCNT) and Multiple-Wall Carbon Nanotubes (MWCNT). The behavior of fluid flow for water based-SWCNT and MWCNT are analyzed through streamlines. Concluding remarks have been developed on behalf of the whole analysis and it is found that engine oil-based CNT have higher skin friction and heat transfer rate as compared to water and ethylene glycol-based CNT.

Using the phase-space imager to analyze partially coherent imaging systems: bright-field, phase contrast, differential interference contrast, differential phase contrast, and spiral phase contrast

NASA Astrophysics Data System (ADS)

Mehta, Shalin B.; Sheppard, Colin J. R.

2010-05-01

Various methods that use large illumination aperture (i.e. partially coherent illumination) have been developed for making transparent (i.e. phase) specimens visible. These methods were developed to provide qualitative contrast rather than quantitative measurement-coherent illumination has been relied upon for quantitative phase analysis. Partially coherent illumination has some important advantages over coherent illumination and can be used for measurement of the specimen's phase distribution. However, quantitative analysis and image computation in partially coherent systems have not been explored fully due to the lack of a general, physically insightful and computationally efficient model of image formation. We have developed a phase-space model that satisfies these requirements. In this paper, we employ this model (called the phase-space imager) to elucidate five different partially coherent systems mentioned in the title. We compute images of an optical fiber under these systems and verify some of them with experimental images. These results and simulated images of a general phase profile are used to compare the contrast and the resolution of the imaging systems. We show that, for quantitative phase imaging of a thin specimen with matched illumination, differential phase contrast offers linear transfer of specimen information to the image. We also show that the edge enhancement properties of spiral phase contrast are compromised significantly as the coherence of illumination is reduced. The results demonstrate that the phase-space imager model provides a useful framework for analysis, calibration, and design of partially coherent imaging methods.

PetIGA: A framework for high-performance isogeometric analysis

DOE PAGES

Dalcin, Lisandro; Collier, Nathaniel; Vignal, Philippe; ...

2016-05-25

We present PetIGA, a code framework to approximate the solution of partial differential equations using isogeometric analysis. PetIGA can be used to assemble matrices and vectors which come from a Galerkin weak form, discretized with Non-Uniform Rational B-spline basis functions. We base our framework on PETSc, a high-performance library for the scalable solution of partial differential equations, which simplifies the development of large-scale scientific codes, provides a rich environment for prototyping, and separates parallelism from algorithm choice. We describe the implementation of PetIGA, and exemplify its use by solving a model nonlinear problem. To illustrate the robustness and flexibility ofmore » PetIGA, we solve some challenging nonlinear partial differential equations that include problems in both solid and fluid mechanics. Lastly, we show strong scaling results on up to 4096 cores, which confirm the suitability of PetIGA for large scale simulations.« less

Diagnostic power of optic disc morphology, peripapillary retinal nerve fiber layer thickness, and macular inner retinal layer thickness in glaucoma diagnosis with fourier-domain optical coherence tomography.

PubMed

Huang, Jehn-Yu; Pekmezci, Melike; Mesiwala, Nisreen; Kao, Andrew; Lin, Shan

2011-02-01

To evaluate the capability of the optic disc, peripapillary retinal nerve fiber layer (P-RNFL), macular inner retinal layer (M-IRL) parameters, and their combination obtained by Fourier-domain optical coherent tomography (OCT) in differentiating a glaucoma suspect from perimetric glaucoma. Two hundred and twenty eyes from 220 patients were enrolled in this study. The optic disc morphology, P-RNFL, and M-IRL were assessed by the Fourier-domain OCT (RTVue OCT, Model RT100, Optovue, Fremont, CA). A linear discriminant function was generated by stepwise linear discriminant analysis on the basis of OCT parameters and demographic factors. The diagnostic power of these parameters was evaluated with receiver operating characteristic (ROC) curve analysis. The diagnostic power in the clinically relevant range (specificity ≥ 80%) was presented as the partial area under the ROC curve (partial AROC). The individual OCT parameter with the largest AROC and partial AROC in the high specificity (≥ 80%) range were cup/disc vertical ratio (AROC = 0.854 and partial AROC = 0.142) for the optic disc parameters, average thickness (AROC = 0.919 and partial AROC = 0.147) for P-RNFL parameters, inferior hemisphere thickness (AROC = 0.871 and partial AROC = 0.138) for M-IRL parameters, respectively. The linear discriminant function further enhanced the ability in detecting perimetric glaucoma (AROC = 0.970 and partial AROC = 0.172). Average P-RNFL thickness is the optimal individual OCT parameter to detect perimetric glaucoma. Simultaneous evaluation on disc morphology, P-RNFL, and M-IRL thickness can improve the diagnostic accuracy in diagnosing glaucoma.

On conforming mixed finite element methods for incompressible viscous flow problems

NASA Technical Reports Server (NTRS)

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

1982-01-01

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

No-go for partially massless spin-2 Yang-Mills

DOE PAGES

Garcia-Saenz, Sebastian; Hinterbichler, Kurt; Joyce, Austin; ...

2016-02-05

There are various no-go results forbidding self-interactions for a single partially massless spin-2 field. Given the photon-like structure of the linear partially massless field, it is natural to ask whether a multiplet of such fields can interact under an internal Yang-Mills like extension of the partially massless symmetry. In this paper, we give two arguments that such a partially massless Yang-Mills theory does not exist. The first is that there is no Yang-Mills like non-abelian deformation of the partially massless symmetry, and the second is that cubic vertices with the appropriate structure constants do not exist.

Transient responses of phosphoric acid fuel cell power plant system. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Lu, Cheng-Yi

1983-01-01

An analytical and computerized study of the steady state and transient response of a phosphoric acid fuel cell (PAFC) system was completed. Parametric studies and sensitivity analyses of the PAFC system's operation were accomplished. Four non-linear dynamic models of the fuel cell stack, reformer, shift converters, and heat exchangers were developed based on nonhomogeneous non-linear partial differential equations, which include the material, component, energy balance, and electrochemical kinetic features. Due to a lack of experimental data for the dynamic response of the components only the steady state results were compared with data from other sources, indicating reasonably good agreement. A steady state simulation of the entire system was developed using, nonlinear ordinary differential equations. The finite difference method and trial-and-error procedures were used to obtain a solution. Using the model, a PAFC system, that was developed under NASA Grant, NCC3-17, was improved through the optimization of the heat exchanger network. Three types of cooling configurations for cell plates were evaluated to obtain the best current density and temperature distributions. The steady state solutions were used as the initial conditions in the dynamic model. The transient response of a simplified PAFC system, which included all of the major components, subjected to a load change was obtained. Due to the length of the computation time for the transient response calculations, analysis on a real-time computer was not possible. A simulation of the real-time calculations was developed on a batch type computer. The transient response characteristics are needed for the optimization of the design and control of the whole PAFC system. All of the models, procedures and simulations were programmed in Fortran and run on IBM 370 computers at Cleveland State University and the NASA Lewis Research Center.

Fast computation of derivative based sensitivities of PSHA models via algorithmic differentiation

NASA Astrophysics Data System (ADS)

Leövey, Hernan; Molkenthin, Christian; Scherbaum, Frank; Griewank, Andreas; Kuehn, Nicolas; Stafford, Peter

2015-04-01

Probabilistic seismic hazard analysis (PSHA) is the preferred tool for estimation of potential ground-shaking hazard due to future earthquakes at a site of interest. A modern PSHA represents a complex framework which combines different models with possible many inputs. Sensitivity analysis is a valuable tool for quantifying changes of a model output as inputs are perturbed, identifying critical input parameters and obtaining insight in the model behavior. Differential sensitivity analysis relies on calculating first-order partial derivatives of the model output with respect to its inputs. Moreover, derivative based global sensitivity measures (Sobol' & Kucherenko '09) can be practically used to detect non-essential inputs of the models, thus restricting the focus of attention to a possible much smaller set of inputs. Nevertheless, obtaining first-order partial derivatives of complex models with traditional approaches can be very challenging, and usually increases the computation complexity linearly with the number of inputs appearing in the models. In this study we show how Algorithmic Differentiation (AD) tools can be used in a complex framework such as PSHA to successfully estimate derivative based sensitivities, as is the case in various other domains such as meteorology or aerodynamics, without no significant increase in the computation complexity required for the original computations. First we demonstrate the feasibility of the AD methodology by comparing AD derived sensitivities to analytically derived sensitivities for a basic case of PSHA using a simple ground-motion prediction equation. In a second step, we derive sensitivities via AD for a more complex PSHA study using a ground motion attenuation relation based on a stochastic method to simulate strong motion. The presented approach is general enough to accommodate more advanced PSHA studies of higher complexity.

An efficient nonlinear finite-difference approach in the computational modeling of the dynamics of a nonlinear diffusion-reaction equation in microbial ecology.

PubMed

Macías-Díaz, J E; Macías, Siegfried; Medina-Ramírez, I E

2013-12-01

In this manuscript, we present a computational model to approximate the solutions of a partial differential equation which describes the growth dynamics of microbial films. The numerical technique reported in this work is an explicit, nonlinear finite-difference methodology which is computationally implemented using Newton's method. Our scheme is compared numerically against an implicit, linear finite-difference discretization of the same partial differential equation, whose computer coding requires an implementation of the stabilized bi-conjugate gradient method. Our numerical results evince that the nonlinear approach results in a more efficient approximation to the solutions of the biofilm model considered, and demands less computer memory. Moreover, the positivity of initial profiles is preserved in the practice by the nonlinear scheme proposed. Copyright © 2013 Elsevier Ltd. All rights reserved.

Identification and compensation of friction for a novel two-axis differential micro-feed system

NASA Astrophysics Data System (ADS)

Du, Fuxin; Zhang, Mingyang; Wang, Zhaoguo; Yu, Chen; Feng, Xianying; Li, Peigang

2018-06-01

Non-linear friction in a conventional drive feed system (CDFS) feeding at low speed is one of the main factors that lead to the complexity of the feed drive. The CDFS will inevitably enter or approach a non-linear creeping work area at extremely low speed. A novel two-axis differential micro-feed system (TDMS) is developed in this paper to overcome the accuracy limitation of CDFS. A dynamic model of TDMS is first established. Then, a novel all-component friction parameter identification method (ACFPIM) using a genetic algorithm (GA) to identify the friction parameters of a TDMS is introduced. The friction parameters of the ball screw and linear motion guides are identified independently using the method, assuring the accurate modelling of friction force at all components. A proportional-derivate feed drive position controller with an observer-based friction compensator is implemented to achieve an accurate trajectory tracking performance. Finally, comparative experiments demonstrate the effectiveness of the TDMS in inhibiting the disadvantageous influence of non-linear friction and the validity of the proposed identification method for TDMS.

A numerical technique for linear elliptic partial differential equations in polygonal domains.

PubMed

Hashemzadeh, P; Fokas, A S; Smitheman, S A

2015-03-08

Integral representations for the solution of linear elliptic partial differential equations (PDEs) can be obtained using Green's theorem. However, these representations involve both the Dirichlet and the Neumann values on the boundary, and for a well-posed boundary-value problem (BVPs) one of these functions is unknown. A new transform method for solving BVPs for linear and integrable nonlinear PDEs usually referred to as the unified transform ( or the Fokas transform ) was introduced by the second author in the late Nineties. For linear elliptic PDEs, this method can be considered as the analogue of Green's function approach but now it is formulated in the complex Fourier plane instead of the physical plane. It employs two global relations also formulated in the Fourier plane which couple the Dirichlet and the Neumann boundary values. These relations can be used to characterize the unknown boundary values in terms of the given boundary data, yielding an elegant approach for determining the Dirichlet to Neumann map . The numerical implementation of the unified transform can be considered as the counterpart in the Fourier plane of the well-known boundary integral method which is formulated in the physical plane. For this implementation, one must choose (i) a suitable basis for expanding the unknown functions and (ii) an appropriate set of complex values, which we refer to as collocation points, at which to evaluate the global relations. Here, by employing a variety of examples we present simple guidelines of how the above choices can be made. Furthermore, we provide concrete rules for choosing the collocation points so that the condition number of the matrix of the associated linear system remains low.

Scaling and scale invariance of conservation laws in Reynolds transport theorem framework

NASA Astrophysics Data System (ADS)

Haltas, Ismail; Ulusoy, Suleyman

2015-07-01

Scale invariance is the case where the solution of a physical process at a specified time-space scale can be linearly related to the solution of the processes at another time-space scale. Recent studies investigated the scale invariance conditions of hydrodynamic processes by applying the one-parameter Lie scaling transformations to the governing equations of the processes. Scale invariance of a physical process is usually achieved under certain conditions on the scaling ratios of the variables and parameters involved in the process. The foundational axioms of hydrodynamics are the conservation laws, namely, conservation of mass, conservation of linear momentum, and conservation of energy from continuum mechanics. They are formulated using the Reynolds transport theorem. Conventionally, Reynolds transport theorem formulates the conservation equations in integral form. Yet, differential form of the conservation equations can also be derived for an infinitesimal control volume. In the formulation of the governing equation of a process, one or more than one of the conservation laws and, some times, a constitutive relation are combined together. Differential forms of the conservation equations are used in the governing partial differential equation of the processes. Therefore, differential conservation equations constitute the fundamentals of the governing equations of the hydrodynamic processes. Applying the one-parameter Lie scaling transformation to the conservation laws in the Reynolds transport theorem framework instead of applying to the governing partial differential equations may lead to more fundamental conclusions on the scaling and scale invariance of the hydrodynamic processes. This study will investigate the scaling behavior and scale invariance conditions of the hydrodynamic processes by applying the one-parameter Lie scaling transformation to the conservation laws in the Reynolds transport theorem framework.

An Entertaining Method of Teaching Concepts of Linear Light Propagation, Reflection and Refraction Using a Simple Optical Mechanism

ERIC Educational Resources Information Center

Yurumezoglu, K.

2009-01-01

An activity has been designed for the purpose of teaching how light is dispersed in a straight line and about the interaction between matter and light as well as the related concepts of shadows, partial shadows, reflection, refraction, primary colours and complementary (secondary) colours, and differentiating the relationship between colours, all…

Remarks on the Non-Linear Differential Equation the Second Derivative of Theta Plus A Sine Theta Equals 0.

ERIC Educational Resources Information Center

Fay, Temple H.; O'Neal, Elizabeth A.

1985-01-01

The authors draw together a variety of facts concerning a nonlinear differential equation and compare the exact solution with approximate solutions. Then they provide an expository introduction to the elliptic sine function suitable for presentation in undergraduate courses on differential equations. (MNS)

Homogeneous partial differential equations for superpositions of indeterminate functions of several variables

NASA Astrophysics Data System (ADS)

Asai, Kazuto

2009-02-01

We determine essentially all partial differential equations satisfied by superpositions of tree type and of a further special type. These equations represent necessary and sufficient conditions for an analytic function to be locally expressible as an analytic superposition of the type indicated. The representability of a real analytic function by a superposition of this type is independent of whether that superposition involves real-analytic functions or C^{\\rho}-functions, where the constant \\rho is determined by the structure of the superposition. We also prove that the function u defined by u^n=xu^a+yu^b+zu^c+1 is generally non-representable in any real (resp. complex) domain as f\\bigl(g(x,y),h(y,z)\\bigr) with twice differentiable f and differentiable g, h (resp. analytic f, g, h).

Approximating a nonlinear advanced-delayed equation from acoustics

NASA Astrophysics Data System (ADS)

Teodoro, M. Filomena

2016-10-01

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

Invariant and partially-invariant solutions of the equations describing a non-stationary and isentropic flow for an ideal and compressible fluid in (3 + 1) dimensions

NASA Astrophysics Data System (ADS)

Grundland, A. M.; Lalague, L.

1996-04-01

This paper presents a new method of constructing, certain classes of solutions of a system of partial differential equations (PDEs) describing the non-stationary and isentropic flow for an ideal compressible fluid. A generalization of the symmetry reduction method to the case of partially-invariant solutions (PISs) has been formulated. We present a new algorithm for constructing PISs and discuss in detail the necessary conditions for the existence of non-reducible PISs. All these solutions have the defect structure 0305-4470/29/8/019/img1 and are computed from four-dimensional symmetric subalgebras. These theoretical considerations are illustrated by several examples. Finally, some new classes of invariant solutions obtained by the symmetry reduction method are included. These solutions represent central, conical, rational, spherical, cylindrical and non-scattering double waves.

Calculation of total electron excitation cross-sections and partial electron ionization cross-sections for the elements. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Green, T. J.

1973-01-01

Computer programs were used to calculate the total electron excitation cross-section for atoms and the partial ionization cross-section. The approximations to the scattering amplitude used are as follows: (1) Born, Bethe, and Modified Bethe for non-exchange excitation; (2) Ochkur for exchange excitation; and (3) Coulomb-Born of non-exchange ionization. The amplitudes are related to the differential cross-sections which are integrated to give the total excitation (or partial ionization) cross-section for the collision. The atomic wave functions used are Hartree-Fock-Slater functions for bound states and the coulomb wave function for the continuum. The programs are presented and the results are examined.

A new analysis of the Fornberg-Whitham equation pertaining to a fractional derivative with Mittag-Leffler-type kernel

NASA Astrophysics Data System (ADS)

Kumar, Devendra; Singh, Jagdev; Baleanu, Dumitru

2018-02-01

The mathematical model of breaking of non-linear dispersive water waves with memory effect is very important in mathematical physics. In the present article, we examine a novel fractional extension of the non-linear Fornberg-Whitham equation occurring in wave breaking. We consider the most recent theory of differentiation involving the non-singular kernel based on the extended Mittag-Leffler-type function to modify the Fornberg-Whitham equation. We examine the existence of the solution of the non-linear Fornberg-Whitham equation of fractional order. Further, we show the uniqueness of the solution. We obtain the numerical solution of the new arbitrary order model of the non-linear Fornberg-Whitham equation with the aid of the Laplace decomposition technique. The numerical outcomes are displayed in the form of graphs and tables. The results indicate that the Laplace decomposition algorithm is a very user-friendly and reliable scheme for handling such type of non-linear problems of fractional order.

The consistency of positive fully fuzzy linear system

NASA Astrophysics Data System (ADS)

Malkawi, Ghassan O.; Alfifi, Hassan Y.

2017-11-01

In this paper, the consistency of fuzziness of positive solution of the n × n fully fuzzy linear system (P - FFLS) is studied based on its associated linear system (P - ALS). That can consist of the whole entries of triangular fuzzy numbers in a linear system without fuzzy operations. The nature of solution is differentiated in case of fuzzy solution, non-fuzzy solution and fuzzy non-positive solution. Moreover, the analysis reveals that the P - ALS is applicable to provide the set of infinite number of solutions. Numerical examples are presented to illustrate the proposed analysis.

Quantization of wave equations and hermitian structures in partial differential varieties

PubMed Central

Paneitz, S. M.; Segal, I. E.

1980-01-01

Sufficiently close to 0, the solution variety of a nonlinear relativistic wave equation—e.g., of the form □ϕ + m2ϕ + gϕp = 0—admits a canonical Lorentz-invariant hermitian structure, uniquely determined by the consideration that the action of the differential scattering transformation in each tangent space be unitary. Similar results apply to linear time-dependent equations or to equations in a curved asymptotically flat space-time. A close relation of the Riemannian structure to the determination of vacuum expectation values is developed and illustrated by an explicit determination of a perturbative 2-point function for the case of interaction arising from curvature. The theory underlying these developments is in part a generalization of that of M. G. Krein and collaborators concerning stability of differential equations in Hilbert space and in part a precise relation between the unitarization of given symplectic linear actions and their full probabilistic quantization. The unique causal structure in the infinite symplectic group is instrumental in these developments. PMID:16592923

On analyticity of linear waves scattered by a layered medium

NASA Astrophysics Data System (ADS)

Nicholls, David P.

2017-10-01

The scattering of linear waves by periodic structures is a crucial phenomena in many branches of applied physics and engineering. In this paper we establish rigorous analytic results necessary for the proper numerical analysis of a class of High-Order Perturbation of Surfaces methods for simulating such waves. More specifically, we prove a theorem on existence and uniqueness of solutions to a system of partial differential equations which model the interaction of linear waves with a multiply layered periodic structure in three dimensions. This result provides hypotheses under which a rigorous numerical analysis could be conducted for recent generalizations to the methods of Operator Expansions, Field Expansions, and Transformed Field Expansions.

Differentiation of uric acid versus non-uric acid kidney stones in the presence of iodine using dual-energy CT

NASA Astrophysics Data System (ADS)

Wang, J.; Qu, M.; Leng, S.; McCollough, C. H.

2010-04-01

In this study, the feasibility of differentiating uric acid from non-uric acid kidney stones in the presence of iodinated contrast material was evaluated using dual-energy CT (DECT). Iodine subtraction was accomplished with a commercial three material decomposition algorithm to create a virtual non-contrast (VNC) image set. VNC images were then used to segment stone regions from tissue background. The DE ratio of each stone was calculated using the CT images acquired at two different energies with DECT using the stone map generated from the VNC images. The performance of DE ratio-based stone differentiation was evaluated at five different iodine concentrations (21, 42, 63, 84 and 105 mg/ml). The DE ratio of stones in iodine solution was found larger than those obtained in non-iodine cases. This is mainly caused by the partial volume effect around the boundary between the stone and iodine solution. The overestimation of the DE ratio leads to substantial overlap between different stone types. To address the partial volume effect, an expectation-maximization (EM) approach was implemented to estimate the contribution of iodine and stone within each image pixel in their mixture area. The DE ratio of each stone was corrected to maximally remove the influence of iodine solutions. The separation of uric-acid and non-uric-acid stone was improved in the presence of iodine solution.

a Non-Overlapping Discretization Method for Partial Differential Equations

NASA Astrophysics Data System (ADS)

Rosas-Medina, A.; Herrera, I.

2013-05-01

Mathematical models of many systems of interest, including very important continuous systems of Engineering and Science, lead to a great variety of partial differential equations whose solution methods are based on the computational processing of large-scale algebraic systems. Furthermore, the incredible expansion experienced by the existing computational hardware and software has made amenable to effective treatment problems of an ever increasing diversity and complexity, posed by engineering and scientific applications. The emergence of parallel computing prompted on the part of the computational-modeling community a continued and systematic effort with the purpose of harnessing it for the endeavor of solving boundary-value problems (BVPs) of partial differential equations. Very early after such an effort began, it was recognized that domain decomposition methods (DDM) were the most effective technique for applying parallel computing to the solution of partial differential equations, since such an approach drastically simplifies the coordination of the many processors that carry out the different tasks and also reduces very much the requirements of information-transmission between them. Ideally, DDMs intend producing algorithms that fulfill the DDM-paradigm; i.e., such that "the global solution is obtained by solving local problems defined separately in each subdomain of the coarse-mesh -or domain-decomposition-". Stated in a simplistic manner, the basic idea is that, when the DDM-paradigm is satisfied, full parallelization can be achieved by assigning each subdomain to a different processor. When intensive DDM research began much attention was given to overlapping DDMs, but soon after attention shifted to non-overlapping DDMs. This evolution seems natural when the DDM-paradigm is taken into account: it is easier to uncouple the local problems when the subdomains are separated. However, an important limitation of non-overlapping domain decompositions, as that concept is usually understood today, is that interface nodes are shared by two or more subdomains of the coarse-mesh and, therefore, even non-overlapping DDMs are actually overlapping when seen from the perspective of the nodes used in the discretization. In this talk we present and discuss a discretization method in which the nodes used are non-overlapping, in the sense that each one of them belongs to one and only one subdomain of the coarse-mesh.

NonMarkov Ito Processes with 1- state memory

NASA Astrophysics Data System (ADS)

McCauley, Joseph L.

2010-08-01

A Markov process, by definition, cannot depend on any previous state other than the last observed state. An Ito process implies the Fokker-Planck and Kolmogorov backward time partial differential eqns. for transition densities, which in turn imply the Chapman-Kolmogorov eqn., but without requiring the Markov condition. We present a class of Ito process superficially resembling Markov processes, but with 1-state memory. In finance, such processes would obey the efficient market hypothesis up through the level of pair correlations. These stochastic processes have been mislabeled in recent literature as 'nonlinear Markov processes'. Inspired by Doob and Feller, who pointed out that the ChapmanKolmogorov eqn. is not restricted to Markov processes, we exhibit a Gaussian Ito transition density with 1-state memory in the drift coefficient that satisfies both of Kolmogorov's partial differential eqns. and also the Chapman-Kolmogorov eqn. In addition, we show that three of the examples from McKean's seminal 1966 paper are also nonMarkov Ito processes. Last, we show that the transition density of the generalized Black-Scholes type partial differential eqn. describes a martingale, and satisfies the ChapmanKolmogorov eqn. This leads to the shortest-known proof that the Green function of the Black-Scholes eqn. with variable diffusion coefficient provides the so-called martingale measure of option pricing.

Response of MDOF strongly nonlinear systems to fractional Gaussian noises.

PubMed

Deng, Mao-Lin; Zhu, Wei-Qiu

2016-08-01

In the present paper, multi-degree-of-freedom strongly nonlinear systems are modeled as quasi-Hamiltonian systems and the stochastic averaging method for quasi-Hamiltonian systems (including quasi-non-integrable, completely integrable and non-resonant, completely integrable and resonant, partially integrable and non-resonant, and partially integrable and resonant Hamiltonian systems) driven by fractional Gaussian noise is introduced. The averaged fractional stochastic differential equations (SDEs) are derived. The simulation results for some examples show that the averaged SDEs can be used to predict the response of the original systems and the simulation time for the averaged SDEs is less than that for the original systems.

Response of MDOF strongly nonlinear systems to fractional Gaussian noises

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

Deng, Mao-Lin; Zhu, Wei-Qiu, E-mail: wqzhu@zju.edu.cn

2016-08-15

In the present paper, multi-degree-of-freedom strongly nonlinear systems are modeled as quasi-Hamiltonian systems and the stochastic averaging method for quasi-Hamiltonian systems (including quasi-non-integrable, completely integrable and non-resonant, completely integrable and resonant, partially integrable and non-resonant, and partially integrable and resonant Hamiltonian systems) driven by fractional Gaussian noise is introduced. The averaged fractional stochastic differential equations (SDEs) are derived. The simulation results for some examples show that the averaged SDEs can be used to predict the response of the original systems and the simulation time for the averaged SDEs is less than that for the original systems.

Investigation of ODE integrators using interactive graphics. [Ordinary Differential Equations

NASA Technical Reports Server (NTRS)

Brown, R. L.

1978-01-01

Two FORTRAN programs using an interactive graphic terminal to generate accuracy and stability plots for given multistep ordinary differential equation (ODE) integrators are described. The first treats the fixed stepsize linear case with complex variable solutions, and generates plots to show accuracy and error response to step driving function of a numerical solution, as well as the linear stability region. The second generates an analog to the stability region for classes of non-linear ODE's as well as accuracy plots. Both systems can compute method coefficients from a simple specification of the method. Example plots are given.

A Tightly Coupled Non-Equilibrium Magneto-Hydrodynamic Model for Inductively Coupled RF Plasmas

DTIC Science & Technology

2016-02-29

development a tightly coupled magneto-hydrodynamic model for Inductively Coupled Radio- Frequency (RF) Plasmas. Non Local Thermodynamic Equilibrium (NLTE...for Inductively Coupled Radio-Frequency (RF) Plasmas. Non Local Thermodynamic Equilibrium (NLTE) effects are described based on a hybrid State-to-State... thermodynamic variable. This choice allows one to hide the non-linearity of the gas (total) thermal conductivity κ and can partially alle- 2 viate numerical

Intrinsic Bayesian Active Contours for Extraction of Object Boundaries in Images

PubMed Central

Srivastava, Anuj

2010-01-01

We present a framework for incorporating prior information about high-probability shapes in the process of contour extraction and object recognition in images. Here one studies shapes as elements of an infinite-dimensional, non-linear quotient space, and statistics of shapes are defined and computed intrinsically using differential geometry of this shape space. Prior models on shapes are constructed using probability distributions on tangent bundles of shape spaces. Similar to the past work on active contours, where curves are driven by vector fields based on image gradients and roughness penalties, we incorporate the prior shape knowledge in the form of vector fields on curves. Through experimental results, we demonstrate the use of prior shape models in the estimation of object boundaries, and their success in handling partial obscuration and missing data. Furthermore, we describe the use of this framework in shape-based object recognition or classification. PMID:21076692

A Spatially Continuous Model of Carbohydrate Digestion and Transport Processes in the Colon

PubMed Central

Moorthy, Arun S.; Brooks, Stephen P. J.; Kalmokoff, Martin; Eberl, Hermann J.

2015-01-01

A spatially continuous mathematical model of transport processes, anaerobic digestion and microbial complexity as would be expected in the human colon is presented. The model is a system of first-order partial differential equations with context determined number of dependent variables, and stiff, non-linear source terms. Numerical simulation of the model is used to elucidate information about the colon-microbiota complex. It is found that the composition of materials on outflow of the model does not well-describe the composition of material in other model locations, and inferences using outflow data varies according to model reactor representation. Additionally, increased microbial complexity allows the total microbial community to withstand major system perturbations in diet and community structure. However, distribution of strains and functional groups within the microbial community can be modified depending on perturbation length and microbial kinetic parameters. Preliminary model extensions and potential investigative opportunities using the computational model are discussed. PMID:26680208

A finite element solution algorithm for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Baker, A. J.

1974-01-01

A finite element solution algorithm is established for the two-dimensional Navier-Stokes equations governing the steady-state kinematics and thermodynamics of a variable viscosity, compressible multiple-species fluid. For an incompressible fluid, the motion may be transient as well. The primitive dependent variables are replaced by a vorticity-streamfunction description valid in domains spanned by rectangular, cylindrical and spherical coordinate systems. Use of derived variables provides a uniformly elliptic partial differential equation description for the Navier-Stokes system, and for which the finite element algorithm is established. Explicit non-linearity is accepted by the theory, since no psuedo-variational principles are employed, and there is no requirement for either computational mesh or solution domain closure regularity. Boundary condition constraints on the normal flux and tangential distribution of all computational variables, as well as velocity, are routinely piecewise enforceable on domain closure segments arbitrarily oriented with respect to a global reference frame.

Multiplicative noise removal through fractional order tv-based model and fast numerical schemes for its approximation

NASA Astrophysics Data System (ADS)

Ullah, Asmat; Chen, Wen; Khan, Mushtaq Ahmad

2017-07-01

This paper introduces a fractional order total variation (FOTV) based model with three different weights in the fractional order derivative definition for multiplicative noise removal purpose. The fractional-order Euler Lagrange equation which is a highly non-linear partial differential equation (PDE) is obtained by the minimization of the energy functional for image restoration. Two numerical schemes namely an iterative scheme based on the dual theory and majorization- minimization algorithm (MMA) are used. To improve the restoration results, we opt for an adaptive parameter selection procedure for the proposed model by applying the trial and error method. We report numerical simulations which show the validity and state of the art performance of the fractional-order model in visual improvement as well as an increase in the peak signal to noise ratio comparing to corresponding methods. Numerical experiments also demonstrate that MMAbased methodology is slightly better than that of an iterative scheme.

L(2) stability for weak solutions of the Navier-Stokes equations in R(3)

NASA Astrophysics Data System (ADS)

Secchi, P.

1985-11-01

We consider the motion of a viscous fluid filling the whole space R3, governed by the classical Navier-Stokes equations (1). Existence of global (in time) regular solutions for that system of non-linear partial differential equations is still an open problem. Up to now, the only available global existence theorem (other than for sufficiently small initial data) is that of weak (turbulent) solutions. From both the mathematical and the physical point of view, an interesting property is the stability of such weak solutions. We assume that v(t,x) is a solution, with initial datum vO(x). We suppose that the initial datum is perturbed and consider one weak solution u corresponding to the new initial velocity. Then we prove that, due to viscosity, the perturbed weak solution u approaches in a suitable norm the unperturbed one, as time goes to + infinity, without smallness assumptions on the initial perturbation.

Cattaneo-Christov Heat Flux Model for MHD Three-Dimensional Flow of Maxwell Fluid over a Stretching Sheet.

PubMed

Rubab, Khansa; Mustafa, M

2016-01-01

This letter investigates the MHD three-dimensional flow of upper-convected Maxwell (UCM) fluid over a bi-directional stretching surface by considering the Cattaneo-Christov heat flux model. This model has tendency to capture the characteristics of thermal relaxation time. The governing partial differential equations even after employing the boundary layer approximations are non linear. Accurate analytic solutions for velocity and temperature distributions are computed through well-known homotopy analysis method (HAM). It is noticed that velocity decreases and temperature rises when stronger magnetic field strength is accounted. Penetration depth of temperature is a decreasing function of thermal relaxation time. The analysis for classical Fourier heat conduction law can be obtained as a special case of the present work. To our knowledge, the Cattaneo-Christov heat flux model law for three-dimensional viscoelastic flow problem is just introduced here.

New imaging algorithm in diffusion tomography

NASA Astrophysics Data System (ADS)

Klibanov, Michael V.; Lucas, Thomas R.; Frank, Robert M.

1997-08-01

A novel imaging algorithm for diffusion/optical tomography is presented for the case of the time dependent diffusion equation. Numerical tests are conducted for ranges of parameters realistic for applications to an early breast cancer diagnosis using ultrafast laser pulses. This is a perturbation-like method which works for both homogeneous a heterogeneous background media. Its main innovation lies in a new approach for a novel linearized problem (LP). Such an LP is derived and reduced to a boundary value problem for a coupled system of elliptic partial differential equations. As is well known, the solution of such a system amounts to the factorization of well conditioned, sparse matrices with few non-zero entries clustered along the diagonal, which can be done very rapidly. Thus, the main advantages of this technique are that it is fast and accurate. The authors call this approach the elliptic systems method (ESM). The ESM can be extended for other data collection schemes.

Effect of partial heating at mid of vertical plate adjacent to porous medium

NASA Astrophysics Data System (ADS)

Mulla, Mohammed Fahimuddin; Pallan, Khalid. M.; Al-Rashed, A. A. A. A.

2018-05-01

Heat and mass transfer in porous medium due to heating of vertical plate at mid-section is analyzed for various physical parameters. The heat and mass transfer in porous medium is modeled with the help of momentum, energy and concentration equations in terms of non-dimensional partial differential equations. The partial differential equations are converted into simpler form of algebraic equations with the help of finite element method. A computer code is developed to assemble the matrix form of algebraic equations into global matrices and then to solve them in an iterative manner to obtain the temperature, concentration and streamline distribution inside the porous medium. It is found that the heat transfer behavior of porous medium heated at middle section is considerably different from other cases.

Fourth order difference methods for hyperbolic IBVP's

NASA Technical Reports Server (NTRS)

Gustafsson, Bertil; Olsson, Pelle

1994-01-01

Fourth order difference approximations of initial-boundary value problems for hyperbolic partial differential equations are considered. We use the method of lines approach with both explicit and compact implicit difference operators in space. The explicit operator satisfies an energy estimate leading to strict stability. For the implicit operator we develop boundary conditions and give a complete proof of strong stability using the Laplace transform technique. We also present numerical experiments for the linear advection equation and Burgers' equation with discontinuities in the solution or in its derivative. The first equation is used for modeling contact discontinuities in fluid dynamics, the second one for modeling shocks and rarefaction waves. The time discretization is done with a third order Runge-Kutta TVD method. For solutions with discontinuities in the solution itself we add a filter based on second order viscosity. In case of the non-linear Burger's equation we use a flux splitting technique that results in an energy estimate for certain different approximations, in which case also an entropy condition is fulfilled. In particular we shall demonstrate that the unsplit conservative form produces a non-physical shock instead of the physically correct rarefaction wave. In the numerical experiments we compare our fourth order methods with a standard second order one and with a third order TVD-method. The results show that the fourth order methods are the only ones that give good results for all the considered test problems.

