Boundary-fitted coordinate systems for numerical solution of partial differential equations - A review

NASA Technical Reports Server (NTRS)

Thompson, J. F.; Warsi, Z. U. A.; Mastin, C. W.

1982-01-01

A comprehensive review of methods of numerically generating curvilinear coordinate systems with coordinate lines coincident with all boundary segments is given. Some general mathematical framework and error analysis common to such coordinate systems is also included. The general categories of generating systems are those based on conformal mapping, orthogonal systems, nearly orthogonal systems, systems produced as the solution of elliptic and hyperbolic partial differential equations, and systems generated algebraically by interpolation among the boundaries. Also covered are the control of coordinate line spacing by functions embedded in the partial differential operators of the generating system and by subsequent stretching transformation. Dynamically adaptive coordinate systems, coupled with the physical solution, and time-dependent systems that follow moving boundaries are treated. References reporting experience using such coordinate systems are reviewed as well as those covering the system development.

Modeling tree crown dynamics with 3D partial differential equations.

PubMed

Beyer, Robert; Letort, Véronique; Cournède, Paul-Henry

2014-01-01

We characterize a tree's spatial foliage distribution by the local leaf area density. Considering this spatially continuous variable allows to describe the spatiotemporal evolution of the tree crown by means of 3D partial differential equations. These offer a framework to rigorously take locally and adaptively acting effects into account, notably the growth toward light. Biomass production through photosynthesis and the allocation to foliage and wood are readily included in this model framework. The system of equations stands out due to its inherent dynamic property of self-organization and spontaneous adaptation, generating complex behavior from even only a few parameters. The density-based approach yields spatially structured tree crowns without relying on detailed geometry. We present the methodological fundamentals of such a modeling approach and discuss further prospects and applications.

A dynamical regularization algorithm for solving inverse source problems of elliptic partial differential equations

NASA Astrophysics Data System (ADS)

Zhang, Ye; Gong, Rongfang; Cheng, Xiaoliang; Gulliksson, Mårten

2018-06-01

This study considers the inverse source problem for elliptic partial differential equations with both Dirichlet and Neumann boundary data. The unknown source term is to be determined by additional boundary conditions. Unlike the existing methods found in the literature, which usually employ the first-order in time gradient-like system (such as the steepest descent methods) for numerically solving the regularized optimization problem with a fixed regularization parameter, we propose a novel method with a second-order in time dissipative gradient-like system and a dynamical selected regularization parameter. A damped symplectic scheme is proposed for the numerical solution. Theoretical analysis is given for both the continuous model and the numerical algorithm. Several numerical examples are provided to show the robustness of the proposed algorithm.

An Introduction to Computational Physics - 2nd Edition

NASA Astrophysics Data System (ADS)

Pang, Tao

2006-01-01

Preface to first edition; Preface; Acknowledgements; 1. Introduction; 2. Approximation of a function; 3. Numerical calculus; 4. Ordinary differential equations; 5. Numerical methods for matrices; 6. Spectral analysis; 7. Partial differential equations; 8. Molecular dynamics simulations; 9. Modeling continuous systems; 10. Monte Carlo simulations; 11. Genetic algorithm and programming; 12. Numerical renormalization; References; Index.

Dynamics of column stability with partial end restraints

NASA Technical Reports Server (NTRS)

Gregory, Peyton B.

1990-01-01

The dynamic behavior of columns with partial end restraints and loads consisting of a dead load and a pulsating load are investigated. The differential equation is solved using a lumped impulse recurrence formula relative to time coupled with a finite difference discretization along the member length. A computer program is written from which the first critical frequencies are found as a function of end stiffness. The case of a pinned ended column compares very well with the exact solution. Also, the natural frequency and buckling load formulas are derived for equal and unequal end restraints.

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.

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.

Dynamic characteristics of a variable-mass flexible missile

NASA Technical Reports Server (NTRS)

Meirovitch, L.; Bankovskis, J.

1970-01-01

The general motion of a variable mass flexible missile with internal flow and aerodynamic forces is considered. The resulting formulation comprises six ordinary differential equations for rigid body motion and three partial differential equations for elastic motion. The simultaneous differential equations are nonlinear and possess time-dependent coefficients. The differential equations are solved by a semi-analytical method leading to a set of purely ordinary differential equations which are then solved numerically. A computer program was developed for the numerical solution and results are presented for a given set of initial conditions.

On time discretizations for spectral methods. [numerical integration of Fourier and Chebyshev methods for dynamic partial differential equations

NASA Technical Reports Server (NTRS)

Gottlieb, D.; Turkel, E.

1980-01-01

New methods are introduced for the time integration of the Fourier and Chebyshev methods of solution for dynamic differential equations. These methods are unconditionally stable, even though no matrix inversions are required. Time steps are chosen by accuracy requirements alone. For the Fourier method both leapfrog and Runge-Kutta methods are considered. For the Chebyshev method only Runge-Kutta schemes are tested. Numerical calculations are presented to verify the analytic results. Applications to the shallow water equations are presented.

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.

Stochastic partial differential fluid equations as a diffusive limit of deterministic Lagrangian multi-time dynamics.

PubMed

Cotter, C J; Gottwald, G A; Holm, D D

2017-09-01

In Holm (Holm 2015 Proc. R. Soc. A 471 , 20140963. (doi:10.1098/rspa.2014.0963)), stochastic fluid equations were derived by employing a variational principle with an assumed stochastic Lagrangian particle dynamics. Here we show that the same stochastic Lagrangian dynamics naturally arises in a multi-scale decomposition of the deterministic Lagrangian flow map into a slow large-scale mean and a rapidly fluctuating small-scale map. We employ homogenization theory to derive effective slow stochastic particle dynamics for the resolved mean part, thereby obtaining stochastic fluid partial equations in the Eulerian formulation. To justify the application of rigorous homogenization theory, we assume mildly chaotic fast small-scale dynamics, as well as a centring condition. The latter requires that the mean of the fluctuating deviations is small, when pulled back to the mean flow.

Dynamical topology and statistical properties of spatiotemporal chaos.

PubMed

Zhuang, Quntao; Gao, Xun; Ouyang, Qi; Wang, Hongli

2012-12-01

For spatiotemporal chaos described by partial differential equations, there are generally locations where the dynamical variable achieves its local extremum or where the time partial derivative of the variable vanishes instantaneously. To a large extent, the location and movement of these topologically special points determine the qualitative structure of the disordered states. We analyze numerically statistical properties of the topologically special points in one-dimensional spatiotemporal chaos. The probability distribution functions for the number of point, the lifespan, and the distance covered during their lifetime are obtained from numerical simulations. Mathematically, we establish a probabilistic model to describe the dynamics of these topologically special points. In spite of the different definitions in different spatiotemporal chaos, the dynamics of these special points can be described in a uniform approach.

Estimating varying coefficients for partial differential equation models.

PubMed

Zhang, Xinyu; Cao, Jiguo; Carroll, Raymond J

2017-09-01

Partial differential equations (PDEs) are used to model complex dynamical systems in multiple dimensions, and their parameters often have important scientific interpretations. In some applications, PDE parameters are not constant but can change depending on the values of covariates, a feature that we call varying coefficients. We propose a parameter cascading method to estimate varying coefficients in PDE models from noisy data. Our estimates of the varying coefficients are shown to be consistent and asymptotically normally distributed. The performance of our method is evaluated by a simulation study and by an empirical study estimating three varying coefficients in a PDE model arising from LIDAR data. © 2017, The International Biometric Society.

An Elementary Introduction to Recently Developed Computational Methods for Solving Singularly Perturbed Partial Differential Equations Arising in Science and Engineering

NASA Astrophysics Data System (ADS)

Kumar, Manoj; Srivastava, Akanksha

2013-01-01

This paper presents a survey of innovative approaches of the most effective computational techniques for solving singular perturbed partial differential equations, which are useful because of their numerical and computer realizations. Many applied problems appearing in semiconductors theory, biochemistry, kinetics, theory of electrical chains, economics, solid mechanics, fluid dynamics, quantum mechanics, and many others can be modelled as singularly perturbed systems. Here, we summarize a wide range of research articles published by numerous researchers during the last ten years to get a better view of the present scenario in this area of research.

On the continuous differentiability of inter-spike intervals of synaptically connected cortical spiking neurons in a neuronal network.

PubMed

Kumar, Gautam; Kothare, Mayuresh V

2013-12-01

We derive conditions for continuous differentiability of inter-spike intervals (ISIs) of spiking neurons with respect to parameters (decision variables) of an external stimulating input current that drives a recurrent network of synaptically connected neurons. The dynamical behavior of individual neurons is represented by a class of discontinuous single-neuron models. We report here that ISIs of neurons in the network are continuously differentiable with respect to decision variables if (1) a continuously differentiable trajectory of the membrane potential exists between consecutive action potentials with respect to time and decision variables and (2) the partial derivative of the membrane potential of spiking neurons with respect to time is not equal to the partial derivative of their firing threshold with respect to time at the time of action potentials. Our theoretical results are supported by showing fulfillment of these conditions for a class of known bidimensional spiking neuron models.

Computation techniques and computer programs to analyze Stirling cycle engines using characteristic dynamic energy equations

NASA Technical Reports Server (NTRS)

Larson, V. H.

1982-01-01

The basic equations that are used to describe the physical phenomena in a Stirling cycle engine are the general energy equations and equations for the conservation of mass and conversion of momentum. These equations, together with the equation of state, an analytical expression for the gas velocity, and an equation for mesh temperature are used in this computer study of Stirling cycle characteristics. The partial differential equations describing the physical phenomena that occurs in a Stirling cycle engine are of the hyperbolic type. The hyperbolic equations have real characteristic lines. By utilizing appropriate points along these curved lines the partial differential equations can be reduced to ordinary differential equations. These equations are solved numerically using a fourth-fifth order Runge-Kutta integration technique.