MIKON 94. International Microwave Conference (10th) Held in Ksiaz, Poland on May 30-June 2, 1994. Volume 3. Invited Papers

DTIC Science & Technology

1994-01-01

linear non -differential equations in series. This makes it easier to control the result, and an exact and accurate solution is obtained without...battery operated and controlled by an industry standard computer 1161. The HF unit contains a step-recovery diode transmitter and two quasi -TEM antennas...16]. All of these procedures can take advantage of exact non -linear analysis or experimental power characterization and are therefore "full non

Compacton solutions in a class of generalized fifth-order Korteweg-de Vries equations.

PubMed

Cooper, F; Hyman, J M; Khare, A

2001-08-01

Solitons play a fundamental role in the evolution of general initial data for quasilinear dispersive partial differential equations, such as the Korteweg-de Vries (KdV), nonlinear Schrödinger, and the Kadomtsev-Petviashvili equations. These integrable equations have linear dispersion and the solitons have infinite support. We have derived and investigate a new KdV-like Hamiltonian partial differential equation from a four-parameter Lagrangian where the nonlinear dispersion gives rise to solitons with compact support (compactons). The new equation does not seem to be integrable and only mass, momentum, and energy seem to be conserved; yet, the solitons display almost the same modal decompositions and structural stability observed in integrable partial differential equations. The compactons formed from arbitrary initial data, are nonlinearly self-stabilizing, and maintain their coherence after multiple collisions. The robustness of these compactons and the inapplicability of the inverse scattering tools, that worked so well for the KdV equation, make it clear that there is a fundamental mechanism underlying the processes beyond integrability. We have found explicit formulas for multiple classes of compact traveling wave solutions. When there are more than one compacton solution for a particular set of parameters, the wider compacton is the minimum of a reduced Hamiltonian and is the only one that is stable.

ELASTIC NET FOR COX'S PROPORTIONAL HAZARDS MODEL WITH A SOLUTION PATH ALGORITHM.

PubMed

Wu, Yichao

2012-01-01

For least squares regression, Efron et al. (2004) proposed an efficient solution path algorithm, the least angle regression (LAR). They showed that a slight modification of the LAR leads to the whole LASSO solution path. Both the LAR and LASSO solution paths are piecewise linear. Recently Wu (2011) extended the LAR to generalized linear models and the quasi-likelihood method. In this work we extend the LAR further to handle Cox's proportional hazards model. The goal is to develop a solution path algorithm for the elastic net penalty (Zou and Hastie (2005)) in Cox's proportional hazards model. This goal is achieved in two steps. First we extend the LAR to optimizing the log partial likelihood plus a fixed small ridge term. Then we define a path modification, which leads to the solution path of the elastic net regularized log partial likelihood. Our solution path is exact and piecewise determined by ordinary differential equation systems.

The fundamentals of adaptive grid movement

NASA Technical Reports Server (NTRS)

Eiseman, Peter R.

1990-01-01

Basic grid point movement schemes are studied. The schemes are referred to as adaptive grids. Weight functions and equidistribution in one dimension are treated. The specification of coefficients in the linear weight, attraction to a given grid or a curve, and evolutionary forces are considered. Curve by curve and finite volume methods are described. The temporal coupling of partial differential equations solvers and grid generators was discussed.

A sensitivity equation approach to shape optimization in fluid flows

NASA Technical Reports Server (NTRS)

Borggaard, Jeff; Burns, John

1994-01-01

A sensitivity equation method to shape optimization problems is applied. An algorithm is developed and tested on a problem of designing optimal forebody simulators for a 2D, inviscid supersonic flow. The algorithm uses a BFGS/Trust Region optimization scheme with sensitivities computed by numerically approximating the linear partial differential equations that determine the flow sensitivities. Numerical examples are presented to illustrate the method.

Optical systolic solutions of linear algebraic equations

NASA Technical Reports Server (NTRS)

Neuman, C. P.; Casasent, D.

1984-01-01

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

Parallel adaptive wavelet collocation method for PDEs

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

Nejadmalayeri, Alireza, E-mail: Alireza.Nejadmalayeri@gmail.com; Vezolainen, Alexei, E-mail: Alexei.Vezolainen@Colorado.edu; Brown-Dymkoski, Eric, E-mail: Eric.Browndymkoski@Colorado.edu

2015-10-01

A parallel adaptive wavelet collocation method for solving a large class of Partial Differential Equations is presented. The parallelization is achieved by developing an asynchronous parallel wavelet transform, which allows one to perform parallel wavelet transform and derivative calculations with only one data synchronization at the highest level of resolution. The data are stored using tree-like structure with tree roots starting at a priori defined level of resolution. Both static and dynamic domain partitioning approaches are developed. For the dynamic domain partitioning, trees are considered to be the minimum quanta of data to be migrated between the processes. This allowsmore » fully automated and efficient handling of non-simply connected partitioning of a computational domain. Dynamic load balancing is achieved via domain repartitioning during the grid adaptation step and reassigning trees to the appropriate processes to ensure approximately the same number of grid points on each process. The parallel efficiency of the approach is discussed based on parallel adaptive wavelet-based Coherent Vortex Simulations of homogeneous turbulence with linear forcing at effective non-adaptive resolutions up to 2048{sup 3} using as many as 2048 CPU cores.« less

A spectral-finite difference solution of the Navier-Stokes equations in three dimensions

NASA Astrophysics Data System (ADS)

Alfonsi, Giancarlo; Passoni, Giuseppe; Pancaldo, Lea; Zampaglione, Domenico

1998-07-01

A new computational code for the numerical integration of the three-dimensional Navier-Stokes equations in their non-dimensional velocity-pressure formulation is presented. The system of non-linear partial differential equations governing the time-dependent flow of a viscous incompressible fluid in a channel is managed by means of a mixed spectral-finite difference method, in which different numerical techniques are applied: Fourier decomposition is used along the homogeneous directions, second-order Crank-Nicolson algorithms are employed for the spatial derivatives in the direction orthogonal to the solid walls and a fourth-order Runge-Kutta procedure is implemented for both the calculation of the convective term and the time advancement. The pressure problem, cast in the Helmholtz form, is solved with the use of a cyclic reduction procedure. No-slip boundary conditions are used at the walls of the channel and cyclic conditions are imposed at the other boundaries of the computing domain.Results are provided for different values of the Reynolds number at several time steps of integration and are compared with results obtained by other authors.

Enhancing sparsity of Hermite polynomial expansions by iterative rotations

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

Yang, Xiu; Lei, Huan; Baker, Nathan A.

2016-02-01

Compressive sensing has become a powerful addition to uncertainty quantification in recent years. This paper identifies new bases for random variables through linear mappings such that the representation of the quantity of interest is more sparse with new basis functions associated with the new random variables. This sparsity increases both the efficiency and accuracy of the compressive sensing-based uncertainty quantification method. Specifically, we consider rotation- based linear mappings which are determined iteratively for Hermite polynomial expansions. We demonstrate the effectiveness of the new method with applications in solving stochastic partial differential equations and high-dimensional (O(100)) problems.

Higher symmetries and exact solutions of linear and nonlinear Schr{umlt o}dinger equation

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

Fushchych, W.I.; Nikitin, A.G.

1997-11-01

A new approach for the analysis of partial differential equations is developed which is characterized by a simultaneous use of higher and conditional symmetries. Higher symmetries of the Schr{umlt o}dinger equation with an arbitrary potential are investigated. Nonlinear determining equations for potentials are solved using reductions to Weierstrass, Painlev{acute e}, and Riccati forms. Algebraic properties of higher order symmetry operators are analyzed. Combinations of higher and conditional symmetries are used to generate families of exact solutions of linear and nonlinear Schr{umlt o}dinger equations. {copyright} {ital 1997 American Institute of Physics.}

Linearized compressible-flow theory for sonic flight speeds

NASA Technical Reports Server (NTRS)

Heaslet, Max A; Lomax, Harvard; Spreiter, John R

1950-01-01

The partial differential equation for the perturbation velocity potential is examined for free-stream Mach numbers close to and equal to one. It is found that, under the assumptions of linearized theory, solutions can be found consistent with the theory for lifting-surface problems both in stationary three-dimensional flow and in unsteady two-dimensional flow. Several examples are solved including a three dimensional swept-back wing and two dimensional harmonically-oscillating wing, both for a free stream Mach number equal to one. Momentum relations for the evaluation of wave and vortex drag are also discussed. (author)

Stability and error estimation for Component Adaptive Grid methods

NASA Technical Reports Server (NTRS)

Oliger, Joseph; Zhu, Xiaolei

1994-01-01

Component adaptive grid (CAG) methods for solving hyperbolic partial differential equations (PDE's) are discussed in this paper. Applying recent stability results for a class of numerical methods on uniform grids. The convergence of these methods for linear problems on component adaptive grids is established here. Furthermore, the computational error can be estimated on CAG's using the stability results. Using these estimates, the error can be controlled on CAG's. Thus, the solution can be computed efficiently on CAG's within a given error tolerance. Computational results for time dependent linear problems in one and two space dimensions are presented.

PAN AIR: A computer program for predicting subsonic or supersonic linear potential flows about arbitrary configurations using a higher order panel method. Volume 1: Theory document (version 1.1)

NASA Technical Reports Server (NTRS)

Magnus, A. E.; Epton, M. A.

1981-01-01

Panel aerodynamics (PAN AIR) is a system of computer programs designed to analyze subsonic and supersonic inviscid flows about arbitrary configurations. A panel method is a program which solves a linear partial differential equation by approximating the configuration surface by a set of panels. An overview of the theory of potential flow in general and PAN AIR in particular is given along with detailed mathematical formulations. Fluid dynamics, the Navier-Stokes equation, and the theory of panel methods were also discussed.

Symmetric linear systems - An application of algebraic systems theory

NASA Technical Reports Server (NTRS)

Hazewinkel, M.; Martin, C.

1983-01-01

Dynamical systems which contain several identical subsystems occur in a variety of applications ranging from command and control systems and discretization of partial differential equations, to the stability augmentation of pairs of helicopters lifting a large mass. Linear models for such systems display certain obvious symmetries. In this paper, we discuss how these symmetries can be incorporated into a mathematical model that utilizes the modern theory of algebraic systems. Such systems are inherently related to the representation theory of algebras over fields. We will show that any control scheme which respects the dynamical structure either implicitly or explicitly uses the underlying algebra.

On the pth moment estimates of solutions to stochastic functional differential equations in the G-framework.

PubMed

Faizullah, Faiz

2016-01-01

The aim of the current paper is to present the path-wise and moment estimates for solutions to stochastic functional differential equations with non-linear growth condition in the framework of G-expectation and G-Brownian motion. Under the nonlinear growth condition, the pth moment estimates for solutions to SFDEs driven by G-Brownian motion are proved. The properties of G-expectations, Hölder's inequality, Bihari's inequality, Gronwall's inequality and Burkholder-Davis-Gundy inequalities are used to develop the above mentioned theory. In addition, the path-wise asymptotic estimates and continuity of pth moment for the solutions to SFDEs in the G-framework, with non-linear growth condition are shown.

Physical origins of current and temperature controlled negative differential resistances in NbO 2

DOE PAGES

Kumar, Suhas; Wang, Ziwen; Davila, Noraica; ...

2017-09-22

Negative differential resistance behavior in oxide memristors, especially those using NbO 2, is gaining renewed interest because of its potential utility in neuromorphic computing. However, there has been a decade-long controversy over whether the negative differential resistance is caused by a relatively low-temperature non-linear transport mechanism or a high-temperature Mott transition. Resolving this issue will enable consistent and robust predictive modeling of this phenomenon for different applications. Here in this paper, we examine NbO 2 memristors that exhibit both a current-controlled and a temperature-controlled negative differential resistance. Through thermal and chemical spectromicroscopy and numerical simulations, we confirm that the formermore » is caused by a ~400 K non-linear-transport-driven instability and the latter is caused by the ~1000 K Mott metal-insulator transition, for which the thermal conductance counter-intuitively decreases in the metallic state relative to the insulating state.« less

Physical origins of current and temperature controlled negative differential resistances in NbO 2

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

Kumar, Suhas; Wang, Ziwen; Davila, Noraica

Negative differential resistance behavior in oxide memristors, especially those using NbO 2, is gaining renewed interest because of its potential utility in neuromorphic computing. However, there has been a decade-long controversy over whether the negative differential resistance is caused by a relatively low-temperature non-linear transport mechanism or a high-temperature Mott transition. Resolving this issue will enable consistent and robust predictive modeling of this phenomenon for different applications. Here in this paper, we examine NbO 2 memristors that exhibit both a current-controlled and a temperature-controlled negative differential resistance. Through thermal and chemical spectromicroscopy and numerical simulations, we confirm that the formermore » is caused by a ~400 K non-linear-transport-driven instability and the latter is caused by the ~1000 K Mott metal-insulator transition, for which the thermal conductance counter-intuitively decreases in the metallic state relative to the insulating state.« less

Unsteady boundary layer flow over a sphere in a porous medium

NASA Astrophysics Data System (ADS)

Mohammad, Nurul Farahain; Waini, Iskandar; Kasim, Abdul Rahman Mohd; Majid, Nurazleen Abdul

2017-08-01

This study focuses on the problem of unsteady boundary layer flow over a sphere in a porous medium. The governing equations which consists of a system of dimensional partial differential equations is applied with dimensionless parameter in order to attain non-dimensional partial differential equations. Later, the similarity transformation is performed in order to attain nonsimilar governing equations. Afterwards, the nonsimilar governing equations are solved numerically by using the Keller-Box method in Octave programme. The effect of porosity parameter is examined on separation time, velocity profile and skin friction of the unsteady flow. The results attained are presented in the form of table and graph.

Reference evapotranspiration forecasting based on local meteorological and global climate information screened by partial mutual information

NASA Astrophysics Data System (ADS)

Fang, Wei; Huang, Shengzhi; Huang, Qiang; Huang, Guohe; Meng, Erhao; Luan, Jinkai

2018-06-01

In this study, reference evapotranspiration (ET0) forecasting models are developed for the least economically developed regions subject to meteorological data scarcity. Firstly, the partial mutual information (PMI) capable of capturing the linear and nonlinear dependence is investigated regarding its utility to identify relevant predictors and exclude those that are redundant through the comparison with partial linear correlation. An efficient input selection technique is crucial for decreasing model data requirements. Then, the interconnection between global climate indices and regional ET0 is identified. Relevant climatic indices are introduced as additional predictors to comprise information regarding ET0, which ought to be provided by meteorological data unavailable. The case study in the Jing River and Beiluo River basins, China, reveals that PMI outperforms the partial linear correlation in excluding the redundant information, favouring the yield of smaller predictor sets. The teleconnection analysis identifies the correlation between Nino 1 + 2 and regional ET0, indicating influences of ENSO events on the evapotranspiration process in the study area. Furthermore, introducing Nino 1 + 2 as predictors helps to yield more accurate ET0 forecasts. A model performance comparison also shows that non-linear stochastic models (SVR or RF with input selection through PMI) do not always outperform linear models (MLR with inputs screen by linear correlation). However, the former can offer quite comparable performance depending on smaller predictor sets. Therefore, efforts such as screening model inputs through PMI and incorporating global climatic indices interconnected with ET0 can benefit the development of ET0 forecasting models suitable for data-scarce regions.

On the boundedness and integration of non-oscillatory solutions of certain linear differential equations of second order.

PubMed

Tunç, Cemil; Tunç, Osman

2016-01-01

In this paper, certain system of linear homogeneous differential equations of second-order is considered. By using integral inequalities, some new criteria for bounded and [Formula: see text]-solutions, upper bounds for values of improper integrals of the solutions and their derivatives are established to the considered system. The obtained results in this paper are considered as extension to the results obtained by Kroopnick (2014) [1]. An example is given to illustrate the obtained results.

Estimation of a partially linear additive model for data from an outcome-dependent sampling design with a continuous outcome

PubMed Central

Tan, Ziwen; Qin, Guoyou; Zhou, Haibo

2016-01-01

Outcome-dependent sampling (ODS) designs have been well recognized as a cost-effective way to enhance study efficiency in both statistical literature and biomedical and epidemiologic studies. A partially linear additive model (PLAM) is widely applied in real problems because it allows for a flexible specification of the dependence of the response on some covariates in a linear fashion and other covariates in a nonlinear non-parametric fashion. Motivated by an epidemiological study investigating the effect of prenatal polychlorinated biphenyls exposure on children's intelligence quotient (IQ) at age 7 years, we propose a PLAM in this article to investigate a more flexible non-parametric inference on the relationships among the response and covariates under the ODS scheme. We propose the estimation method and establish the asymptotic properties of the proposed estimator. Simulation studies are conducted to show the improved efficiency of the proposed ODS estimator for PLAM compared with that from a traditional simple random sampling design with the same sample size. The data of the above-mentioned study is analyzed to illustrate the proposed method. PMID:27006375

A Solution Space for a System of Null-State Partial Differential Equations: Part 2

NASA Astrophysics Data System (ADS)

Flores, Steven M.; Kleban, Peter

2015-01-01

This article is the second of four that completely and rigorously characterize a solution space for a homogeneous system of 2 N + 3 linear partial differential equations in 2 N variables that arises in conformal field theory (CFT) and multiple Schramm-Löwner evolution (SLE). The system comprises 2 N null-state equations and three conformal Ward identities which govern CFT correlation functions of 2 N one-leg boundary operators. In the first article (Flores and Kleban, Commun Math Phys, arXiv:1212.2301, 2012), we use methods of analysis and linear algebra to prove that dim , with C N the Nth Catalan number. The analysis of that article is complete except for the proof of a lemma that it invokes. The purpose of this article is to provide that proof. The lemma states that if every interval among ( x 2, x 3), ( x 3, x 4),…,( x 2 N-1, x 2 N ) is a two-leg interval of (defined in Flores and Kleban, Commun Math Phys, arXiv:1212.2301, 2012), then F vanishes. Proving this lemma by contradiction, we show that the existence of such a nonzero function implies the existence of a non-vanishing CFT two-point function involving primary operators with different conformal weights, an impossibility. This proof (which is rigorous in spite of our occasional reference to CFT) involves two different types of estimates, those that give the asymptotic behavior of F as the length of one interval vanishes, and those that give this behavior as the lengths of two intervals vanish simultaneously. We derive these estimates by using Green functions to rewrite certain null-state PDEs as integral equations, combining other null-state PDEs to obtain Schauder interior estimates, and then repeatedly integrating the integral equations with these estimates until we obtain optimal bounds. Estimates in which two interval lengths vanish simultaneously divide into two cases: two adjacent intervals and two non-adjacent intervals. The analysis of the latter case is similar to that for one vanishing interval length. In contrast, the analysis of the former case is more complicated, involving a Green function that contains the Jacobi heat kernel as its essential ingredient.

Formal Integrals and Noether Operators of Nonlinear Hyperbolic Partial Differential Systems Admitting a Rich Set of Symmetries

NASA Astrophysics Data System (ADS)

Startsev, Sergey Ya.

2017-05-01

The paper is devoted to hyperbolic (generally speaking, non-Lagrangian and nonlinear) partial differential systems possessing a full set of differential operators that map any function of one independent variable into a symmetry of the corresponding system. We demonstrate that a system has the above property if and only if this system admits a full set of formal integrals (i.e., differential operators which map symmetries into integrals of the system). As a consequence, such systems possess both direct and inverse Noether operators (in the terminology of a work by B. Fuchssteiner and A.S. Fokas who have used these terms for operators that map cosymmetries into symmetries and perform transformations in the opposite direction). Systems admitting Noether operators are not exhausted by Euler-Lagrange systems and the systems with formal integrals. In particular, a hyperbolic system admits an inverse Noether operator if a differential substitution maps this system into a system possessing an inverse Noether operator.

Face-selective regions show invariance to linear, but not to non-linear, changes in facial images.

PubMed

Baseler, Heidi A; Young, Andrew W; Jenkins, Rob; Mike Burton, A; Andrews, Timothy J

2016-12-01

Familiar face recognition is remarkably invariant across huge image differences, yet little is understood concerning how image-invariant recognition is achieved. To investigate the neural correlates of invariance, we localized the core face-responsive regions and then compared the pattern of fMR-adaptation to different stimulus transformations in each region to behavioural data demonstrating the impact of the same transformations on familiar face recognition. In Experiment 1, we compared linear transformations of size and aspect ratio to a non-linear transformation affecting only part of the face. We found that adaptation to facial identity in face-selective regions showed invariance to linear changes, but there was no invariance to non-linear changes. In Experiment 2, we measured the sensitivity to non-linear changes that fell within the normal range of variation across face images. We found no adaptation to facial identity for any of the non-linear changes in the image, including to faces that varied in different levels of caricature. These results show a compelling difference in the sensitivity to linear compared to non-linear image changes in face-selective regions of the human brain that is only partially consistent with their effect on behavioural judgements of identity. We conclude that while regions such as the FFA may well be involved in the recognition of face identity, they are more likely to contribute to some form of normalisation that underpins subsequent recognition than to form the neural substrate of recognition per se. Copyright © 2016 Elsevier Ltd. All rights reserved.

A Double-Blinded, Randomized Comparison of Medetomidine-Tiletamine-Zolazepam and Dexmedetomidine-Tiletamine-Zolazepam Anesthesia in Free-Ranging Brown Bears (Ursus Arctos)

PubMed Central

Cattet, Marc; Zedrosser, Andreas; Stenhouse, Gordon B.; Küker, Susanne; Evans, Alina L.; Arnemo, Jon M.

2017-01-01

We compared anesthetic features, blood parameters, and physiological responses to either medetomidine-tiletamine-zolazepam or dexmedetomidine-tiletamine-zolazepam using a double-blinded, randomized experimental design during 40 anesthetic events of free-ranging brown bears (Ursus arctos) either captured by helicopter in Sweden or by culvert trap in Canada. Induction was smooth and predictable with both anesthetic protocols. Induction time, the need for supplemental drugs to sustain anesthesia, and capture-related stress were analyzed using generalized linear models, but anesthetic protocol did not differentially affect these variables. Arterial blood gases and acid-base status, and physiological responses were examined using linear mixed models. We documented acidemia (pH of arterial blood < 7.35), hypoxemia (partial pressure of arterial oxygen < 80 mmHg), and hypercapnia (partial pressure of arterial carbon dioxide ≥ 45 mmHg) with both protocols. Arterial pH and oxygen partial pressure were similar between groups with the latter improving markedly after oxygen supplementation (p < 0.001). We documented dose-dependent effects of both anesthetic protocols on induction time and arterial oxygen partial pressure. The partial pressure of arterial carbon dioxide increased as respiratory rate increased with medetomidine-tiletamine-zolazepam, but not with dexmedetomidine-tiletamine-zolazepam, demonstrating a differential drug effect. Differences in heart rate, respiratory rate, and rectal temperature among bears could not be attributed to the anesthetic protocol. Heart rate increased with increasing rectal temperature (p < 0.001) and ordinal day of capture (p = 0.002). Respiratory rate was significantly higher in bears captured by helicopter in Sweden than in bears captured by culvert trap in Canada (p < 0.001). Rectal temperature significantly decreased over time (p ≤ 0.05). Overall, we did not find any benefit of using dexmedetomidine-tiletamine-zolazepam instead of medetomidine-tiletamine-zolazepam in the anesthesia of brown bears. Both drug combinations appeared to be safe and reliable for the anesthesia of free-ranging brown bears captured by helicopter or by culvert trap. PMID:28118413

PDE-based geophysical modelling using finite elements: examples from 3D resistivity and 2D magnetotellurics

NASA Astrophysics Data System (ADS)

Schaa, R.; Gross, L.; du Plessis, J.

2016-04-01

We present a general finite-element solver, escript, tailored to solve geophysical forward and inverse modeling problems in terms of partial differential equations (PDEs) with suitable boundary conditions. Escript’s abstract interface allows geoscientists to focus on solving the actual problem without being experts in numerical modeling. General-purpose finite element solvers have found wide use especially in engineering fields and find increasing application in the geophysical disciplines as these offer a single interface to tackle different geophysical problems. These solvers are useful for data interpretation and for research, but can also be a useful tool in educational settings. This paper serves as an introduction into PDE-based modeling with escript where we demonstrate in detail how escript is used to solve two different forward modeling problems from applied geophysics (3D DC resistivity and 2D magnetotellurics). Based on these two different cases, other geophysical modeling work can easily be realized. The escript package is implemented as a Python library and allows the solution of coupled, linear or non-linear, time-dependent PDEs. Parallel execution for both shared and distributed memory architectures is supported and can be used without modifications to the scripts.

Dynamics from a mathematical model of a two-state gas laser

NASA Astrophysics Data System (ADS)

Kleanthous, Antigoni; Hua, Tianshu; Manai, Alexandre; Yawar, Kamran; Van Gorder, Robert A.

2018-05-01

Motivated by recent work in the area, we consider the behavior of solutions to a nonlinear PDE model of a two-state gas laser. We first review the derivation of the two-state gas laser model, before deriving a non-dimensional model given in terms of coupled nonlinear partial differential equations. We then classify the steady states of this system, in order to determine the possible long-time asymptotic solutions to this model, as well as corresponding stability results, showing that the only uniform steady state (the zero motion state) is unstable, while a linear profile in space is stable. We then provide numerical simulations for the full unsteady model. We show for a wide variety of initial conditions that the solutions tend toward the stable linear steady state profiles. We also consider traveling wave solutions, and determine the unique wave speed (in terms of the other model parameters) which allows wave-like solutions to exist. Despite some similarities between the model and the inviscid Burger's equation, the solutions we obtain are much more regular than the solutions to the inviscid Burger's equation, with no evidence of shock formation or loss of regularity.

Substrate mass transfer: analytical approach for immobilized enzyme reactions

NASA Astrophysics Data System (ADS)

Senthamarai, R.; Saibavani, T. N.

2018-04-01

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

Geometry of Conservation Laws for a Class of Parabolic Partial Differential Equations

NASA Astrophysics Data System (ADS)

Clelland, Jeanne Nielsen

1996-08-01

I consider the problem of computing the space of conservation laws for a second-order, parabolic partial differential equation for one function of three independent variables. The PDE is formulated as an exterior differential system {cal I} on a 12 -manifold M, and its conservation laws are identified with the vector space of closed 3-forms in the infinite prolongation of {cal I} modulo the so -called "trivial" conservation laws. I use the tools of exterior differential systems and Cartan's method of equivalence to study the structure of the space of conservation laws. My main result is:. Theorem. Any conservation law for a second-order, parabolic PDE for one function of three independent variables can be represented by a closed 3-form in the differential ideal {cal I} on the original 12-manifold M. I show that if a nontrivial conservation law exists, then {cal I} has a deprolongation to an equivalent system {cal J} on a 7-manifold N, and any conservation law for {cal I} can be expressed as a closed 3-form on N which lies in {cal J}. Furthermore, any such system in the real analytic category is locally equivalent to a system generated by a (parabolic) equation of the formA(u _{xx}u_{yy}-u_sp {xy}{2}) + B_1u_{xx }+2B_2u_{xy} +B_3u_ {yy}+C=0crwhere A, B_{i}, C are functions of x, y, t, u, u_{x}, u _{y}, u_{t}. I compute the space of conservation laws for several examples, and I begin the process of analyzing the general case using Cartan's method of equivalence. I show that the non-linearizable equation u_{t} = {1over2}e ^{-u}(u_{xx}+u_ {yy})has an infinite-dimensional space of conservation laws. This stands in contrast to the two-variable case, for which Bryant and Griffiths showed that any equation whose space of conservation laws has dimension 4 or more is locally equivalent to a linear equation, i.e., is linearizable.

Geometry of Optimal Paths around Focal Singular Surfaces in Differential Games

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

Melikyan, Arik; Bernhard, Pierre

2005-06-15

We investigate a special type of singularity in non-smooth solutions of first-order partial differential equations, with emphasis on Isaacs' equation. This type, called focal manifold, is characterized by the incoming trajectory fields on the two sides and a discontinuous gradient. We provide a complete set of constructive equations under various hypotheses on the singularity, culminating with the case where no a priori hypothesis on its geometry is known, and where the extremal trajectory fields need not be collinear. We show two examples of differential games exhibiting non-collinear fields of extremal trajectories on the focal manifold, one with a transversal approachmore » and one with a tangential approach.« less

Krylov subspace methods - Theory, algorithms, and applications

NASA Technical Reports Server (NTRS)

Sad, Youcef

1990-01-01

Projection methods based on Krylov subspaces for solving various types of scientific problems are reviewed. The main idea of this class of methods when applied to a linear system Ax = b, is to generate in some manner an approximate solution to the original problem from the so-called Krylov subspace span. Thus, the original problem of size N is approximated by one of dimension m, typically much smaller than N. Krylov subspace methods have been very successful in solving linear systems and eigenvalue problems and are now becoming popular for solving nonlinear equations. The main ideas in Krylov subspace methods are shown and their use in solving linear systems, eigenvalue problems, parabolic partial differential equations, Liapunov matrix equations, and nonlinear system of equations are discussed.

The application of Green's theorem to the solution of boundary-value problems in linearized supersonic wing theory

NASA Technical Reports Server (NTRS)

Heaslet, Max A; Lomax, Harvard

1950-01-01

Following the introduction of the linearized partial differential equation for nonsteady three-dimensional compressible flow, general methods of solution are given for the two and three-dimensional steady-state and two-dimensional unsteady-state equations. It is also pointed out that, in the absence of thickness effects, linear theory yields solutions consistent with the assumptions made when applied to lifting-surface problems for swept-back plan forms at sonic speeds. The solutions of the particular equations are determined in all cases by means of Green's theorem, and thus depend on the use of Green's equivalent layer of sources, sinks, and doublets. Improper integrals in the supersonic theory are treated by means of Hadamard's "finite part" technique.

A soft body as a reservoir: case studies in a dynamic model of octopus-inspired soft robotic arm.

PubMed

Nakajima, Kohei; Hauser, Helmut; Kang, Rongjie; Guglielmino, Emanuele; Caldwell, Darwin G; Pfeifer, Rolf

2013-01-01

The behaviors of the animals or embodied agents are characterized by the dynamic coupling between the brain, the body, and the environment. This implies that control, which is conventionally thought to be handled by the brain or a controller, can partially be outsourced to the physical body and the interaction with the environment. This idea has been demonstrated in a number of recently constructed robots, in particular from the field of "soft robotics". Soft robots are made of a soft material introducing high-dimensionality, non-linearity, and elasticity, which often makes the robots difficult to control. Biological systems such as the octopus are mastering their complex bodies in highly sophisticated manners by capitalizing on their body dynamics. We will demonstrate that the structure of the octopus arm cannot only be exploited for generating behavior but also, in a sense, as a computational resource. By using a soft robotic arm inspired by the octopus we show in a number of experiments how control is partially incorporated into the physical arm's dynamics and how the arm's dynamics can be exploited to approximate non-linear dynamical systems and embed non-linear limit cycles. Future application scenarios as well as the implications of the results for the octopus biology are also discussed.

A soft body as a reservoir: case studies in a dynamic model of octopus-inspired soft robotic arm

PubMed Central

Nakajima, Kohei; Hauser, Helmut; Kang, Rongjie; Guglielmino, Emanuele; Caldwell, Darwin G.; Pfeifer, Rolf

2013-01-01

The behaviors of the animals or embodied agents are characterized by the dynamic coupling between the brain, the body, and the environment. This implies that control, which is conventionally thought to be handled by the brain or a controller, can partially be outsourced to the physical body and the interaction with the environment. This idea has been demonstrated in a number of recently constructed robots, in particular from the field of “soft robotics”. Soft robots are made of a soft material introducing high-dimensionality, non-linearity, and elasticity, which often makes the robots difficult to control. Biological systems such as the octopus are mastering their complex bodies in highly sophisticated manners by capitalizing on their body dynamics. We will demonstrate that the structure of the octopus arm cannot only be exploited for generating behavior but also, in a sense, as a computational resource. By using a soft robotic arm inspired by the octopus we show in a number of experiments how control is partially incorporated into the physical arm's dynamics and how the arm's dynamics can be exploited to approximate non-linear dynamical systems and embed non-linear limit cycles. Future application scenarios as well as the implications of the results for the octopus biology are also discussed. PMID:23847526

Techniques in Linear and Nonlinear Partial Differential Equations

DTIC Science & Technology

1991-10-21

theory. J. Grotowski (a student) studied the heat flow approach to harmonic maps betv:een manifolds: between spheres. and from the ball B’ in R 3 into...T. Yau; S. Kichenessamy: F. H. Lin. L. Sadun: Wu. Sigue; Yi. Fang. Also these graduate students: Li, Cong Ming, received Ph.D. in 1989. J. Grotowski . received Ph.D. in 1990. I. Birindelli, working on Ph.D. thesis. 5

Direct Linearization and Adjoint Approaches to Evaluation of Atmospheric Weighting Functions and Surface Partial Derivatives: General Principles, Synergy and Areas of Application

NASA Technical Reports Server (NTRS)

Ustino, Eugene A.

2006-01-01

This slide presentation reviews the observable radiances as functions of atmospheric parameters and of surface parameters; the mathematics of atmospheric weighting functions (WFs) and surface partial derivatives (PDs) are presented; and the equation of the forward radiative transfer (RT) problem is presented. For non-scattering atmospheres this can be done analytically, and all WFs and PDs can be computed analytically using the direct linearization approach. For scattering atmospheres, in general case, the solution of the forward RT problem can be obtained only numerically, but we need only two numerical solutions: one of the forward RT problem and one of the adjoint RT problem to compute all WFs and PDs we can think of. In this presentation we discuss applications of both the linearization and adjoint approaches

SAGUARO: a finite-element computer program for partially saturated porous flow problems

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

Eaton, R.R.; Gartling, D.K.; Larson, D.E.

1983-06-01

SAGUARO is a finite element computer program designed to calculate two-dimensional flow of mass and energy through porous media. The media may be saturated or partially saturated. SAGUARO solves the parabolic time-dependent mass transport equation which accounts for the presence of partially saturated zones through the use of highly non-linear material characteristic curves. The energy equation accounts for the possibility of partially saturated regions by adjusting the thermal capacitances and thermal conductivities according to the volume fraction of water present in the local pores. Program capabilities, user instructions and a sample problem are presented in this manual.

Linear response formula for piecewise expanding unimodal maps

NASA Astrophysics Data System (ADS)

Baladi, Viviane; Smania, Daniel

2008-04-01

The average R(t)=\\int \\varphi\\,\\rmd \\mu_t of a smooth function phiv with respect to the SRB measure μt of a smooth one-parameter family ft of piecewise expanding interval maps is not always Lipschitz (Baladi 2007 Commun. Math. Phys. 275 839-59, Mazzolena 2007 Master's Thesis Rome 2, Tor Vergata). We prove that if ft is tangent to the topological class of f, and if ∂t ft|t = 0 = X circle f, then R(t) is differentiable at zero, and R'(0) coincides with the resummation proposed (Baladi 2007) of the (a priori divergent) series \\sum_{n=0}^\\infty \\int X(y) \\partial_y (\\varphi \\circ f^n)(y)\\,\\rmd \\mu_0(y) given by Ruelle's conjecture. In fact, we show that t map μt is differentiable within Radon measures. Linear response is violated if and only if ft is transversal to the topological class of f.