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.

Stochastic partial differential fluid equations as a diffusive limit of deterministic Lagrangian multi-time dynamics

PubMed Central

Cotter, C. J.

2017-01-01

In Holm (Holm 2015 Proc. R. Soc. A 471, 20140963. (doi:10.1098/rspa.2014.0963)), stochastic fluid equations were derived by employing a variational principle with an assumed stochastic Lagrangian particle dynamics. Here we show that the same stochastic Lagrangian dynamics naturally arises in a multi-scale decomposition of the deterministic Lagrangian flow map into a slow large-scale mean and a rapidly fluctuating small-scale map. We employ homogenization theory to derive effective slow stochastic particle dynamics for the resolved mean part, thereby obtaining stochastic fluid partial equations in the Eulerian formulation. To justify the application of rigorous homogenization theory, we assume mildly chaotic fast small-scale dynamics, as well as a centring condition. The latter requires that the mean of the fluctuating deviations is small, when pulled back to the mean flow. PMID:28989316

Amniotic-Fluid Stem Cells: Growth Dynamics and Differentiation Potential after a CD-117-Based Selection Procedure

PubMed Central

Arnhold, S.; Glüer, S.; Hartmann, K.; Raabe, O.; Addicks, K.; Wenisch, S.; Hoopmann, M.

2011-01-01

Amniotic fluid (AF) has become an interesting source of fetal stem cells. However, AF contains heterogeneous and multiple, partially differentiated cell types. After isolation from the amniotic fluid, cells were characterized regarding their morphology and growth dynamics. They were sorted by magnetic associated cell sorting using the surface marker CD 117. In order to show stem cell characteristics such as pluripotency and to evaluate a possible therapeutic application of these cells, AF fluid-derived stem cells were differentiated along the adipogenic, osteogenic, and chondrogenic as well as the neuronal lineage under hypoxic conditions. Our findings reveal that magnetic associated cell sorting (MACS) does not markedly influence growth characteristics as demonstrated by the generation doubling time. There was, however, an effect regarding an altered adipogenic, osteogenic, and chondrogenic differentiation capacity in the selected cell fraction. In contrast, in the unselected cell population neuronal differentiation is enhanced. PMID:21437196

Differential Equations Models to Study Quorum Sensing.

PubMed

Pérez-Velázquez, Judith; Hense, Burkhard A

2018-01-01

Mathematical models to study quorum sensing (QS) have become an important tool to explore all aspects of this type of bacterial communication. A wide spectrum of mathematical tools and methods such as dynamical systems, stochastics, and spatial models can be employed. In this chapter, we focus on giving an overview of models consisting of differential equations (DE), which can be used to describe changing quantities, for example, the dynamics of one or more signaling molecule in time and space, often in conjunction with bacterial growth dynamics. The chapter is divided into two sections: ordinary differential equations (ODE) and partial differential equations (PDE) models of QS. Rates of change are represented mathematically by derivatives, i.e., in terms of DE. ODE models allow describing changes in one independent variable, for example, time. PDE models can be used to follow changes in more than one independent variable, for example, time and space. Both types of models often consist of systems (i.e., more than one equation) of equations, such as equations for bacterial growth and autoinducer concentration dynamics. Almost from the onset, mathematical modeling of QS using differential equations has been an interdisciplinary endeavor and many of the works we revised here will be placed into their biological context.

Mathematical Methods in Wave Propagation: Part 2--Non-Linear Wave Front Analysis

ERIC Educational Resources Information Center

Jeffrey, Alan

1971-01-01

The paper presents applications and methods of analysis for non-linear hyperbolic partial differential equations. The paper is concluded by an account of wave front analysis as applied to the piston problem of gas dynamics. (JG)

Dynamic characteristics of a two-stage variable-mass flexible missile with internal flow

NASA Technical Reports Server (NTRS)

Meirovitch, L.; Bankovskis, J.

1972-01-01

A general formulation of the dynamical problems associated with powered flight of a two stage flexible, variable-mass missile with internal flow, discrete masses, and aerodynamic forces is presented. The formulation comprises six ordinary differential equations for the rigid body motion, 3n ordinary differential equations for the n discrete masses and three partial differential equations with the appropriate boundary conditions for the elastic motion. This set of equations is modified to represent a single stage flexible, variable-mass missile with internal flow and aerodynamic forces. The rigid-body motion consists then of three translations and three rotations, whereas the elastic motion is defined by one longitudinal and two flexural displacements, the latter about two orthogonal transverse axes. The differential equations are nonlinear and, in addition, they possess time-dependent coefficients due to the mass variation.

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

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 Tribute to J. C. Sprott

NASA Astrophysics Data System (ADS)

Nazarimehr, Fahimeh; Jafari, Sajad; Chen, Guanrong; Kapitaniak, Tomasz; Kuznetsov, Nikolay V.; Leonov, Gennady A.; Li, Chunbiao; Wei, Zhouchao

2017-12-01

In honor of his 75th birthday, we review the prominent works of Professor Julien Clinton Sprott in chaos and nonlinear dynamics. We categorize his works into three important groups. The first and most important group is identifying new dynamical systems with special properties. He has proposed different chaotic maps, flows, complex variable systems, nonautonomous systems, partial differential equations, fractional-order systems, delay differential systems, spatiotemporal systems, artificial neural networks, and chaotic electrical circuits. He has also studied dynamical properties of complex systems such as bifurcations and basins of attraction. He has done work on generating fractal art. He has examined models of real-world systems that exhibit chaos. The second group of his works comprise control and synchronization of chaos. Finally, the third group is extracting dynamical properties of systems using time-series analysis. This paper highlights the impact of Sprott’s work on the promotion of nonlinear dynamics.

Molecular dynamics on diffusive time scales from the phase-field-crystal equation.

PubMed

Chan, Pak Yuen; Goldenfeld, Nigel; Dantzig, Jon

2009-03-01

We extend the phase-field-crystal model to accommodate exact atomic configurations and vacancies by requiring the order parameter to be non-negative. The resulting theory dictates the number of atoms and describes the motion of each of them. By solving the dynamical equation of the model, which is a partial differential equation, we are essentially performing molecular dynamics simulations on diffusive time scales. To illustrate this approach, we calculate the two-point correlation function of a fluid.

Multisynchronization of Coupled Heterogeneous Genetic Oscillator Networks via Partial Impulsive Control.

PubMed

He, Ding-Xin; Ling, Guang; Guan, Zhi-Hong; Hu, Bin; Liao, Rui-Quan

2018-02-01

This paper focuses on the collective dynamics of multisynchronization among heterogeneous genetic oscillators under a partial impulsive control strategy. The coupled nonidentical genetic oscillators are modeled by differential equations with uncertainties. The definition of multisynchronization is proposed to describe some more general synchronization behaviors in the real. Considering that each genetic oscillator consists of a large number of biochemical molecules, we design a more manageable impulsive strategy for dynamic networks to achieve multisynchronization. Not all the molecules but only a small fraction of them in each genetic oscillator are controlled at each impulsive instant. Theoretical analysis of multisynchronization is carried out by the control theory approach, and a sufficient condition of partial impulsive controller for multisynchronization with given error bounds is established. At last, numerical simulations are exploited to demonstrate the effectiveness of our results.

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.

Simplified method for numerical modeling of fiber lasers.

PubMed

Shtyrina, O V; Yarutkina, I A; Fedoruk, M P

2014-12-29

A simplified numerical approach to modeling of dissipative dispersion-managed fiber lasers is examined. We present a new numerical iteration algorithm for finding the periodic solutions of the system of nonlinear ordinary differential equations describing the intra-cavity dynamics of the dissipative soliton characteristics in dispersion-managed fiber lasers. We demonstrate that results obtained using simplified model are in good agreement with full numerical modeling based on the corresponding partial differential equations.

Dynamics of temporally localized states in passively mode-locked semiconductor lasers

NASA Astrophysics Data System (ADS)

Schelte, C.; Javaloyes, J.; Gurevich, S. V.

2018-05-01

We study the emergence and the stability of temporally localized structures in the output of a semiconductor laser passively mode locked by a saturable absorber in the long-cavity regime. For large yet realistic values of the linewidth enhancement factor, we disclose the existence of secondary dynamical instabilities where the pulses develop regular and subsequent irregular temporal oscillations. By a detailed bifurcation analysis we show that additional solution branches that consist of multipulse (molecules) solutions exist. We demonstrate that the various solution curves for the single and multipeak pulses can splice and intersect each other via transcritical bifurcations, leading to a complex web of solutions. Our analysis is based on a generic model of mode locking that consists of a time-delayed dynamical system, but also on a much more numerically efficient, yet approximate, partial differential equation. We compare the results of the bifurcation analysis of both models in order to assess up to which point the two approaches are equivalent. We conclude our analysis by the study of the influence of group velocity dispersion, which is only possible in the framework of the partial differential equation model, and we show that it may have a profound impact on the dynamics of the localized states.

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.

Statistical theory for the Kardar-Parisi-Zhang equation in (1+1) dimensions.

PubMed

Masoudi, A A; Shahbazi, F; Davoudi, J; Tabar, M Reza Rahimi

2002-02-01

The Kardar-Parisi-Zhang (KPZ) equation in (1+1) dimensions dynamically develops sharply connected valley structures within which the height derivative is not continuous. We develop a statistical theory for the KPZ equation in (1+1) dimensions driven with a random forcing that is white in time and Gaussian-correlated in space. A master equation is derived for the joint probability density function of height difference and height gradient P(h-h*, partial differential(x)h,t) when the forcing correlation length is much smaller than the system size and much larger than the typical sharp valley width. In the time scales before the creation of the sharp valleys, we find the exact generating function of h-h* and partial differential(x)h. The time scale of the sharp valley formation is expressed in terms of the force characteristics. In the stationary state, when the sharp valleys are fully developed, finite-size corrections to the scaling laws of the structure functions left angle bracket(h-h*)(n)(partial differential(x)h)(m)right angle bracket are also obtained.