A finite difference method for the solution of the transonic flow around harmonically oscillating wings

NASA Technical Reports Server (NTRS)

Ehlers, E. F.

1974-01-01

A finite difference method for the solution of the transonic flow about a harmonically oscillating wing is presented. The partial differential equation for the unsteady transonic flow was linearized by dividing the flow into separate steady and unsteady perturbation velocity potentials and by assuming small amplitudes of harmonic oscillation. The resulting linear differential equation is of mixed type, being elliptic or hyperbolic whereever the steady flow equation is elliptic or hyperbolic. Central differences were used for all derivatives except at supersonic points where backward differencing was used for the streamwise direction. Detailed formulas and procedures are described in sufficient detail for programming on high speed computers. To test the method, the problem of the oscillating flap on a NACA 64A006 airfoil was programmed. The numerical procedure was found to be stable and convergent even in regions of local supersonic flow with shocks.

Method and apparatus for calibrating a linear variable differential transformer

DOEpatents

Pokrywka, Robert J [North Huntingdon, PA

2005-01-18

A calibration apparatus for calibrating a linear variable differential transformer (LVDT) having an armature positioned in au LVDT armature orifice, and the armature able to move along an axis of movement. The calibration apparatus includes a heating mechanism with an internal chamber, a temperature measuring mechanism for measuring the temperature of the LVDT, a fixture mechanism with an internal chamber for at least partially accepting the LVDT and for securing the LVDT within the heating mechanism internal chamber, a moving mechanism for moving the armature, a position measurement mechanism for measuring the position of the armature, and an output voltage measurement mechanism. A method for calibrating an LVDT, including the steps of: powering the LVDT; heating the LVDT to a desired temperature; measuring the position of the armature with respect to the armature orifice; and measuring the output voltage of the LVDT.

Spectral modification of seismic waves propagating through solids exhibiting a resonance frequency: a 1-D coupled wave propagation-oscillation model

NASA Astrophysics Data System (ADS)

Frehner, Marcel; Schmalholz, Stefan M.; Podladchikov, Yuri

2009-02-01

A 1-D model is presented that couples the microscale oscillations of non-wetting fluid blobs in a partially saturated poroelastic medium with the macroscale wave propagation through the elastic skeleton. The fluid oscillations are caused by surface tension forces that act as the restoring forces driving the oscillations. The oscillations are described mathematically with the equation for a linear oscillator and the wave propagation is described with the 1-D elastic wave equation. Coupling is done using Hamilton's variational principle for continuous systems. The resulting linear system of two partial differential equations is solved numerically with explicit finite differences. Numerical simulations are used to analyse the effect of solids exhibiting internal oscillations, and consequently a resonance frequency, on seismic waves propagating through such media. The phase velocity dispersion relation shows a higher phase velocity in the high-frequency limit and a lower phase velocity in the low-frequency limit. At the resonance frequency a singularity in the dispersion relation occurs. Seismic waves can initiate oscillations of the fluid by transferring energy from solid to fluid at the resonance frequency. Due to this transfer, the spectral amplitude of the solid particle velocity decreases at the resonance frequency. After initiation, the oscillatory movement of the fluid continuously transfers energy at the resonance frequency back to the solid. Therefore, the spectral amplitude of the solid particle velocity is increased at the resonance frequency. Once initiated, fluid oscillations decrease in amplitude with increasing time. Consequently, the spectral peak of the solid particle velocity at the resonance frequency decreases with time.

Stable isotope ratios of carbon and nitrogen and mercury concentrations in 13 toothed whale species taken from the western Pacific Ocean off Japan.

PubMed

Endo, Tetsuya; Hisamichi, Yohsuke; Kimura, Osamu; Haraguchi, Koichi; Lavery, Shane; Dalebout, Merel L; Funahashi, Naoko; Baker, C Scott

2010-04-01

Stable isotope ratios of carbon (partial differential(13)C) and nitrogen (partial differential(15)N) and total mercury (T-Hg) concentrations were measured in red meat samples from 11 odontocete species (toothed whales, dolphins, and porpoises) sold in Japan (n = 96) and in muscle samples from stranded killer whales (n = 6) and melon-headed whales (n = 15), and the analytical data for these species were classified into three regions (northern, central, and southern Japan) depending on the locations in which they were caught or stranded. The partial differential(15)N in the samples from southern Japan tended to be lower than that in samples from the north, whereas both partial differential(13)C and T-Hg concentrations in samples from the south tended to higher than those in samples from northern Japan. Negative correlations were found between the partial differential(13)C and partial differential(15)N values and between the partial differential(15)N value and T-Hg concentrations in the combined samples all three regions (gamma= -0.238, n = 117, P < 0.01). The partial differential(13)C, partial differential(15)N, and T-Hg concentrations in the samples varied more by habitat than by species. Spatial variations in partial differential(13)C, partial differential(15)N, and T-Hg concentrations in the ocean may be the cause of these phenomena.

Toward lattice fractional vector calculus

NASA Astrophysics Data System (ADS)

Tarasov, Vasily E.

2014-09-01

An analog of fractional vector calculus for physical lattice models is suggested. We use an approach based on the models of three-dimensional lattices with long-range inter-particle interactions. The lattice analogs of fractional partial derivatives are represented by kernels of lattice long-range interactions, where the Fourier series transformations of these kernels have a power-law form with respect to wave vector components. In the continuum limit, these lattice partial derivatives give derivatives of non-integer order with respect to coordinates. In the three-dimensional description of the non-local continuum, the fractional differential operators have the form of fractional partial derivatives of the Riesz type. As examples of the applications of the suggested lattice fractional vector calculus, we give lattice models with long-range interactions for the fractional Maxwell equations of non-local continuous media and for the fractional generalization of the Mindlin and Aifantis continuum models of gradient elasticity.

miRNA Temporal Analyzer (mirnaTA): a bioinformatics tool for identifying differentially expressed microRNAs in temporal studies using normal quantile transformation.

PubMed

Cer, Regina Z; Herrera-Galeano, J Enrique; Anderson, Joseph J; Bishop-Lilly, Kimberly A; Mokashi, Vishwesh P

2014-01-01

Understanding the biological roles of microRNAs (miRNAs) is a an active area of research that has produced a surge of publications in PubMed, particularly in cancer research. Along with this increasing interest, many open-source bioinformatics tools to identify existing and/or discover novel miRNAs in next-generation sequencing (NGS) reads become available. While miRNA identification and discovery tools are significantly improved, the development of miRNA differential expression analysis tools, especially in temporal studies, remains substantially challenging. Further, the installation of currently available software is non-trivial and steps of testing with example datasets, trying with one's own dataset, and interpreting the results require notable expertise and time. Subsequently, there is a strong need for a tool that allows scientists to normalize raw data, perform statistical analyses, and provide intuitive results without having to invest significant efforts. We have developed miRNA Temporal Analyzer (mirnaTA), a bioinformatics package to identify differentially expressed miRNAs in temporal studies. mirnaTA is written in Perl and R (Version 2.13.0 or later) and can be run across multiple platforms, such as Linux, Mac and Windows. In the current version, mirnaTA requires users to provide a simple, tab-delimited, matrix file containing miRNA name and count data from a minimum of two to a maximum of 20 time points and three replicates. To recalibrate data and remove technical variability, raw data is normalized using Normal Quantile Transformation (NQT), and linear regression model is used to locate any miRNAs which are differentially expressed in a linear pattern. Subsequently, remaining miRNAs which do not fit a linear model are further analyzed in two different non-linear methods 1) cumulative distribution function (CDF) or 2) analysis of variances (ANOVA). After both linear and non-linear analyses are completed, statistically significant miRNAs (P < 0.05) are plotted as heat maps using hierarchical cluster analysis and Euclidean distance matrix computation methods. mirnaTA is an open-source, bioinformatics tool to aid scientists in identifying differentially expressed miRNAs which could be further mined for biological significance. It is expected to provide researchers with a means of interpreting raw data to statistical summaries in a fast and intuitive manner.

HAM2D: 2D Shearing Box Model

NASA Astrophysics Data System (ADS)

Gammie, Charles F.; Guan, Xiaoyue

2012-10-01

HAM solves non-relativistic hyperbolic partial differential equations in conservative form using high-resolution shock-capturing techniques. This version of HAM has been configured to solve the magnetohydrodynamic equations of motion in axisymmetry to evolve a shearing box model.

Numerical solution of a non-linear conservation law applicable to the interior dynamics of partially molten planets

NASA Astrophysics Data System (ADS)

Bower, Dan J.; Sanan, Patrick; Wolf, Aaron S.

2018-01-01

The energy balance of a partially molten rocky planet can be expressed as a non-linear diffusion equation using mixing length theory to quantify heat transport by both convection and mixing of the melt and solid phases. Crucially, in this formulation the effective or eddy diffusivity depends on the entropy gradient, ∂S / ∂r , as well as entropy itself. First we present a simplified model with semi-analytical solutions that highlights the large dynamic range of ∂S / ∂r -around 12 orders of magnitude-for physically-relevant parameters. It also elucidates the thermal structure of a magma ocean during the earliest stage of crystal formation. This motivates the development of a simple yet stable numerical scheme able to capture the large dynamic range of ∂S / ∂r and hence provide a flexible and robust method for time-integrating the energy equation. Using insight gained from the simplified model, we consider a full model, which includes energy fluxes associated with convection, mixing, gravitational separation, and conduction that all depend on the thermophysical properties of the melt and solid phases. This model is discretised and evolved by applying the finite volume method (FVM), allowing for extended precision calculations and using ∂S / ∂r as the solution variable. The FVM is well-suited to this problem since it is naturally energy conserving, flexible, and intuitive to incorporate arbitrary non-linear fluxes that rely on lookup data. Special attention is given to the numerically challenging scenario in which crystals first form in the centre of a magma ocean. The computational framework we devise is immediately applicable to modelling high melt fraction phenomena in Earth and planetary science research. Furthermore, it provides a template for solving similar non-linear diffusion equations that arise in other science and engineering disciplines, particularly for non-linear functional forms of the diffusion coefficient.

Bayesian analysis of non-linear differential equation models with application to a gut microbial ecosystem.

PubMed

Lawson, Daniel J; Holtrop, Grietje; Flint, Harry

2011-07-01

Process models specified by non-linear dynamic differential equations contain many parameters, which often must be inferred from a limited amount of data. We discuss a hierarchical Bayesian approach combining data from multiple related experiments in a meaningful way, which permits more powerful inference than treating each experiment as independent. The approach is illustrated with a simulation study and example data from experiments replicating the aspects of the human gut microbial ecosystem. A predictive model is obtained that contains prediction uncertainty caused by uncertainty in the parameters, and we extend the model to capture situations of interest that cannot easily be studied experimentally. Copyright © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Realization of preconditioned Lanczos and conjugate gradient algorithms on optical linear algebra processors.

PubMed

Ghosh, A

1988-08-01

Lanczos and conjugate gradient algorithms are important in computational linear algebra. In this paper, a parallel pipelined realization of these algorithms on a ring of optical linear algebra processors is described. The flow of data is designed to minimize the idle times of the optical multiprocessor and the redundancy of computations. The effects of optical round-off errors on the solutions obtained by the optical Lanczos and conjugate gradient algorithms are analyzed, and it is shown that optical preconditioning can improve the accuracy of these algorithms substantially. Algorithms for optical preconditioning and results of numerical experiments on solving linear systems of equations arising from partial differential equations are discussed. Since the Lanczos algorithm is used mostly with sparse matrices, a folded storage scheme to represent sparse matrices on spatial light modulators is also described.

Complex partial status epilepticus: a recurrent problem.

PubMed Central

Cockerell, O C; Walker, M C; Sander, J W; Shorvon, S D

1994-01-01

Twenty patients with complex partial status epilepticus were identified retrospectively from a specialist neurology hospital. Seventeen patients experienced recurrent episodes of complex partial status epilepticus, often occurring at regular intervals, usually over many years, and while being treated with effective anti-epileptic drugs. No unifying cause for the recurrences, and no common epilepsy aetiologies, were identified. In spite of the frequency of recurrence and length of history, none of the patients showed any marked evidence of cognitive or neurological deterioration. Complex partial status epilepticus is more common than is generally recognised, should be differentiated from other forms of non-convulsive status, and is often difficult to treat. PMID:8021671

Numerical simulation of the wave-induced non-linear bending moment of ships

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

Xia, J.; Wang, Z.; Gu, X.

1995-12-31

Ships traveling in moderate or rough seas may experience non-linear bending moments due to flare effect and slamming loads. The numerical simulation of the total wave-induced bending moment contributed from both the wave frequency component induced by wave forces and the high frequency whipping component induced by slamming actions is very important in predicting the responses and ensuring the safety of the ship in rough seas. The time simulation is also useful for the reliability analysis of ship girder strength. The present paper discusses four different methods of the numerical simulation of wave-induced non-linear vertical bending moment of ships recentlymore » developed in CSSRC, including the hydroelastic integral-differential method (HID), the hydroelastic differential analysis method (HDA), the combined seakeeping and structural forced vibration method (CSFV), and the modified CSFV method (MCSFV). Numerical predictions are compared with the experimental results obtained from the elastic ship model test of S-175 container ship in regular and irregular waves presented by Watanabe Ueno and Sawada (1989).« less

Self-organizing biochemical cycle in dynamic feedback with soil structure

NASA Astrophysics Data System (ADS)

Vasilyeva, Nadezda; Vladimirov, Artem; Smirnov, Alexander; Matveev, Sergey; Tyrtyshnikov, Evgeniy; Yudina, Anna; Milanovskiy, Evgeniy; Shein, Evgeniy

2016-04-01

In the present study we perform bifurcation analysis of a physically-based mathematical model of self-organized structures in soil (Vasilyeva et al., 2015). The state variables in this model included microbial biomass, two organic matter types, oxygen, carbon dioxide, water content and capillary pore size. According to our previous experimental studies, organic matter affinity to water is an important property affecting soil structure. Therefore, organic matter wettability was taken as principle distinction between organic matter types in this model. It considers general known biological feedbacks with soil physical properties formulated as a system of parabolic type non-linear partial differential equations with elements of discrete modeling for water and pore formation. The model shows complex behavior, involving emergence of temporal and spatial irregular auto-oscillations from initially homogeneous distributions. The energy of external impact on a system was defined by a constant oxygen level on the boundary. Non-linear as opposed to linear oxygen diffusion gives possibility of modeling anaerobic micro-zones formation (organic matter conservation mechanism). For the current study we also introduced population competition of three different types of microorganisms according to their mobility/feeding (diffusive, moving and fungal growth). The strongly non-linear system was solved and parameterized by time-optimized algorithm combining explicit and implicit (matrix form of Thomas algorithm) methods considering the time for execution of the evaluated time-step according to accuracy control. The integral flux of the CO2 state variable was used as a macroscopic parameter to describe system as a whole and validation was carried out on temperature series of moisture dependence for soil heterotrophic respiration data. Thus, soil heterotrophic respiration can be naturally modeled as an integral result of complex dynamics on microscale, arising from biological processes formulated as a sum of state variables products, with no need to introduce any saturation functions, such as Mikhaelis-Menten type kinetics, inside the model. Analyzed dynamic soil model is being further developed to describe soil structure formation and its effect on organic matter decomposition at macro-scale, to predict changes with external perturbations. To link micro- and macro-scales we additionally model soil particles aggregation process. The results from local biochemical soil organic matter cycle serve as inputs to aggregation process, while the output aggregate size distributions define physical properties in the soil profile, these in turn serve as dynamic parameters in local biochemical cycles. The additional formulation is a system of non-linear ordinary differential equations, including Smoluchowski-type equations for aggregation and reaction kinetics equations for coagulation/adsorption/adhesion processes. Vasilyeva N.A., Ingtem J.G., Silaev D.A. Nonlinear dynamical model of microbial growth in soil medium. Computational Mathematics and Modeling, vol. 49, p.31-44, 2015 (in Russian). English version is expected in corresponding vol.27, issue 2, 2016.

Multi-scale modeling of the CD8 immune response

NASA Astrophysics Data System (ADS)

Barbarroux, Loic; Michel, Philippe; Adimy, Mostafa; Crauste, Fabien

2016-06-01

During the primary CD8 T-Cell immune response to an intracellular pathogen, CD8 T-Cells undergo exponential proliferation and continuous differentiation, acquiring cytotoxic capabilities to address the infection and memorize the corresponding antigen. After cleaning the organism, the only CD8 T-Cells left are antigen-specific memory cells whose role is to respond stronger and faster in case they are presented this very same antigen again. That is how vaccines work: a small quantity of a weakened pathogen is introduced in the organism to trigger the primary response, generating corresponding memory cells in the process, giving the organism a way to defend himself in case it encounters the same pathogen again. To investigate this process, we propose a non linear, multi-scale mathematical model of the CD8 T-Cells immune response due to vaccination using a maturity structured partial differential equation. At the intracellular scale, the level of expression of key proteins is modeled by a delay differential equation system, which gives the speeds of maturation for each cell. The population of cells is modeled by a maturity structured equation whose speeds are given by the intracellular model. We focus here on building the model, as well as its asymptotic study. Finally, we display numerical simulations showing the model can reproduce the biological dynamics of the cell population for both the primary response and the secondary responses.

Multi-scale modeling of the CD8 immune response

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

Barbarroux, Loic, E-mail: loic.barbarroux@doctorant.ec-lyon.fr; Ecole Centrale de Lyon, 36 avenue Guy de Collongue, 69134 Ecully; Michel, Philippe, E-mail: philippe.michel@ec-lyon.fr

During the primary CD8 T-Cell immune response to an intracellular pathogen, CD8 T-Cells undergo exponential proliferation and continuous differentiation, acquiring cytotoxic capabilities to address the infection and memorize the corresponding antigen. After cleaning the organism, the only CD8 T-Cells left are antigen-specific memory cells whose role is to respond stronger and faster in case they are presented this very same antigen again. That is how vaccines work: a small quantity of a weakened pathogen is introduced in the organism to trigger the primary response, generating corresponding memory cells in the process, giving the organism a way to defend himself inmore » case it encounters the same pathogen again. To investigate this process, we propose a non linear, multi-scale mathematical model of the CD8 T-Cells immune response due to vaccination using a maturity structured partial differential equation. At the intracellular scale, the level of expression of key proteins is modeled by a delay differential equation system, which gives the speeds of maturation for each cell. The population of cells is modeled by a maturity structured equation whose speeds are given by the intracellular model. We focus here on building the model, as well as its asymptotic study. Finally, we display numerical simulations showing the model can reproduce the biological dynamics of the cell population for both the primary response and the secondary responses.« less

Low dose reconstruction algorithm for differential phase contrast imaging.

PubMed

Wang, Zhentian; Huang, Zhifeng; Zhang, Li; Chen, Zhiqiang; Kang, Kejun; Yin, Hongxia; Wang, Zhenchang; Marco, Stampanoni

2011-01-01

Differential phase contrast imaging computed tomography (DPCI-CT) is a novel x-ray inspection method to reconstruct the distribution of refraction index rather than the attenuation coefficient in weakly absorbing samples. In this paper, we propose an iterative reconstruction algorithm for DPCI-CT which benefits from the new compressed sensing theory. We first realize a differential algebraic reconstruction technique (DART) by discretizing the projection process of the differential phase contrast imaging into a linear partial derivative matrix. In this way the compressed sensing reconstruction problem of DPCI reconstruction can be transformed to a resolved problem in the transmission imaging CT. Our algorithm has the potential to reconstruct the refraction index distribution of the sample from highly undersampled projection data. Thus it can significantly reduce the dose and inspection time. The proposed algorithm has been validated by numerical simulations and actual experiments.

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.

Linear-stability theory of thermocapillary convection in a model of float-zone crystal growth

NASA Technical Reports Server (NTRS)

Neitzel, G. P.; Chang, K.-T.; Jankowski, D. F.; Mittelmann, H. D.

1992-01-01

Linear-stability theory has been applied to a basic state of thermocapillary convection in a model half-zone to determine values of the Marangoni number above which instability is guaranteed. The basic state must be determined numerically since the half-zone is of finite, O(1) aspect ratio with two-dimensional flow and temperature fields. This, in turn, means that the governing equations for disturbance quantities will remain partial differential equations. The disturbance equations are treated by a staggered-grid discretization scheme. Results are presented for a variety of parameters of interest in the problem, including both terrestrial and microgravity cases.

A semigroup approach to the strong ergodic theorem of the multistate stable population process.

PubMed

Inaba, H

1988-01-01

"In this paper we first formulate the dynamics of multistate stable population processes as a partial differential equation. Next, we rewrite this equation as an abstract differential equation in a Banach space, and solve it by using the theory of strongly continuous semigroups of bounded linear operators. Subsequently, we investigate the asymptotic behavior of this semigroup to show the strong ergodic theorem which states that there exists a stable distribution independent of the initial distribution. Finally, we introduce the dual problem in order to obtain a logical definition for the reproductive value and we discuss its applications." (SUMMARY IN FRE) excerpt

Analysis and synthesis of distributed-lumped-active networks by digital computer

NASA Technical Reports Server (NTRS)

1973-01-01

The use of digital computational techniques in the analysis and synthesis of DLA (distributed lumped active) networks is considered. This class of networks consists of three distinct types of elements, namely, distributed elements (modeled by partial differential equations), lumped elements (modeled by algebraic relations and ordinary differential equations), and active elements (modeled by algebraic relations). Such a characterization is applicable to a broad class of circuits, especially including those usually referred to as linear integrated circuits, since the fabrication techniques for such circuits readily produce elements which may be modeled as distributed, as well as the more conventional lumped and active ones.

Quantification and parametrization of non-linearity effects by higher-order sensitivity terms in scattered light differential optical absorption spectroscopy

NASA Astrophysics Data System (ADS)

Puķīte, Jānis; Wagner, Thomas

2016-05-01

We address the application of differential optical absorption spectroscopy (DOAS) of scattered light observations in the presence of strong absorbers (in particular ozone), for which the absorption optical depth is a non-linear function of the trace gas concentration. This is the case because Beer-Lambert law generally does not hold for scattered light measurements due to many light paths contributing to the measurement. While in many cases linear approximation can be made, for scenarios with strong absorptions non-linear effects cannot always be neglected. This is especially the case for observation geometries, for which the light contributing to the measurement is crossing the atmosphere under spatially well-separated paths differing strongly in length and location, like in limb geometry. In these cases, often full retrieval algorithms are applied to address the non-linearities, requiring iterative forward modelling of absorption spectra involving time-consuming wavelength-by-wavelength radiative transfer modelling. In this study, we propose to describe the non-linear effects by additional sensitivity parameters that can be used e.g. to build up a lookup table. Together with widely used box air mass factors (effective light paths) describing the linear response to the increase in the trace gas amount, the higher-order sensitivity parameters eliminate the need for repeating the radiative transfer modelling when modifying the absorption scenario even in the presence of a strong absorption background. While the higher-order absorption structures can be described as separate fit parameters in the spectral analysis (so-called DOAS fit), in practice their quantitative evaluation requires good measurement quality (typically better than that available from current measurements). Therefore, we introduce an iterative retrieval algorithm correcting for the higher-order absorption structures not yet considered in the DOAS fit as well as the absorption dependence on temperature and scattering processes.

Numerical simulation of Forchheimer flow to a partially penetrating well with a mixed-type boundary condition

NASA Astrophysics Data System (ADS)

Mathias, Simon A.; Wen, Zhang

2015-05-01

This article presents a numerical study to investigate the combined role of partial well penetration (PWP) and non-Darcy effects concerning the performance of groundwater production wells. A finite difference model is developed in MATLAB to solve the two-dimensional mixed-type boundary value problem associated with flow to a partially penetrating well within a cylindrical confined aquifer. Non-Darcy effects are incorporated using the Forchheimer equation. The model is verified by comparison to results from existing semi-analytical solutions concerning the same problem but assuming Darcy's law. A sensitivity analysis is presented to explore the problem of concern. For constant pressure production, Non-Darcy effects lead to a reduction in production rate, as compared to an equivalent problem solved using Darcy's law. For fully penetrating wells, this reduction in production rate becomes less significant with time. However, for partially penetrating wells, the reduction in production rate persists for much larger times. For constant production rate scenarios, the combined effect of PWP and non-Darcy flow takes the form of a constant additional drawdown term. An approximate solution for this loss term is obtained by performing linear regression on the modeling results.

Heat Source/Sink in a Magneto-Hydrodynamic Non-Newtonian Fluid Flow in a Porous Medium: Dual Solutions.

PubMed

Hayat, Tasawar; Awais, Muhammad; Imtiaz, Amna

2016-01-01

This communication deals with the properties of heat source/sink in a magneto-hydrodynamic flow of a non-Newtonian fluid immersed in a porous medium. Shrinking phenomenon along with the permeability of the wall is considered. Mathematical modelling is performed to convert the considered physical process into set of coupled nonlinear mathematical equations. Suitable transformations are invoked to convert the set of partial differential equations into nonlinear ordinary differential equations which are tackled numerically for the solution computations. It is noted that dual solutions for various physical parameters exist which are analyzed in detail.

Functional differentiability in time-dependent quantum mechanics.

PubMed

Penz, Markus; Ruggenthaler, Michael

2015-03-28

In this work, we investigate the functional differentiability of the time-dependent many-body wave function and of derived quantities with respect to time-dependent potentials. For properly chosen Banach spaces of potentials and wave functions, Fréchet differentiability is proven. From this follows an estimate for the difference of two solutions to the time-dependent Schrödinger equation that evolve under the influence of different potentials. Such results can be applied directly to the one-particle density and to bounded operators, and present a rigorous formulation of non-equilibrium linear-response theory where the usual Lehmann representation of the linear-response kernel is not valid. Further, the Fréchet differentiability of the wave function provides a new route towards proving basic properties of time-dependent density-functional theory.

An algorithm for solving the perturbed gas dynamic equations

NASA Technical Reports Server (NTRS)

Davis, Sanford

1993-01-01

The present application of a compact, higher-order central-difference approximation to the linearized Euler equations illustrates the multimodal character of these equations by means of computations for acoustic, vortical, and entropy waves. Such dissipationless central-difference methods are shown to propagate waves exhibiting excellent phase and amplitude resolution on the basis of relatively large time-steps; they can be applied to wave problems governed by systems of first-order partial differential equations.

Mixed, charge and heat noises in thermoelectric nanosystems

NASA Astrophysics Data System (ADS)

Crépieux, Adeline; Michelini, Fabienne

2015-01-01

Mixed, charge and heat current fluctuations as well as thermoelectric differential conductances are considered for non-interacting nanosystems connected to reservoirs. Using the Landauer-Büttiker formalism, we derive general expressions for these quantities and consider their possible relationships in the entire ranges of temperature, voltage and coupling to the environment or reservoirs. We introduce a dimensionless quantity given by the ratio between the product of mixed noises and the product of charge and heat noises, distinguishing between the auto-ratio defined in the same reservoir and the cross-ratio between distinct reservoirs. From the linear response regime to the high-voltage regime, we further specify the analytical expressions of differential conductances, noises and ratios of noises, and examine their behavior in two concrete nanosystems: a quantum point contact in an ohmic environment and a single energy level quantum dot connected to reservoirs. In the linear response regime, we find that these ratios are equal to each other and are simply related to the figure of merit. They can be expressed in terms of differential conductances with the help of the fluctuation-dissipation theorem. In the non-linear regime, these ratios radically distinguish between themselves as the auto-ratio remains bounded by one, while the cross-ratio exhibits rich and complex behaviors. In the quantum dot nanosystem, we moreover demonstrate that the thermoelectric efficiency can be expressed as a ratio of noises in the non-linear Schottky regime. In the intermediate voltage regime, the cross-ratio changes sign and diverges, which evidences a change of sign in the heat cross-noise.

Mixed, charge and heat noises in thermoelectric nanosystems.

PubMed

Crépieux, Adeline; Michelini, Fabienne

2015-01-14

Mixed, charge and heat current fluctuations as well as thermoelectric differential conductances are considered for non-interacting nanosystems connected to reservoirs. Using the Landauer-Büttiker formalism, we derive general expressions for these quantities and consider their possible relationships in the entire ranges of temperature, voltage and coupling to the environment or reservoirs. We introduce a dimensionless quantity given by the ratio between the product of mixed noises and the product of charge and heat noises, distinguishing between the auto-ratio defined in the same reservoir and the cross-ratio between distinct reservoirs. From the linear response regime to the high-voltage regime, we further specify the analytical expressions of differential conductances, noises and ratios of noises, and examine their behavior in two concrete nanosystems: a quantum point contact in an ohmic environment and a single energy level quantum dot connected to reservoirs. In the linear response regime, we find that these ratios are equal to each other and are simply related to the figure of merit. They can be expressed in terms of differential conductances with the help of the fluctuation-dissipation theorem. In the non-linear regime, these ratios radically distinguish between themselves as the auto-ratio remains bounded by one, while the cross-ratio exhibits rich and complex behaviors. In the quantum dot nanosystem, we moreover demonstrate that the thermoelectric efficiency can be expressed as a ratio of noises in the non-linear Schottky regime. In the intermediate voltage regime, the cross-ratio changes sign and diverges, which evidences a change of sign in the heat cross-noise.

Rheological Behavior of Entangled Polystyrene-Polyhedral Oligosilsesquioxane (POSS) Copolymer

DTIC Science & Technology

2006-08-24

analysis. The effects of the presence of tethered POSS cages on the glass transition were studied using differential scanning...studies mainly focused on the effect of the long chain branches (LCBs) on the linear and non- linear rheological properties. How spherical cage -like...apparent activation energy increasing with increasing iBuPOSS loading. Like linear polymeric coil branches, the iBuPOSS cage plays a negative effect on

Dynamic Towed Array Models and State Estimation for Underwater Target Tracking

DTIC Science & Technology

2013-09-01

adjusting the value of 2q impacts how much non-linear acceleration the model can handle. In [22] it is shown that the best value for 2q is generated...partial_brng_x1 = (-deltaY) / ((deltaY)^2 + (deltaX)^2); partial_brng_x3 = (deltaX) / ((deltaY)^2 + (deltaX)^2); H11 = partial_brng_x1; H13 ...freq_recHat]; H11 = -deltaY/Rng^2; H13 = deltaX/Rng^2; Mult = xhat(5)/Sound_Spd; T1 = Mult*deltaY/Rng^3; T2 = ((deltaVx)*(deltaY)-(deltaVy

Free Vibration Analysis of a Spinning Flexible DISK-SPINDLE System Supported by Ball Bearing and Flexible Shaft Using the Finite Element Method and Substructure Synthesis

NASA Astrophysics Data System (ADS)

JANG, G. H.; LEE, S. H.; JUNG, M. S.

2002-03-01

Free vibration of a spinning flexible disk-spindle system supported by ball bearing and flexible shaft is analyzed by using Hamilton's principle, FEM and substructure synthesis. The spinning disk is described by using the Kirchhoff plate theory and von Karman non-linear strain. The rotating spindle and stationary shaft are modelled by Rayleigh beam and Euler beam respectively. Using Hamilton's principle and including the rigid body translation and tilting motion, partial differential equations of motion of the spinning flexible disk and spindle are derived consistently to satisfy the geometric compatibility in the internal boundary between substructures. FEM is used to discretize the derived governing equations, and substructure synthesis is introduced to assemble each component of the disk-spindle-bearing-shaft system. The developed method is applied to the spindle system of a computer hard disk drive with three disks, and modal testing is performed to verify the simulation results. The simulation result agrees very well with the experimental one. This research investigates critical design parameters in an HDD spindle system, i.e., the non-linearity of a spinning disk and the flexibility and boundary condition of a stationary shaft, to predict the free vibration characteristics accurately. The proposed method may be effectively applied to predict the vibration characteristics of a spinning flexible disk-spindle system supported by ball bearing and flexible shaft in the various forms of computer storage device, i.e., FDD, CD, HDD and DVD.

A partial differential equation model and its reduction to an ordinary differential equation model for prostate tumor growth under intermittent hormone therapy.

PubMed

Tao, Youshan; Guo, Qian; Aihara, Kazuyuki

2014-10-01

Hormonal therapy with androgen suppression is a common treatment for advanced prostate tumors. The emergence of androgen-independent cells, however, leads to a tumor relapse under a condition of long-term androgen deprivation. Clinical trials suggest that intermittent androgen suppression (IAS) with alternating on- and off-treatment periods can delay the relapse when compared with continuous androgen suppression (CAS). In this paper, we propose a mathematical model for prostate tumor growth under IAS therapy. The model elucidates initial hormone sensitivity, an eventual relapse of a tumor under CAS therapy, and a delay of a relapse under IAS therapy, which are due to the coexistence of androgen-dependent cells, androgen-independent cells resulting from reversible changes by adaptation, and androgen-independent cells resulting from irreversible changes by genetic mutations. The model is formulated as a free boundary problem of partial differential equations that describe the evolution of populations of the abovementioned three types of cells during on-treatment periods and off-treatment periods. Moreover, the model can be transformed into a piecewise linear ordinary differential equation model by introducing three new volume variables, and the study of the resulting model may help to devise optimal IAS schedules.

Simultaneous source and attenuation reconstruction in SPECT using ballistic and single scattering data

NASA Astrophysics Data System (ADS)

Courdurier, M.; Monard, F.; Osses, A.; Romero, F.

2015-09-01

In medical single-photon emission computed tomography (SPECT) imaging, we seek to simultaneously obtain the internal radioactive sources and the attenuation map using not only ballistic measurements but also first-order scattering measurements and assuming a very specific scattering regime. The problem is modeled using the radiative transfer equation by means of an explicit non-linear operator that gives the ballistic and scattering measurements as a function of the radioactive source and attenuation distributions. First, by differentiating this non-linear operator we obtain a linearized inverse problem. Then, under regularity hypothesis for the source distribution and attenuation map and considering small attenuations, we rigorously prove that the linear operator is invertible and we compute its inverse explicitly. This allows proof of local uniqueness for the non-linear inverse problem. Finally, using the previous inversion result for the linear operator, we propose a new type of iterative algorithm for simultaneous source and attenuation recovery for SPECT based on the Neumann series and a Newton-Raphson algorithm.

A comparative entropy based analysis of Cu and Fe3O4/methanol Powell-Eyring nanofluid in solar thermal collectors subjected to thermal radiation, variable thermal conductivity and impact of different nanoparticles shape

NASA Astrophysics Data System (ADS)

Jamshed, Wasim; Aziz, Asim

2018-06-01

The efficiency of any nanofluid based thermal solar system depend on the thermophysical properties of the operating fluids, type and shape of nanoparticles, nanoparticles volumetric concentration in the base fluid and the geometry/length of the system in which fluid is flowing. The recent research in the field of thermal solar energy has been focused to increase the efficiency of solar thermal collector systems. In the present research a simplified mathematical model is studied for inclusion in the thermal solar systems with the aim to improve the overall efficiency of the system. The flow of Powell-Eyring nanofluid is induced by non-uniform stretching of porous horizontal surface with fluid occupying a space over the surface. The thermal conductivity of the nanofluid is to vary as a linear function of temperature and the thermal radiation is to travel a short distance in the optically thick nanofluid. Numerical scheme of Keller box is implemented on the system of nonlinear ordinary differential equations, which are resultant after application of similarity transformation to governing nonlinear partial differential equations. The impact of non dimensional physical parameters appearing in the system have been observed on velocity and temperature profiles along with the entropy of the system. The velocity gradient (skin friction coefficient) and the strength of convective heat exchange (Nusselt number) are also investigated.

A meta-analysis of cambium phenology and growth: linear and non-linear patterns in conifers of the northern hemisphere.

PubMed

Rossi, Sergio; Anfodillo, Tommaso; Cufar, Katarina; Cuny, Henri E; Deslauriers, Annie; Fonti, Patrick; Frank, David; Gricar, Jozica; Gruber, Andreas; King, Gregory M; Krause, Cornelia; Morin, Hubert; Oberhuber, Walter; Prislan, Peter; Rathgeber, Cyrille B K

2013-12-01

Ongoing global warming has been implicated in shifting phenological patterns such as the timing and duration of the growing season across a wide variety of ecosystems. Linear models are routinely used to extrapolate these observed shifts in phenology into the future and to estimate changes in associated ecosystem properties such as net primary productivity. Yet, in nature, linear relationships may be special cases. Biological processes frequently follow more complex, non-linear patterns according to limiting factors that generate shifts and discontinuities, or contain thresholds beyond which responses change abruptly. This study investigates to what extent cambium phenology is associated with xylem growth and differentiation across conifer species of the northern hemisphere. Xylem cell production is compared with the periods of cambial activity and cell differentiation assessed on a weekly time scale on histological sections of cambium and wood tissue collected from the stems of nine species in Canada and Europe over 1-9 years per site from 1998 to 2011. The dynamics of xylogenesis were surprisingly homogeneous among conifer species, although dispersions from the average were obviously observed. Within the range analysed, the relationships between the phenological timings were linear, with several slopes showing values close to or not statistically different from 1. The relationships between the phenological timings and cell production were distinctly non-linear, and involved an exponential pattern. The trees adjust their phenological timings according to linear patterns. Thus, shifts of one phenological phase are associated with synchronous and comparable shifts of the successive phases. However, small increases in the duration of xylogenesis could correspond to a substantial increase in cell production. The findings suggest that the length of the growing season and the resulting amount of growth could respond differently to changes in environmental conditions.

Data-driven discovery of partial differential equations.

PubMed

Rudy, Samuel H; Brunton, Steven L; Proctor, Joshua L; Kutz, J Nathan

2017-04-01

We propose a sparse regression method capable of discovering the governing partial differential equation(s) of a given system by time series measurements in the spatial domain. The regression framework relies on sparsity-promoting techniques to select the nonlinear and partial derivative terms of the governing equations that most accurately represent the data, bypassing a combinatorially large search through all possible candidate models. The method balances model complexity and regression accuracy by selecting a parsimonious model via Pareto analysis. Time series measurements can be made in an Eulerian framework, where the sensors are fixed spatially, or in a Lagrangian framework, where the sensors move with the dynamics. The method is computationally efficient, robust, and demonstrated to work on a variety of canonical problems spanning a number of scientific domains including Navier-Stokes, the quantum harmonic oscillator, and the diffusion equation. Moreover, the method is capable of disambiguating between potentially nonunique dynamical terms by using multiple time series taken with different initial data. Thus, for a traveling wave, the method can distinguish between a linear wave equation and the Korteweg-de Vries equation, for instance. The method provides a promising new technique for discovering governing equations and physical laws in parameterized spatiotemporal systems, where first-principles derivations are intractable.

A scalable variational inequality approach for flow through porous media models with pressure-dependent viscosity

NASA Astrophysics Data System (ADS)

Mapakshi, N. K.; Chang, J.; Nakshatrala, K. B.

2018-04-01

Mathematical models for flow through porous media typically enjoy the so-called maximum principles, which place bounds on the pressure field. It is highly desirable to preserve these bounds on the pressure field in predictive numerical simulations, that is, one needs to satisfy discrete maximum principles (DMP). Unfortunately, many of the existing formulations for flow through porous media models do not satisfy DMP. This paper presents a robust, scalable numerical formulation based on variational inequalities (VI), to model non-linear flows through heterogeneous, anisotropic porous media without violating DMP. VI is an optimization technique that places bounds on the numerical solutions of partial differential equations. To crystallize the ideas, a modification to Darcy equations by taking into account pressure-dependent viscosity will be discretized using the lowest-order Raviart-Thomas (RT0) and Variational Multi-scale (VMS) finite element formulations. It will be shown that these formulations violate DMP, and, in fact, these violations increase with an increase in anisotropy. It will be shown that the proposed VI-based formulation provides a viable route to enforce DMP. Moreover, it will be shown that the proposed formulation is scalable, and can work with any numerical discretization and weak form. A series of numerical benchmark problems are solved to demonstrate the effects of heterogeneity, anisotropy and non-linearity on DMP violations under the two chosen formulations (RT0 and VMS), and that of non-linearity on solver convergence for the proposed VI-based formulation. Parallel scalability on modern computational platforms will be illustrated through strong-scaling studies, which will prove the efficiency of the proposed formulation in a parallel setting. Algorithmic scalability as the problem size is scaled up will be demonstrated through novel static-scaling studies. The performed static-scaling studies can serve as a guide for users to be able to select an appropriate discretization for a given problem size.

Polyhydroxyester films obtained by non-catalyzed melt-polycondensation of natural occurring fatty polyhydroxyacids.

NASA Astrophysics Data System (ADS)

Benitez, Jose; Heredia-Guerrero, José; Guzman-Puyol, Susana; Barthel, Markus; Dominguez, Eva; Heredia, Antonio

2015-08-01

Free-standing polyesters films from mono and polyhydroxylated fatty acids (C16 and C18) have been obtained by non-catalyzed melt-condensation polymerization in air at 150°C. Chemical characterization by Fourier Transform Infrared Spectroscopy (FTIR) and 13C Magic Angle Spinning Nuclear Magnetic Resonance (13C MAS-NMR) has confirmed the formation of the corresponding esters and the occurrence of hydroxyl partial oxidation which extent depends on the type of hydroxylation of the monomer (primary or secondary). Generally, polyester films obtained are hydrophobic, insoluble in common solvents, amorphous and infusible as revealed by X-ray Diffraction (XRD) and Differential Scanning Calorimetry (DSC). In ?-polyhydroxy acids, esterification reaction with primary hydroxyls is preferential and, therefore, the structure can be defined as linear with variable branching depending on the amount of esterified secondary hydroxyls. The occurrence side oxidative reactions like the diol cleavage are responsible for chain cross-linking. Films are thermally stable up to 200-250°C though this limit can be extended up to 300°C in the absence of ester bonds involving secondary hydroxyls. By analogy with natural occurring fatty polyesters (i.e. cutin in higher plants) these polymers are proposed as biodegradable and non-toxic barrier films or coatings to be used, for instance, in food packing

Variational Theory of Motion of Curved, Twisted and Extensible Elastic Rods

DTIC Science & Technology

1993-01-18

nonlinear theory such as questions of existence of solutions and global behavior have been carried out by Antman (1976). His basic work entitled "The...Aerosp. Ens. Q017/018 16 REFERENCES Antman , S.S., "Ordinary Differential Equations of Non-Linear ElastIcity 1: Foundatious of the Theories of Non-Linearly...Elutic rods and Shells," A.R.M.A. 61 (1976), 307-351. Antman , S.S., "The Theory of Rods", Handbuch der Physik, Vol. Vla/2, Springer-Verlq, Berlin

Fourier Series and Elliptic Functions

ERIC Educational Resources Information Center

Fay, Temple H.

2003-01-01

Non-linear second-order differential equations whose solutions are the elliptic functions "sn"("t, k"), "cn"("t, k") and "dn"("t, k") are investigated. Using "Mathematica", high precision numerical solutions are generated. From these data, Fourier coefficients are determined yielding approximate formulas for these non-elementary functions that are…

A non-linear dimension reduction methodology for generating data-driven stochastic input models

NASA Astrophysics Data System (ADS)

Ganapathysubramanian, Baskar; Zabaras, Nicholas

2008-06-01

Stochastic analysis of random heterogeneous media (polycrystalline materials, porous media, functionally graded materials) provides information of significance only if realistic input models of the topology and property variations are used. This paper proposes a framework to construct such input stochastic models for the topology and thermal diffusivity variations in heterogeneous media using a data-driven strategy. Given a set of microstructure realizations (input samples) generated from given statistical information about the medium topology, the framework constructs a reduced-order stochastic representation of the thermal diffusivity. This problem of constructing a low-dimensional stochastic representation of property variations is analogous to the problem of manifold learning and parametric fitting of hyper-surfaces encountered in image processing and psychology. Denote by M the set of microstructures that satisfy the given experimental statistics. A non-linear dimension reduction strategy is utilized to map M to a low-dimensional region, A. We first show that M is a compact manifold embedded in a high-dimensional input space Rn. An isometric mapping F from M to a low-dimensional, compact, connected set A⊂Rd(d≪n) is constructed. Given only a finite set of samples of the data, the methodology uses arguments from graph theory and differential geometry to construct the isometric transformation F:M→A. Asymptotic convergence of the representation of M by A is shown. This mapping F serves as an accurate, low-dimensional, data-driven representation of the property variations. The reduced-order model of the material topology and thermal diffusivity variations is subsequently used as an input in the solution of stochastic partial differential equations that describe the evolution of dependant variables. A sparse grid collocation strategy (Smolyak algorithm) is utilized to solve these stochastic equations efficiently. We showcase the methodology by constructing low-dimensional input stochastic models to represent thermal diffusivity in two-phase microstructures. This model is used in analyzing the effect of topological variations of two-phase microstructures on the evolution of temperature in heat conduction processes.

An Obstruction to the Integrability of a Class of Non-linear Wave Equations by 1-Stable Cartan Characteristics

NASA Astrophysics Data System (ADS)

Fackerell, E. D.; Hartley, D.; Tucker, R. W.

We examine in detail the Cauchy problem for a class of non-linear hyperbolic equations in two independent variables. This class is motivated by the analysis of the dynamics of a line of non-linearly coupled particles by Fermi, Pasta, and Ulam and extends the recent investigation of this problem by Gardner and Kamran. We find conditions for the existence of a 1-stable Cartan characteristic of a Pfaffian exterior differential system whose integral curves provide a solution to the Cauchy problem. The same obstruction to involution is exposed in Darboux's method of integration and the two approaches are compared. A class of particular solutions to the obstruction is constructed.

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.

Spontaneous collective synchronization in the Kuramoto model with additional non-local interactions

NASA Astrophysics Data System (ADS)

Gupta, Shamik

2017-10-01

In the context of the celebrated Kuramoto model of globally-coupled phase oscillators of distributed natural frequencies, which serves as a paradigm to investigate spontaneous collective synchronization in many-body interacting systems, we report on a very rich phase diagram in presence of thermal noise and an additional non-local interaction on a one-dimensional periodic lattice. Remarkably, the phase diagram involves both equilibrium and non-equilibrium phase transitions. In two contrasting limits of the dynamics, we obtain exact analytical results for the phase transitions. These two limits correspond to (i) the absence of thermal noise, when the dynamics reduces to that of a non-linear dynamical system, and (ii) the oscillators having the same natural frequency, when the dynamics becomes that of a statistical system in contact with a heat bath and relaxing to a statistical equilibrium state. In the former case, our exact analysis is based on the use of the so-called Ott-Antonsen ansatz to derive a reduced set of nonlinear partial differential equations for the macroscopic evolution of the system. Our results for the case of statistical equilibrium are on the other hand obtained by extending the well-known transfer matrix approach for nearest-neighbor Ising model to consider non-local interactions. The work offers a case study of exact analysis in many-body interacting systems. The results obtained underline the crucial role of additional non-local interactions in either destroying or enhancing the possibility of observing synchrony in mean-field systems exhibiting spontaneous synchronization.

Application of differential transformation method for solving dengue transmission mathematical model

NASA Astrophysics Data System (ADS)

Ndii, Meksianis Z.; Anggriani, Nursanti; Supriatna, Asep K.

2018-03-01

The differential transformation method (DTM) is a semi-analytical numerical technique which depends on Taylor series and has application in many areas including Biomathematics. The aim of this paper is to employ the differential transformation method (DTM) to solve system of non-linear differential equations for dengue transmission mathematical model. Analytical and numerical solutions are determined and the results are compared to that of Runge-Kutta method. We found a good agreement between DTM and Runge-Kutta method.

ELASTIC NET FOR COX’S PROPORTIONAL HAZARDS MODEL WITH A SOLUTION PATH ALGORITHM

PubMed Central

Wu, Yichao

2012-01-01

For least squares regression, Efron et al. (2004) proposed an efficient solution path algorithm, the least angle regression (LAR). They showed that a slight modification of the LAR leads to the whole LASSO solution path. Both the LAR and LASSO solution paths are piecewise linear. Recently Wu (2011) extended the LAR to generalized linear models and the quasi-likelihood method. In this work we extend the LAR further to handle Cox’s proportional hazards model. The goal is to develop a solution path algorithm for the elastic net penalty (Zou and Hastie (2005)) in Cox’s proportional hazards model. This goal is achieved in two steps. First we extend the LAR to optimizing the log partial likelihood plus a fixed small ridge term. Then we define a path modification, which leads to the solution path of the elastic net regularized log partial likelihood. Our solution path is exact and piecewise determined by ordinary differential equation systems. PMID:23226932

Chaotic Oscillations of Second Order Linear Hyperbolic Equations with Nonlinear Boundary Conditions: A Factorizable but Noncommutative Case

NASA Astrophysics Data System (ADS)

Li, Liangliang; Huang, Yu; Chen, Goong; Huang, Tingwen

If a second order linear hyperbolic partial differential equation in one-space dimension can be factorized as a product of two first order operators and if the two first order operators commute, with one boundary condition being the van der Pol type and the other being linear, one can establish the occurrence of chaos when the parameters enter a certain regime [Chen et al., 2014]. However, if the commutativity of the two first order operators fails to hold, then the treatment in [Chen et al., 2014] no longer works and significant new challenges arise in determining nonlinear boundary conditions that engenders chaos. In this paper, we show that by incorporating a linear memory effect, a nonlinear van der Pol boundary condition can cause chaotic oscillations when the parameter enters a certain regime. Numerical simulations illustrating chaotic oscillations are also presented.

CPDES3: A preconditioned conjugate gradient solver for linear asymmetric matrix equations arising from coupled partial differential equations in three dimensions

NASA Astrophysics Data System (ADS)

Anderson, D. V.; Koniges, A. E.; Shumaker, D. E.

1988-11-01

Many physical problems require the solution of coupled partial differential equations on three-dimensional domains. When the time scales of interest dictate an implicit discretization of the equations a rather complicated global matrix system needs solution. The exact form of the matrix depends on the choice of spatial grids and on the finite element or finite difference approximations employed. CPDES3 allows each spatial operator to have 7, 15, 19, or 27 point stencils and allows for general couplings between all of the component PDE's and it automatically generates the matrix structures needed to perform the algorithm. The resulting sparse matrix equation is solved by either the preconditioned conjugate gradient (CG) method or by the preconditioned biconjugate gradient (BCG) algorithm. An arbitrary number of component equations are permitted only limited by available memory. In the sub-band representation used, we generate an algorithm that is written compactly in terms of indirect induces which is vectorizable on some of the newer scientific computers.

CPDES2: A preconditioned conjugate gradient solver for linear asymmetric matrix equations arising from coupled partial differential equations in two dimensions

NASA Astrophysics Data System (ADS)

Anderson, D. V.; Koniges, A. E.; Shumaker, D. E.

1988-11-01

Many physical problems require the solution of coupled partial differential equations on two-dimensional domains. When the time scales of interest dictate an implicit discretization of the equations a rather complicated global matrix system needs solution. The exact form of the matrix depends on the choice of spatial grids and on the finite element or finite difference approximations employed. CPDES2 allows each spatial operator to have 5 or 9 point stencils and allows for general couplings between all of the component PDE's and it automatically generates the matrix structures needed to perform the algorithm. The resulting sparse matrix equation is solved by either the preconditioned conjugate gradient (CG) method or by the preconditioned biconjugate gradient (BCG) algorithm. An arbitrary number of component equations are permitted only limited by available memory. In the sub-band representation used, we generate an algorithm that is written compactly in terms of indirect indices which is vectorizable on some of the newer scientific computers.

Transformation elastodynamics and cloaking for flexural waves

NASA Astrophysics Data System (ADS)

Colquitt, D. J.; Brun, M.; Gei, M.; Movchan, A. B.; Movchan, N. V.; Jones, I. S.

2014-12-01

The paper addresses an important issue of cloaking transformations for fourth-order partial differential equations representing flexural waves in thin elastic plates. It is shown that, in contrast with the Helmholtz equation, the general form of the partial differential equation is not invariant with respect to the cloaking transformation. The significant result of this paper is the analysis of the transformed equation and its interpretation in the framework of the linear theory of pre-stressed plates. The paper provides a formal framework for transformation elastodynamics as applied to elastic plates. Furthermore, an algorithm is proposed for designing a broadband square cloak for flexural waves, which employs a regularised push-out transformation. Illustrative numerical examples show high accuracy and efficiency of the proposed cloaking algorithm. In particular, a physical configuration involving a perturbation of an interference pattern generated by two coherent sources is presented. It is demonstrated that the perturbation produced by a cloaked defect is negligibly small even for such a delicate interference pattern.

A multi-domain spectral method for time-fractional differential equations

NASA Astrophysics Data System (ADS)

Chen, Feng; Xu, Qinwu; Hesthaven, Jan S.

2015-07-01

This paper proposes an approach for high-order time integration within a multi-domain setting for time-fractional differential equations. Since the kernel is singular or nearly singular, two main difficulties arise after the domain decomposition: how to properly account for the history/memory part and how to perform the integration accurately. To address these issues, we propose a novel hybrid approach for the numerical integration based on the combination of three-term-recurrence relations of Jacobi polynomials and high-order Gauss quadrature. The different approximations used in the hybrid approach are justified theoretically and through numerical examples. Based on this, we propose a new multi-domain spectral method for high-order accurate time integrations and study its stability properties by identifying the method as a generalized linear method. Numerical experiments confirm hp-convergence for both time-fractional differential equations and time-fractional partial differential equations.

Solutions to an advanced functional partial differential equation of the pantograph type

PubMed Central

Zaidi, Ali A.; Van Brunt, B.; Wake, G. C.

2015-01-01

A model for cells structured by size undergoing growth and division leads to an initial boundary value problem that involves a first-order linear partial differential equation with a functional term. Here, size can be interpreted as DNA content or mass. It has been observed experimentally and shown analytically that solutions for arbitrary initial cell distributions are asymptotic as time goes to infinity to a certain solution called the steady size distribution. The full solution to the problem for arbitrary initial distributions, however, is elusive owing to the presence of the functional term and the paucity of solution techniques for such problems. In this paper, we derive a solution to the problem for arbitrary initial cell distributions. The method employed exploits the hyperbolic character of the underlying differential operator, and the advanced nature of the functional argument to reduce the problem to a sequence of simple Cauchy problems. The existence of solutions for arbitrary initial distributions is established along with uniqueness. The asymptotic relationship with the steady size distribution is established, and because the solution is known explicitly, higher-order terms in the asymptotics can be readily obtained. PMID:26345391

Solutions to an advanced functional partial differential equation of the pantograph type.

PubMed

Zaidi, Ali A; Van Brunt, B; Wake, G C

2015-07-08

A model for cells structured by size undergoing growth and division leads to an initial boundary value problem that involves a first-order linear partial differential equation with a functional term. Here, size can be interpreted as DNA content or mass. It has been observed experimentally and shown analytically that solutions for arbitrary initial cell distributions are asymptotic as time goes to infinity to a certain solution called the steady size distribution. The full solution to the problem for arbitrary initial distributions, however, is elusive owing to the presence of the functional term and the paucity of solution techniques for such problems. In this paper, we derive a solution to the problem for arbitrary initial cell distributions. The method employed exploits the hyperbolic character of the underlying differential operator, and the advanced nature of the functional argument to reduce the problem to a sequence of simple Cauchy problems. The existence of solutions for arbitrary initial distributions is established along with uniqueness. The asymptotic relationship with the steady size distribution is established, and because the solution is known explicitly, higher-order terms in the asymptotics can be readily obtained.

On the design of experiments for determining ternary mixture free energies from static light scattering data using a nonlinear partial differential equation

PubMed Central

Wahle, Chris W.; Ross, David S.; Thurston, George M.

2012-01-01

We mathematically design sets of static light scattering experiments to provide for model-independent measurements of ternary liquid mixing free energies to a desired level of accuracy. A parabolic partial differential equation (PDE), linearized from the full nonlinear PDE [D. Ross, G. Thurston, and C. Lutzer, J. Chem. Phys. 129, 064106 (2008)10.1063/1.2937902], describes how data noise affects the free energies to be inferred. The linearized PDE creates a net of spacelike characteristic curves and orthogonal, timelike curves in the composition triangle, and this net governs diffusion of information coming from light scattering measurements to the free energy. Free energy perturbations induced by a light scattering perturbation diffuse along the characteristic curves and towards their concave sides, with a diffusivity that is proportional to the local characteristic curvature radius. Consequently, static light scattering can determine mixing free energies in regions with convex characteristic curve boundaries, given suitable boundary data. The dielectric coefficient is a Lyapunov function for the dynamical system whose trajectories are PDE characteristics. Information diffusion is heterogeneous and system-dependent in the composition triangle, since the characteristics depend on molecular interactions and are tangent to liquid-liquid phase separation coexistence loci at critical points. We find scaling relations that link free energy accuracy, total measurement time, the number of samples, and the interpolation method, and identify the key quantitative tradeoffs between devoting time to measuring more samples, or fewer samples more accurately. For each total measurement time there are optimal sample numbers beyond which more will not improve free energy accuracy. We estimate the degree to which many-point interpolation and optimized measurement concentrations can improve accuracy and save time. For a modest light scattering setup, a sample calculation shows that less than two minutes of measurement time is, in principle, sufficient to determine the dimensionless mixing free energy of a non-associating ternary mixture to within an integrated error norm of 0.003. These findings establish a quantitative framework for designing light scattering experiments to determine the Gibbs free energy of ternary liquid mixtures. PMID:22830693

Optimal control of a coupled partial and ordinary differential equations system for the assimilation of polarimetry Stokes vector measurements in tokamak free-boundary equilibrium reconstruction with application to ITER

NASA Astrophysics Data System (ADS)

Faugeras, Blaise; Blum, Jacques; Heumann, Holger; Boulbe, Cédric

2017-08-01

The modelization of polarimetry Faraday rotation measurements commonly used in tokamak plasma equilibrium reconstruction codes is an approximation to the Stokes model. This approximation is not valid for the foreseen ITER scenarios where high current and electron density plasma regimes are expected. In this work a method enabling the consistent resolution of the inverse equilibrium reconstruction problem in the framework of non-linear free-boundary equilibrium coupled to the Stokes model equation for polarimetry is provided. Using optimal control theory we derive the optimality system for this inverse problem. A sequential quadratic programming (SQP) method is proposed for its numerical resolution. Numerical experiments with noisy synthetic measurements in the ITER tokamak configuration for two test cases, the second of which is an H-mode plasma, show that the method is efficient and that the accuracy of the identification of the unknown profile functions is improved compared to the use of classical Faraday measurements.

Final Report: Subcontract B623868 Algebraic Multigrid solvers for coupled PDE systems

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

Brannick, J.

The Pennsylvania State University (“Subcontractor”) continued to work on the design of algebraic multigrid solvers for coupled systems of partial differential equations (PDEs) arising in numerical modeling of various applications, with a main focus on solving the Dirac equation arising in Quantum Chromodynamics (QCD). The goal of the proposed work was to develop combined geometric and algebraic multilevel solvers that are robust and lend themselves to efficient implementation on massively parallel heterogeneous computers for these QCD systems. The research in these areas built on previous works, focusing on the following three topics: (1) the development of parallel full-multigrid (PFMG) andmore » non-Galerkin coarsening techniques in this frame work for solving the Wilson Dirac system; (2) the use of these same Wilson MG solvers for preconditioning the Overlap and Domain Wall formulations of the Dirac equation; and (3) the design and analysis of algebraic coarsening algorithms for coupled PDE systems including Stokes equation, Maxwell equation and linear elasticity.« less

On the complete and partial integrability of non-Hamiltonian systems

NASA Astrophysics Data System (ADS)

Bountis, T. C.; Ramani, A.; Grammaticos, B.; Dorizzi, B.

1984-11-01

The methods of singularity analysis are applied to several third order non-Hamiltonian systems of physical significance including the Lotka-Volterra equations, the three-wave interaction and the Rikitake dynamo model. Complete integrability is defined and new completely integrable systems are discovered by means of the Painlevé property. In all these cases we obtain integrals, which reduce the equations either to a final quadrature or to an irreducible second order ordinary differential equation (ODE) solved by Painlevé transcendents. Relaxing the Painlevé property we find many partially integrable cases whose movable singularities are poles at leading order, with In( t- t0) terms entering at higher orders. In an Nth order, generalized Rössler model a precise relation is established between the partial fulfillment of the Painlevé conditions and the existence of N - 2 integrals of the motion.

Parse Completion: A Study of an Inductive Domain

DTIC Science & Technology

1987-07-01

for Right Linear and Chomsky Normal Form grammars in detail. These two grammar classes were chosen as they can capture the classes of Regular and...Linear and Chomsky Normal Form grammars the allowed RHS formats could be divided into those which introduced new non-terminals and those which reused... Chomsky Normal Form grammars can both be shown to define a partial order over the set of grammars consistent with the examples. (Note that this is a

Stability of elastic bending and torsion of uniform cantilever rotor blades in hover with variable structural coupling

NASA Technical Reports Server (NTRS)

Hodges, D. H., Roberta.

1976-01-01

The stability of elastic flap bending, lead-lag bending, and torsion of uniform, untwisted, cantilever rotor blades without chordwise offsets between the elastic, mass, tension, and areodynamic center axes is investigated for the hovering flight condition. The equations of motion are obtained by simplifying the general, nonlinear, partial differential equations of motion of an elastic rotating cantilever blade. The equations are adapted for a linearized stability analysis in the hovering flight condition by prescribing aerodynamic forces, applying Galerkin's method, and linearizing the resulting ordinary differential equations about the equilibrium operating condition. The aerodynamic forces are obtained from strip theory based on a quasi-steady approximation of two-dimensional unsteady airfoil theory. Six coupled mode shapes, calculated from free vibration about the equilibrium operating condition, are used in the linearized stability analysis. The study emphasizes the effects of two types of structural coupling that strongly influence the stability of hingeless rotor blades. The first structural coupling is the linear coupling between flap and lead-lag bending of the rotor blade. The second structural coupling is a nonlinear coupling between flap bending, lead-lag bending, and torsion deflections. Results are obtained for a wide variety of hingeless rotor configurations and operating conditions in order to provide a reasonably complete picture of hingeless rotor blade stability characteristics.

Collective effect of personal behavior induced preventive measures and differential rate of transmission on spread of epidemics

NASA Astrophysics Data System (ADS)

Sagar, Vikram; Zhao, Yi

2017-02-01

In the present work, the effect of personal behavior induced preventive measures is studied on the spread of epidemics over scale free networks that are characterized by the differential rate of disease transmission. The role of personal behavior induced preventive measures is parameterized in terms of variable λ, which modulates the number of concurrent contacts a node makes with the fraction of its neighboring nodes. The dynamics of the disease is described by a non-linear Susceptible Infected Susceptible model based upon the discrete time Markov Chain method. The network mean field approach is generalized to account for the effect of non-linear coupling between the aforementioned factors on the collective dynamics of nodes. The upper bound estimates of the disease outbreak threshold obtained from the mean field theory are found to be in good agreement with the corresponding non-linear stochastic model. From the results of parametric study, it is shown that the epidemic size has inverse dependence on the preventive measures (λ). It has also been shown that the increase in the average degree of the nodes lowers the time of spread and enhances the size of epidemics.

Appraisal of jump distributions in ensemble-based sampling algorithms

NASA Astrophysics Data System (ADS)

Dejanic, Sanda; Scheidegger, Andreas; Rieckermann, Jörg; Albert, Carlo

2017-04-01

Sampling Bayesian posteriors of model parameters is often required for making model-based probabilistic predictions. For complex environmental models, standard Monte Carlo Markov Chain (MCMC) methods are often infeasible because they require too many sequential model runs. Therefore, we focused on ensemble methods that use many Markov chains in parallel, since they can be run on modern cluster architectures. Little is known about how to choose the best performing sampler, for a given application. A poor choice can lead to an inappropriate representation of posterior knowledge. We assessed two different jump moves, the stretch and the differential evolution move, underlying, respectively, the software packages EMCEE and DREAM, which are popular in different scientific communities. For the assessment, we used analytical posteriors with features as they often occur in real posteriors, namely high dimensionality, strong non-linear correlations or multimodality. For posteriors with non-linear features, standard convergence diagnostics based on sample means can be insufficient. Therefore, we resorted to an entropy-based convergence measure. We assessed the samplers by means of their convergence speed, robustness and effective sample sizes. For posteriors with strongly non-linear features, we found that the stretch move outperforms the differential evolution move, w.r.t. all three aspects.

Miscible gravitational instability of initially stable horizontal interface in a porous medium: Non-monotonic density profiles

NASA Astrophysics Data System (ADS)

Kim, Min Chan

2014-11-01

To simulate a CO2 sequestration process, some researchers employed a water/propylene glycol (PPG) system which shows a non-monotonic density profile. Motivated by this fact, the stability of the diffusion layer of two miscible fluids saturated in a porous medium is analyzed. For a non-monotonic density profile system, linear stability equations are derived in a global domain, and then transformed into a system of ordinary differential equations in an infinite domain. Initial growth rate analysis is conducted without the quasi-steady state approximation (QSSA) and shows that initially the system is unconditionally stable for the least stable disturbance. For the time evolving case, the ordinary differential equations are solved applying the eigen-analysis and numerical shooting scheme with and without the QSSA. To support these theoretical results, direct numerical simulations are conducted using the Fourier spectral method. The results of theoretical linear stability analyses and numerical simulations validate one another. The present linear and nonlinear analyses show that the water/PPG system is more unstable than the CO2/brine one, and the flow characteristics of these two systems are quite different from each other.

Enceladus's crust as a non-uniform thin shell: I tidal deformations

NASA Astrophysics Data System (ADS)

Beuthe, Mikael

2018-03-01

The geologic activity at Enceladus's south pole remains unexplained, though tidal deformations are probably the ultimate cause. Recent gravity and libration data indicate that Enceladus's icy crust floats on a global ocean, is rather thin, and has a strongly non-uniform thickness. Tidal effects are enhanced by crustal thinning at the south pole, so that realistic models of tidal tectonics and dissipation should take into account the lateral variations of shell structure. I construct here the theory of non-uniform viscoelastic thin shells, allowing for depth-dependent rheology and large lateral variations of shell thickness and rheology. Coupling to tides yields two 2D linear partial differential equations of the fourth order on the sphere which take into account self-gravity, density stratification below the shell, and core viscoelasticity. If the shell is laterally uniform, the solution agrees with analytical formulas for tidal Love numbers; errors on displacements and stresses are less than 5% and 15%, respectively, if the thickness is less than 10% of the radius. If the shell is non-uniform, the tidal thin shell equations are solved as a system of coupled linear equations in a spherical harmonic basis. Compared to finite element models, thin shell predictions are similar for the deformations due to Enceladus's pressurized ocean, but differ for the tides of Ganymede. If Enceladus's shell is conductive with isostatic thickness variations, surface stresses are approximately inversely proportional to the local shell thickness. The radial tide is only moderately enhanced at the south pole. The combination of crustal thinning and convection below the poles can amplify south polar stresses by a factor of 10, but it cannot explain the apparent time lag between the maximum plume brightness and the opening of tiger stripes. In a second paper, I will study the impact of a non-uniform crust on tidal dissipation.

Differentiating fatty and non-fatty tissue using photoacoustic imaging

NASA Astrophysics Data System (ADS)

Pan, Leo; Rohling, Robert; Abolmaesumi, Purang; Salcudean, Septimiu; Tang, Shuo

2014-03-01

In this paper, we demonstrate a temporal-domain intensity-based photoacoustic imaging method that can differentiate between fatty and non-fatty tissues. PA pressure intensity is partly dependent on the tissue's speed of sound, which increases as temperature increases in non-fatty tissue and decreases in fatty tissue. Therefore, by introducing a temperature change in the tissue and subsequently monitoring the change of the PA intensity, it is possible to distinguish between the two types of tissue. A commercial ultrasound system with a 128-element 5-14 MHz linear array transducer and a tunable ND:YAG laser were used to produce PA images. Ex-vivo bovine fat and porcine liver tissues were precooled to below 10°C and then warmed to room-temperature over ~1 hour period. A thermocouple monitored the temperature rise while PA images were acquired at 0.5°C intervals. The averaged intensity of the illuminated tissue region at each temperature interval was plotted and linearly fitted. Liver samples showed a mean increase of 2.82 %/°C, whereas bovine fat had a mean decrease of 6.24 %/°C. These results demonstrate that this method has the potential to perform tissue differentiation in the temporal-domain.

A counting-weighted calibration method for a field-programmable-gate-array-based time-to-digital converter

NASA Astrophysics Data System (ADS)

Chen, Yuan-Ho

2017-05-01

In this work, we propose a counting-weighted calibration method for field-programmable-gate-array (FPGA)-based time-to-digital converter (TDC) to provide non-linearity calibration for use in positron emission tomography (PET) scanners. To deal with the non-linearity in FPGA, we developed a counting-weighted delay line (CWD) to count the delay time of the delay cells in the TDC in order to reduce the differential non-linearity (DNL) values based on code density counts. The performance of the proposed CWD-TDC with regard to linearity far exceeds that of TDC with a traditional tapped delay line (TDL) architecture, without the need for nonlinearity calibration. When implemented in a Xilinx Vertix-5 FPGA device, the proposed CWD-TDC achieved time resolution of 60 ps with integral non-linearity (INL) and DNL of [-0.54, 0.24] and [-0.66, 0.65] least-significant-bit (LSB), respectively. This is a clear indication of the suitability of the proposed FPGA-based CWD-TDC for use in PET scanners.

Three-dimensional instabilities of natural convection between two differentially heated vertical plates: Linear and nonlinear complementary approaches

NASA Astrophysics Data System (ADS)

Gao, Zhenlan; Podvin, Berengere; Sergent, Anne; Xin, Shihe; Chergui, Jalel

2018-05-01

The transition to the chaos of the air flow between two vertical plates maintained at different temperatures is studied in the Boussinesq approximation. After the first bifurcation at critical Rayleigh number Rac, the flow consists of two-dimensional (2D) corotating rolls. The stability of the 2D rolls is examined, confronting linear predictions with nonlinear integration. In all cases the 2D rolls are destabilized in the spanwise direction. Efficient linear stability analysis based on an Arnoldi method shows competition between two eigenmodes, corresponding to different spanwise wavelengths and different types of roll distortion. Nonlinear integration shows that the lower-wave-number mode is always dominant. A partial route to chaos is established through the nonlinear simulations. The flow becomes temporally chaotic for Ra =1.05 Rac , but remains characterized by the spatial patterns identified by linear stability analysis. This highlights the complementary role of linear stability analysis and nonlinear simulation.