Sensitivity analysis of dynamic biological systems with time-delays.

PubMed

Wu, Wu Hsiung; Wang, Feng Sheng; Chang, Maw Shang

2010-10-15

Mathematical modeling has been applied to the study and analysis of complex biological systems for a long time. Some processes in biological systems, such as the gene expression and feedback control in signal transduction networks, involve a time delay. These systems are represented as delay differential equation (DDE) models. Numerical sensitivity analysis of a DDE model by the direct method requires the solutions of model and sensitivity equations with time-delays. The major effort is the computation of Jacobian matrix when computing the solution of sensitivity equations. The computation of partial derivatives of complex equations either by the analytic method or by symbolic manipulation is time consuming, inconvenient, and prone to introduce human errors. To address this problem, an automatic approach to obtain the derivatives of complex functions efficiently and accurately is necessary. We have proposed an efficient algorithm with an adaptive step size control to compute the solution and dynamic sensitivities of biological systems described by ordinal differential equations (ODEs). The adaptive direct-decoupled algorithm is extended to solve the solution and dynamic sensitivities of time-delay systems describing by DDEs. To save the human effort and avoid the human errors in the computation of partial derivatives, an automatic differentiation technique is embedded in the extended algorithm to evaluate the Jacobian matrix. The extended algorithm is implemented and applied to two realistic models with time-delays: the cardiovascular control system and the TNF-α signal transduction network. The results show that the extended algorithm is a good tool for dynamic sensitivity analysis on DDE models with less user intervention. By comparing with direct-coupled methods in theory, the extended algorithm is efficient, accurate, and easy to use for end users without programming background to do dynamic sensitivity analysis on complex biological systems with time-delays.

Observing spatio-temporal dynamics of excitable media using reservoir computing

NASA Astrophysics Data System (ADS)

Zimmermann, Roland S.; Parlitz, Ulrich

2018-04-01

We present a dynamical observer for two dimensional partial differential equation models describing excitable media, where the required cross prediction from observed time series to not measured state variables is provided by Echo State Networks receiving input from local regions in space, only. The efficacy of this approach is demonstrated for (noisy) data from a (cubic) Barkley model and the Bueno-Orovio-Cherry-Fenton model describing chaotic electrical wave propagation in cardiac tissue.

Dynamic modeling of spacecraft in a collisionless plasma

NASA Technical Reports Server (NTRS)

Katz, I.; Parks, D. E.; Wang, S. S.; Wilson, A.

1977-01-01

A new computational model is described which can simulate the charging of complex geometrical objects in three dimensions. Two sample calculations are presented. In the first problem, the capacitance to infinity of a complex object similar to a satellite with solar array paddles is calculated. The second problem concerns the dynamical charging of a conducting cube partially covered with a thin dielectric film. In this calculation, the photoemission results in differential charging of the object.

Dispersive models describing mosquitoes’ population dynamics

NASA Astrophysics Data System (ADS)

Yamashita, W. M. S.; Takahashi, L. T.; Chapiro, G.

2016-08-01

The global incidences of dengue and, more recently, zica virus have increased the interest in studying and understanding the mosquito population dynamics. Understanding this dynamics is important for public health in countries where climatic and environmental conditions are favorable for the propagation of these diseases. This work is based on the study of nonlinear mathematical models dealing with the life cycle of the dengue mosquito using partial differential equations. We investigate the existence of traveling wave solutions using semi-analytical method combining dynamical systems techniques and numerical integration. Obtained solutions are validated through numerical simulations using finite difference schemes.

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.

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

Simulation of Stochastic Processes by Coupled ODE-PDE

NASA Technical Reports Server (NTRS)

Zak, Michail

2008-01-01

A document discusses the emergence of randomness in solutions of coupled, fully deterministic ODE-PDE (ordinary differential equations-partial differential equations) due to failure of the Lipschitz condition as a new phenomenon. It is possible to exploit the special properties of ordinary differential equations (represented by an arbitrarily chosen, dynamical system) coupled with the corresponding Liouville equations (used to describe the evolution of initial uncertainties in terms of joint probability distribution) in order to simulate stochastic processes with the proscribed probability distributions. The important advantage of the proposed approach is that the simulation does not require a random-number generator.

Optimization of CMOS image sensor utilizing variable temporal multisampling partial transfer technique to achieve full-frame high dynamic range with superior low light and stop motion capability

NASA Astrophysics Data System (ADS)

Kabir, Salman; Smith, Craig; Armstrong, Frank; Barnard, Gerrit; Schneider, Alex; Guidash, Michael; Vogelsang, Thomas; Endsley, Jay

2018-03-01

Differential binary pixel technology is a threshold-based timing, readout, and image reconstruction method that utilizes the subframe partial charge transfer technique in a standard four-transistor (4T) pixel CMOS image sensor to achieve a high dynamic range video with stop motion. This technology improves low light signal-to-noise ratio (SNR) by up to 21 dB. The method is verified in silicon using a Taiwan Semiconductor Manufacturing Company's 65 nm 1.1 μm pixel technology 1 megapixel test chip array and is compared with a traditional 4 × oversampling technique using full charge transfer to show low light SNR superiority of the presented technology.

Numerical solution of a coupled pair of elliptic equations from solid state electronics

NASA Technical Reports Server (NTRS)

Phillips, T. N.

1983-01-01

Iterative methods are considered for the solution of a coupled pair of second order elliptic partial differential equations which arise in the field of solid state electronics. A finite difference scheme is used which retains the conservative form of the differential equations. Numerical solutions are obtained in two ways, by multigrid and dynamic alternating direction implicit methods. Numerical results are presented which show the multigrid method to be an efficient way of solving this problem.

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 method for solution of the Euler-Bernoulli beam equation in flexible-link robotic systems

NASA Technical Reports Server (NTRS)

Tzes, Anthony P.; Yurkovich, Stephen; Langer, F. Dieter

1989-01-01

An efficient numerical method for solving the partial differential equation (PDE) governing the flexible manipulator control dynamics is presented. A finite-dimensional model of the equation is obtained through discretization in both time and space coordinates by using finite-difference approximations to the PDE. An expert program written in the Macsyma symbolic language is utilized in order to embed the boundary conditions into the program, accounting for a mass carried at the tip of the manipulator. The advantages of the proposed algorithm are many, including the ability to (1) include any distributed actuation term in the partial differential equation, (2) provide distributed sensing of the beam displacement, (3) easily modify the boundary conditions through an expert program, and (4) modify the structure for running under a multiprocessor environment.

Workload Characterization of CFD Applications Using Partial Differential Equation Solvers

NASA Technical Reports Server (NTRS)

Waheed, Abdul; Yan, Jerry; Saini, Subhash (Technical Monitor)

1998-01-01

Workload characterization is used for modeling and evaluating of computing systems at different levels of detail. We present workload characterization for a class of Computational Fluid Dynamics (CFD) applications that solve Partial Differential Equations (PDEs). This workload characterization focuses on three high performance computing platforms: SGI Origin2000, EBM SP-2, a cluster of Intel Pentium Pro bases PCs. We execute extensive measurement-based experiments on these platforms to gather statistics of system resource usage, which results in workload characterization. Our workload characterization approach yields a coarse-grain resource utilization behavior that is being applied for performance modeling and evaluation of distributed high performance metacomputing systems. In addition, this study enhances our understanding of interactions between PDE solver workloads and high performance computing platforms and is useful for tuning these applications.

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.

A multiscale computational model of spatially resolved calcium cycling in cardiac myocytes: from detailed cleft dynamics to the whole cell concentration profiles

PubMed Central

Vierheller, Janine; Neubert, Wilhelm; Falcke, Martin; Gilbert, Stephen H.; Chamakuri, Nagaiah

2015-01-01

Mathematical modeling of excitation-contraction coupling (ECC) in ventricular cardiac myocytes is a multiscale problem, and it is therefore difficult to develop spatially detailed simulation tools. ECC involves gradients on the length scale of 100 nm in dyadic spaces and concentration profiles along the 100 μm of the whole cell, as well as the sub-millisecond time scale of local concentration changes and the change of lumenal Ca2+ content within tens of seconds. Our concept for a multiscale mathematical model of Ca2+ -induced Ca2+ release (CICR) and whole cardiomyocyte electrophysiology incorporates stochastic simulation of individual LC- and RyR-channels, spatially detailed concentration dynamics in dyadic clefts, rabbit membrane potential dynamics, and a system of partial differential equations for myoplasmic and lumenal free Ca2+ and Ca2+-binding molecules in the bulk of the cell. We developed a novel computational approach to resolve the concentration gradients from dyadic space to cell level by using a quasistatic approximation within the dyad and finite element methods for integrating the partial differential equations. We show whole cell Ca2+-concentration profiles using three previously published RyR-channel Markov schemes. PMID:26441674

State-resolved differential and integral cross sections for the Ne + H{sub 2}{sup +} (v = 0–2, j = 0) → NeH{sup +} + H reaction

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

Wu, Hui; Yao, Cui-Xia; He, Xiao-Hu

State-to-state quantum dynamic calculations for the proton transfer reaction Ne + H{sub 2}{sup +} (v = 0–2, j = 0) are performed on the most accurate LZHH potential energy surface, with the product Jacobi coordinate based time-dependent wave packet method including the Coriolis coupling. The J = 0 reaction probabilities for the title reaction agree well with previous results in a wide range of collision energy of 0.2-1.2 eV. Total integral cross sections are in reasonable agreement with the available experiment data. Vibrational excitation of the reactant is much more efficient in enhancing the reaction cross sections than translational andmore » rotational excitation. Total differential cross sections are found to be forward-backward peaked with strong oscillations, which is the indication of the complex-forming mechanism. As the collision energy increases, state-resolved differential cross section changes from forward-backward symmetric peaked to forward scattering biased. This forward bias can be attributed to the larger J partial waves, which makes the reaction like an abstraction process. Differential cross sections summed over two different sets of J partial waves for the v = 0 reaction at the collision energy of 1.2 eV are plotted to illustrate the importance of large J partial waves in the forward bias of the differential cross sections.« less

Mathematical Model of Bubble Sloshing Dynamics for Cryogenic Liquid Helium in Orbital Spacecraft Dewar Container

NASA Technical Reports Server (NTRS)

Hung, R. J.; Pan, H. L.

1995-01-01

A generalized mathematical model is investigated of sloshing dynamics for dewar containers, partially filled with a liquid of cryogenic superfluid helium 2, driven by both gravity gradient and jitter accelerations applicable to two types of scientific spacecrafts, which are eligible to carry out spinning motion and/or slew motion to perform scientific observations during normal spacecraft operation. Two examples are given for the Gravity Probe-B (GP-B) with spinning motion, and the Advanced X-Ray Astrophysics Facility-Spectroscopy (AXAF-S) with slew motion, which are responsible for the sloshing dynamics. Explicit mathematical expressions for the modelling of sloshing dynamics to cover these forces acting on the spacecraft fluid systems are derived. The numerical computation of sloshing dynamics will be based on the noninertial frame spacecraft bound coordinate, and we will solve the time-dependent three-dimensional formulations of partial differential equations subject to initial and boundary conditions. Explicit mathematical expressions of boundary conditions lo cover capillary force effects on the liquid-vapor interface in microgravity environments are also derived. Results of the simulations of the mathematical model are illustrated.

Dynamics of embedded curves by doubly-nonlocal reaction-diffusion systems

NASA Astrophysics Data System (ADS)

von Brecht, James H.; Blair, Ryan

2017-11-01

We study a class of nonlocal, energy-driven dynamical models that govern the motion of closed, embedded curves from both an energetic and dynamical perspective. Our energetic results provide a variety of ways to understand physically motivated energetic models in terms of more classical, combinatorial measures of complexity for embedded curves. This line of investigation culminates in a family of complexity bounds that relate a rather broad class of models to a generalized, or weighted, variant of the crossing number. Our dynamic results include global well-posedness of the associated partial differential equations, regularity of equilibria for these flows as well as a more detailed investigation of dynamics near such equilibria. Finally, we explore a few global dynamical properties of these models numerically.

An evolution infinity Laplace equation modelling dynamic elasto-plastic torsion

NASA Astrophysics Data System (ADS)

Messelmi, Farid

2017-12-01

We consider in this paper a parabolic partial differential equation involving the infinity Laplace operator and a Leray-Lions operator with no coercitive assumption. We prove the existence and uniqueness of the corresponding approached problem and we show that at the limit the solution solves the parabolic variational inequality arising in the elasto-plastic torsion problem.

Wavelet-based spectral finite element dynamic analysis for an axially moving Timoshenko beam

NASA Astrophysics Data System (ADS)

Mokhtari, Ali; Mirdamadi, Hamid Reza; Ghayour, Mostafa

2017-08-01

In this article, wavelet-based spectral finite element (WSFE) model is formulated for time domain and wave domain dynamic analysis of an axially moving Timoshenko beam subjected to axial pretension. The formulation is similar to conventional FFT-based spectral finite element (SFE) model except that Daubechies wavelet basis functions are used for temporal discretization of the governing partial differential equations into a set of ordinary differential equations. The localized nature of Daubechies wavelet basis functions helps to rule out problems of SFE model due to periodicity assumption, especially during inverse Fourier transformation and back to time domain. The high accuracy of WSFE model is then evaluated by comparing its results with those of conventional finite element and SFE results. The effects of moving beam speed and axial tensile force on vibration and wave characteristics, and static and dynamic stabilities of moving beam are investigated.

Bifurcation Analysis of an Electrostatically Actuated Nano-Beam Based on Modified Couple Stress Theory

NASA Astrophysics Data System (ADS)

Rezaei Kivi, Araz; Azizi, Saber; Norouzi, Peyman

2017-12-01

In this paper, the nonlinear size-dependent static and dynamic behavior of an electrostatically actuated nano-beam is investigated. A fully clamped nano-beam is considered for the modeling of the deformable electrode of the NEMS. The governing differential equation of the motion is derived using Hamiltonian principle based on couple stress theory; a non-classical theory for considering length scale effects. The nonlinear partial differential equation of the motion is discretized to a nonlinear Duffing type ODE's using Galerkin method. Static and dynamic pull-in instabilities obtained by both classical theory and MCST are compared. At the second stage of analysis, shooting technique is utilized to obtain the frequency response curve, and to capture the periodic solutions of the motion; the stability of the periodic solutions are gained by Floquet theory. The nonlinear dynamic behavior of the deformable electrode due to the AC harmonic accompanied with size dependency is investigated.

Influence of human behavior on cholera dynamics

PubMed Central

Wang, Xueying; Gao, Daozhou; Wang, Jin

2015-01-01

This paper is devoted to studying the impact of human behavior on cholera infection. We start with a cholera ordinary differential equation (ODE) model that incorporates human behavior via modeling disease prevalence dependent contact rates for direct and indirect transmissions and infectious host shedding. Local and global dynamics of the model are analyzed with respect to the basic reproduction number. We then extend the ODE model to a reaction-convection-diffusion partial differential equation (PDE) model that accounts for the movement of both human hosts and bacteria. Particularly, we investigate the cholera spreading speed by analyzing the traveling wave solutions of the PDE model, and disease threshold dynamics by numerically evaluating the basic reproduction number of the PDE model. Our results show that human behavior can reduce (a) the endemic and epidemic levels, (b) cholera spreading speeds and (c) the risk of infection (characterized by the basic reproduction number). PMID:26119824

Parameter Estimation of Partial Differential Equation Models.

PubMed

Xun, Xiaolei; Cao, Jiguo; Mallick, Bani; Carroll, Raymond J; Maity, Arnab

2013-01-01

Partial differential equation (PDE) models are commonly used to model complex dynamic systems in applied sciences such as biology and finance. The forms of these PDE models are usually proposed by experts based on their prior knowledge and understanding of the dynamic system. Parameters in PDE models often have interesting scientific interpretations, but their values are often unknown, and need to be estimated from the measurements of the dynamic system in the present of measurement errors. Most PDEs used in practice have no analytic solutions, and can only be solved with numerical methods. Currently, methods for estimating PDE parameters require repeatedly solving PDEs numerically under thousands of candidate parameter values, and thus the computational load is high. In this article, we propose two methods to estimate parameters in PDE models: a parameter cascading method and a Bayesian approach. In both methods, the underlying dynamic process modeled with the PDE model is represented via basis function expansion. For the parameter cascading method, we develop two nested levels of optimization to estimate the PDE parameters. For the Bayesian method, we develop a joint model for data and the PDE, and develop a novel hierarchical model allowing us to employ Markov chain Monte Carlo (MCMC) techniques to make posterior inference. Simulation studies show that the Bayesian method and parameter cascading method are comparable, and both outperform other available methods in terms of estimation accuracy. The two methods are demonstrated by estimating parameters in a PDE model from LIDAR data.

Recent disruption of an asteroid from the Eos family

NASA Astrophysics Data System (ADS)

Novaković, B.; Tsirvoulis, G.

2014-07-01

A key difficulty with searching for partially differentiated asteroids arises from the fact that a crust covers the exterior of the body, and, consequently, should hide the melted interior. This motivates an alternative approach of examining members of asteroid families, i.e., fragments of single large bodies, many of which were in the size regime capable of igneous differentiation, that have been disrupted by catastrophic collisions. Such families could provide a stratigraphic cross section across the interior of the parent asteroid [1]. With more than 10,000 known members, the Eos dynamical family is one of the most numerous and earliest recognized asteroid families [2]. Interestingly, the estimated ˜220-km-diameter parent body [3] is well within the size range capable of differentiation. Thus, existing family members should contain fragments of the deep interior. The Eos family has the highest diversity of taxonomic classes than any other known family [4]. Many members are of K spectral type, which is uncommon outside the family, and is similar to the spectra of CV, CK, CO, and CR carbonaceous chondrites [5]. This diversity leads to the suggestion that the Eos parent body was partially differentiated [4,6]. Thus, the Eos family may not only be a remnant of a partially differentiated parent body, but it could be the source of the CV-CK meteorite group. Here we report the discovery of a young subfamily of the Eos asteroid family. It may help understanding the mineralogical nature of the Eos asteroid family and of its parent body. By applying the hierarchical clustering method [7], we find an extremely compact 16-body cluster within the borders of the Eos family. We name the cluster (6733) 1992 EF, after its largest member. The statistical significance of this new cluster is estimated to be above 99%, indicating that its members share a common origin. All members of the cluster are found to be dynamically stable over long timescales. Backward numerical orbital integrations are used to set an upper limit of the age of the cluster to be only 4 Myr.

Computing generalized Langevin equations and generalized Fokker-Planck equations.

PubMed

Darve, Eric; Solomon, Jose; Kia, Amirali

2009-07-07

The Mori-Zwanzig formalism is an effective tool to derive differential equations describing the evolution of a small number of resolved variables. In this paper we present its application to the derivation of generalized Langevin equations and generalized non-Markovian Fokker-Planck equations. We show how long time scales rates and metastable basins can be extracted from these equations. Numerical algorithms are proposed to discretize these equations. An important aspect is the numerical solution of the orthogonal dynamics equation which is a partial differential equation in a high dimensional space. We propose efficient numerical methods to solve this orthogonal dynamics equation. In addition, we present a projection formalism of the Mori-Zwanzig type that is applicable to discrete maps. Numerical applications are presented from the field of Hamiltonian systems.