Aeroelastic loads prediction for an arrow wing. Task 3: Evaluation of the Boeing three-dimensional leading-edge vortex code

NASA Technical Reports Server (NTRS)

Manro, M. E.

1983-01-01

Two separated flow computer programs and a semiempirical method for incorporating the experimentally measured separated flow effects into a linear aeroelastic analysis were evaluated. The three dimensional leading edge vortex (LEV) code is evaluated. This code is an improved panel method for three dimensional inviscid flow over a wing with leading edge vortex separation. The governing equations are the linear flow differential equation with nonlinear boundary conditions. The solution is iterative; the position as well as the strength of the vortex is determined. Cases for both full and partial span vortices were executed. The predicted pressures are good and adequately reflect changes in configuration.

Numerical analysis for the fractional diffusion and fractional Buckmaster equation by the two-step Laplace Adam-Bashforth method

NASA Astrophysics Data System (ADS)

Jain, Sonal

2018-01-01

In this paper, we aim to use the alternative numerical scheme given by Gnitchogna and Atangana for solving partial differential equations with integer and non-integer differential operators. We applied this method to fractional diffusion model and fractional Buckmaster models with non-local fading memory. The method yields a powerful numerical algorithm for fractional order derivative to implement. Also we present in detail the stability analysis of the numerical method for solving the diffusion equation. This proof shows that this method is very stable and also converges very quickly to exact solution and finally some numerical simulation is presented.

Heat Source/Sink in a Magneto-Hydrodynamic Non-Newtonian Fluid Flow in a Porous Medium: Dual Solutions

PubMed Central

Hayat, Tasawar; Awais, Muhammad; Imtiaz, Amna

2016-01-01

This communication deals with the properties of heat source/sink in a magneto-hydrodynamic flow of a non-Newtonian fluid immersed in a porous medium. Shrinking phenomenon along with the permeability of the wall is considered. Mathematical modelling is performed to convert the considered physical process into set of coupled nonlinear mathematical equations. Suitable transformations are invoked to convert the set of partial differential equations into nonlinear ordinary differential equations which are tackled numerically for the solution computations. It is noted that dual solutions for various physical parameters exist which are analyzed in detail. PMID:27598314

Green functions and Langevin equations for nonlinear diffusion equations: A comment on ‘Markov processes, Hurst exponents, and nonlinear diffusion equations’ by Bassler et al.

NASA Astrophysics Data System (ADS)

Frank, T. D.

2008-02-01

We discuss two central claims made in the study by Bassler et al. [K.E. Bassler, G.H. Gunaratne, J.L. McCauley, Physica A 369 (2006) 343]. Bassler et al. claimed that Green functions and Langevin equations cannot be defined for nonlinear diffusion equations. In addition, they claimed that nonlinear diffusion equations are linear partial differential equations disguised as nonlinear ones. We review bottom-up and top-down approaches that have been used in the literature to derive Green functions for nonlinear diffusion equations and, in doing so, show that the first claim needs to be revised. We show that the second claim as well needs to be revised. To this end, we point out similarities and differences between non-autonomous linear Fokker-Planck equations and autonomous nonlinear Fokker-Planck equations. In this context, we raise the question whether Bassler et al.’s approach to financial markets is physically plausible because it necessitates the introduction of external traders and causes. Such external entities can easily be eliminated when taking self-organization principles and concepts of nonextensive thermostatistics into account and modeling financial processes by means of nonlinear Fokker-Planck equations.

Numerical solution of nonlinear partial differential equations of mixed type. [finite difference approximation

NASA Technical Reports Server (NTRS)

Jameson, A.

1976-01-01

A review is presented of some recently developed numerical methods for the solution of nonlinear equations of mixed type. The methods considered use finite difference approximations to the differential equation. Central difference formulas are employed in the subsonic zone and upwind difference formulas are used in the supersonic zone. The relaxation method for the small disturbance equation is discussed and a description is given of difference schemes for the potential flow equation in quasi-linear form. Attention is also given to difference schemes for the potential flow equation in conservation form, the analysis of relaxation schemes by the time dependent analogy, the accelerated iterative method, and three-dimensional calculations.

Darboux theorems and Wronskian formulas for integrable systems I. Constrained KP flows

NASA Astrophysics Data System (ADS)

Oevel, W.

1993-05-01

Generalizations of the classical Darboux theorem are established for pseudo-differential scattering operators of the form L = limit∑i=0N u i∂ i + limitΣi=1m Φ i∂ -1limitΨi†i. Iteration of the Darboux transformations leads to a gauge transformed operator with coefficients given by Wronskian formulas involving a set of eigenfunctions of L. Nonlinear integrable partial differential equations are associated with the scattering operator L which arise as a symmetry reduction of the multicomponent KP hierarchy. With a suitable linear time evolution for the eigenfunctions the Darboux transformation is used to obtain solutions of the integrable equations in terms of Wronskian determinants.

A new methodology for determination of macroscopic transport parameters in drying porous media

NASA Astrophysics Data System (ADS)

Attari Moghaddam, A.; Kharaghani, A.; Tsotsas, E.; Prat, M.

2015-12-01

Two main approaches have been used to model the drying process: The first approach considers the partially saturated porous medium as a continuum and partial differential equations are used to describe the mass, momentum and energy balances of the fluid phases. The continuum-scale models (CM) obtained by this approach involve constitutive laws which require effective material properties, such as the diffusivity, permeability, and thermal conductivity which are often determined by experiments. The second approach considers the material at the pore scale, where the void space is represented by a network of pores (PN). Micro- or nanofluidics models used in each pore give rise to a large system of ordinary differential equations with degrees of freedom at each node of the pore network. In this work, the moisture transport coefficient (D), the pseudo desorption isotherm inside the network and at the evaporative surface are estimated from the post-processing of the three-dimensional pore network drying simulations for fifteen realizations of the pore space geometry from a given probability distribution. A slice sampling method is used in order to extract these parameters from PN simulations. The moisture transport coefficient obtained in this way is shown in Fig. 1a. The minimum of average D values demonstrates the transition between liquid dominated moisture transport region and vapor dominated moisture transport region; a similar behavior has been observed in previous experimental findings. A function is fitted to the average D values and then is fed into the non-linear moisture diffusion equation. The saturation profiles obtained from PN and CM simulations are shown in Fig. 1b. Figure 1: (a) extracted moisture transport coefficient during drying for fifteen realizations of the pore network, (b) average moisture profiles during drying obtained from PN and CM simulations.

Numerical modeling of bubble dynamics in viscoelastic media with relaxation

NASA Astrophysics Data System (ADS)

Warnez, M. T.; Johnsen, E.

2015-06-01

Cavitation occurs in a variety of non-Newtonian fluids and viscoelastic materials. The large-amplitude volumetric oscillations of cavitation bubbles give rise to high temperatures and pressures at collapse, as well as induce large and rapid deformation of the surroundings. In this work, we develop a comprehensive numerical framework for spherical bubble dynamics in isotropic media obeying a wide range of viscoelastic constitutive relationships. Our numerical approach solves the compressible Keller-Miksis equation with full thermal effects (inside and outside the bubble) when coupled to a highly generalized constitutive relationship (which allows Newtonian, Kelvin-Voigt, Zener, linear Maxwell, upper-convected Maxwell, Jeffreys, Oldroyd-B, Giesekus, and Phan-Thien-Tanner models). For the latter two models, partial differential equations (PDEs) must be solved in the surrounding medium; for the remaining models, we show that the PDEs can be reduced to ordinary differential equations. To solve the general constitutive PDEs, we present a Chebyshev spectral collocation method, which is robust even for violent collapse. Combining this numerical approach with theoretical analysis, we simulate bubble dynamics in various viscoelastic media to determine the impact of relaxation time, a constitutive parameter, on the associated physics. Relaxation time is found to increase bubble growth and permit rebounds driven purely by residual stresses in the surroundings. Different regimes of oscillations occur depending on the relaxation time.

A numerical solution for a variable-order reaction-diffusion model by using fractional derivatives with non-local and non-singular kernel

NASA Astrophysics Data System (ADS)

Coronel-Escamilla, A.; Gómez-Aguilar, J. F.; Torres, L.; Escobar-Jiménez, R. F.

2018-02-01

A reaction-diffusion system can be represented by the Gray-Scott model. The reaction-diffusion dynamic is described by a pair of time and space dependent Partial Differential Equations (PDEs). In this paper, a generalization of the Gray-Scott model by using variable-order fractional differential equations is proposed. The variable-orders were set as smooth functions bounded in (0 , 1 ] and, specifically, the Liouville-Caputo and the Atangana-Baleanu-Caputo fractional derivatives were used to express the time differentiation. In order to find a numerical solution of the proposed model, the finite difference method together with the Adams method were applied. The simulations results showed the chaotic behavior of the proposed model when different variable-orders are applied.

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

Choi, Cheong R.

The structural changes of kinetic Alfvén solitary waves (KASWs) due to higher-order terms are investigated. While the first-order differential equation for KASWs provides the dispersion relation for kinetic Alfvén waves, the second-order differential equation describes the structural changes of the solitary waves due to higher-order nonlinearity. The reductive perturbation method is used to obtain the second-order and third-order partial differential equations; then, Kodama and Taniuti's technique [J. Phys. Soc. Jpn. 45, 298 (1978)] is applied in order to remove the secularities in the third-order differential equations and derive a linear second-order inhomogeneous differential equation. The solution to this new second-ordermore » equation indicates that, as the amplitude increases, the hump-type Korteweg-de Vries solution is concentrated more around the center position of the soliton and that dip-type structures form near the two edges of the soliton. This result has a close relationship with the interpretation of the complex KASW structures observed in space with satellites.« less

Reducing the duality gap in partially convex programming

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

Correa, R.

1994-12-31

We consider the non-linear minimization program {alpha} = min{sub z{element_of}D, x{element_of}C}{l_brace}f{sub 0}(z, x) : f{sub i}(z, x) {<=} 0, i {element_of} {l_brace}1, ..., m{r_brace}{r_brace} where f{sub i}(z, {center_dot}) are convex functions, C is convex and D is compact. Following Ben-Tal, Eiger and Gershowitz we prove the existence of a partial dual program whose optimum is arbitrarily close to {alpha}. The idea, corresponds to the branching principle in Branch and Bound methods. We describe such a kind of algorithm for obtaining the desired partial dual.

Burst and inter-burst duration statistics as empirical test of long-range memory in the financial markets

NASA Astrophysics Data System (ADS)

Gontis, V.; Kononovicius, A.

2017-10-01

We address the problem of long-range memory in the financial markets. There are two conceptually different ways to reproduce power-law decay of auto-correlation function: using fractional Brownian motion as well as non-linear stochastic differential equations. In this contribution we address this problem by analyzing empirical return and trading activity time series from the Forex. From the empirical time series we obtain probability density functions of burst and inter-burst duration. Our analysis reveals that the power-law exponents of the obtained probability density functions are close to 3 / 2, which is a characteristic feature of the one-dimensional stochastic processes. This is in a good agreement with earlier proposed model of absolute return based on the non-linear stochastic differential equations derived from the agent-based herding model.

The large discretization step method for time-dependent partial differential equations

NASA Technical Reports Server (NTRS)

Haras, Zigo; Taasan, Shlomo

1995-01-01

A new method for the acceleration of linear and nonlinear time dependent calculations is presented. It is based on the Large Discretization Step (LDS) approximation, defined in this work, which employs an extended system of low accuracy schemes to approximate a high accuracy discrete approximation to a time dependent differential operator. Error bounds on such approximations are derived. These approximations are efficiently implemented in the LDS methods for linear and nonlinear hyperbolic equations, presented here. In these algorithms the high and low accuracy schemes are interpreted as the same discretization of a time dependent operator on fine and coarse grids, respectively. Thus, a system of correction terms and corresponding equations are derived and solved on the coarse grid to yield the fine grid accuracy. These terms are initialized by visiting the fine grid once in many coarse grid time steps. The resulting methods are very general, simple to implement and may be used to accelerate many existing time marching schemes.

GPU computing with Kaczmarz’s and other iterative algorithms for linear systems

PubMed Central

Elble, Joseph M.; Sahinidis, Nikolaos V.; Vouzis, Panagiotis

2009-01-01

The graphics processing unit (GPU) is used to solve large linear systems derived from partial differential equations. The differential equations studied are strongly convection-dominated, of various sizes, and common to many fields, including computational fluid dynamics, heat transfer, and structural mechanics. The paper presents comparisons between GPU and CPU implementations of several well-known iterative methods, including Kaczmarz’s, Cimmino’s, component averaging, conjugate gradient normal residual (CGNR), symmetric successive overrelaxation-preconditioned conjugate gradient, and conjugate-gradient-accelerated component-averaged row projections (CARP-CG). Computations are preformed with dense as well as general banded systems. The results demonstrate that our GPU implementation outperforms CPU implementations of these algorithms, as well as previously studied parallel implementations on Linux clusters and shared memory systems. While the CGNR method had begun to fall out of favor for solving such problems, for the problems studied in this paper, the CGNR method implemented on the GPU performed better than the other methods, including a cluster implementation of the CARP-CG method. PMID:20526446

Teaching Modeling with Partial Differential Equations: Several Successful Approaches

ERIC Educational Resources Information Center

Myers, Joseph; Trubatch, David; Winkel, Brian

2008-01-01

We discuss the introduction and teaching of partial differential equations (heat and wave equations) via modeling physical phenomena, using a new approach that encompasses constructing difference equations and implementing these in a spreadsheet, numerically solving the partial differential equations using the numerical differential equation…

Partner symmetries and non-invariant solutions of four-dimensional heavenly equations

NASA Astrophysics Data System (ADS)

Malykh, A. A.; Nutku, Y.; Sheftel, M. B.

2004-07-01

We extend our method of partner symmetries to the hyperbolic complex Monge-Ampère equation and the second heavenly equation of Plebañski. We show the existence of partner symmetries and derive the relations between them. For certain simple choices of partner symmetries the resulting differential constraints together with the original heavenly equations are transformed to systems of linear equations by an appropriate Legendre transformation. The solutions of these linear equations are generically non-invariant. As a consequence we obtain explicitly new classes of heavenly metrics without Killing vectors.

Rotating Flow of Magnetite-Water Nanofluid over a Stretching Surface Inspired by Non-Linear Thermal Radiation.

PubMed

Mustafa, M; Mushtaq, A; Hayat, T; Alsaedi, A

2016-01-01

Present study explores the MHD three-dimensional rotating flow and heat transfer of ferrofluid induced by a radiative surface. The base fluid is considered as water with magnetite-Fe3O4 nanoparticles. Novel concept of non-linear radiative heat flux is considered which produces a non-linear energy equation in temperature field. Conventional transformations are employed to obtain the self-similar form of the governing differential system. The arising system involves an interesting temperature ratio parameter which is an indicator of small/large temperature differences in the flow. Numerical simulations with high precision are determined by well-known shooting approach. Both uniform stretching and rotation have significant impact on the solutions. The variation in velocity components with the nanoparticle volume fraction is non-monotonic. Local Nusselt number in Fe3O4-water ferrofluid is larger in comparison to the pure fluid even at low particle concentration.

Flat connections and nonlocal conserved quantities in irrational conformal field theory

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

Halpern, M.B.; Obers, N.A.

1995-03-01

Irrational conformal field theory (ICFT) includes rational conformal field theory as a small subspace, and the affine-Virasoro Ward identities describe the biconformal correlators of ICFT. The Ward identities are reformulated as an equivalent linear partial differential system with flat connections and new nonlocal conserved quantities. As examples of the formulation, the system of flat connections is solved for the coset correlators, the correlators of the affine-Sugawara nests, and the high-level [ital n]-point correlators of ICFT.

Numerical study of a matrix-free trust-region SQP method for equality constrained optimization.

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

Heinkenschloss, Matthias; Ridzal, Denis; Aguilo, Miguel Antonio

2011-12-01

This is a companion publication to the paper 'A Matrix-Free Trust-Region SQP Algorithm for Equality Constrained Optimization' [11]. In [11], we develop and analyze a trust-region sequential quadratic programming (SQP) method that supports the matrix-free (iterative, in-exact) solution of linear systems. In this report, we document the numerical behavior of the algorithm applied to a variety of equality constrained optimization problems, with constraints given by partial differential equations (PDEs).

Transactions of the Army Conference on Applied Mathematics and Computing (2nd) Held at Washington, DC on 22-25 May 1984

DTIC Science & Technology

1985-02-01

0 Here Q denotes the midplane of the plate ?assumed to be a Lipschitzian) with a smooth boundary ", and H (Q) and H (Q) are the Hilbert spaces of...using a reproducing kernel Hilbert space approach, Weinert [8,9] et al, developed a structural correspondence between spline interpolation and linear...597 A Mesh Moving Technique for Time Dependent Partial Differential Equations in Two Space Dimensions David C. Arney and Joseph

Singular growth shapes in turbulent field theories

NASA Astrophysics Data System (ADS)

Conrado, Claudine V.; Bohr, Tomas

1994-05-01

In this work we study deterministic, turbulent partial differential equations (the Kuramoto-Sivashinsky equation and generalizations) with initial conditions which are nonzero only in a small region. We demonstrate that the asymptotic state has a well-defined growth shape, which can be determined by the combination of nonlinear growth velocities, and front propagation governed by the linear instabilities. We show that the growth shapes are, in general, singular and that a new type of instability occurs when the growth shape becomes discontinuous.

Non-Darcian flow to a partially penetrating well in a confined aquifer with a finite-thickness skin

NASA Astrophysics Data System (ADS)

Feng, Qinggao; Wen, Zhang

2016-08-01

Non-Darcian flow to a partially penetrating well in a confined aquifer with a finite-thickness skin was investigated. The Izbash equation is used to describe the non-Darcian flow in the horizontal direction, and the vertical flow is described as Darcian. The solution for the newly developed non-Darcian flow model can be obtained by applying the linearization procedure in conjunction with the Laplace transform and the finite Fourier cosine transform. The flow model combines the effects of the non-Darcian flow, partial penetration of the well, and the finite thickness of the well skin. The results show that the depression cone spread is larger for the Darcian flow than for the non-Darcian flow. The drawdowns within the skin zone for a fully penetrating well are smaller than those for the partially penetrating well. The skin type and skin thickness have great impact on the drawdown in the skin zone, while they have little influence on drawdown in the formation zone. The sensitivity analysis indicates that the drawdown in the formation zone is sensitive to the power index ( n), the length of well screen ( w), the apparent radial hydraulic conductivity of the formation zone ( K r2), and the specific storage of the formation zone ( S s2) at early times, and it is very sensitive to the parameters n, w and K r2 at late times, especially to n, while it is not sensitive to the skin thickness ( r s).

Tumor necrosis factor-alpha antagonists: differential clinical effects by different biotechnological molecules.

PubMed

Licastro, F; Chiappelli, M; Ianni, M; Porcellini, E

2009-01-01

Inhibitors of tumor necrosis factor-alpha have deeply changed the therapy of several inflammatory human diseases. For instance, clinical management of rheumatoid arthritis, psoriatic arthritis and ankylosing spondylitis have profoundly benefited after the introduction of new therapeutic tools, such as antagonist of TNF-alpha molecule. These drugs include etanercept, a soluble TNF-alpha receptor antagonist, three anti-TNF-alpha antibodies, adalimumab, infliximab, golimumab and certolizumab a humanized Fab fragment combined with polyethylene glycol. These compounds efficiently inhibit several TNF-alpha biological-mediated effects, however, they have also shown differential clinical efficacy in several trials from different autoimmune diseases. It is of clinical relevance that non-responders to one of these drugs often positively responded to another. Different mechanisms of action and diversity in pharmacokinetics of these three compounds may partially explain different clinical effects. However, partially diverse pathogenetic mechanisms in different diseases also contribute to differential therapeutic responses. Therefore, these apparently homogeneous agents can not be considered equivalent in their clinically efficacy. Differential therapeutic actions of these drugs may be advantageously used in clinical practice and further improve the great potential of individual TNF-alpha inhibitors.

Multigrid Methods for Fully Implicit Oil Reservoir Simulation

NASA Technical Reports Server (NTRS)

Molenaar, J.

1996-01-01

In this paper we consider the simultaneous flow of oil and water in reservoir rock. This displacement process is modeled by two basic equations: the material balance or continuity equations and the equation of motion (Darcy's law). For the numerical solution of this system of nonlinear partial differential equations there are two approaches: the fully implicit or simultaneous solution method and the sequential solution method. In the sequential solution method the system of partial differential equations is manipulated to give an elliptic pressure equation and a hyperbolic (or parabolic) saturation equation. In the IMPES approach the pressure equation is first solved, using values for the saturation from the previous time level. Next the saturations are updated by some explicit time stepping method; this implies that the method is only conditionally stable. For the numerical solution of the linear, elliptic pressure equation multigrid methods have become an accepted technique. On the other hand, the fully implicit method is unconditionally stable, but it has the disadvantage that in every time step a large system of nonlinear algebraic equations has to be solved. The most time-consuming part of any fully implicit reservoir simulator is the solution of this large system of equations. Usually this is done by Newton's method. The resulting systems of linear equations are then either solved by a direct method or by some conjugate gradient type method. In this paper we consider the possibility of applying multigrid methods for the iterative solution of the systems of nonlinear equations. There are two ways of using multigrid for this job: either we use a nonlinear multigrid method or we use a linear multigrid method to deal with the linear systems that arise in Newton's method. So far only a few authors have reported on the use of multigrid methods for fully implicit simulations. Two-level FAS algorithm is presented for the black-oil equations, and linear multigrid for two-phase flow problems with strong heterogeneities and anisotropies is studied. Here we consider both possibilities. Moreover we present a novel way for constructing the coarse grid correction operator in linear multigrid algorithms. This approach has the advantage in that it preserves the sparsity pattern of the fine grid matrix and it can be extended to systems of equations in a straightforward manner. We compare the linear and nonlinear multigrid algorithms by means of a numerical experiment.

Viability and neural differentiation of mesenchymal stem cells derived from the umbilical cord following perinatal asphyxia.

PubMed

Aly, H; Mohsen, L; Badrawi, N; Gabr, H; Ali, Z; Akmal, D

2012-09-01

Hypoxia-ischemia is the leading cause of neurological handicaps in newborns worldwide. Mesenchymal stem cells (MSCs) collected from fresh cord blood of asphyxiated newborns have the potential to regenerate damaged neural tissues. The aim of this study was to examine the capacity for MSCs to differentiate into neural tissue that could subsequently be used for autologous transplantation. We collected cord blood samples from full-term newborns with perinatal hypoxemia (n=27), healthy newborns (n=14) and non-hypoxic premature neonates (n=14). Mononuclear cells were separated, counted, and then analyzed by flow cytometry to assess various stem cell populations. MSCs were isolated by plastic adherence and characterized by morphology. Cells underwent immunophenotyping and trilineage differentiation potential. They were then cultured in conditions favoring neural differentiation. Neural lineage commitment was detected using immunohistochemical staining for glial fibrillary acidic protein, tubulin III and oligodendrocyte marker O4 antibodies. Mononuclear cell count and viability did not differ among the three groups of infants. Neural differentiation was best demonstrated in the cells derived from hypoxia-ischemia term neonates, of which 69% had complete and 31% had partial neural differentiation. Cells derived from preterm neonates had the least amount of neural differentiation, whereas partial differentiation was observed in only 12%. These findings support the potential utilization of umbilical cord stem cells as a source for autologous transplant in asphyxiated neonates.

Data-driven discovery of partial differential equations

PubMed Central

Rudy, Samuel H.; Brunton, Steven L.; Proctor, Joshua L.; Kutz, J. Nathan

2017-01-01

We propose a sparse regression method capable of discovering the governing partial differential equation(s) of a given system by time series measurements in the spatial domain. The regression framework relies on sparsity-promoting techniques to select the nonlinear and partial derivative terms of the governing equations that most accurately represent the data, bypassing a combinatorially large search through all possible candidate models. The method balances model complexity and regression accuracy by selecting a parsimonious model via Pareto analysis. Time series measurements can be made in an Eulerian framework, where the sensors are fixed spatially, or in a Lagrangian framework, where the sensors move with the dynamics. The method is computationally efficient, robust, and demonstrated to work on a variety of canonical problems spanning a number of scientific domains including Navier-Stokes, the quantum harmonic oscillator, and the diffusion equation. Moreover, the method is capable of disambiguating between potentially nonunique dynamical terms by using multiple time series taken with different initial data. Thus, for a traveling wave, the method can distinguish between a linear wave equation and the Korteweg–de Vries equation, for instance. The method provides a promising new technique for discovering governing equations and physical laws in parameterized spatiotemporal systems, where first-principles derivations are intractable. PMID:28508044

The Laguerre finite difference one-way equation solver

NASA Astrophysics Data System (ADS)

Terekhov, Andrew V.

2017-05-01

This paper presents a new finite difference algorithm for solving the 2D one-way wave equation with a preliminary approximation of a pseudo-differential operator by a system of partial differential equations. As opposed to the existing approaches, the integral Laguerre transform instead of Fourier transform is used. After carrying out the approximation of spatial variables it is possible to obtain systems of linear algebraic equations with better computing properties and to reduce computer costs for their solution. High accuracy of calculations is attained at the expense of employing finite difference approximations of higher accuracy order that are based on the dispersion-relationship-preserving method and the Richardson extrapolation in the downward continuation direction. The numerical experiments have verified that as compared to the spectral difference method based on Fourier transform, the new algorithm allows one to calculate wave fields with a higher degree of accuracy and a lower level of numerical noise and artifacts including those for non-smooth velocity models. In the context of solving the geophysical problem the post-stack migration for velocity models of the types Syncline and Sigsbee2A has been carried out. It is shown that the images obtained contain lesser noise and are considerably better focused as compared to those obtained by the known Fourier Finite Difference and Phase-Shift Plus Interpolation methods. There is an opinion that purely finite difference approaches do not allow carrying out the seismic migration procedure with sufficient accuracy, however the results obtained disprove this statement. For the supercomputer implementation it is proposed to use the parallel dichotomy algorithm when solving systems of linear algebraic equations with block-tridiagonal matrices.

Measurement and characterization of slippage and slip-law using a rigorous analysis in dynamics of oscillating rheometer: Newtonian fluid

NASA Astrophysics Data System (ADS)

Azese, Martin Ndi

2018-02-01

This article presents a rigorous calculation involving velocity slip of Newtonian fluid where we analyze and solve the unsteady Navier-Stokes equation with emphasis on its rheological implication. The goal of which is to model a simple yet effective non-invasive way of quantifying and characterizing slippage. Indeed this contrasts with previous techniques that exhibit inherent limitations whereby injecting foreign objects usually alter the flow. This problem is built on the Couette rheological flow system such that μ-Newton force and μ-stress are captured and processed to obtain wall slip. Our model leads to a linear partial differential equation and upon enforcing linear-Navier slip boundary conditions (BC) yields inhomogeneous and unsteady "Robin-type" BC. A dimensional analysis reveals salient dimensionless parameters: Roshko, Strouhal, and Reynolds while highlighting slip-numbers from BC. We also solve the slip-free case to corroborate and validate our results. Several graphs are generated showing slip effects, particularly, studying how slip-numbers, a key input, differentiate themselves to the outputs. We also confirm this in a graphical fashion by presenting the flow profile across channel width, velocity, and stress at both walls. A perturbation scheme is introduced to calculate long-time behavior when the system seats for long. More importantly, in the end, we justify the existence of a reverse mechanism, where an inverse transformation like Fourier transform uses the output data to retrieve slip-numbers and slip law, thus quantifying and characterizing slip. Therefore, we not only substantiate our analysis, but we also justify our claim, measurement and characterization, and theorize realizability of our proposition.

Cortical pitch response components show differential sensitivity to native and nonnative pitch contours

PubMed Central

Krishnan, Ananthanarayan; Gandour, Jackson T.; Suresh, Chandan H.

2015-01-01

The aim of this study is to evaluate how nonspeech pitch contours of varying shape influence latency and amplitude of cortical pitch-specific response (CPR) components differentially as a function of language experience. Stimuli included time-varying, high rising Mandarin Tone 2 (T2) and linear rising ramp (Linear), and steady-state (Flat). Both the latency and magnitude of CPR components were differentially modulated by (i) the overall trajectory of pitch contours (time-varying vs. steady-state), (ii) their pitch acceleration rates (changing vs. constant), and (iii) their linguistic status (lexical vs. non-lexical). T2 elicited larger amplitude than Linear in both language groups, but size of the effect was larger in Chinese than English. The magnitude of CPR components elicited by T2 were larger for Chinese than English at the right temporal electrode site. Using the CPR, we provide evidence in support of experience-dependent modulation of dynamic pitch contours at an early stage of sensory processing. PMID:25306506

Wideband pulse amplifiers for the NECTAr chip

NASA Astrophysics Data System (ADS)

Sanuy, A.; Delagnes, E.; Gascon, D.; Sieiro, X.; Bolmont, J.; Corona, P.; Feinstein, F.; Glicenstein, J.-F.; Naumann, C. L.; Nayman, P.; Ribó, M.; Tavernet, J.-P.; Toussenel, F.; Vincent, P.; Vorobiov, S.

2012-12-01

The NECTAr collaboration's FE option for the camera of the CTA is a 16 bits and 1-3 GS/s sampling chip based on analog memories including most of the readout functions. This works describes the input amplifiers of the NECTAr ASIC. A fully differential wideband amplifier, with voltage gain up to 20 V/V and a BW of 400 MHz. As it is impossible to design a fully differential OpAmp with an 8 GHz GBW product in a 0.35 CMOS technology, an alternative implementation based on HF linearized transconductors is explored. The output buffer is a class AB miller operational amplifier, with special non-linear current boost.

Multiple imputation of covariates by fully conditional specification: Accommodating the substantive model

PubMed Central

Seaman, Shaun R; White, Ian R; Carpenter, James R

2015-01-01

Missing covariate data commonly occur in epidemiological and clinical research, and are often dealt with using multiple imputation. Imputation of partially observed covariates is complicated if the substantive model is non-linear (e.g. Cox proportional hazards model), or contains non-linear (e.g. squared) or interaction terms, and standard software implementations of multiple imputation may impute covariates from models that are incompatible with such substantive models. We show how imputation by fully conditional specification, a popular approach for performing multiple imputation, can be modified so that covariates are imputed from models which are compatible with the substantive model. We investigate through simulation the performance of this proposal, and compare it with existing approaches. Simulation results suggest our proposal gives consistent estimates for a range of common substantive models, including models which contain non-linear covariate effects or interactions, provided data are missing at random and the assumed imputation models are correctly specified and mutually compatible. Stata software implementing the approach is freely available. PMID:24525487

Computational analysis of non-Newtonian boundary layer flow of nanofluid past a semi-infinite vertical plate with partial slip

NASA Astrophysics Data System (ADS)

Amanulla, C. H.; Nagendra, N.; Suryanarayana Reddy, M.

2018-03-01

An analysis of this paper is examined, two-dimensional, laminar with heat and mass transfer of natural convective nanofluid flow past a semi-infinite vertical plate surface with velocity and thermal slip effects are studied theoretically. The coupled governing partial differential equations are transformed to ordinary differential equations by using non-similarity transformations. The obtained ordinary differential equations are solved numerically by a well-known method named as Keller Box Method (KBM). The influences of the emerging parameters i.e. Casson fluid parameter (β), Brownian motion parameter (Nb), thermophoresis parameter (Nt), Buoyancy ratio parameter (N), Lewis number (Le), Prandtl number (Pr), Velocity slip factor (Sf) and Thermal slip factor (ST) on velocity, temperature and nano-particle concentration distributions is illustrated graphically and interpreted at length. The major sources of nanoparticle migration in Nanofluids are Thermophoresis and Brownian motion. A suitable agreement with existing published literature is made and an excellent agreement is observed for the limiting case and also validation of solutions with a Nakamura tridiagonal method has been included. It is observed that nanoparticle concentrations on surface decreases with an increase in slip parameter. The study is relevant to enrobing processes for electric-conductive nano-materials, of potential use in aerospace and other industries.

The consentaneous model of the financial markets exhibiting spurious nature of long-range memory

NASA Astrophysics Data System (ADS)

Gontis, V.; Kononovicius, A.

2018-09-01

It is widely accepted that there is strong persistence in the volatility of financial time series. The origin of the observed persistence, or long-range memory, is still an open problem as the observed phenomenon could be a spurious effect. Earlier we have proposed the consentaneous model of the financial markets based on the non-linear stochastic differential equations. The consentaneous model successfully reproduces empirical probability and power spectral densities of volatility. This approach is qualitatively different from models built using fractional Brownian motion. In this contribution we investigate burst and inter-burst duration statistics of volatility in the financial markets employing the consentaneous model. Our analysis provides an evidence that empirical statistical properties of burst and inter-burst duration can be explained by non-linear stochastic differential equations driving the volatility in the financial markets. This serves as an strong argument that long-range memory in finance can have spurious nature.

Noise-induced modulation of the relaxation kinetics around a non-equilibrium steady state of non-linear chemical reaction networks.

PubMed

Ramaswamy, Rajesh; Sbalzarini, Ivo F; González-Segredo, Nélido

2011-01-28

Stochastic effects from correlated noise non-trivially modulate the kinetics of non-linear chemical reaction networks. This is especially important in systems where reactions are confined to small volumes and reactants are delivered in bursts. We characterise how the two noise sources confinement and burst modulate the relaxation kinetics of a non-linear reaction network around a non-equilibrium steady state. We find that the lifetimes of species change with burst input and confinement. Confinement increases the lifetimes of all species that are involved in any non-linear reaction as a reactant. Burst monotonically increases or decreases lifetimes. Competition between burst-induced and confinement-induced modulation may hence lead to a non-monotonic modulation. We quantify lifetime as the integral of the time autocorrelation function (ACF) of concentration fluctuations around a non-equilibrium steady state of the reaction network. Furthermore, we look at the first and second derivatives of the ACF, each of which is affected in opposite ways by burst and confinement. This allows discriminating between these two noise sources. We analytically derive the ACF from the linear Fokker-Planck approximation of the chemical master equation in order to establish a baseline for the burst-induced modulation at low confinement. Effects of higher confinement are then studied using a partial-propensity stochastic simulation algorithm. The results presented here may help understand the mechanisms that deviate stochastic kinetics from its deterministic counterpart. In addition, they may be instrumental when using fluorescence-lifetime imaging microscopy (FLIM) or fluorescence-correlation spectroscopy (FCS) to measure confinement and burst in systems with known reaction rates, or, alternatively, to correct for the effects of confinement and burst when experimentally measuring reaction rates.

A meta-analysis of cambium phenology and growth: linear and non-linear patterns in conifers of the northern hemisphere

PubMed Central

Rossi, Sergio; Anfodillo, Tommaso; Čufar, Katarina; Cuny, Henri E.; Deslauriers, Annie; Fonti, Patrick; Frank, David; Gričar, Jožica; Gruber, Andreas; King, Gregory M.; Krause, Cornelia; Morin, Hubert; Oberhuber, Walter; Prislan, Peter; Rathgeber, Cyrille B. K.