Spectral methods for partial differential equations

NASA Technical Reports Server (NTRS)

Hussaini, M. Y.; Streett, C. L.; Zang, T. A.

1983-01-01

Origins of spectral methods, especially their relation to the Method of Weighted Residuals, are surveyed. Basic Fourier, Chebyshev, and Legendre spectral concepts are reviewed, and demonstrated through application to simple model problems. Both collocation and tau methods are considered. These techniques are then applied to a number of difficult, nonlinear problems of hyperbolic, parabolic, elliptic, and mixed type. Fluid dynamical applications are emphasized.

European Science Notes Information Bulletin Reports on Current European and Middle Eastern Science

DTIC Science & Technology

1992-01-01

evclopment in the Abbey-Polymer Processing and Properties ................... 524 J, Magill Corrosion and Protection Centre at the University of...34* Software Engineering and microprocessors and communication chips. The Information Processing Systems recently announced T9000 microprocessor will...computational fluid dynamics, struc- In addition to general and special-purpose tural mechanics, partial differential equations, processing , Europe has a

Autonomous selection of PDE inpainting techniques vs. exemplar inpainting techniques for void fill of high resolution digital surface models

NASA Astrophysics Data System (ADS)

Rahmes, Mark; Yates, J. Harlan; Allen, Josef DeVaughn; Kelley, Patrick

2007-04-01

High resolution Digital Surface Models (DSMs) may contain voids (missing data) due to the data collection process used to obtain the DSM, inclement weather conditions, low returns, system errors/malfunctions for various collection platforms, and other factors. DSM voids are also created during bare earth processing where culture and vegetation features have been extracted. The Harris LiteSite TM Toolkit handles these void regions in DSMs via two novel techniques. We use both partial differential equations (PDEs) and exemplar based inpainting techniques to accurately fill voids. The PDE technique has its origin in fluid dynamics and heat equations (a particular subset of partial differential equations). The exemplar technique has its origin in texture analysis and image processing. Each technique is optimally suited for different input conditions. The PDE technique works better where the area to be void filled does not have disproportionately high frequency data in the neighborhood of the boundary of the void. Conversely, the exemplar based technique is better suited for high frequency areas. Both are autonomous with respect to detecting and repairing void regions. We describe a cohesive autonomous solution that dynamically selects the best technique as each void is being repaired.

The mu-derivative and its applications to finding exact solutions of the Cahn-Hilliard, Korteveg-de Vries, and Burgers equations.

PubMed

Mitlin, Vlad

2005-10-15

A new transformation termed the mu-derivative is introduced. Applying it to the Cahn-Hilliard equation yields dynamical exact solutions. It is shown that the mu-transformed Cahn-Hilliard equation can be presented in a separable form. This transformation also yields dynamical exact solutions and separable forms for other nonlinear models such as the modified Korteveg-de Vries and the Burgers equations. The general structure of a nonlinear partial differential equation that becomes separable upon applying the mu-derivative is described.

Solitary Waves, Periodic Peakons and Pseudo-Peakons of the Nonlinear Acoustic Wave Model in Rotating Magnetized Plasma

NASA Astrophysics Data System (ADS)

Li, Jibin

The dynamical model of the nonlinear acoustic wave in rotating magnetized plasma is governed by a partial differential equation system. Its traveling system is a singular traveling wave system of first class depending on two parameters. By using the bifurcation theory and method of dynamical systems and the theory of singular traveling wave systems, in this paper, we show that there exist parameter groups such that this singular system has pseudo-peakons, periodic peakons and compactons as well as different solitary wave solutions.

Periodic Peakons, Pseudo-Peakons and Compactons of Ion-Acoustic Wave Model in Electronegative Plasmas with Electrons Featuring Tsallis Distribution

NASA Astrophysics Data System (ADS)

Li, Jibin

The dynamical model of the nonlinear ion-acoustic oscillations is governed by a partial differential equation system. Its traveling system is just a singular traveling wave system of first class depending on four parameters. By using the method of dynamical systems and the theory of singular traveling wave systems, in this paper, we show that there exist parameter groups such that this singular system has pseudo-peakons, periodic peakons and compactons as well as kink and anti-kink wave solutions.

Reactive multi-particle collision dynamics with reactive boundary conditions

NASA Astrophysics Data System (ADS)

Sayyidmousavi, Alireza; Rohlf, Katrin

2018-07-01

In the present study, an off-lattice particle-based method called the reactive multi-particle collision (RMPC) dynamics is extended to model reaction-diffusion systems with reactive boundary conditions in which the a priori diffusion coefficient of the particles needs to be maintained throughout the simulation. To this end, the authors have made use of the so-called bath particles whose purpose is only to ensure proper diffusion of the main particles in the system. In order to model partial adsorption by a reactive boundary in the RMPC, the probability of a particle being adsorbed, once it hits the boundary, is calculated by drawing an analogy between the RMPC and Brownian Dynamics. The main advantages of the RMPC compared to other molecular based methods are less computational cost as well as conservation of mass, energy and momentum in the collision and free streaming steps. The proposed approach is tested on three reaction-diffusion systems and very good agreement with the solutions to their corresponding partial differential equations is observed.

ML-Space: Hybrid Spatial Gillespie and Particle Simulation of Multi-Level Rule-Based Models in Cell Biology.

PubMed

Bittig, Arne T; Uhrmacher, Adelinde M

2017-01-01

Spatio-temporal dynamics of cellular processes can be simulated at different levels of detail, from (deterministic) partial differential equations via the spatial Stochastic Simulation algorithm to tracking Brownian trajectories of individual particles. We present a spatial simulation approach for multi-level rule-based models, which includes dynamically hierarchically nested cellular compartments and entities. Our approach ML-Space combines discrete compartmental dynamics, stochastic spatial approaches in discrete space, and particles moving in continuous space. The rule-based specification language of ML-Space supports concise and compact descriptions of models and to adapt the spatial resolution of models easily.

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.

A new computational method for reacting hypersonic flows

NASA Astrophysics Data System (ADS)

Niculescu, M. L.; Cojocaru, M. G.; Pricop, M. V.; Fadgyas, M. C.; Pepelea, D.; Stoican, M. G.

2017-07-01

Hypersonic gas dynamics computations are challenging due to the difficulties to have reliable and robust chemistry models that are usually added to Navier-Stokes equations. From the numerical point of view, it is very difficult to integrate together Navier-Stokes equations and chemistry model equations because these partial differential equations have different specific time scales. For these reasons, almost all known finite volume methods fail shortly to solve this second order partial differential system. Unfortunately, the heating of Earth reentry vehicles such as space shuttles and capsules is very close linked to endothermic chemical reactions. A better prediction of wall heat flux leads to smaller safety coefficient for thermal shield of space reentry vehicle; therefore, the size of thermal shield decreases and the payload increases. For these reasons, the present paper proposes a new computational method based on chemical equilibrium, which gives accurate prediction of hypersonic heating in order to support the Earth reentry capsule design.

On the identification of continuous vibrating systems modelled by hyperbolic partial differential equations

NASA Technical Reports Server (NTRS)

Udwadia, F. E.; Garba, J. A.

1983-01-01

This paper deals with the identification of spatially varying parameters in systems of finite spatial extent which can be described by second order hyperbolic differential equations. Two questions have been addressed. The first deals with 'partial identification' and inquires into the possibility of retrieving all the eigenvalues of the system from response data obtained at one location x-asterisk epsilon (0, 1). The second deals with the identification of the distributed coefficients rho(x), a(x) and b(x). Sufficient conditions for unique identification of all the eigenvalues of the system are obtained, and conditions under which the coefficients can be uniquely identified using suitable response data obtained at one point in the spatial domain are determined. Application of the results and their usefulness is demonstrated in the identification of the properties of tall building structural systems subjected to dynamic load environments.

OBSERVING LYAPUNOV EXPONENTS OF INFINITE-DIMENSIONAL DYNAMICAL SYSTEMS

PubMed Central

OTT, WILLIAM; RIVAS, MAURICIO A.; WEST, JAMES

2016-01-01

Can Lyapunov exponents of infinite-dimensional dynamical systems be observed by projecting the dynamics into ℝN using a ‘typical’ nonlinear projection map? We answer this question affirmatively by developing embedding theorems for compact invariant sets associated with C1 maps on Hilbert spaces. Examples of such discrete-time dynamical systems include time-T maps and Poincaré return maps generated by the solution semigroups of evolution partial differential equations. We make every effort to place hypotheses on the projected dynamics rather than on the underlying infinite-dimensional dynamical system. In so doing, we adopt an empirical approach and formulate checkable conditions under which a Lyapunov exponent computed from experimental data will be a Lyapunov exponent of the infinite-dimensional dynamical system under study (provided the nonlinear projection map producing the data is typical in the sense of prevalence). PMID:28066028

OBSERVING LYAPUNOV EXPONENTS OF INFINITE-DIMENSIONAL DYNAMICAL SYSTEMS.

PubMed

Ott, William; Rivas, Mauricio A; West, James

2015-12-01

Can Lyapunov exponents of infinite-dimensional dynamical systems be observed by projecting the dynamics into ℝ N using a 'typical' nonlinear projection map? We answer this question affirmatively by developing embedding theorems for compact invariant sets associated with C 1 maps on Hilbert spaces. Examples of such discrete-time dynamical systems include time- T maps and Poincaré return maps generated by the solution semigroups of evolution partial differential equations. We make every effort to place hypotheses on the projected dynamics rather than on the underlying infinite-dimensional dynamical system. In so doing, we adopt an empirical approach and formulate checkable conditions under which a Lyapunov exponent computed from experimental data will be a Lyapunov exponent of the infinite-dimensional dynamical system under study (provided the nonlinear projection map producing the data is typical in the sense of prevalence).

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…

Improved Sensitivity Relations in State Constrained Optimal Control

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

Bettiol, Piernicola, E-mail: piernicola.bettiol@univ-brest.fr; Frankowska, Hélène, E-mail: frankowska@math.jussieu.fr; Vinter, Richard B., E-mail: r.vinter@imperial.ac.uk

2015-04-15

Sensitivity relations in optimal control provide an interpretation of the costate trajectory and the Hamiltonian, evaluated along an optimal trajectory, in terms of gradients of the value function. While sensitivity relations are a straightforward consequence of standard transversality conditions for state constraint free optimal control problems formulated in terms of control-dependent differential equations with smooth data, their verification for problems with either pathwise state constraints, nonsmooth data, or for problems where the dynamic constraint takes the form of a differential inclusion, requires careful analysis. In this paper we establish validity of both ‘full’ and ‘partial’ sensitivity relations for an adjointmore » state of the maximum principle, for optimal control problems with pathwise state constraints, where the underlying control system is described by a differential inclusion. The partial sensitivity relation interprets the costate in terms of partial Clarke subgradients of the value function with respect to the state variable, while the full sensitivity relation interprets the couple, comprising the costate and Hamiltonian, as the Clarke subgradient of the value function with respect to both time and state variables. These relations are distinct because, for nonsmooth data, the partial Clarke subdifferential does not coincide with the projection of the (full) Clarke subdifferential on the relevant coordinate space. We show for the first time (even for problems without state constraints) that a costate trajectory can be chosen to satisfy the partial and full sensitivity relations simultaneously. The partial sensitivity relation in this paper is new for state constraint problems, while the full sensitivity relation improves on earlier results in the literature (for optimal control problems formulated in terms of Lipschitz continuous multifunctions), because a less restrictive inward pointing hypothesis is invoked in the proof, and because it is validated for a stronger set of necessary conditions.« less

Dynamics and Collapse in a Power System Model with Voltage Variation: The Damping Effect.

PubMed

Ma, Jinpeng; Sun, Yong; Yuan, Xiaoming; Kurths, Jürgen; Zhan, Meng

2016-01-01

Complex nonlinear phenomena are investigated in a basic power system model of the single-machine-infinite-bus (SMIB) with a synchronous generator modeled by a classical third-order differential equation including both angle dynamics and voltage dynamics, the so-called flux decay equation. In contrast, for the second-order differential equation considering the angle dynamics only, it is the classical swing equation. Similarities and differences of the dynamics generated between the third-order model and the second-order one are studied. We mainly find that, for positive damping, these two models show quite similar behavior, namely, stable fixed point, stable limit cycle, and their coexistence for different parameters. However, for negative damping, the second-order system can only collapse, whereas for the third-order model, more complicated behavior may happen, such as stable fixed point, limit cycle, quasi-periodicity, and chaos. Interesting partial collapse phenomena for angle instability only and not for voltage instability are also found here, including collapse from quasi-periodicity and from chaos etc. These findings not only provide a basic physical picture for power system dynamics in the third-order model incorporating voltage dynamics, but also enable us a deeper understanding of the complex dynamical behavior and even leading to a design of oscillation damping in electric power systems.

Algorithm for Stabilizing a POD-Based Dynamical System

NASA Technical Reports Server (NTRS)

Kalb, Virginia L.

2010-01-01

This algorithm provides a new way to improve the accuracy and asymptotic behavior of a low-dimensional system based on the proper orthogonal decomposition (POD). Given a data set representing the evolution of a system of partial differential equations (PDEs), such as the Navier-Stokes equations for incompressible flow, one may obtain a low-dimensional model in the form of ordinary differential equations (ODEs) that should model the dynamics of the flow. Temporal sampling of the direct numerical simulation of the PDEs produces a spatial time series. The POD extracts the temporal and spatial eigenfunctions of this data set. Truncated to retain only the most energetic modes followed by Galerkin projection of these modes onto the PDEs obtains a dynamical system of ordinary differential equations for the time-dependent behavior of the flow. In practice, the steps leading to this system of ODEs entail numerically computing first-order derivatives of the mean data field and the eigenfunctions, and the computation of many inner products. This is far from a perfect process, and often results in the lack of long-term stability of the system and incorrect asymptotic behavior of the model. This algorithm describes a new stabilization method that utilizes the temporal eigenfunctions to derive correction terms for the coefficients of the dynamical system to significantly reduce these errors.

The 1D Richards' equation in two layered soils: a Filippov approach to treat discontinuities

NASA Astrophysics Data System (ADS)

Berardi, Marco; Difonzo, Fabio; Vurro, Michele; Lopez, Luciano

2018-05-01

The infiltration process into the soil is generally modeled by the Richards' partial differential equation (PDE). In this paper a new approach for modeling the infiltration process through the interface of two different soils is proposed, where the interface is seen as a discontinuity surface defined by suitable state variables. Thus, the original 1D Richards' PDE, enriched by a particular choice of the boundary conditions, is first approximated by means of a time semidiscretization, that is by means of the transversal method of lines (TMOL). In such a way a sequence of discontinuous initial value problems, described by a sequence of second order differential systems in the space variable, is derived. Then, Filippov theory on discontinuous dynamical systems may be applied in order to study the relevant dynamics of the problem. The numerical integration of the semidiscretized differential system will be performed by using a one-step method, which employs an event driven procedure to locate the discontinuity surface and to adequately change the vector field.

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

Computationally efficient statistical differential equation modeling using homogenization

USGS Publications Warehouse

Hooten, Mevin B.; Garlick, Martha J.; Powell, James A.

2013-01-01

Statistical models using partial differential equations (PDEs) to describe dynamically evolving natural systems are appearing in the scientific literature with some regularity in recent years. Often such studies seek to characterize the dynamics of temporal or spatio-temporal phenomena such as invasive species, consumer-resource interactions, community evolution, and resource selection. Specifically, in the spatial setting, data are often available at varying spatial and temporal scales. Additionally, the necessary numerical integration of a PDE may be computationally infeasible over the spatial support of interest. We present an approach to impose computationally advantageous changes of support in statistical implementations of PDE models and demonstrate its utility through simulation using a form of PDE known as “ecological diffusion.” We also apply a statistical ecological diffusion model to a data set involving the spread of mountain pine beetle (Dendroctonus ponderosae) in Idaho, USA.

On the slow dynamics of near-field acoustically levitated objects under High excitation frequencies

NASA Astrophysics Data System (ADS)

Ilssar, Dotan; Bucher, Izhak

2015-10-01

This paper introduces a simplified analytical model describing the governing dynamics of near-field acoustically levitated objects. The simplification converts the equation of motion coupled with the partial differential equation of a compressible fluid, into a compact, second order ordinary differential equation, where the local stiffness and damping are transparent. The simplified model allows one to more easily analyse and design near-field acoustic levitation based systems, and it also helps to devise closed-loop controller algorithms for such systems. Near-field acoustic levitation employs fast ultrasonic vibrations of a driving surface and exploits the viscosity and the compressibility of a gaseous medium to achieve average, load carrying pressure. It is demonstrated that the slow dynamics dominates the transient behaviour, while the time-scale associated with the fast, ultrasonic excitation has a small presence in the oscillations of the levitated object. Indeed, the present paper formulates the slow dynamics under an ultrasonic excitation without the need to explicitly consider the latter. The simplified model is compared with a numerical scheme based on Reynolds equation and with experiments, both showing reasonably good results.

Partial Thermalization of Correlations in pA and AA collisionss

NASA Astrophysics Data System (ADS)

Gavin, Sean; Moschelli, George; Zin, Christopher

2017-09-01

Correlations born before the onset of hydrodynamic flow can leave observable traces on the final state particles. Measurement of these correlations can yield important information on the isotropization and thermalization process. Starting with Israel-Stewart hydrodynamics and Boltzmann-like kinetic theory in the presence of dynamic Langevin noise, we derive new partial differential equations for two-particle correlation functions. To illustrate how these equations can be used, we study the effect of thermalization on long range correlations. We show quite generally that two particle correlations at early times depend on S, the average probability that a parton suffers no interactions. We extract S from transverse momentum fluctuations measured in Pb+Pb collisions and predict the degree of partial thermalization in pA experiments. NSF-PHY-1207687.

Strange quark condensate in the nucleon in 2 + 1 flavor QCD.

PubMed

Toussaint, D; Freeman, W

2009-09-18

We calculate the "strange quark content of the nucleon," , which is important for interpreting the results of some dark matter detection experiments. The method is to evaluate quark-line disconnected correlations on the MILC lattice ensembles, which include the effects of dynamical light and strange quarks. After continuum and chiral extrapolations, the result is = 0.69(7)_{stat}(9)_{syst}, in the modified minimal subtraction scheme (2 GeV) regularization, or for the renormalization scheme invariant form, m_{s} partial differentialM_{N}/ partial differentialm_{s} = 59(6)(8) MeV.

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.

Constraints on the rheology of the partially molten mantle from numerical models of laboratory experiments

NASA Astrophysics Data System (ADS)

Rudge, J. F.; Alisic Jewell, L.; Rhebergen, S.; Katz, R. F.; Wells, G. N.