2013-01-01

Background and Aims Ongoing global warming has been implicated in shifting phenological patterns such as the timing and duration of the growing season across a wide variety of ecosystems. Linear models are routinely used to extrapolate these observed shifts in phenology into the future and to estimate changes in associated ecosystem properties such as net primary productivity. Yet, in nature, linear relationships may be special cases. Biological processes frequently follow more complex, non-linear patterns according to limiting factors that generate shifts and discontinuities, or contain thresholds beyond which responses change abruptly. This study investigates to what extent cambium phenology is associated with xylem growth and differentiation across conifer species of the northern hemisphere. Methods Xylem cell production is compared with the periods of cambial activity and cell differentiation assessed on a weekly time scale on histological sections of cambium and wood tissue collected from the stems of nine species in Canada and Europe over 1–9 years per site from 1998 to 2011. Key Results The dynamics of xylogenesis were surprisingly homogeneous among conifer species, although dispersions from the average were obviously observed. Within the range analysed, the relationships between the phenological timings were linear, with several slopes showing values close to or not statistically different from 1. The relationships between the phenological timings and cell production were distinctly non-linear, and involved an exponential pattern Conclusions The trees adjust their phenological timings according to linear patterns. Thus, shifts of one phenological phase are associated with synchronous and comparable shifts of the successive phases. However, small increases in the duration of xylogenesis could correspond to a substantial increase in cell production. The findings suggest that the length of the growing season and the resulting amount of growth could respond differently to changes in environmental conditions. PMID:24201138

Unification of the general non-linear sigma model and the Virasoro master equation

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

Boer, J. de; Halpern, M.B.

1997-06-01

The Virasoro master equation describes a large set of conformal field theories known as the affine-Virasoro constructions, in the operator algebra (affinie Lie algebra) of the WZW model, while the einstein equations of the general non-linear sigma model describe another large set of conformal field theories. This talk summarizes recent work which unifies these two sets of conformal field theories, together with a presumable large class of new conformal field theories. The basic idea is to consider spin-two operators of the form L{sub ij}{partial_derivative}x{sup i}{partial_derivative}x{sup j} in the background of a general sigma model. The requirement that these operators satisfymore » the Virasoro algebra leads to a set of equations called the unified Einstein-Virasoro master equation, in which the spin-two spacetime field L{sub ij} cuples to the usual spacetime fields of the sigma model. The one-loop form of this unified system is presented, and some of its algebraic and geometric properties are discussed.« less

A non-linear study of fluctuating fluid flow on MHD mixed convection through a vertical permeable plate

NASA Astrophysics Data System (ADS)

Babu, R. Suresh; Rushi Kumar, B.

2017-11-01

In this paper, an analytical solution for an unsteady (independent of time), MHD mixed convection, two-dimensional (x and y), laminar, viscous flow of an incompressible fluid through a vertical permeable plate in a porous medium was developed with these assumptions:(i) the suction velocity (which is normal to the plate)and the free stream velocity both fluctuate with respect to time with a fixed mean; (ii) the wall temperature is constant;(iii) difference between the temperature of the plate and the free stream is moderately large due to the free convection currents. Based on the physical configuration of the model, the governing equations are derived and are non-dimensionalize using dimensionless parameters. The resultant nonlinear partial differential equations are solved using double regular perturbation technique analytically. The results are computed numerically to understand the behaviour of the fluid (i.e., effects of MHD, viscosity, body force etc.) for various non-dimensional parameters involving like Grashof number Gr, Prandtl number Pr, Hartmann number M, Eckert number E, the Viscous ratio λ and so on for velocity and temperature. These results are found to be in good agreement with known results available in the literature in the absence of few physical parameters. The numerical values of the above said flow is discussed through graphs on velocity and temperature.

A numerical study of coarsening in the two-dimensional complex Ginzburg-Landau equation

NASA Astrophysics Data System (ADS)

Liu, Weigang; Tauber, Uwe

The complex Ginzburg-Landau equation with additive noise is a stochastic partial differential equation that describes a remarkably wide range of physical systems: coupled non-linear oscillators subject to external noise near a Hopf bifurcation instability; spontaneous structure formation in non-equilibrium systems, e.g., in cyclically competing populations; and driven-dissipative Bose-Einstein condensation, realized in open systems on the interface of quantum optics and many-body physics. We employ a finite-difference method to numerically solve the noisy complex Ginzburg-Landau equation on a two-dimensional domain with the goal to investigate the coarsening dynamics following a quench from a strongly fluctuating defect turbulence phase to a long-range ordered phase. We start from a simplified amplitude equation, solve it numerically, and then study the spatio-temporal behavior characterized by the spontaneous creation and annihilation of topological defects (spiral waves). We check our simulation results against the known dynamical phase diagram in this non-equilibrium system, tentatively analyze the coarsening kinetics following sudden quenches, and characterize the ensuing aging scaling behavior. In addition, we aim to use Voronoi triangulation to study the cellular structure in the phase turbulence and frozen states. This research is supported by the U. S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Science and Engineering under Award DE-FG02-09ER46613.

Measuring partial fluorescence yield using filtered detectors.

PubMed

Boyko, T D; Green, R J; Moewes, A; Regier, T Z

2014-07-01

Typically, X-ray absorption near-edge structure measurements aim to probe the linear attenuation coefficient. These measurements are often carried out using partial fluorescence yield techniques that rely on detectors having photon energy discrimination improving the sensitivity and the signal-to-background ratio of the measured spectra. However, measuring the partial fluorescence yield in the soft X-ray regime with reasonable efficiency requires solid-state detectors, which have limitations due to the inherent dead-time while measuring. Alternatively, many of the available detectors that are not energy dispersive do not suffer from photon count rate limitations. A filter placed in front of one of these detectors will make the energy-dependent efficiency non-linear, thereby changing the responsivity of the detector. It is shown that using an array of filtered X-ray detectors is a viable method for measuring soft X-ray partial fluorescence yield spectra without dead-time. The feasibility of this technique is further demonstrated using α-Fe2O3 as an example and it is shown that this detector technology could vastly improve the photon collection efficiency at synchrotrons and that these detectors will allow experiments to be completed with a much lower photon flux reducing X-ray-induced damage.

The Seismic Tool-Kit (STK): an open source software for seismology and signal processing.

NASA Astrophysics Data System (ADS)

Reymond, Dominique

2016-04-01

We present an open source software project (GNU public license), named STK: Seismic ToolKit, that is dedicated mainly for seismology and signal processing. The STK project that started in 2007, is hosted by SourceForge.net, and count more than 19 500 downloads at the date of writing. The STK project is composed of two main branches: First, a graphical interface dedicated to signal processing (in the SAC format (SAC_ASCII and SAC_BIN): where the signal can be plotted, zoomed, filtered, integrated, derivated, ... etc. (a large variety of IFR and FIR filter is proposed). The estimation of spectral density of the signal are performed via the Fourier transform, with visualization of the Power Spectral Density (PSD) in linear or log scale, and also the evolutive time-frequency representation (or sonagram). The 3-components signals can be also processed for estimating their polarization properties, either for a given window, or either for evolutive windows along the time. This polarization analysis is useful for extracting the polarized noises, differentiating P waves, Rayleigh waves, Love waves, ... etc. Secondly, a panel of Utilities-Program are proposed for working in a terminal mode, with basic programs for computing azimuth and distance in spherical geometry, inter/auto-correlation, spectral density, time-frequency for an entire directory of signals, focal planes, and main components axis, radiation pattern of P waves, Polarization analysis of different waves (including noize), under/over-sampling the signals, cubic-spline smoothing, and linear/non linear regression analysis of data set. A MINimum library of Linear AlGebra (MIN-LINAG) is also provided for computing the main matrix process like: QR/QL decomposition, Cholesky solve of linear system, finding eigen value/eigen vectors, QR-solve/Eigen-solve of linear equations systems ... etc. STK is developed in C/C++, mainly under Linux OS, and it has been also partially implemented under MS-Windows. Usefull links: http://sourceforge.net/projects/seismic-toolkit/ http://sourceforge.net/p/seismic-toolkit/wiki/browse_pages/

Adaptive learning in complex reproducing kernel Hilbert spaces employing Wirtinger's subgradients.

PubMed

Bouboulis, Pantelis; Slavakis, Konstantinos; Theodoridis, Sergios

2012-03-01

This paper presents a wide framework for non-linear online supervised learning tasks in the context of complex valued signal processing. The (complex) input data are mapped into a complex reproducing kernel Hilbert space (RKHS), where the learning phase is taking place. Both pure complex kernels and real kernels (via the complexification trick) can be employed. Moreover, any convex, continuous and not necessarily differentiable function can be used to measure the loss between the output of the specific system and the desired response. The only requirement is the subgradient of the adopted loss function to be available in an analytic form. In order to derive analytically the subgradients, the principles of the (recently developed) Wirtinger's calculus in complex RKHS are exploited. Furthermore, both linear and widely linear (in RKHS) estimation filters are considered. To cope with the problem of increasing memory requirements, which is present in almost all online schemes in RKHS, the sparsification scheme, based on projection onto closed balls, has been adopted. We demonstrate the effectiveness of the proposed framework in a non-linear channel identification task, a non-linear channel equalization problem and a quadrature phase shift keying equalization scheme, using both circular and non circular synthetic signal sources.

Almost periodic solutions to difference equations

NASA Technical Reports Server (NTRS)

Bayliss, A.

1975-01-01

The theory of Massera and Schaeffer relating the existence of unique almost periodic solutions of an inhomogeneous linear equation to an exponential dichotomy for the homogeneous equation was completely extended to discretizations by a strongly stable difference scheme. In addition it is shown that the almost periodic sequence solution will converge to the differential equation solution. The preceding theory was applied to a class of exponentially stable partial differential equations to which one can apply the Hille-Yoshida theorem. It is possible to prove the existence of unique almost periodic solutions of the inhomogeneous equation (which can be approximated by almost periodic sequences) which are the solutions to appropriate discretizations. Two methods of discretizations are discussed: the strongly stable scheme and the Lax-Wendroff scheme.

A numerical algorithm for optimal feedback gains in high dimensional LQR problems

NASA Technical Reports Server (NTRS)

Banks, H. T.; Ito, K.

1986-01-01

A hybrid method for computing the feedback gains in linear quadratic regulator problems is proposed. The method, which combines the use of a Chandrasekhar type system with an iteration of the Newton-Kleinman form with variable acceleration parameter Smith schemes, is formulated so as to efficiently compute directly the feedback gains rather than solutions of an associated Riccati equation. The hybrid method is particularly appropriate when used with large dimensional systems such as those arising in approximating infinite dimensional (distributed parameter) control systems (e.g., those governed by delay-differential and partial differential equations). Computational advantage of the proposed algorithm over the standard eigenvector (Potter, Laub-Schur) based techniques are discussed and numerical evidence of the efficacy of our ideas presented.

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

Predicting the composition of red wine blends using an array of multicomponent Peptide-based sensors.

PubMed

Ghanem, Eman; Hopfer, Helene; Navarro, Andrea; Ritzer, Maxwell S; Mahmood, Lina; Fredell, Morgan; Cubley, Ashley; Bolen, Jessica; Fattah, Rabia; Teasdale, Katherine; Lieu, Linh; Chua, Tedmund; Marini, Federico; Heymann, Hildegarde; Anslyn, Eric V

2015-05-20

Differential sensing using synthetic receptors as mimics of the mammalian senses of taste and smell is a powerful approach for the analysis of complex mixtures. Herein, we report on the effectiveness of a cross-reactive, supramolecular, peptide-based sensing array in differentiating and predicting the composition of red wine blends. Fifteen blends of Cabernet Sauvignon, Merlot and Cabernet Franc, in addition to the mono varietals, were used in this investigation. Linear Discriminant Analysis (LDA) showed a clear differentiation of blends based on tannin concentration and composition where certain mono varietals like Cabernet Sauvignon seemed to contribute less to the overall characteristics of the blend. Partial Least Squares (PLS) Regression and cross validation were used to build a predictive model for the responses of the receptors to eleven binary blends and the three mono varietals. The optimized model was later used to predict the percentage of each mono varietal in an independent test set composted of four tri-blends with a 15% average error. A partial least square regression model using the mouth-feel and taste descriptive sensory attributes of the wine blends revealed a strong correlation of the receptors to perceived astringency, which is indicative of selective binding to polyphenols in wine.

An almost symmetric Strang splitting scheme for nonlinear evolution equations.

PubMed

Einkemmer, Lukas; Ostermann, Alexander

2014-07-01

In this paper we consider splitting methods for the time integration of parabolic and certain classes of hyperbolic partial differential equations, where one partial flow cannot be computed exactly. Instead, we use a numerical approximation based on the linearization of the vector field. This is of interest in applications as it allows us to apply splitting methods to a wider class of problems from the sciences. However, in the situation described, the classic Strang splitting scheme, while still being a method of second order, is not longer symmetric. This, in turn, implies that the construction of higher order methods by composition is limited to order three only. To remedy this situation, based on previous work in the context of ordinary differential equations, we construct a class of Strang splitting schemes that are symmetric up to a desired order. We show rigorously that, under suitable assumptions on the nonlinearity, these methods are of second order and can then be used to construct higher order methods by composition. In addition, we illustrate the theoretical results by conducting numerical experiments for the Brusselator system and the KdV equation.

An almost symmetric Strang splitting scheme for nonlinear evolution equations☆

PubMed Central

Einkemmer, Lukas; Ostermann, Alexander

2014-01-01

In this paper we consider splitting methods for the time integration of parabolic and certain classes of hyperbolic partial differential equations, where one partial flow cannot be computed exactly. Instead, we use a numerical approximation based on the linearization of the vector field. This is of interest in applications as it allows us to apply splitting methods to a wider class of problems from the sciences. However, in the situation described, the classic Strang splitting scheme, while still being a method of second order, is not longer symmetric. This, in turn, implies that the construction of higher order methods by composition is limited to order three only. To remedy this situation, based on previous work in the context of ordinary differential equations, we construct a class of Strang splitting schemes that are symmetric up to a desired order. We show rigorously that, under suitable assumptions on the nonlinearity, these methods are of second order and can then be used to construct higher order methods by composition. In addition, we illustrate the theoretical results by conducting numerical experiments for the Brusselator system and the KdV equation. PMID:25844017

Research on odor interaction between aldehyde compounds via a partial differential equation (PDE) model.

PubMed

Yan, Luchun; Liu, Jiemin; Qu, Chen; Gu, Xingye; Zhao, Xia

2015-01-28

In order to explore the odor interaction of binary odor mixtures, a series of odor intensity evaluation tests were performed using both individual components and binary mixtures of aldehydes. Based on the linear relation between the logarithm of odor activity value and odor intensity of individual substances, the relationship between concentrations of individual constituents and their joint odor intensity was investigated by employing a partial differential equation (PDE) model. The obtained results showed that the binary odor interaction was mainly influenced by the mixing ratio of two constituents, but not the concentration level of an odor sample. Besides, an extended PDE model was also proposed on the basis of the above experiments. Through a series of odor intensity matching tests for several different binary odor mixtures, the extended PDE model was proved effective at odor intensity prediction. Furthermore, odorants of the same chemical group and similar odor type exhibited similar characteristics in the binary odor interaction. The overall results suggested that the PDE model is a more interpretable way of demonstrating the odor interactions of binary odor mixtures.

Tensor calculus in polar coordinates using Jacobi polynomials

NASA Astrophysics Data System (ADS)

Vasil, Geoffrey M.; Burns, Keaton J.; Lecoanet, Daniel; Olver, Sheehan; Brown, Benjamin P.; Oishi, Jeffrey S.

2016-11-01

Spectral methods are an efficient way to solve partial differential equations on domains possessing certain symmetries. The utility of a method depends strongly on the choice of spectral basis. In this paper we describe a set of bases built out of Jacobi polynomials, and associated operators for solving scalar, vector, and tensor partial differential equations in polar coordinates on a unit disk. By construction, the bases satisfy regularity conditions at r = 0 for any tensorial field. The coordinate singularity in a disk is a prototypical case for many coordinate singularities. The work presented here extends to other geometries. The operators represent covariant derivatives, multiplication by azimuthally symmetric functions, and the tensorial relationship between fields. These arise naturally from relations between classical orthogonal polynomials, and form a Heisenberg algebra. Other past work uses more specific polynomial bases for solving equations in polar coordinates. The main innovation in this paper is to use a larger set of possible bases to achieve maximum bandedness of linear operations. We provide a series of applications of the methods, illustrating their ease-of-use and accuracy.

Optimal analytic method for the nonlinear Hasegawa-Mima equation

NASA Astrophysics Data System (ADS)

Baxter, Mathew; Van Gorder, Robert A.; Vajravelu, Kuppalapalle

2014-05-01

The Hasegawa-Mima equation is a nonlinear partial differential equation that describes the electric potential due to a drift wave in a plasma. In the present paper, we apply the method of homotopy analysis to a slightly more general Hasegawa-Mima equation, which accounts for hyper-viscous damping or viscous dissipation. First, we outline the method for the general initial/boundary value problem over a compact rectangular spatial domain. We use a two-stage method, where both the convergence control parameter and the auxiliary linear operator are optimally selected to minimize the residual error due to the approximation. To do the latter, we consider a family of operators parameterized by a constant which gives the decay rate of the solutions. After outlining the general method, we consider a number of concrete examples in order to demonstrate the utility of this approach. The results enable us to study properties of the initial/boundary value problem for the generalized Hasegawa-Mima equation. In several cases considered, we are able to obtain solutions with extremely small residual errors after relatively few iterations are computed (residual errors on the order of 10-15 are found in multiple cases after only three iterations). The results demonstrate that selecting a parameterized auxiliary linear operator can be extremely useful for minimizing residual errors when used concurrently with the optimal homotopy analysis method, suggesting that this approach can prove useful for a number of nonlinear partial differential equations arising in physics and nonlinear mechanics.

A simplified computer program for the prediction of the linear stability behavior of liquid propellant combustors

NASA Technical Reports Server (NTRS)

Mitchell, C. E.; Eckert, K.

1979-01-01

A program for predicting the linear stability of liquid propellant rocket engines is presented. The underlying model assumptions and analytical steps necessary for understanding the program and its input and output are also given. The rocket engine is modeled as a right circular cylinder with an injector with a concentrated combustion zone, a nozzle, finite mean flow, and an acoustic admittance, or the sensitive time lag theory. The resulting partial differential equations are combined into two governing integral equations by the use of the Green's function method. These equations are solved using a successive approximation technique for the small amplitude (linear) case. The computational method used as well as the various user options available are discussed. Finally, a flow diagram, sample input and output for a typical application and a complete program listing for program MODULE are presented.

The use of Galerkin finite-element methods to solve mass-transport equations

USGS Publications Warehouse

Grove, David B.

1977-01-01

The partial differential equation that describes the transport and reaction of chemical solutes in porous media was solved using the Galerkin finite-element technique. These finite elements were superimposed over finite-difference cells used to solve the flow equation. Both convection and flow due to hydraulic dispersion were considered. Linear and Hermite cubic approximations (basis functions) provided satisfactory results: however, the linear functions were computationally more efficient for two-dimensional problems. Successive over relaxation (SOR) and iteration techniques using Tchebyschef polynomials were used to solve the sparce matrices generated using the linear and Hermite cubic functions, respectively. Comparisons of the finite-element methods to the finite-difference methods, and to analytical results, indicated that a high degree of accuracy may be obtained using the method outlined. The technique was applied to a field problem involving an aquifer contaminated with chloride, tritium, and strontium-90. (Woodard-USGS)

Hierarchical cluster-based partial least squares regression (HC-PLSR) is an efficient tool for metamodelling of nonlinear dynamic models.

PubMed

Tøndel, Kristin; Indahl, Ulf G; Gjuvsland, Arne B; Vik, Jon Olav; Hunter, Peter; Omholt, Stig W; Martens, Harald

2011-06-01

Deterministic dynamic models of complex biological systems contain a large number of parameters and state variables, related through nonlinear differential equations with various types of feedback. A metamodel of such a dynamic model is a statistical approximation model that maps variation in parameters and initial conditions (inputs) to variation in features of the trajectories of the state variables (outputs) throughout the entire biologically relevant input space. A sufficiently accurate mapping can be exploited both instrumentally and epistemically. Multivariate regression methodology is a commonly used approach for emulating dynamic models. However, when the input-output relations are highly nonlinear or non-monotone, a standard linear regression approach is prone to give suboptimal results. We therefore hypothesised that a more accurate mapping can be obtained by locally linear or locally polynomial regression. We present here a new method for local regression modelling, Hierarchical Cluster-based PLS regression (HC-PLSR), where fuzzy C-means clustering is used to separate the data set into parts according to the structure of the response surface. We compare the metamodelling performance of HC-PLSR with polynomial partial least squares regression (PLSR) and ordinary least squares (OLS) regression on various systems: six different gene regulatory network models with various types of feedback, a deterministic mathematical model of the mammalian circadian clock and a model of the mouse ventricular myocyte function. Our results indicate that multivariate regression is well suited for emulating dynamic models in systems biology. The hierarchical approach turned out to be superior to both polynomial PLSR and OLS regression in all three test cases. The advantage, in terms of explained variance and prediction accuracy, was largest in systems with highly nonlinear functional relationships and in systems with positive feedback loops. HC-PLSR is a promising approach for metamodelling in systems biology, especially for highly nonlinear or non-monotone parameter to phenotype maps. The algorithm can be flexibly adjusted to suit the complexity of the dynamic model behaviour, inviting automation in the metamodelling of complex systems.

Hierarchical Cluster-based Partial Least Squares Regression (HC-PLSR) is an efficient tool for metamodelling of nonlinear dynamic models

PubMed Central

2011-01-01

Background Deterministic dynamic models of complex biological systems contain a large number of parameters and state variables, related through nonlinear differential equations with various types of feedback. A metamodel of such a dynamic model is a statistical approximation model that maps variation in parameters and initial conditions (inputs) to variation in features of the trajectories of the state variables (outputs) throughout the entire biologically relevant input space. A sufficiently accurate mapping can be exploited both instrumentally and epistemically. Multivariate regression methodology is a commonly used approach for emulating dynamic models. However, when the input-output relations are highly nonlinear or non-monotone, a standard linear regression approach is prone to give suboptimal results. We therefore hypothesised that a more accurate mapping can be obtained by locally linear or locally polynomial regression. We present here a new method for local regression modelling, Hierarchical Cluster-based PLS regression (HC-PLSR), where fuzzy C-means clustering is used to separate the data set into parts according to the structure of the response surface. We compare the metamodelling performance of HC-PLSR with polynomial partial least squares regression (PLSR) and ordinary least squares (OLS) regression on various systems: six different gene regulatory network models with various types of feedback, a deterministic mathematical model of the mammalian circadian clock and a model of the mouse ventricular myocyte function. Results Our results indicate that multivariate regression is well suited for emulating dynamic models in systems biology. The hierarchical approach turned out to be superior to both polynomial PLSR and OLS regression in all three test cases. The advantage, in terms of explained variance and prediction accuracy, was largest in systems with highly nonlinear functional relationships and in systems with positive feedback loops. Conclusions HC-PLSR is a promising approach for metamodelling in systems biology, especially for highly nonlinear or non-monotone parameter to phenotype maps. The algorithm can be flexibly adjusted to suit the complexity of the dynamic model behaviour, inviting automation in the metamodelling of complex systems. PMID:21627852

Non-linear dynamic characteristics and optimal control of giant magnetostrictive film subjected to in-plane stochastic excitation

NASA Astrophysics Data System (ADS)

Zhu, Z. W.; Zhang, W. D.; Xu, J.

2014-03-01

The non-linear dynamic characteristics and optimal control of a giant magnetostrictive film (GMF) subjected to in-plane stochastic excitation were studied. Non-linear differential items were introduced to interpret the hysteretic phenomena of the GMF, and the non-linear dynamic model of the GMF subjected to in-plane stochastic excitation was developed. The stochastic stability was analysed, and the probability density function was obtained. The condition of stochastic Hopf bifurcation and noise-induced chaotic response were determined, and the fractal boundary of the system's safe basin was provided. The reliability function was solved from the backward Kolmogorov equation, and an optimal control strategy was proposed in the stochastic dynamic programming method. Numerical simulation shows that the system stability varies with the parameters, and stochastic Hopf bifurcation and chaos appear in the process; the area of the safe basin decreases when the noise intensifies, and the boundary of the safe basin becomes fractal; the system reliability improved through stochastic optimal control. Finally, the theoretical and numerical results were proved by experiments. The results are helpful in the engineering applications of GMF.

Non-linear hydrodynamical evolution of rotating relativistic stars: numerical methods and code tests

NASA Astrophysics Data System (ADS)

Font, José A.; Stergioulas, Nikolaos; Kokkotas, Kostas D.

2000-04-01

We present numerical hydrodynamical evolutions of rapidly rotating relativistic stars, using an axisymmetric, non-linear relativistic hydrodynamics code. We use four different high-resolution shock-capturing (HRSC) finite-difference schemes (based on approximate Riemann solvers) and compare their accuracy in preserving uniformly rotating stationary initial configurations in long-term evolutions. Among these four schemes, we find that the third-order piecewise parabolic method scheme is superior in maintaining the initial rotation law in long-term evolutions, especially near the surface of the star. It is further shown that HRSC schemes are suitable for the evolution of perturbed neutron stars and for the accurate identification (via Fourier transforms) of normal modes of oscillation. This is demonstrated for radial and quadrupolar pulsations in the non-rotating limit, where we find good agreement with frequencies obtained with a linear perturbation code. The code can be used for studying small-amplitude or non-linear pulsations of differentially rotating neutron stars, while our present results serve as testbed computations for three-dimensional general-relativistic evolution codes.

Evaluation of Uncertainty in Runoff Analysis Incorporating Theory of Stochastic Process

NASA Astrophysics Data System (ADS)

Yoshimi, Kazuhiro; Wang, Chao-Wen; Yamada, Tadashi

2015-04-01

The aim of this paper is to provide a theoretical framework of uncertainty estimate on rainfall-runoff analysis based on theory of stochastic process. SDE (stochastic differential equation) based on this theory has been widely used in the field of mathematical finance due to predict stock price movement. Meanwhile, some researchers in the field of civil engineering have investigated by using this knowledge about SDE (stochastic differential equation) (e.g. Kurino et.al, 1999; Higashino and Kanda, 2001). However, there have been no studies about evaluation of uncertainty in runoff phenomenon based on comparisons between SDE (stochastic differential equation) and Fokker-Planck equation. The Fokker-Planck equation is a partial differential equation that describes the temporal variation of PDF (probability density function), and there is evidence to suggest that SDEs and Fokker-Planck equations are equivalent mathematically. In this paper, therefore, the uncertainty of discharge on the uncertainty of rainfall is explained theoretically and mathematically by introduction of theory of stochastic process. The lumped rainfall-runoff model is represented by SDE (stochastic differential equation) due to describe it as difference formula, because the temporal variation of rainfall is expressed by its average plus deviation, which is approximated by Gaussian distribution. This is attributed to the observed rainfall by rain-gauge station and radar rain-gauge system. As a result, this paper has shown that it is possible to evaluate the uncertainty of discharge by using the relationship between SDE (stochastic differential equation) and Fokker-Planck equation. Moreover, the results of this study show that the uncertainty of discharge increases as rainfall intensity rises and non-linearity about resistance grows strong. These results are clarified by PDFs (probability density function) that satisfy Fokker-Planck equation about discharge. It means the reasonable discharge can be estimated based on the theory of stochastic processes, and it can be applied to the probabilistic risk of flood management.

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Probabilistic density function method for nonlinear dynamical systems driven by colored noise

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

Barajas-Solano, David A.; Tartakovsky, Alexandre M.

2016-05-01

We present a probability density function (PDF) method for a system of nonlinear stochastic ordinary differential equations driven by colored noise. The method provides an integro-differential equation for the temporal evolution of the joint PDF of the system's state, which we close by means of a modified Large-Eddy-Diffusivity-type closure. Additionally, we introduce the generalized local linearization (LL) approximation for deriving a computable PDF equation in the form of the second-order partial differential equation (PDE). We demonstrate the proposed closure and localization accurately describe the dynamics of the PDF in phase space for systems driven by noise with arbitrary auto-correlation time.more » We apply the proposed PDF method to the analysis of a set of Kramers equations driven by exponentially auto-correlated Gaussian colored noise to study the dynamics and stability of a power grid.« less

Simulation of creep effects in framework of a geometrically nonlinear endochronic theory of inelasticity

NASA Astrophysics Data System (ADS)

Zabavnikova, T. A.; Kadashevich, Yu. I.; Pomytkin, S. P.

2018-05-01

A geometric non-linear endochronic theory of inelasticity in tensor parametric form is considered. In the framework of this theory, the creep strains are modelled. The effect of various schemes of applying stresses and changing of material properties on the development of creep strains is studied. The constitutive equations of the model are represented by non-linear systems of ordinary differential equations which are solved in MATLAB environment by implicit difference method. Presented results demonstrate a good qualitative agreement of theoretical data and experimental observations including the description of the tertiary creep and pre-fracture of materials.

Comparison between two meshless methods based on collocation technique for the numerical solution of four-species tumor growth model

NASA Astrophysics Data System (ADS)

Dehghan, Mehdi; Mohammadi, Vahid

2017-03-01

As is said in [27], the tumor-growth model is the incorporation of nutrient within the mixture as opposed to being modeled with an auxiliary reaction-diffusion equation. The formulation involves systems of highly nonlinear partial differential equations of surface effects through diffuse-interface models [27]. Simulations of this practical model using numerical methods can be applied for evaluating it. The present paper investigates the solution of the tumor growth model with meshless techniques. Meshless methods are applied based on the collocation technique which employ multiquadrics (MQ) radial basis function (RBFs) and generalized moving least squares (GMLS) procedures. The main advantages of these choices come back to the natural behavior of meshless approaches. As well as, a method based on meshless approach can be applied easily for finding the solution of partial differential equations in high-dimension using any distributions of points on regular and irregular domains. The present paper involves a time-dependent system of partial differential equations that describes four-species tumor growth model. To overcome the time variable, two procedures will be used. One of them is a semi-implicit finite difference method based on Crank-Nicolson scheme and another one is based on explicit Runge-Kutta time integration. The first case gives a linear system of algebraic equations which will be solved at each time-step. The second case will be efficient but conditionally stable. The obtained numerical results are reported to confirm the ability of these techniques for solving the two and three-dimensional tumor-growth equations.

The algebraic criteria for the stability of control systems

NASA Technical Reports Server (NTRS)

Cremer, H.; Effertz, F. H.

1986-01-01

This paper critically examines the standard algebraic criteria for the stability of linear control systems and their proofs, reveals important previously unnoticed connections, and presents new representations. Algebraic stability criteria have also acquired significance for stability studies of non-linear differential equation systems by the Krylov-Bogoljubov-Magnus Method, and allow realization conditions to be determined for classes of broken rational functions as frequency characteristics of electrical network.

Near-infrared Raman spectroscopy for estimating biochemical changes associated with different pathological conditions of cervix

NASA Astrophysics Data System (ADS)

Daniel, Amuthachelvi; Prakasarao, Aruna; Ganesan, Singaravelu

2018-02-01

The molecular level changes associated with oncogenesis precede the morphological changes in cells and tissues. Hence molecular level diagnosis would promote early diagnosis of the disease. Raman spectroscopy is capable of providing specific spectral signature of various biomolecules present in the cells and tissues under various pathological conditions. The aim of this work is to develop a non-linear multi-class statistical methodology for discrimination of normal, neoplastic and malignant cells/tissues. The tissues were classified as normal, pre-malignant and malignant by employing Principal Component Analysis followed by Artificial Neural Network (PC-ANN). The overall accuracy achieved was 99%. Further, to get an insight into the quantitative biochemical composition of the normal, neoplastic and malignant tissues, a linear combination of the major biochemicals by non-negative least squares technique was fit to the measured Raman spectra of the tissues. This technique confirms the changes in the major biomolecules such as lipids, nucleic acids, actin, glycogen and collagen associated with the different pathological conditions. To study the efficacy of this technique in comparison with histopathology, we have utilized Principal Component followed by Linear Discriminant Analysis (PC-LDA) to discriminate the well differentiated, moderately differentiated and poorly differentiated squamous cell carcinoma with an accuracy of 94.0%. And the results demonstrated that Raman spectroscopy has the potential to complement the good old technique of histopathology.

Soil thaw effects on river discharge recessions of a subarctic catchment

NASA Astrophysics Data System (ADS)

Ploum, Stefan; Lyon, Steve; Teuling, Ryan; van der Velde, Ype

2017-04-01

Thawing permafrost in circumpolar regions is likely to change subsurface hydrology. In high latitude areas continuous permafrost is expected to partially thaw leading to sporadic permafrost with deeper groundwater flow paths. Moreover, freeze-thaw cycles of the shallow subsurface are likely to increase. River discharge recession analysis can be particularly useful to understand the hydrological effects of a thawing Arctic. Here we examine river discharge recessions of the Abiskojokka, a 560 km2 watershed with sporadic permafrost, using a river discharge record of 30 years (1985 - 2015). Snow observation records were used to separate river recessions in snowmelt and snowfree periods. We found significant differences between recessions during the snowmelt and snowfree seasons. During the snowmelt, recessions were close to linear (b=1.11), while during the snowfree period, recessions were more non-linear (b=1.54). Typically, non-linearity has been found to increase with discharge magnitude, while we observed the opposite (snowfree periods tend to have lower discharges than the snowmelt periods). We explain these contrasting results by hypothesizing that increased connectivity (increasing magnitude and number of water flow paths) between groundwater and stream leads to higher non-linearity. In temperate catchments without frozen soils, connectivity tends to increase with increasing discharge. In contrast, in Arctic systems, where soils are frozen, connectivity between groundwater and stream is limited. Therefore, thawing of frozen soils is expected to increase connectivity and thus non-linearity of river discharges. We tested this hypothesis with a detailed analysis of all spring flood recessions. Years with cold soil temperatures (b=1.08) and years with a below median snowpack depth were found to have progressively linear slopes (b=1.08 and 1.01 respectively). On the other hand, years with warm soil conditions show increasingly non-linear recessions (b=1.67). Although limited in spatial extent, these results further support our connectivity hypothesis, which predicts increasing non-linearity of river discharges (higher discharge peaks and lower low flows under the same precipitation regime) as permafrost thaws.

Vibration analysis of partially cracked plate submerged in fluid

NASA Astrophysics Data System (ADS)

Soni, Shashank; Jain, N. K.; Joshi, P. V.

2018-01-01

The present work proposes an analytical model for vibration analysis of partially cracked rectangular plates coupled with fluid medium. The governing equation of motion for the isotropic plate based on the classical plate theory is modified to accommodate a part through continuous line crack according to simplified line spring model. The influence of surrounding fluid medium is incorporated in the governing equation in the form of inertia effects based on velocity potential function and Bernoulli's equations. Both partially and totally submerged plate configurations are considered. The governing equation also considers the in-plane stretching due to lateral deflection in the form of in-plane forces which introduces geometric non-linearity into the system. The fundamental frequencies are evaluated by expressing the lateral deflection in terms of modal functions. The assessment of the present results is carried out for intact submerged plate as to the best of the author's knowledge the literature lacks in analytical results for submerged cracked plates. New results for fundamental frequencies are presented as affected by crack length, fluid level, fluid density and immersed depth of plate. By employing the method of multiple scales, the frequency response and peak amplitude of the cracked structure is analyzed. The non-linear frequency response curves show the phenomenon of bending hardening or softening and the effect of fluid dynamic pressure on the response of the cracked plate.