2015-12-01

One of the fundamental components in any dynamical model of melt transport is the rheology of partially molten rock. This rheology is poorly understood, and one way in which a better understanding can be obtained is by comparing the results of laboratory deformation experiments to numerical models. Here we present a comparison between numerical models and the laboratory setup of Qi et al. 2013 (EPSL), where a cylinder of partially molten rock containing rigid spherical inclusions was placed under torsion. We have replicated this setup in a finite element model which solves the partial differential equations describing the mechanical process of compaction. These computationally-demanding 3D simulations are only possible due to the recent development of a new preconditioning method for the equations of magma dynamics. The experiments show a distinct pattern of melt-rich and melt-depleted regions around the inclusions. In our numerical models, the pattern of melt varies with key rheological parameters, such as the ratio of bulk to shear viscosity, and the porosity- and strain-rate-dependence of the shear viscosity. These observed melt patterns therefore have the potential to constrain rheological properties. While there are many similarities between the experiments and the numerical models, there are also important differences, which highlight the need for better models of the physics of two-phase mantle/magma dynamics. In particular, the laboratory experiments display more pervasive melt-rich bands than is seen in our numerics.

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).

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.

Lunar and Planetary Science XXXV: Terrestrial Planets: Building Blocks and Differentiation

NASA Technical Reports Server (NTRS)

2004-01-01

The session "Terrestrial Planets: Building Blocks and Differentiation: included the following topics:Magnesium Isotopes in the Earth, Moon, Mars, and Pallasite Parent Body: High-Precision Analysis of Olivine by Laser-Ablation Multi-Collector ICPMS; Meteoritic Constraints on Collision Rates in the Primordial Asteroid Belt and Its Origin; New Constraints on the Origin of the Highly Siderophile Elements in the Earth's Upper Mantle; Further Lu-Hf and Sm-Nd Isotopic Data on Planetary Materials and Consequences for Planetary Differentiation; A Deep Lunar Magma Ocean Based on Neodymium, Strontium and Hafnium Isotope Mass Balance Partial Resetting on Hf-W System by Giant Impacts; On the Problem of Metal-Silicate Equilibration During Planet Formation: Significance for Hf-W Chronometry ; Solid Metal-Liquid Metal Partitioning of Pt, Re, and Os: The Effect of Carbon; Siderophile Element Abundances in Fe-S-Ni-O Melts Segregated from Partially Molten Ordinary Chondrite Under Dynamic Conditions; Activity Coefficients of Silicon in Iron-Nickel Alloys: Experimental Determination and Relevance for Planetary Differentiation; Reinvestigation of the Ni and Co Metal-Silicate Partitioning; Metal/Silicate Paritioning of P, Ga, and W at High Pressures and Temperatures: Dependence on Silicate Melt Composition; and Closure of the Fe-S-Si Liquid Miscibility Gap at High Pressure and Its Implications for Planetary Core Formation.

Implicit finite difference methods on composite grids

NASA Technical Reports Server (NTRS)

Mastin, C. Wayne

1987-01-01

Techniques for eliminating time lags in the implicit finite-difference solution of partial differential equations are investigated analytically, with a focus on transient fluid dynamics problems on overlapping multicomponent grids. The fundamental principles of the approach are explained, and the method is shown to be applicable to both rectangular and curvilinear grids. Numerical results for sample problems are compared with exact solutions in graphs, and good agreement is demonstrated.

Modelling the aggregation process of cellular slime mold by the chemical attraction.

PubMed

Atangana, Abdon; Vermeulen, P D

2014-01-01

We put into exercise a comparatively innovative analytical modus operandi, the homotopy decomposition method (HDM), for solving a system of nonlinear partial differential equations arising in an attractor one-dimensional Keller-Segel dynamics system. Numerical solutions are given and some properties show evidence of biologically practical reliance on the parameter values. The reliability of HDM and the reduction in computations give HDM a wider applicability.

Using some results about the Lie evolution of differential operators to obtain the Fokker-Planck equation for non-Hamiltonian dynamical systems of interest

NASA Astrophysics Data System (ADS)

Bianucci, Marco

2018-05-01

Finding the generalized Fokker-Planck Equation (FPE) for the reduced probability density function of a subpart of a given complex system is a classical issue of statistical mechanics. Zwanzig projection perturbation approach to this issue leads to the trouble of resumming a series of commutators of differential operators that we show to correspond to solving the Lie evolution of first order differential operators along the unperturbed Liouvillian of the dynamical system of interest. In this paper, we develop in a systematic way the procedure to formally solve this problem. In particular, here we show which the basic assumptions are, concerning the dynamical system of interest, necessary for the Lie evolution to be a group on the space of first order differential operators, and we obtain the coefficients of the so-evolved operators. It is thus demonstrated that if the Liouvillian of the system of interest is not a first order differential operator, in general, the FPE structure breaks down and the master equation contains all the power of the partial derivatives, up to infinity. Therefore, this work shed some light on the trouble of the ubiquitous emergence of both thermodynamics from microscopic systems and regular regression laws at macroscopic scales. However these results are very general and can be applied also in other contexts that are non-Hamiltonian as, for example, geophysical fluid dynamics, where important events, like El Niño, can be considered as large time scale phenomena emerging from the observation of few ocean degrees of freedom of a more complex system, including the interaction with the atmosphere.

Measles metapopulation dynamics: a gravity model for epidemiological coupling and dynamics.

PubMed

Xia, Yingcun; Bjørnstad, Ottar N; Grenfell, Bryan T

2004-08-01

Infectious diseases provide a particularly clear illustration of the spatiotemporal underpinnings of consumer-resource dynamics. The paradigm is provided by extremely contagious, acute, immunizing childhood infections. Partially synchronized, unstable oscillations are punctuated by local extinctions. This, in turn, can result in spatial differentiation in the timing of epidemics and, depending on the nature of spatial contagion, may result in traveling waves. Measles epidemics are one of a few systems documented well enough to reveal all of these properties and how they are affected by spatiotemporal variations in population structure and demography. On the basis of a gravity coupling model and a time series susceptible-infected-recovered (TSIR) model for local dynamics, we propose a metapopulation model for regional measles dynamics. The model can capture all the major spatiotemporal properties in prevaccination epidemics of measles in England and Wales.

From the big five to the general factor of personality: a dynamic approach.

PubMed

Micó, Joan C; Amigó, Salvador; Caselles, Antonio

2014-10-28

An integrating and dynamic model of personality that allows predicting the response of the basic factors of personality, such as the Big Five Factors (B5F) or the general factor of personality (GFP) to acute doses of drug is presented in this paper. Personality has a dynamic nature, i.e., as a consequence of a stimulus, the GFP dynamics as well as each one of the B5F of personality dynamics can be explained by the same model (a system of three coupled differential equations). From this invariance hypothesis, a partial differential equation, whose solution relates the GFP with each one of the B5F, is deduced. From this dynamic approach, a co-evolution of the GFP and each one of the B5F occurs, rather than an unconnected evolution, as a consequence of the same stimulus. The hypotheses and deductions are validated through an experimental design centered on the individual, where caffeine is the considered stimulus. Thus, as much from a theoretical point of view as from an applied one, the models here proposed open a new perspective in the understanding and study of personality like a global system that interacts intimately with the environment, being a clear bet for the high level inter-disciplinary research.

Vibration analysis of beams traversed by uniform partially distributed moving masses

NASA Astrophysics Data System (ADS)

Esmailzadeh, E.; Ghorashi, M.

1995-07-01

An investigation into the dynamic behavior of beams with simply supported boundary conditions, carrying either uniform partially distributed moving masses or forces, has been carried out. The present analysis in its general form may well be applied to beams with various boundary conditions. However, the results from the computer simulation model given in this paper are for beams with simply supported end conditions. Results from the numerical solutions of the differential equations of motion are shown graphically and their close agreement, in some extreme cases, with those published previously by the authors is demonstrated. It is shown that the inertial effect of the moving mass is of importance in the dynamic behavior of such structures. Moreover, when considering the maximum deflection for the mid-span of the beam, the critical speeds of the moving load have been evaluated. It is also verified that the length of the distributed moving mass affects the dynamic response considerably. These effects are shown to be of significant practical importance when designing beam-type structures such as long suspension and railway bridges.

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

Sloshing dynamics on rotating helium dewar tank

NASA Technical Reports Server (NTRS)

Hung, R. J.

1993-01-01

The generalized mathematical formulation of sloshing dynamics for partially filled liquid of cryogenic superfluid helium II in dewar containers driven by both the gravity gradient and jitter accelerations applicable to scientific spacecraft which is eligible to carry out spinning motion and/or slew motion for the purpose to perform scientific observation during the normal spacecraft operation are investigated. An example is given with Gravity Probe-B (GP-B) spacecraft which is responsible for the sloshing dynamics. The jitter accelerations include slew motion, spinning motion, atmospheric drag on the spacecraft, spacecraft attitude motions arising from machinery vibrations, thruster firing, pointing control of spacecraft, crew motion, etc. Explicit mathematical expressions to cover these forces acting on the spacecraft fluid systems are derived. The numerical computation of sloshing dynamics were based on the non-inertia frame spacecraft bound coordinate, and solve time dependent, three-dimensional formulations of partial differential equations subject to initial and boundary conditions. The explicit mathematical expressions of boundary conditions to cover capillary force effect on the liquid vapor interface in microgravity environments are also derived. The formulations of fluid moment and angular moment fluctuations in fluid profiles induced by the sloshing dynamics, together with fluid stress and moment fluctuations exerted on the spacecraft dewar containers were derived. Results were widely published in the open journals.

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.

Extent of reaction in open systems with multiple heterogeneous reactions

USGS Publications Warehouse

Friedly, John C.