Variable selection in near-infrared spectroscopy: benchmarking of feature selection methods on biodiesel data.

PubMed

Balabin, Roman M; Smirnov, Sergey V

2011-04-29

During the past several years, near-infrared (near-IR/NIR) spectroscopy has increasingly been adopted as an analytical tool in various fields from petroleum to biomedical sectors. The NIR spectrum (above 4000 cm(-1)) of a sample is typically measured by modern instruments at a few hundred of wavelengths. Recently, considerable effort has been directed towards developing procedures to identify variables (wavelengths) that contribute useful information. Variable selection (VS) or feature selection, also called frequency selection or wavelength selection, is a critical step in data analysis for vibrational spectroscopy (infrared, Raman, or NIRS). In this paper, we compare the performance of 16 different feature selection methods for the prediction of properties of biodiesel fuel, including density, viscosity, methanol content, and water concentration. The feature selection algorithms tested include stepwise multiple linear regression (MLR-step), interval partial least squares regression (iPLS), backward iPLS (BiPLS), forward iPLS (FiPLS), moving window partial least squares regression (MWPLS), (modified) changeable size moving window partial least squares (CSMWPLS/MCSMWPLSR), searching combination moving window partial least squares (SCMWPLS), successive projections algorithm (SPA), uninformative variable elimination (UVE, including UVE-SPA), simulated annealing (SA), back-propagation artificial neural networks (BP-ANN), Kohonen artificial neural network (K-ANN), and genetic algorithms (GAs, including GA-iPLS). Two linear techniques for calibration model building, namely multiple linear regression (MLR) and partial least squares regression/projection to latent structures (PLS/PLSR), are used for the evaluation of biofuel properties. A comparison with a non-linear calibration model, artificial neural networks (ANN-MLP), is also provided. Discussion of gasoline, ethanol-gasoline (bioethanol), and diesel fuel data is presented. The results of other spectroscopic techniques application, such as Raman, ultraviolet-visible (UV-vis), or nuclear magnetic resonance (NMR) spectroscopies, can be greatly improved by an appropriate feature selection choice. Copyright © 2011 Elsevier B.V. All rights reserved.

The shear-Hall instability in newborn neutron stars

NASA Astrophysics Data System (ADS)

Kondić, T.; Rüdiger, G.; Hollerbach, R.

2011-11-01

Aims: In the first few minutes of a newborn neutron star's life the Hall effect and differential rotation may both be important. We demonstrate that these two ingredients are sufficient for generating a "shear-Hall instability" and for studying its excitation conditions, growth rates, and characteristic magnetic field patterns. Methods: We numerically solve the induction equation in a spherical shell, with a kinematically prescribed differential rotation profile Ω(s), where s is the cylindrical radius. The Hall term is linearized about an imposed uniform axial field. The linear stability of individual azimuthal modes, both axisymmetric and non-axisymmetric, is then investigated. Results: For the shear-Hall instability to occur, the axial field must be parallel to the rotation axis if Ω(s) decreases outward, whereas if Ω(s) increases outward it must be anti-parallel. The instability draws its energy from the differential rotation, and occurs on the short rotational timescale rather than on the much longer Hall timescale. It operates most efficiently if the Hall time is comparable to the diffusion time. Depending on the precise field strengths B0, either axisymmetric or non-axisymmetric modes may be the most unstable. Conclusions: Even if the differential rotation in newborn neutron stars is quenched within minutes, the shear-Hall instability may nevertheless amplify any seed magnetic fields by many orders of magnitude.

Comparison of linear and nonlinear models for coherent hemodynamics spectroscopy (CHS)

NASA Astrophysics Data System (ADS)

Sassaroli, Angelo; Kainerstorfer, Jana; Fantini, Sergio

2015-03-01

A recently proposed linear time-invariant hemodynamic model for coherent hemodynamics spectroscopy1 (CHS) relates the tissue concentrations of oxy- and deoxy-hemoglobin (outputs of the system) to given dynamics of the tissue blood volume, blood flow and rate constant of oxygen diffusion (inputs of the system). This linear model was derived in the limit of "small" perturbations in blood flow velocity. We have extended this model to a more general model (which will be referred to as the nonlinear extension to the original model) that yields the time-dependent changes of oxy and deoxy-hemoglobin concentrations in response to arbitrary dynamic changes in capillary blood flow velocity. The nonlinear extension to the model relies on a general solution of the partial differential equation that governs the spatio-temporal behavior of oxygen saturation of hemoglobin in capillaries and venules on the basis of dynamic (or time resolved) blood transit time. We show preliminary results where the CHS spectra obtained from the linear and nonlinear models are compared to quantify the limits of applicability of the linear model.

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.

Variational formulation for dissipative continua and an incremental J-integral

NASA Astrophysics Data System (ADS)

Rahaman, Md. Masiur; Dhas, Bensingh; Roy, D.; Reddy, J. N.

2018-01-01

Our aim is to rationally formulate a proper variational principle for dissipative (viscoplastic) solids in the presence of inertia forces. As a first step, a consistent linearization of the governing nonlinear partial differential equations (PDEs) is carried out. An additional set of complementary (adjoint) equations is then formed to recover an underlying variational structure for the augmented system of linearized balance laws. This makes it possible to introduce an incremental Lagrangian such that the linearized PDEs, including the complementary equations, become the Euler-Lagrange equations. Continuous groups of symmetries of the linearized PDEs are computed and an analysis is undertaken to identify the variational groups of symmetries of the linearized dissipative system. Application of Noether's theorem leads to the conservation laws (conserved currents) of motion corresponding to the variational symmetries. As a specific outcome, we exploit translational symmetries of the functional in the material space and recover, via Noether's theorem, an incremental J-integral for viscoplastic solids in the presence of inertia forces. Numerical demonstrations are provided through a two-dimensional plane strain numerical simulation of a compact tension specimen of annealed mild steel under dynamic loading.

Kernel PLS-SVC for Linear and Nonlinear Discrimination

NASA Technical Reports Server (NTRS)

Rosipal, Roman; Trejo, Leonard J.; Matthews, Bryan

2003-01-01

A new methodology for discrimination is proposed. This is based on kernel orthonormalized partial least squares (PLS) dimensionality reduction of the original data space followed by support vector machines for classification. Close connection of orthonormalized PLS and Fisher's approach to linear discrimination or equivalently with canonical correlation analysis is described. This gives preference to use orthonormalized PLS over principal component analysis. Good behavior of the proposed method is demonstrated on 13 different benchmark data sets and on the real world problem of the classification finger movement periods versus non-movement periods based on electroencephalogram.

On a difficulty in eigenfunction expansion solutions for the start-up of fluid flow

NASA Astrophysics Data System (ADS)

Christov, Ivan C.

2015-11-01

Most mathematics and engineering textbooks describe the process of ``subtracting off'' the steady state of a linear parabolic partial differential equation as a technique for obtaining a boundary-value problem with homogeneous boundary conditions that can be solved by separation of variables (i.e., eigenfunction expansions). While this method produces the correct solution for the start-up of the flow of, e.g., a Newtonian fluid between parallel plates, it can lead to erroneous solutions to the corresponding problem for a class of non-Newtonian fluids. We show that the reason for this is the non-rigorous enforcement of the start-up condition in the textbook approach, which leads to a violation of the principle of causality. Nevertheless, these boundary-value problems can be solved correctly using eigenfunction expansions, and we present the formulation that makes this possible (in essence, an application of Duhamel's principle). The solutions obtained by this new approach are shown to agree identically with those obtained by using the Laplace transform in time only, a technique that enforces the proper start-up condition implicitly (hence, the same error cannot be committed). Supported, in part, by NSF Grant DMS-1104047 and the U.S. DOE (Contract No. DE-AC52-06NA25396) through the LANL/LDRD Program.

A comparison of two adaptive multivariate analysis methods (PLSR and ANN) for winter wheat yield forecasting using Landsat-8 OLI images

NASA Astrophysics Data System (ADS)

Chen, Pengfei; Jing, Qi

2017-02-01

An assumption that the non-linear method is more reasonable than the linear method when canopy reflectance is used to establish the yield prediction model was proposed and tested in this study. For this purpose, partial least squares regression (PLSR) and artificial neural networks (ANN), represented linear and non-linear analysis method, were applied and compared for wheat yield prediction. Multi-period Landsat-8 OLI images were collected at two different wheat growth stages, and a field campaign was conducted to obtain grain yields at selected sampling sites in 2014. The field data were divided into a calibration database and a testing database. Using calibration data, a cross-validation concept was introduced for the PLSR and ANN model construction to prevent over-fitting. All models were tested using the test data. The ANN yield-prediction model produced R2, RMSE and RMSE% values of 0.61, 979 kg ha-1, and 10.38%, respectively, in the testing phase, performing better than the PLSR yield-prediction model, which produced R2, RMSE, and RMSE% values of 0.39, 1211 kg ha-1, and 12.84%, respectively. Non-linear method was suggested as a better method for yield prediction.

Note on Solutions to a Class of Nonlinear Singular Integro-Differential Equations,

DTIC Science & Technology

1986-08-01

KdV) ut + 2uu x +Uxx x a 0, (1) the sine-Gordon equation Uxt a sin u, (2) and the Kadomtsev - Petviashvili (KP) equation (Ut + 2uu x + UXXx)x -3a 2u yy...SOUIN OA LSFNN ! /" / M.. \\boiz A.S ::-:- and ,M.O.. .- :1/1 / NOTE ON SOLUTIONS TO A CLASS OF NON \\ / LINEAR SINGULAR INTEGRO-DIFFERENTIA[ EQUATIONS by...important nonlinear evolution equations which can be linearized. Many of these equations fall into the category of linearization via soliton theory and

Non-destructive imaging of spinor Bose-Einstein condensates

NASA Astrophysics Data System (ADS)

Samson, E.; Vinit, Anshuman; Raman, Chandra

2013-05-01

We present a non-destructive differential imaging technique that enables the observation of the spatial distribution of the magnetization in a spinor Bose-Einstein condensate (BEC) through a Faraday rotation protocol. In our procedure, we utilize a linearly polarized, far-detuned laser beam as our imaging probe, and upon interaction with the condensate, the beam's polarization direction undergoes Faraday rotation. A differential measurement of the orthogonal polarization components of the rotated beam provides a spatial map of the net magnetization density within the BEC. The non-destructive aspect of this method allows for continuous imaging of the condensate. This imaging technique will prove useful in experimental BEC studies, such as spatially resolved magnetometry using ultracold atoms, and non-destructive imaging of non-equilibrium behavior of antiferromagnetic spinor condensates. This work was supported by the DARPA QuASAR program through a grant from ARO.

A Novel Approach to Solve Linearized Stellar Pulsation Equations

NASA Astrophysics Data System (ADS)

Bard, Christopher; Teitler, S.

2011-01-01

We present a new approach to modeling linearized, non-radial pulsations in differentially rotating, massive stars. As a first step in this direction, we consider adiabatic pulsations and adopt the Cowling approximation that perturbations of the gravitational potential and its radial derivative are negligible. The angular dependence of the pulsation modes is expressed as a series expansion of associated Legendre polynomials; the resulting coupled system of differential equations is then solved by finding the eigenfrequencies at which the determinant of a characteristic matrix vanishes. Our method improves on previous treatments by removing the requirement that an arbitrary normalization be applied to the eigenfunctions; this brings the benefit of improved numerical robustness.

Gesellschaft fuer angewandte Mathematik und Mechanik, Annual Scientific Meeting, Technische Universitaet Berlin, Berlin, West Germany, April 8-11, 1980, Reports. Parts 1 & 2

NASA Astrophysics Data System (ADS)

1981-04-01

The main topics discussed were related to nonparametric statistics, plane and antiplane states in finite elasticity, free-boundary-variational inequalities, the numerical solution of free boundary-value problems, discrete and combinatorial optimization, mathematical modelling in fluid mechanics, a survey and comparison regarding thermodynamic theories, invariant and almost invariant subspaces in linear systems with applications to disturbance isolation, nonlinear acoustics, and methods of function theory in the case of partial differential equations, giving particular attention to elliptic problems in the plane.

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

Ashraf, M. Bilal, E-mail: bilalashraf-qau@yahoo.com; Hayat, T.; Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80257, Jeddah 21589

Three dimensional radiative flow of Maxwell fluid over an inclined stretching surface with convective boundary condition is investigated. Heat and mass transfer analysis is taken into account with thermophoresis effects. Similarity transformations are utilized to reduce the partial differential equations into ordinary differential equations. Series solutions of velocity, temperature and concentration are developed. Influence of different parameters Biot number, therrmophoretic parameter, Deborah number, ratio parameter, inclined stretching angle, radiation parameter, mixed convection parameter and concentration buoyancy parameter on the non-dimensional velocity components, temperature and concentration are plotted and discussed in detail. Physical quantities of interests are tabulated and examined.

A Bifurcation Problem for a Nonlinear Partial Differential Equation of Parabolic Type,

DTIC Science & Technology

NONLINEAR DIFFERENTIAL EQUATIONS, INTEGRATION), (*PARTIAL DIFFERENTIAL EQUATIONS, BOUNDARY VALUE PROBLEMS), BANACH SPACE , MAPPING (TRANSFORMATIONS), SET THEORY, TOPOLOGY, ITERATIONS, STABILITY, THEOREMS

Numerical modeling of bubble dynamics in viscoelastic media with relaxation

PubMed Central

Warnez, M. T.; Johnsen, E.

2015-01-01

Cavitation occurs in a variety of non-Newtonian fluids and viscoelastic materials. The large-amplitude volumetric oscillations of cavitation bubbles give rise to high temperatures and pressures at collapse, as well as induce large and rapid deformation of the surroundings. In this work, we develop a comprehensive numerical framework for spherical bubble dynamics in isotropic media obeying a wide range of viscoelastic constitutive relationships. Our numerical approach solves the compressible Keller–Miksis equation with full thermal effects (inside and outside the bubble) when coupled to a highly generalized constitutive relationship (which allows Newtonian, Kelvin–Voigt, Zener, linear Maxwell, upper-convected Maxwell, Jeffreys, Oldroyd-B, Giesekus, and Phan-Thien-Tanner models). For the latter two models, partial differential equations (PDEs) must be solved in the surrounding medium; for the remaining models, we show that the PDEs can be reduced to ordinary differential equations. To solve the general constitutive PDEs, we present a Chebyshev spectral collocation method, which is robust even for violent collapse. Combining this numerical approach with theoretical analysis, we simulate bubble dynamics in various viscoelastic media to determine the impact of relaxation time, a constitutive parameter, on the associated physics. Relaxation time is found to increase bubble growth and permit rebounds driven purely by residual stresses in the surroundings. Different regimes of oscillations occur depending on the relaxation time. PMID:26130967

On the suitability of the Thellier method of palaeointensity determinations on pseudo-single-domain and multidomain grains

NASA Astrophysics Data System (ADS)

Shcherbakov, V. P.; Shcherbakova, V. V.

2001-07-01

We report an experimental and theoretical study of non-linear Arai-Nagata diagrams for samples containing pseudo-single-domain (PSD) and multidomain (MD) magnetite. Our aim is to reveal the physical reasons for the deviation of these plots from ideal straight lines. Contrary to expectations, the concavity of the Arai-Nagata diagrams is not related to the two most noticeable violations of the Thellier laws documented for non-single-domain particles: the tail of partial thermoremanence and the dependence of the magnitude of pTRM on the thermal history of the sample. Indeed, the contributions from these two factors mutually cancel each other. Phenomenologically, the non-linear Arai-Nagata plots occur because samples during low-temperature stages of the Thellier procedure lose too much remanence and recover too little of it. The excessive loss of the previously imparted total TRM is due at least partly to some partial demagnetization of high-temperature TRM components and to progressive stabilization of domain structure during the repetitive heatings to moderate temperatures that form the basis of the Thellier procedure. For natural MD samples a linear fit to the low-temperature data points on the Arai-Nagata plots leads to a palaeointensity overestimated by as much as 60 per cent. The samples containing hydrothermally grown or crushed and sieved MD magnetite provide low-temperature apparent palaeointensities two to three times larger than the correct value. For small PSD samples the overestimate is less than 10-20 per cent and, in general, PSD samples can be used for the palaeointensity determinations.

Differences in postural tremor dynamics with age and neurological disease.

PubMed

Morrison, Steven; Newell, Karl M; Kavanagh, Justin J

2017-06-01

The overlap of dominant tremor frequencies and similarly amplified tremor observed for Parkinson's disease (PD) and essential tremor (ET) means differentiating between these pathologies is often difficult. As tremor exhibits non-linear properties, employing both linear and non-linear analyses may help distinguish between the tremor dynamics of aging, PD and ET. This study was designed to examine postural tremor in healthy older adults, PD and ET using standard linear and non-linear metrics. Hand and finger postural tremor was recorded in 15 healthy older adults (64 ± 6 years), 15 older individuals with PD (63 ± 6 years), and 10 persons with ET (68 ± 7 years). Linear measures of amplitude, frequency, and between-limb coupling (coherence) were performed. Non-linear measures of regularity (ApEn) and coupling (Cross-ApEn) were also used. Additionally, receiver operating characteristic analyses were performed for those measures that were significantly different between all groups. The results revealed that the linear measures only showed significant differences between the healthy adults and ET/PD persons, but no differences between the two neurological groups. Coherence showed higher bilateral coupling for ET but no differences in inter-limb coupling between PD and healthy subjects. However, ApEn values for finger tremor revealed significant differences between all groups, with tremor for ET persons being more regular (lower ApEn) overall. Similarly, Cross-ApEn results also showed differences between all groups, with ET persons showing strongest inter-limb coupling followed by PD and elderly. Overall, our findings point to the diagnostic potential for non-linear measures of coupling and tremor structure as biomarkers for discriminating between ET, PD and healthy persons.

Histological Grading of Hepatocellular Carcinomas with Intravoxel Incoherent Motion Diffusion-weighted Imaging: Inconsistent Results Depending on the Fitting Method.

PubMed

Ichikawa, Shintaro; Motosugi, Utaroh; Hernando, Diego; Morisaka, Hiroyuki; Enomoto, Nobuyuki; Matsuda, Masanori; Onishi, Hiroshi

2018-04-10

To compare the abilities of three intravoxel incoherent motion (IVIM) imaging approximation methods to discriminate the histological grade of hepatocellular carcinomas (HCCs). Fifty-eight patients (60 HCCs) underwent IVIM imaging with 11 b-values (0-1000 s/mm 2 ). Slow (D) and fast diffusion coefficients (D * ) and the perfusion fraction (f) were calculated for the HCCs using the mean signal intensities in regions of interest drawn by two radiologists. Three approximation methods were used. First, all three parameters were obtained simultaneously using non-linear fitting (method A). Second, D was obtained using linear fitting (b = 500 and 1000), followed by non-linear fitting for D * and f (method B). Third, D was obtained by linear fitting, f was obtained using the regression line intersection and signals at b = 0, and non-linear fitting was used for D * (method C). A receiver operating characteristic analysis was performed to reveal the abilities of these methods to distinguish poorly-differentiated from well-to-moderately-differentiated HCCs. Inter-reader agreements were assessed using intraclass correlation coefficients (ICCs). The measurements of D, D * , and f in methods B and C (Az-value, 0.658-0.881) had better discrimination abilities than did those in method A (Az-value, 0.527-0.607). The ICCs of D and f were good to excellent (0.639-0.835) with all methods. The ICCs of D * were moderate with methods B (0.580) and C (0.463) and good with method A (0.705). The IVIM parameters may vary depending on the fitting methods, and therefore, further technical refinement may be needed.

Geologic Evolution of North America: Geologic features suggest that the continent has grown and differentiated through geologic time.

PubMed

Engel, A E

1963-04-12

The oldest decipherable rock complexes within continents (more than 2.5 billion years old) are largely basaltic volcanics and graywacke. Recent and modern analogs are the island arcs formed along and adjacent to the unstable interface of continental and oceanic crusts. The major interfacial reactions (orogenies) incorporate pre-existing sial, oceanic crust, and mantle into crust of a more continental type. Incipient stages of continental evolution, more than 3 billion years ago, remain obscure. They may involve either a cataclysmic granite-forming event or a succession of volcanic-sedimentary and granite-forming cycles. Intermediate and recent stages of continental evolution, as indicated by data for North America, involve accretion of numerous crustal interfaces with fragments of adjacent continental crust and their partial melting, reinjection, elevation, unroofing, and stabilization. Areas of relict provinces defined by ages of granites suggest that continental growth is approximately linear. But the advanced differentiation found in many provinces and the known overlaps permit wide deviation from linearity in the direction of a more explosive early or intermediate growth.

Local polynomial chaos expansion for linear differential equations with high dimensional random inputs

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

Chen, Yi; Jakeman, John; Gittelson, Claude

2015-01-08

In this paper we present a localized polynomial chaos expansion for partial differential equations (PDE) with random inputs. In particular, we focus on time independent linear stochastic problems with high dimensional random inputs, where the traditional polynomial chaos methods, and most of the existing methods, incur prohibitively high simulation cost. Furthermore, the local polynomial chaos method employs a domain decomposition technique to approximate the stochastic solution locally. In each subdomain, a subdomain problem is solved independently and, more importantly, in a much lower dimensional random space. In a postprocesing stage, accurate samples of the original stochastic problems are obtained frommore » the samples of the local solutions by enforcing the correct stochastic structure of the random inputs and the coupling conditions at the interfaces of the subdomains. Overall, the method is able to solve stochastic PDEs in very large dimensions by solving a collection of low dimensional local problems and can be highly efficient. In our paper we present the general mathematical framework of the methodology and use numerical examples to demonstrate the properties of the method.« less

On hyperbolicity and Gevrey well-posedness. Part two: Scalar or degenerate transitions

NASA Astrophysics Data System (ADS)

Morisse, Baptiste

2018-04-01

For first-order quasi-linear systems of partial differential equations, we formulate an assumption of a transition from initial hyperbolicity to ellipticity. This assumption bears on the principal symbol of the first-order operator. Under such an assumption, we prove a strong Hadamard instability for the associated Cauchy problem, namely an instantaneous defect of Hölder continuity of the flow from Gσ to L2, with 0 < σ <σ0, the limiting Gevrey index σ0 depending on the nature of the transition. We restrict here to scalar transitions, and non-scalar transitions in which the boundary of the hyperbolic zone satisfies a flatness condition. As in our previous work for initially elliptic Cauchy problems [B. Morisse, On hyperbolicity and Gevrey well-posedness. Part one: the elliptic case, arxiv:arXiv:1611.07225], the instability follows from a long-time Cauchy-Kovalevskaya construction for highly oscillating solutions. This extends recent work of N. Lerner, T. Nguyen, and B. Texier [The onset of instability in first-order systems, to appear in J. Eur. Math. Soc.].

Lax Integrability and the Peakon Problem for the Modified Camassa-Holm Equation

NASA Astrophysics Data System (ADS)

Chang, Xiangke; Szmigielski, Jacek

2018-02-01

Peakons are special weak solutions of a class of nonlinear partial differential equations modelling non-linear phenomena such as the breakdown of regularity and the onset of shocks. We show that the natural concept of weak solutions in the case of the modified Camassa-Holm equation studied in this paper is dictated by the distributional compatibility of its Lax pair and, as a result, it differs from the one proposed and used in the literature based on the concept of weak solutions used for equations of the Burgers type. Subsequently, we give a complete construction of peakon solutions satisfying the modified Camassa-Holm equation in the sense of distributions; our approach is based on solving certain inverse boundary value problem, the solution of which hinges on a combination of classical techniques of analysis involving Stieltjes' continued fractions and multi-point Padé approximations. We propose sufficient conditions needed to ensure the global existence of peakon solutions and analyze the large time asymptotic behaviour whose special features include a formation of pairs of peakons that share asymptotic speeds, as well as Toda-like sorting property.

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

Ghafarian, M.; Ariaei, A., E-mail: ariaei@eng.ui.ac.ir

The free vibration analysis of a multiple rotating nanobeams' system applying the nonlocal Eringen elasticity theory is presented. Multiple nanobeams' systems are of great importance in nano-optomechanical applications. At nanoscale, the nonlocal effects become non-negligible. According to the nonlocal Euler-Bernoulli beam theory, the governing partial differential equations are derived by incorporating the nonlocal scale effects. Assuming a structure of n parallel nanobeams, the vibration of the system is described by a coupled set of n partial differential equations. The method involves a change of variables to uncouple the equations and the differential transform method as an efficient mathematical technique tomore » solve the nonlocal governing differential equations. Then a number of parametric studies are conducted to assess the effect of the nonlocal scaling parameter, rotational speed, boundary conditions, hub radius, and the stiffness coefficients of the elastic interlayer media on the vibration behavior of the coupled rotating multiple-carbon-nanotube-beam system. It is revealed that the bending vibration of the system is significantly influenced by the rotational speed, elastic mediums, and the nonlocal scaling parameters. This model is validated by comparing the results with those available in the literature. The natural frequencies are in a reasonably good agreement with the reported results.« less

Stability analysis of a time-periodic 2-dof MEMS structure

NASA Astrophysics Data System (ADS)

Kniffka, Till Jochen; Welte, Johannes; Ecker, Horst

2012-11-01

Microelectromechanical systems (MEMS) are becoming important for all kinds of industrial applications. Among them are filters in communication devices, due to the growing demand for efficient and accurate filtering of signals. In recent developments single degree of freedom (1-dof) oscillators, that are operated at a parametric resonances, are employed for such tasks. Typically vibration damping is low in such MEM systems. While parametric excitation (PE) is used so far to take advantage of a parametric resonance, this contribution suggests to also exploit parametric anti-resonances in order to improve the damping behavior of such systems. Modeling aspects of a 2-dof MEM system and first results of the analysis of the non-linear and the linearized system are the focus of this paper. In principle the investigated system is an oscillating mechanical system with two degrees of freedom x = [x1x2]T that can be described by Mx+Cx+K1x+K3(x2)x+Fes(x,V(t)) = 0. The system is inherently non-linear because of the cubic mechanical stiffness K3 of the structure, but also because of electrostatic forces (1+cos(ωt))Fes(x) that act on the system. Electrostatic forces are generated by comb drives and are proportional to the applied time-periodic voltage V(t). These drives also provide the means to introduce time-periodic coefficients, i.e. parametric excitation (1+cos(ωt)) with frequency ω. For a realistic MEM system the coefficients of the non-linear set of differential equations need to be scaled for efficient numerical treatment. The final mathematical model is a set of four non-linear time-periodic homogeneous differential equations of first order. Numerical results are obtained from two different methods. The linearized time-periodic (LTP) system is studied by calculating the Monodromy matrix of the system. The eigenvalues of this matrix decide on the stability of the LTP-system. To study the unabridged non-linear system, the bifurcation software ManLab is employed. Continuation analysis including stability evaluations are executed and show the frequency ranges for which the 2-dof system becomes unstable due to parametric resonances. Moreover, the existence of frequency intervals are shown where enhanced damping for the system is observed for this MEMS. The results from the stability studies are confirmed by simulation results.

A non-linear dimension reduction methodology for generating data-driven stochastic input models

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

Ganapathysubramanian, Baskar; Zabaras, Nicholas

Stochastic analysis of random heterogeneous media (polycrystalline materials, porous media, functionally graded materials) provides information of significance only if realistic input models of the topology and property variations are used. This paper proposes a framework to construct such input stochastic models for the topology and thermal diffusivity variations in heterogeneous media using a data-driven strategy. Given a set of microstructure realizations (input samples) generated from given statistical information about the medium topology, the framework constructs a reduced-order stochastic representation of the thermal diffusivity. This problem of constructing a low-dimensional stochastic representation of property variations is analogous to the problem ofmore » manifold learning and parametric fitting of hyper-surfaces encountered in image processing and psychology. Denote by M the set of microstructures that satisfy the given experimental statistics. A non-linear dimension reduction strategy is utilized to map M to a low-dimensional region, A. We first show that M is a compact manifold embedded in a high-dimensional input space R{sup n}. An isometric mapping F from M to a low-dimensional, compact, connected set A is contained in R{sup d}(d<

Glass promotes the differentiation of neuronal and non-neuronal cell types in the Drosophila eye

PubMed Central

Morrison, Carolyn A.; Chen, Hao; Cook, Tiffany; Brown, Stuart

2018-01-01

Transcriptional regulators can specify different cell types from a pool of equivalent progenitors by activating distinct developmental programs. The Glass transcription factor is expressed in all progenitors in the developing Drosophila eye, and is maintained in both neuronal and non-neuronal cell types. Glass is required for neuronal progenitors to differentiate as photoreceptors, but its role in non-neuronal cone and pigment cells is unknown. To determine whether Glass activity is limited to neuronal lineages, we compared the effects of misexpressing it in neuroblasts of the larval brain and in epithelial cells of the wing disc. Glass activated overlapping but distinct sets of genes in these neuronal and non-neuronal contexts, including markers of photoreceptors, cone cells and pigment cells. Coexpression of other transcription factors such as Pax2, Eyes absent, Lozenge and Escargot enabled Glass to induce additional genes characteristic of the non-neuronal cell types. Cell type-specific glass mutations generated in cone or pigment cells using somatic CRISPR revealed autonomous developmental defects, and expressing Glass specifically in these cells partially rescued glass mutant phenotypes. These results indicate that Glass is a determinant of organ identity that acts in both neuronal and non-neuronal cells to promote their differentiation into functional components of the eye. PMID:29324767

Continuation Methods for Qualitative Analysis of Aircraft Dynamics

NASA Technical Reports Server (NTRS)

Cummings, Peter A.

2004-01-01

A class of numerical methods for constructing bifurcation curves for systems of coupled, non-linear ordinary differential equations is presented. Foundations are discussed, and several variations are outlined along with their respective capabilities. Appropriate background material from dynamical systems theory is presented.

Linear and nonlinear stability criteria for compressible MHD flows in a gravitational field

NASA Astrophysics Data System (ADS)

Moawad, S. M.; Moawad

2013-10-01

The equilibrium and stability properties of ideal magnetohydrodynamics (MHD) of compressible flow in a gravitational field with a translational symmetry are investigated. Variational principles for the steady-state equations are formulated. The MHD equilibrium equations are obtained as critical points of a conserved Lyapunov functional. This functional consists of the sum of the total energy, the mass, the circulation along field lines (cross helicity), the momentum, and the magnetic helicity. In the unperturbed case, the equilibrium states satisfy a nonlinear second-order partial differential equation (PDE) associated with hydrodynamic Bernoulli law. The PDE can be an elliptic or a parabolic equation depending on increasing the poloidal flow speed. Linear and nonlinear Lyapunov stability conditions under translational symmetric perturbations are established for the equilibrium states.

The numerical dynamic for highly nonlinear partial differential equations

NASA Technical Reports Server (NTRS)

Lafon, A.; Yee, H. C.

1992-01-01

Problems associated with the numerical computation of highly nonlinear equations in computational fluid dynamics are set forth and analyzed in terms of the potential ranges of spurious behaviors. A reaction-convection equation with a nonlinear source term is employed to evaluate the effects related to spatial and temporal discretizations. The discretization of the source term is described according to several methods, and the various techniques are shown to have a significant effect on the stability of the spurious solutions. Traditional linearized stability analyses cannot provide the level of confidence required for accurate fluid dynamics computations, and the incorporation of nonlinear analysis is proposed. Nonlinear analysis based on nonlinear dynamical systems complements the conventional linear approach and is valuable in the analysis of hypersonic aerodynamics and combustion phenomena.

An efficient method for solving the steady Euler equations

NASA Technical Reports Server (NTRS)

Liou, M.-S.

1986-01-01

An efficient numerical procedure for solving a set of nonlinear partial differential equations, the steady Euler equations, using Newton's linearization procedure is presented. A theorem indicating quadratic convergence for the case of differential equations is demonstrated. A condition for the domain of quadratic convergence Omega(2) is obtained which indicates that whether an approximation lies in Omega(2) depends on the rate of change and the smoothness of the flow vectors, and hence is problem-dependent. The choice of spatial differencing, of particular importance for the present method, is discussed. The treatment of boundary conditions is addressed, and the system of equations resulting from the foregoing analysis is summarized and solution strategies are discussed. The convergence of calculated solutions is demonstrated by comparing them with exact solutions to one and two-dimensional problems.

Four points function fitted and first derivative procedure for determining the end points in potentiometric titration curves: statistical analysis and method comparison.

PubMed

Kholeif, S A

2001-06-01

A new method that belongs to the differential category for determining the end points from potentiometric titration curves is presented. It uses a preprocess to find first derivative values by fitting four data points in and around the region of inflection to a non-linear function, and then locate the end point, usually as a maximum or minimum, using an inverse parabolic interpolation procedure that has an analytical solution. The behavior and accuracy of the sigmoid and cumulative non-linear functions used are investigated against three factors. A statistical evaluation of the new method using linear least-squares method validation and multifactor data analysis are covered. The new method is generally applied to symmetrical and unsymmetrical potentiometric titration curves, and the end point is calculated using numerical procedures only. It outperforms the "parent" regular differential method in almost all factors levels and gives accurate results comparable to the true or estimated true end points. Calculated end points from selected experimental titration curves compatible with the equivalence point category of methods, such as Gran or Fortuin, are also compared with the new method.

A neuro approach to solve fuzzy Riccati differential equations

NASA Astrophysics Data System (ADS)

Shahrir, Mohammad Shazri; Kumaresan, N.; Kamali, M. Z. M.; Ratnavelu, Kurunathan

2015-10-01

There are many applications of optimal control theory especially in the area of control systems in engineering. In this paper, fuzzy quadratic Riccati differential equation is estimated using neural networks (NN). Previous works have shown reliable results using Runge-Kutta 4th order (RK4). The solution can be achieved by solving the 1st Order Non-linear Differential Equation (ODE) that is found commonly in Riccati differential equation. Research has shown improved results relatively to the RK4 method. It can be said that NN approach shows promising results with the advantage of continuous estimation and improved accuracy that can be produced over RK4.

A neuro approach to solve fuzzy Riccati differential equations

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

Shahrir, Mohammad Shazri, E-mail: mshazri@gmail.com; Telekom Malaysia, R&D TM Innovation Centre, LingkaranTeknokrat Timur, 63000 Cyberjaya, Selangor; Kumaresan, N., E-mail: drnk2008@gmail.com

There are many applications of optimal control theory especially in the area of control systems in engineering. In this paper, fuzzy quadratic Riccati differential equation is estimated using neural networks (NN). Previous works have shown reliable results using Runge-Kutta 4th order (RK4). The solution can be achieved by solving the 1st Order Non-linear Differential Equation (ODE) that is found commonly in Riccati differential equation. Research has shown improved results relatively to the RK4 method. It can be said that NN approach shows promising results with the advantage of continuous estimation and improved accuracy that can be produced over RK4.

Inductive Linear-Position Sensor/Limit-Sensor Units

NASA Technical Reports Server (NTRS)

Alhom, Dean; Howard, David; Smith, Dennis; Dutton, Kenneth

2007-01-01

A new sensor provides an absolute position measurement. A schematic view of a motorized linear-translation stage that contains, at each end, an electronic unit that functions as both (1) a non-contact sensor that measures the absolute position of the stage and (2) a non-contact equivalent of a limit switch that is tripped when the stage reaches the nominal limit position. The need for such an absolute linear position-sensor/limit-sensor unit arises in the case of a linear-translation stage that is part of a larger system in which the actual stopping position of the stage (relative to the nominal limit position) must be known. Because inertia inevitably causes the stage to run somewhat past the nominal limit position, tripping of a standard limit switch or other limit sensor does not provide the required indication of the actual stopping position. This innovative sensor unit operates on an electromagnetic-induction principle similar to that of linear variable differential transformers (LVDTs)

The numerical solution of ordinary differential equations by the Taylor series method

NASA Technical Reports Server (NTRS)

Silver, A. H.; Sullivan, E.

1973-01-01

A programming implementation of the Taylor series method is presented for solving ordinary differential equations. The compiler is written in PL/1, and the target language is FORTRAN IV. The reduction of a differential system to rational form is described along with the procedures required for automatic numerical integration. The Taylor method is compared with two other methods for a number of differential equations. Algorithms using the Taylor method to find the zeroes of a given differential equation and to evaluate partial derivatives are presented. An annotated listing of the PL/1 program which performs the reduction and code generation is given. Listings of the FORTRAN routines used by the Taylor series method are included along with a compilation of all the recurrence formulas used to generate the Taylor coefficients for non-rational functions.

On the hierarchy of partially invariant submodels of differential equations

NASA Astrophysics Data System (ADS)

Golovin, Sergey V.

2008-07-01

It is noted that the partially invariant solution (PIS) of differential equations in many cases can be represented as an invariant reduction of some PISs of the higher rank. This introduces a hierarchic structure in the set of all PISs of a given system of differential equations. An equivalence of the two-step and the direct ways of construction of PISs is proved. The hierarchy simplifies the process of enumeration and analysis of partially invariant submodels to the given system of differential equations. In this framework, the complete classification of regular partially invariant solutions of ideal MHD equations is given.

Solution of differential equations by application of transformation groups

NASA Technical Reports Server (NTRS)

Driskell, C. N., Jr.; Gallaher, L. J.; Martin, R. H., Jr.

1968-01-01

Report applies transformation groups to the solution of systems of ordinary differential equations and partial differential equations. Lies theorem finds an integrating factor for appropriate invariance group or groups can be found and can be extended to partial differential equations.

Application of ANNs approach for wave-like and heat-like equations

NASA Astrophysics Data System (ADS)

Jafarian, Ahmad; Baleanu, Dumitru

2017-12-01

Artificial neural networks are data processing systems which originate from human brain tissue studies. The remarkable abilities of these networks help us to derive desired results from complicated raw data. In this study, we intend to duplicate an efficient iterative method to the numerical solution of two famous partial differential equations, namely the wave-like and heat-like problems. It should be noted that many physical phenomena such as coupling currents in a flat multi-strand two-layer super conducting cable, non-homogeneous elastic waves in soils and earthquake stresses, are described by initial-boundary value wave and heat partial differential equations with variable coefficients. To the numerical solution of these equations, a combination of the power series method and artificial neural networks approach, is used to seek an appropriate bivariate polynomial solution of the mentioned initial-boundary value problem. Finally, several computer simulations confirmed the theoretical results and demonstrating applicability of the method.

Investigation of Solitary wave solutions for Vakhnenko-Parkes equation via exp-function and Exp(-ϕ(ξ))-expansion method.

PubMed

Roshid, Harun-Or; Kabir, Md Rashed; Bhowmik, Rajandra Chadra; Datta, Bimal Kumar

2014-01-01

In this paper, we have described two dreadfully important methods to solve nonlinear partial differential equations which are known as exp-function and the exp(-ϕ(ξ)) -expansion method. Recently, there are several methods to use for finding analytical solutions of the nonlinear partial differential equations. The methods are diverse and useful for solving the nonlinear evolution equations. With the help of these methods, we are investigated the exact travelling wave solutions of the Vakhnenko- Parkes equation. The obtaining soliton solutions of this equation are described many physical phenomena for weakly nonlinear surface and internal waves in a rotating ocean. Further, three-dimensional plots of the solutions such as solitons, singular solitons, bell type solitary wave i.e. non-topological solitons solutions and periodic solutions are also given to visualize the dynamics of the equation.

Tower of London test: a comparison between conventional statistic approach and modelling based on artificial neural network in differentiating fronto-temporal dementia from Alzheimer's disease.

PubMed

Franceschi, Massimo; Caffarra, Paolo; Savarè, Rita; Cerutti, Renata; Grossi, Enzo

2011-01-01

The early differentiation of Alzheimer's disease (AD) from frontotemporal dementia (FTD) may be difficult. The Tower of London (ToL), thought to assess executive functions such as planning and visuo-spatial working memory, could help in this purpose. Twentytwo Dementia Centers consecutively recruited patients with early FTD or AD. ToL performances of these groups were analyzed using both the conventional statistical approaches and the Artificial Neural Networks (ANNs) modelling. Ninety-four non aphasic FTD and 160 AD patients were recruited. ToL Accuracy Score (AS) significantly (p < 0.05) differentiated FTD from AD patients. However, the discriminant validity of AS checked by ROC curve analysis, yielded no significant results in terms of sensitivity and specificity (AUC 0.63). The performances of the 12 Success Subscores (SS) together with age, gender and schooling years were entered into advanced ANNs developed by Semeion Institute. The best ANNs were selected and submitted to ROC curves. The non-linear model was able to discriminate FTD from AD with an average AUC for 7 independent trials of 0.82. The use of hidden information contained in the different items of ToL and the non linear processing of the data through ANNs allows a high discrimination between FTD and AD in individual patients.

Single-cell topological RNA-Seq analysis reveals insights into cellular differentiation and development

PubMed Central

Rizvi, Abbas H.; Camara, Pablo G.; Kandror, Elena K.; Roberts, Thomas J.; Schieren, Ira; Maniatis, Tom; Rabadan, Raul

2017-01-01

Transcriptional programs control cellular lineage commitment and differentiation during development. Understanding cell fate has been advanced by studying single-cell RNA-seq, but is limited by the assumptions of current analytic methods regarding the structure of data. We present single-cell topological data analysis (scTDA), an algorithm for topology-based computational analyses to study temporal, unbiased transcriptional regulation. Compared to other methods, scTDA is a non-linear, model-independent, unsupervised statistical framework that can characterize transient cellular states. We applied scTDA to the analysis of murine embryonic stem cell (mESC) differentiation in vitro in response to inducers of motor neuron differentiation. scTDA resolved asynchrony and continuity in cellular identity over time, and identified four transient states (pluripotent, precursor, progenitor, and fully differentiated cells) based on changes in stage-dependent combinations of transcription factors, RNA-binding proteins and long non-coding RNAs. scTDA can be applied to study asynchronous cellular responses to either developmental cues or environmental perturbations. PMID:28459448

Social inequality, lifestyles and health - a non-linear canonical correlation analysis based on the approach of Pierre Bourdieu.

PubMed

Grosse Frie, Kirstin; Janssen, Christian

2009-01-01

Based on the theoretical and empirical approach of Pierre Bourdieu, a multivariate non-linear method is introduced as an alternative way to analyse the complex relationships between social determinants and health. The analysis is based on face-to-face interviews with 695 randomly selected respondents aged 30 to 59. Variables regarding socio-economic status, life circumstances, lifestyles, health-related behaviour and health were chosen for the analysis. In order to determine whether the respondents can be differentiated and described based on these variables, a non-linear canonical correlation analysis (OVERALS) was performed. The results can be described on three dimensions; Eigenvalues add up to the fit of 1.444, which can be interpreted as approximately 50 % of explained variance. The three-dimensional space illustrates correspondences between variables and provides a framework for interpretation based on latent dimensions, which can be described by age, education, income and gender. Using non-linear canonical correlation analysis, health characteristics can be analysed in conjunction with socio-economic conditions and lifestyles. Based on Bourdieus theoretical approach, the complex correlations between these variables can be more substantially interpreted and presented.

Non-linear dynamic characteristics and optimal control of giant magnetostrictive film subjected to in-plane stochastic excitation

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

Zhu, Z. W., E-mail: zhuzhiwen@tju.edu.cn; Tianjin Key Laboratory of Non-linear Dynamics and Chaos Control, 300072, Tianjin; Zhang, W. D., E-mail: zhangwenditju@126.com

2014-03-15

The non-linear dynamic characteristics and optimal control of a giant magnetostrictive film (GMF) subjected to in-plane stochastic excitation were studied. Non-linear differential items were introduced to interpret the hysteretic phenomena of the GMF, and the non-linear dynamic model of the GMF subjected to in-plane stochastic excitation was developed. The stochastic stability was analysed, and the probability density function was obtained. The condition of stochastic Hopf bifurcation and noise-induced chaotic response were determined, and the fractal boundary of the system's safe basin was provided. The reliability function was solved from the backward Kolmogorov equation, and an optimal control strategy was proposedmore » in the stochastic dynamic programming method. Numerical simulation shows that the system stability varies with the parameters, and stochastic Hopf bifurcation and chaos appear in the process; the area of the safe basin decreases when the noise intensifies, and the boundary of the safe basin becomes fractal; the system reliability improved through stochastic optimal control. Finally, the theoretical and numerical results were proved by experiments. The results are helpful in the engineering applications of GMF.« less

Boosting Bayesian parameter inference of stochastic differential equation models with methods from statistical physics

NASA Astrophysics Data System (ADS)

Albert, Carlo; Ulzega, Simone; Stoop, Ruedi

2016-04-01

Measured time-series of both precipitation and runoff are known to exhibit highly non-trivial statistical properties. For making reliable probabilistic predictions in hydrology, it is therefore desirable to have stochastic models with output distributions that share these properties. When parameters of such models have to be inferred from data, we also need to quantify the associated parametric uncertainty. For non-trivial stochastic models, however, this latter step is typically very demanding, both conceptually and numerically, and always never done in hydrology. Here, we demonstrate that methods developed in statistical physics make a large class of stochastic differential equation (SDE) models amenable to a full-fledged Bayesian parameter inference. For concreteness we demonstrate these methods by means of a simple yet non-trivial toy SDE model. We consider a natural catchment that can be described by a linear reservoir, at the scale of observation. All the neglected processes are assumed to happen at much shorter time-scales and are therefore modeled with a Gaussian white noise term, the standard deviation of which is assumed to scale linearly with the system state (water volume in the catchment). Even for constant input, the outputs of this simple non-linear SDE model show a wealth of desirable statistical properties, such as fat-tailed distributions and long-range correlations. Standard algorithms for Bayesian inference fail, for models of this kind, because their likelihood functions are extremely high-dimensional intractable integrals over all possible model realizations. The use of Kalman filters is illegitimate due to the non-linearity of the model. Particle filters could be used but become increasingly inefficient with growing number of data points. Hamiltonian Monte Carlo algorithms allow us to translate this inference problem to the problem of simulating the dynamics of a statistical mechanics system and give us access to most sophisticated methods that have been developed in the statistical physics community over the last few decades. We demonstrate that such methods, along with automated differentiation algorithms, allow us to perform a full-fledged Bayesian inference, for a large class of SDE models, in a highly efficient and largely automatized manner. Furthermore, our algorithm is highly parallelizable. For our toy model, discretized with a few hundred points, a full Bayesian inference can be performed in a matter of seconds on a standard PC.

Simultaneous quaternion estimation (QUEST) and bias determination

NASA Technical Reports Server (NTRS)

Markley, F. Landis

1989-01-01

Tests of a new method for the simultaneous estimation of spacecraft attitude and sensor biases, based on a quaternion estimation algorithm minimizing Wahba's loss function are presented. The new method is compared with a conventional batch least-squares differential correction algorithm. The estimates are based on data from strapdown gyros and star trackers, simulated with varying levels of Gaussian noise for both inertially-fixed and Earth-pointing reference attitudes. Both algorithms solve for the spacecraft attitude and the gyro drift rate biases. They converge to the same estimates at the same rate for inertially-fixed attitude, but the new algorithm converges more slowly than the differential correction for Earth-pointing attitude. The slower convergence of the new method for non-zero attitude rates is believed to be due to the use of an inadequate approximation for a partial derivative matrix. The new method requires about twice the computational effort of the differential correction. Improving the approximation for the partial derivative matrix in the new method is expected to improve its convergence at the cost of increased computational effort.

High-order Newton-penalty algorithms

NASA Astrophysics Data System (ADS)

Dussault, Jean-Pierre

2005-10-01

Recent efforts in differentiable non-linear programming have been focused on interior point methods, akin to penalty and barrier algorithms. In this paper, we address the classical equality constrained program solved using the simple quadratic loss penalty function/algorithm. The suggestion to use extrapolations to track the differentiable trajectory associated with penalized subproblems goes back to the classic monograph of Fiacco & McCormick. This idea was further developed by Gould who obtained a two-steps quadratically convergent algorithm using prediction steps and Newton correction. Dussault interpreted the prediction step as a combined extrapolation with respect to the penalty parameter and the residual of the first order optimality conditions. Extrapolation with respect to the residual coincides with a Newton step.We explore here higher-order extrapolations, thus higher-order Newton-like methods. We first consider high-order variants of the Newton-Raphson method applied to non-linear systems of equations. Next, we obtain improved asymptotic convergence results for the quadratic loss penalty algorithm by using high-order extrapolation steps.

A hybrid credibility-based fuzzy multiple objective optimisation to differential pricing and inventory policies with arbitrage consideration

NASA Astrophysics Data System (ADS)

Ghasemy Yaghin, R.; Fatemi Ghomi, S. M. T.; Torabi, S. A.

2015-10-01

In most markets, price differentiation mechanisms enable manufacturers to offer different prices for their products or services in different customer segments; however, the perfect price discrimination is usually impossible for manufacturers. The importance of accounting for uncertainty in such environments spurs an interest to develop appropriate decision-making tools to deal with uncertain and ill-defined parameters in joint pricing and lot-sizing problems. This paper proposes a hybrid bi-objective credibility-based fuzzy optimisation model including both quantitative and qualitative objectives to cope with these issues. Taking marketing and lot-sizing decisions into account simultaneously, the model aims to maximise the total profit of manufacturer and to improve service aspects of retailing simultaneously to set different prices with arbitrage consideration. After applying appropriate strategies to defuzzify the original model, the resulting non-linear multi-objective crisp model is then solved by a fuzzy goal programming method. An efficient stochastic search procedure using particle swarm optimisation is also proposed to solve the non-linear crisp model.

Integral method for transient He II heat transfer in a semi-infinite domain

NASA Astrophysics Data System (ADS)

Baudouy, B.

2002-05-01

Integral methods are suited to solve a non-linear system of differential equations where the non-linearity can be found either in the differential equations or in the boundary conditions. Though they are approximate methods, they have proven to give simple solutions with acceptable accuracy for transient heat transfer in He II. Taking in account the temperature dependence of thermal properties, direct solutions are found without the need of adjusting a parameter. Previously, we have presented a solution for the clamped heat flux and in the present study this method is used to accommodate the clamped-temperature problem. In the case of constant thermal properties, this method yields results that are within a few percent of the exact solution for the heat flux at the axis origin. We applied this solution to analyze recovery from burnout and find an agreement within 10% at low heat flux, whereas at high heat flux the model deviates from the experimental data suggesting the need for a more refined thermal model.

Heat transfer in porous medium embedded with vertical plate: Non-equilibrium approach - Part A

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

Badruddin, Irfan Anjum; Quadir, G. A.

2016-06-08

Heat transfer in a porous medium embedded with vertical flat plate is investigated by using thermal non-equilibrium model. Darcy model is employed to simulate the flow inside porous medium. It is assumed that the heat transfer takes place by natural convection and radiation. The vertical plate is maintained at isothermal temperature. The governing partial differential equations are converted into non-dimensional form and solved numerically using finite element method. Results are presented in terms of isotherms and streamlines for various parameters such as heat transfer coefficient parameter, thermal conductivity ratio, and radiation parameter.

From stochastic processes to numerical methods: A new scheme for solving reaction subdiffusion fractional partial differential equations

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

Angstmann, C.N.; Donnelly, I.C.; Henry, B.I., E-mail: B.Henry@unsw.edu.au

We have introduced a new explicit numerical method, based on a discrete stochastic process, for solving a class of fractional partial differential equations that model reaction subdiffusion. The scheme is derived from the master equations for the evolution of the probability density of a sum of discrete time random walks. We show that the diffusion limit of the master equations recovers the fractional partial differential equation of interest. This limiting procedure guarantees the consistency of the numerical scheme. The positivity of the solution and stability results are simply obtained, provided that the underlying process is well posed. We also showmore » that the method can be applied to standard reaction–diffusion equations. This work highlights the broader applicability of using discrete stochastic processes to provide numerical schemes for partial differential equations, including fractional partial differential equations.« less

Global Regularity for the Fractional Euler Alignment System

NASA Astrophysics Data System (ADS)

Do, Tam; Kiselev, Alexander; Ryzhik, Lenya; Tan, Changhui

2018-04-01

We study a pressureless Euler system with a non-linear density-dependent alignment term, originating in the Cucker-Smale swarming models. The alignment term is dissipative in the sense that it tends to equilibrate the velocities. Its density dependence is natural: the alignment rate increases in the areas of high density due to species discomfort. The diffusive term has the order of a fractional Laplacian {(-partial _{xx})^{α/2}, α \\in (0, 1)}. The corresponding Burgers equation with a linear dissipation of this type develops shocks in a finite time. We show that the alignment nonlinearity enhances the dissipation, and the solutions are globally regular for all {α \\in (0, 1)}. To the best of our knowledge, this is the first example of such regularization due to the non-local nonlinear modulation of dissipation.

Reciprocal links among differential parenting, perceived partiality, and self-worth: a three-wave longitudinal study.

PubMed

Shebloski, Barbara; Conger, Katherine J; Widaman, Keith F

2005-12-01

This study examined reciprocal links between parental differential treatment, siblings' perception of partiality, and self-worth with 3 waves of data from 384 adolescent sibling dyads. Results suggest that birth-order status was significantly associated with self-worth and perception of maternal and paternal differential treatment. There was a consistent across-time effect of self-worth on perception of parental partiality for later born siblings, but not earlier born siblings, and a consistent effect of differential treatment on perception of partiality for earlier born but not later born siblings. The results contribute new insight into the associations between perception of differential parenting and adolescents' adjustment and the role of birth order. Copyright 2006 APA, all rights reserved).

Robust global identifiability theory using potentials--Application to compartmental models.

PubMed

Wongvanich, N; Hann, C E; Sirisena, H R

2015-04-01

This paper presents a global practical identifiability theory for analyzing and identifying linear and nonlinear compartmental models. The compartmental system is prolonged onto the potential jet space to formulate a set of input-output equations that are integrals in terms of the measured data, which allows for robust identification of parameters without requiring any simulation of the model differential equations. Two classes of linear and non-linear compartmental models are considered. The theory is first applied to analyze the linear nitrous oxide (N2O) uptake model. The fitting accuracy of the identified models from differential jet space and potential jet space identifiability theories is compared with a realistic noise level of 3% which is derived from sensor noise data in the literature. The potential jet space approach gave a match that was well within the coefficient of variation. The differential jet space formulation was unstable and not suitable for parameter identification. The proposed theory is then applied to a nonlinear immunological model for mastitis in cows. In addition, the model formulation is extended to include an iterative method which allows initial conditions to be accurately identified. With up to 10% noise, the potential jet space theory predicts the normalized population concentration infected with pathogens, to within 9% of the true curve. Copyright © 2015 Elsevier Inc. All rights reserved.

Comparing Consider-Covariance Analysis with Sigma-Point Consider Filter and Linear-Theory Consider Filter Formulations

NASA Technical Reports Server (NTRS)

Lisano, Michael E.

2007-01-01

Recent literature in applied estimation theory reflects growing interest in the sigma-point (also called unscented ) formulation for optimal sequential state estimation, often describing performance comparisons with extended Kalman filters as applied to specific dynamical problems [c.f. 1, 2, 3]. Favorable attributes of sigma-point filters are described as including a lower expected error for nonlinear even non-differentiable dynamical systems, and a straightforward formulation not requiring derivation or implementation of any partial derivative Jacobian matrices. These attributes are particularly attractive, e.g. in terms of enabling simplified code architecture and streamlined testing, in the formulation of estimators for nonlinear spaceflight mechanics systems, such as filter software onboard deep-space robotic spacecraft. As presented in [4], the Sigma-Point Consider Filter (SPCF) algorithm extends the sigma-point filter algorithm to the problem of consider covariance analysis. Considering parameters in a dynamical system, while estimating its state, provides an upper bound on the estimated state covariance, which is viewed as a conservative approach to designing estimators for problems of general guidance, navigation and control. This is because, whether a parameter in the system model is observable or not, error in the knowledge of the value of a non-estimated parameter will increase the actual uncertainty of the estimated state of the system beyond the level formally indicated by the covariance of an estimator that neglects errors or uncertainty in that parameter. The equations for SPCF covariance evolution are obtained in a fashion similar to the derivation approach taken with standard (i.e. linearized or extended) consider parameterized Kalman filters (c.f. [5]). While in [4] the SPCF and linear-theory consider filter (LTCF) were applied to an illustrative linear dynamics/linear measurement problem, in the present work examines the SPCF as applied to nonlinear sequential consider covariance analysis, i.e. in the presence of nonlinear dynamics and nonlinear measurements. A simple SPCF for orbit determination, exemplifying an algorithm hosted in the guidance, navigation and control (GN&C) computer processor of a hypothetical robotic spacecraft, was implemented, and compared with an identically-parameterized (standard) extended, consider-parameterized Kalman filter. The onboard filtering scenario examined is a hypothetical spacecraft orbit about a small natural body with imperfectly-known mass. The formulations, relative complexities, and performances of the filters are compared and discussed.

Dynamics of curved fronts in systems with power-law memory

NASA Astrophysics Data System (ADS)

Abu Hamed, M.; Nepomnyashchy, A. A.

2016-08-01

The dynamics of a curved front in a plane between two stable phases with equal potentials is modeled via two-dimensional fractional in time partial differential equation. A closed equation governing a slow motion of a small-curvature front is derived and applied for two typical examples of the potential function. Approximate axisymmetric and non-axisymmetric solutions are obtained.

JDINAC: joint density-based non-parametric differential interaction network analysis and classification using high-dimensional sparse omics data.

PubMed

Ji, Jiadong; He, Di; Feng, Yang; He, Yong; Xue, Fuzhong; Xie, Lei

2017-10-01

A complex disease is usually driven by a number of genes interwoven into networks, rather than a single gene product. Network comparison or differential network analysis has become an important means of revealing the underlying mechanism of pathogenesis and identifying clinical biomarkers for disease classification. Most studies, however, are limited to network correlations that mainly capture the linear relationship among genes, or rely on the assumption of a parametric probability distribution of gene measurements. They are restrictive in real application. We propose a new Joint density based non-parametric Differential Interaction Network Analysis and Classification (JDINAC) method to identify differential interaction patterns of network activation between two groups. At the same time, JDINAC uses the network biomarkers to build a classification model. The novelty of JDINAC lies in its potential to capture non-linear relations between molecular interactions using high-dimensional sparse data as well as to adjust confounding factors, without the need of the assumption of a parametric probability distribution of gene measurements. Simulation studies demonstrate that JDINAC provides more accurate differential network estimation and lower classification error than that achieved by other state-of-the-art methods. We apply JDINAC to a Breast Invasive Carcinoma dataset, which includes 114 patients who have both tumor and matched normal samples. The hub genes and differential interaction patterns identified were consistent with existing experimental studies. Furthermore, JDINAC discriminated the tumor and normal sample with high accuracy by virtue of the identified biomarkers. JDINAC provides a general framework for feature selection and classification using high-dimensional sparse omics data. R scripts available at https://github.com/jijiadong/JDINAC. lxie@iscb.org. Supplementary data are available at Bioinformatics online. © The Author (2017). Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com

DOUAR: A new three-dimensional creeping flow numerical model for the solution of geological problems

NASA Astrophysics Data System (ADS)

Braun, Jean; Thieulot, Cédric; Fullsack, Philippe; DeKool, Marthijn; Beaumont, Christopher; Huismans, Ritske

2008-12-01

We present a new finite element code for the solution of the Stokes and energy (or heat transport) equations that has been purposely designed to address crustal-scale to mantle-scale flow problems in three dimensions. Although it is based on an Eulerian description of deformation and flow, the code, which we named DOUAR ('Earth' in Breton language), has the ability to track interfaces and, in particular, the free surface, by using a dual representation based on a set of particles placed on the interface and the computation of a level set function on the nodes of the finite element grid, thus ensuring accuracy and efficiency. The code also makes use of a new method to compute the dynamic Delaunay triangulation connecting the particles based on non-Euclidian, curvilinear measure of distance, ensuring that the density of particles remains uniform and/or dynamically adapted to the curvature of the interface. The finite element discretization is based on a non-uniform, yet regular octree division of space within a unit cube that allows efficient adaptation of the finite element discretization, i.e. in regions of strong velocity gradient or high interface curvature. The finite elements are cubes (the leaves of the octree) in which a q1- p0 interpolation scheme is used. Nodal incompatibilities across faces separating elements of differing size are dealt with by introducing linear constraints among nodal degrees of freedom. Discontinuities in material properties across the interfaces are accommodated by the use of a novel method (which we called divFEM) to integrate the finite element equations in which the elemental volume is divided by a local octree to an appropriate depth (resolution). A variety of rheologies have been implemented including linear, non-linear and thermally activated creep and brittle (or plastic) frictional deformation. A simple smoothing operator has been defined to avoid checkerboard oscillations in pressure that tend to develop when using a highly irregular octree discretization and the tri-linear (or q1- p0) finite element. A three-dimensional cloud of particles is used to track material properties that depend on the integrated history of deformation (the integrated strain, for example); its density is variable and dynamically adapted to the computed flow. The large system of algebraic equations that results from the finite element discretization and linearization of the basic partial differential equations is solved using a multi-frontal massively parallel direct solver that can efficiently factorize poorly conditioned systems resulting from the highly non-linear rheology and the presence of the free surface. The code is almost entirely parallelized. We present example results including the onset of a Rayleigh-Taylor instability, the indentation of a rigid-plastic material and the formation of a fold beneath a free eroding surface, that demonstrate the accuracy, efficiency and appropriateness of the new code to solve complex geodynamical problems in three dimensions.

Utility of p57 immunohistochemistry in differentiating between complete mole, partial mole & non-molar or hydropic abortus.

PubMed

Samadder, Abhimanyu; Kar, Rakhee

2017-01-01

There is considerable inter-observer variability in the diagnosis of molar pregnancies by histomorphological examination of products of conception (POC). The p57KIP2 gene is paternally imprinted and expressed from the maternal allele. On immunohistochemistry (IHC) with p57, complete mole (CM) shows absent staining whereas hydropic abortus (HA) and partial mole (PM) show positive staining. This study was undertaken to evaluate the role of p57 IHC along with histomorphology in differentiating between CM, PM and non-molar or HA. This was a cross-sectional study over a period of three and a half years on archival material. Detailed histomorphological review along with p57 IHC was carried out in 28 diagnosed cases (23 CM, 4 PM and 1 molar pregnancy not categorized) and 25 controls of four normal placentas and 21 POC (8 non-hydropic and 13 HA). In 14.8 per cent (4/27) cases, there was discordance in accurate subtyping of molar pregnancy. One case of CM showed inconsistent IHC pattern. In 15.4 per cent (2/13) HA, molar pregnancy was final diagnosis. After final review, there were 25 CM, five PM, 22 non-molar controls including 10 HA and one not assigned (PM/HA). IHC with p57 was negative in 96 per cent CM and positive in 100 and 95 per cent PM and non-molar controls, respectively. This study showed that negative p57KIP2 immunostaining reliably identified CM and could be used in association with the histological findings to distinguish CM from its mimics.

Experimental feedback linearisation of a vibrating system with a non-smooth nonlinearity

NASA Astrophysics Data System (ADS)

Lisitano, D.; Jiffri, S.; Bonisoli, E.; Mottershead, J. E.

2018-03-01

Input-output partial feedback linearisation is demonstrated experimentally for the first time on a system with non-smooth nonlinearity, a laboratory three degrees of freedom lumped mass system with a piecewise-linear spring. The output degree of freedom is located away from the nonlinearity so that the partial feedback linearisation possesses nonlinear internal dynamics. The dynamic behaviour of the linearised part is specified by eigenvalue assignment and an investigation of the zero dynamics is carried out to confirm stability of the overall system. A tuned numerical model is developed for use in the controller and to produce numerical outputs for comparison with experimental closed-loop results. A new limitation of the feedback linearisation method is discovered in the case of lumped mass systems - that the input and output must share the same degrees of freedom.

An application of the Maslov complex germ method to the one-dimensional nonlocal Fisher-KPP equation

NASA Astrophysics Data System (ADS)

Shapovalov, A. V.; Trifonov, A. Yu.

A semiclassical approximation approach based on the Maslov complex germ method is considered in detail for the one-dimensional nonlocal Fisher-Kolmogorov-Petrovskii-Piskunov (Fisher-KPP) equation under the supposition of weak diffusion. In terms of the semiclassical formalism developed, the original nonlinear equation is reduced to an associated linear partial differential equation and some algebraic equations for the coefficients of the linear equation with a given accuracy of the asymptotic parameter. The solutions of the nonlinear equation are constructed from the solutions of both the linear equation and the algebraic equations. The solutions of the linear problem are found with the use of symmetry operators. A countable family of the leading terms of the semiclassical asymptotics is constructed in explicit form. The semiclassical asymptotics are valid by construction in a finite time interval. We construct asymptotics which are different from the semiclassical ones and can describe evolution of the solutions of the Fisher-KPP equation at large times. In the example considered, an initial unimodal distribution becomes multimodal, which can be treated as an example of a space structure.

Computing rates of Markov models of voltage-gated ion channels by inverting partial differential equations governing the probability density functions of the conducting and non-conducting states.

PubMed

Tveito, Aslak; Lines, Glenn T; Edwards, Andrew G; McCulloch, Andrew

2016-07-01

Markov models are ubiquitously used to represent the function of single ion channels. However, solving the inverse problem to construct a Markov model of single channel dynamics from bilayer or patch-clamp recordings remains challenging, particularly for channels involving complex gating processes. Methods for solving the inverse problem are generally based on data from voltage clamp measurements. Here, we describe an alternative approach to this problem based on measurements of voltage traces. The voltage traces define probability density functions of the functional states of an ion channel. These probability density functions can also be computed by solving a deterministic system of partial differential equations. The inversion is based on tuning the rates of the Markov models used in the deterministic system of partial differential equations such that the solution mimics the properties of the probability density function gathered from (pseudo) experimental data as well as possible. The optimization is done by defining a cost function to measure the difference between the deterministic solution and the solution based on experimental data. By evoking the properties of this function, it is possible to infer whether the rates of the Markov model are identifiable by our method. We present applications to Markov model well-known from the literature. Copyright © 2016 The Authors. Published by Elsevier Inc. All rights reserved.

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.

A canonical form of the equation of motion of linear dynamical systems

NASA Astrophysics Data System (ADS)

Kawano, Daniel T.; Salsa, Rubens Goncalves; Ma, Fai; Morzfeld, Matthias

2018-03-01

The equation of motion of a discrete linear system has the form of a second-order ordinary differential equation with three real and square coefficient matrices. It is shown that, for almost all linear systems, such an equation can always be converted by an invertible transformation into a canonical form specified by two diagonal coefficient matrices associated with the generalized acceleration and displacement. This canonical form of the equation of motion is unique up to an equivalence class for non-defective systems. As an important by-product, a damped linear system that possesses three symmetric and positive definite coefficients can always be recast as an undamped and decoupled system.

Identifiability of large-scale non-linear dynamic network models applied to the ADM1-case study.

PubMed

Nimmegeers, Philippe; Lauwers, Joost; Telen, Dries; Logist, Filip; Impe, Jan Van

2017-06-01

In this work, both the structural and practical identifiability of the Anaerobic Digestion Model no. 1 (ADM1) is investigated, which serves as a relevant case study of large non-linear dynamic network models. The structural identifiability is investigated using the probabilistic algorithm, adapted to deal with the specifics of the case study (i.e., a large-scale non-linear dynamic system of differential and algebraic equations). The practical identifiability is analyzed using a Monte Carlo parameter estimation procedure for a 'non-informative' and 'informative' experiment, which are heuristically designed. The model structure of ADM1 has been modified by replacing parameters by parameter combinations, to provide a generally locally structurally identifiable version of ADM1. This means that in an idealized theoretical situation, the parameters can be estimated accurately. Furthermore, the generally positive structural identifiability results can be explained from the large number of interconnections between the states in the network structure. This interconnectivity, however, is also observed in the parameter estimates, making uncorrelated parameter estimations in practice difficult. Copyright © 2017. Published by Elsevier Inc.

Confinement properties of tokamak plasmas with extended regions of low magnetic shear

NASA Astrophysics Data System (ADS)

Graves, J. P.; Cooper, W. A.; Kleiner, A.; Raghunathan, M.; Neto, E.; Nicolas, T.; Lanthaler, S.; Patten, H.; Pfefferle, D.; Brunetti, D.; Lutjens, H.

2017-10-01

Extended regions of low magnetic shear can be advantageous to tokamak plasmas. But the core and edge can be susceptible to non-resonant ideal fluctuations due to the weakened restoring force associated with magnetic field line bending. This contribution shows how saturated non-linear phenomenology, such as 1 / 1 Long Lived Modes, and Edge Harmonic Oscillations associated with QH-modes, can be modelled accurately using the non-linear stability code XTOR, the free boundary 3D equilibrium code VMEC, and non-linear analytic theory. That the equilibrium approach is valid is particularly valuable because it enables advanced particle confinement studies to be undertaken in the ordinarily difficult environment of strongly 3D magnetic fields. The VENUS-LEVIS code exploits the Fourier description of the VMEC equilibrium fields, such that full Lorenzian and guiding centre approximated differential operators in curvilinear angular coordinates can be evaluated analytically. Consequently, the confinement properties of minority ions such as energetic particles and high Z impurities can be calculated accurately over slowing down timescales in experimentally relevant 3D plasmas.

Spillover, nonlinearity, and flexible structures

NASA Technical Reports Server (NTRS)

Bass, Robert W.; Zes, Dean

1991-01-01

Many systems whose evolution in time is governed by Partial Differential Equations (PDEs) are linearized around a known equilibrium before Computer Aided Control Engineering (CACE) is considered. In this case, there are infinitely many independent vibrational modes, and it is intuitively evident on physical grounds that infinitely many actuators would be needed in order to control all modes. A more precise, general formulation of this grave difficulty (spillover problem) is due to A.V. Balakrishnan. A possible route to circumvention of this difficulty lies in leaving the PDE in its original nonlinear form, and adding the essentially finite dimensional control action prior to linearization. One possibly applicable technique is the Liapunov Schmidt rigorous reduction of singular infinite dimensional implicit function problems to finite dimensional implicit function problems. Omitting details of Banach space rigor, the formalities of this approach are given.