1991-01-01

The familiar batch concept of extent of reaction is reexamined for systems of reactions occurring in open systems. Because species concentrations change as a result of transport processes as well as reactions in open systems, the extent of reaction has been less useful in practice in these applications. It is shown that by defining the extent of the equivalent batch reaction and a second contribution to the extent of reaction due to the transport processes, it is possible to treat the description of the dynamics of flow through porous media accompanied by many chemical reactions in a uniform, concise manner. This approach tends to isolate the reaction terms among themselves and away from the model partial differential equations, thereby enabling treatment of large problems involving both equilibrium and kinetically controlled reactions. Implications on the number of coupled partial differential equations necessary to be solved and on numerical algorithms for solving such problems are discussed. Examples provided illustrate the theory applied to solute transport in groundwater flow.

Bounding the solutions of parametric weakly coupled second-order semilinear parabolic partial differential equations

DOE PAGES

Azunre, P.

2016-09-21

Here in this paper, two novel techniques for bounding the solutions of parametric weakly coupled second-order semilinear parabolic partial differential equations are developed. The first provides a theorem to construct interval bounds, while the second provides a theorem to construct lower bounds convex and upper bounds concave in the parameter. The convex/concave bounds can be significantly tighter than the interval bounds because of the wrapping effect suffered by interval analysis in dynamical systems. Both types of bounds are computationally cheap to construct, requiring solving auxiliary systems twice and four times larger than the original system, respectively. An illustrative numerical examplemore » of bound construction and use for deterministic global optimization within a simple serial branch-and-bound algorithm, implemented numerically using interval arithmetic and a generalization of McCormick's relaxation technique, is presented. Finally, problems within the important class of reaction-diffusion systems may be optimized with these tools.« less

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

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.

Wavelet and adaptive methods for time dependent problems and applications in aerosol dynamics

NASA Astrophysics Data System (ADS)

Guo, Qiang

Time dependent partial differential equations (PDEs) are widely used as mathematical models of environmental problems. Aerosols are now clearly identified as an important factor in many environmental aspects of climate and radiative forcing processes, as well as in the health effects of air quality. The mathematical models for the aerosol dynamics with respect to size distribution are nonlinear partial differential and integral equations, which describe processes of condensation, coagulation and deposition. Simulating the general aerosol dynamic equations on time, particle size and space exhibits serious difficulties because the size dimension ranges from a few nanometer to several micrometer while the spatial dimension is usually described with kilometers. Therefore, it is an important and challenging task to develop efficient techniques for solving time dependent dynamic equations. In this thesis, we develop and analyze efficient wavelet and adaptive methods for the time dependent dynamic equations on particle size and further apply them to the spatial aerosol dynamic systems. Wavelet Galerkin method is proposed to solve the aerosol dynamic equations on time and particle size due to the fact that aerosol distribution changes strongly along size direction and the wavelet technique can solve it very efficiently. Daubechies' wavelets are considered in the study due to the fact that they possess useful properties like orthogonality, compact support, exact representation of polynomials to a certain degree. Another problem encountered in the solution of the aerosol dynamic equations results from the hyperbolic form due to the condensation growth term. We propose a new characteristic-based fully adaptive multiresolution numerical scheme for solving the aerosol dynamic equation, which combines the attractive advantages of adaptive multiresolution technique and the characteristics method. On the aspect of theoretical analysis, the global existence and uniqueness of solutions of continuous time wavelet numerical methods for the nonlinear aerosol dynamics are proved by using Schauder's fixed point theorem and the variational technique. Optimal error estimates are derived for both continuous and discrete time wavelet Galerkin schemes. We further derive reliable and efficient a posteriori error estimate which is based on stable multiresolution wavelet bases and an adaptive space-time algorithm for efficient solution of linear parabolic differential equations. The adaptive space refinement strategies based on the locality of corresponding multiresolution processes are proved to converge. At last, we develop efficient numerical methods by combining the wavelet methods proposed in previous parts and the splitting technique to solve the spatial aerosol dynamic equations. Wavelet methods along the particle size direction and the upstream finite difference method along the spatial direction are alternately used in each time interval. Numerical experiments are taken to show the effectiveness of our developed methods.

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.

Numerical investigations of two-phase flow with dynamic capillary pressure in porous media via a moving mesh method

NASA Astrophysics Data System (ADS)

Zhang, Hong; Zegeling, Paul Andries

2017-09-01

Motivated by observations of saturation overshoot, this paper investigates numerical modeling of two-phase flow in porous media incorporating dynamic capillary pressure. The effects of the dynamic capillary coefficient, the infiltrating flux rate and the initial and boundary values are systematically studied using a traveling wave ansatz and efficient numerical methods. The traveling wave solutions may exhibit monotonic, non-monotonic or plateau-shaped behavior. Special attention is paid to the non-monotonic profiles. The traveling wave results are confirmed by numerically solving the partial differential equation using an accurate adaptive moving mesh solver. Comparisons between the computed solutions using the Brooks-Corey model and the laboratory measurements of saturation overshoot verify the effectiveness of our approach.

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

Variational Solutions and Random Dynamical Systems to SPDEs Perturbed by Fractional Gaussian Noise

PubMed Central

Zeng, Caibin; Yang, Qigui; Cao, Junfei

2014-01-01

This paper deals with the following type of stochastic partial differential equations (SPDEs) perturbed by an infinite dimensional fractional Brownian motion with a suitable volatility coefficient Φ: dX(t) = A(X(t))dt+Φ(t)dB H(t), where A is a nonlinear operator satisfying some monotonicity conditions. Using the variational approach, we prove the existence and uniqueness of variational solutions to such system. Moreover, we prove that this variational solution generates a random dynamical system. The main results are applied to a general type of nonlinear SPDEs and the stochastic generalized p-Laplacian equation. PMID:24574903

Complex groundwater flow systems as traveling agent models

PubMed Central

Padilla, Pablo; Escolero, Oscar; González, Tomas; Morales-Casique, Eric; Osorio-Olvera, Luis

2014-01-01

Analyzing field data from pumping tests, we show that as with many other natural phenomena, groundwater flow exhibits complex dynamics described by 1/f power spectrum. This result is theoretically studied within an agent perspective. Using a traveling agent model, we prove that this statistical behavior emerges when the medium is complex. Some heuristic reasoning is provided to justify both spatial and dynamic complexity, as the result of the superposition of an infinite number of stochastic processes. Even more, we show that this implies that non-Kolmogorovian probability is needed for its study, and provide a set of new partial differential equations for groundwater flow. PMID:25337455

A study analysis of cable-body systems totally immersed in a fluid stream

NASA Technical Reports Server (NTRS)

Delaurier, J. D.

1972-01-01

A general stability analysis of a cable-body system immersed in a fluid stream is presented. The analytical portion of this analysis treats the system as being essentially a cable problem, with the body dynamics giving the end conditions. The mathematical form of the analysis consists of partial differential wave equations, with the end and auxiliary conditions being determined from the body equations of motion. The equations uncouple to give a lateral problem and a longitudinal problem as in first order airplane dynamics. A series of tests on a tethered wind tunnel model provide a comparison of the theory with experiment.

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.

Optimal moving grids for time-dependent partial differential equations

NASA Technical Reports Server (NTRS)

Wathen, A. J.

1989-01-01

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 partial differential equation solutions in the least squares norm.

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.

Embedding dynamical networks into distributed models

NASA Astrophysics Data System (ADS)

Innocenti, Giacomo; Paoletti, Paolo

2015-07-01

Large networks of interacting dynamical systems are well-known for the complex behaviours they are able to display, even when each node features a quite simple dynamics. Despite examples of such networks being widespread both in nature and in technological applications, the interplay between the local and the macroscopic behaviour, through the interconnection topology, is still not completely understood. Moreover, traditional analytical methods for dynamical response analysis fail because of the intrinsically large dimension of the phase space of the network which makes the general problem intractable. Therefore, in this paper we develop an approach aiming to condense all the information in a compact description based on partial differential equations. By focusing on propagative phenomena, rigorous conditions under which the original network dynamical properties can be successfully analysed within the proposed framework are derived as well. A network of Fitzhugh-Nagumo systems is finally used to illustrate the effectiveness of the proposed method.

The Modelling of Axially Translating Flexible Beams

NASA Astrophysics Data System (ADS)

Theodore, R. J.; Arakeri, J. H.; Ghosal, A.

1996-04-01

The axially translating flexible beam with a prismatic joint can be modelled by using the Euler-Bernoulli beam equation together with the convective terms. In general, the method of separation of variables cannot be applied to solve this partial differential equation. In this paper, a non-dimensional form of the Euler Bernoulli beam equation is presented, obtained by using the concept of group velocity, and also the conditions under which separation of variables and assumed modes method can be used. The use of clamped-mass boundary conditions leads to a time-dependent frequency equation for the translating flexible beam. A novel method is presented for solving this time dependent frequency equation by using a differential form of the frequency equation. The assume mode/Lagrangian formulation of dynamics is employed to derive closed form equations of motion. It is shown by using Lyapunov's first method that the dynamic responses of flexural modal variables become unstable during retraction of the flexible beam, which the dynamic response during extension of the beam is stable. Numerical simulation results are presented for the uniform axial motion induced transverse vibration for a typical flexible beam.

The mitochondrial elongation factors MIEF1 and MIEF2 exert partially distinct functions in mitochondrial dynamics

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

Liu, Tong; Yu, Rong; Jin, Shao-Bo

2013-11-01

Mitochondria are dynamic organelles whose morphology is regulated by a complex balance of fission and fusion processes, and we still know relatively little about how mitochondrial dynamics is regulated. MIEF1 (also called MiD51) has recently been characterized as a key regulator of mitochondrial dynamics and in this report we explore the functions of its paralog MIEF2 (also called MiD49), to learn to what extent MIEF2 is functionally distinct from MIEF1. We show that MIEF1 and MIEF2 have many functions in common. Both are anchored in the mitochondrial outer membrane, recruit Drp1 from the cytoplasm to the mitochondrial surface and causemore » mitochondrial fusion, and MIEF2, like MIEF1, can interact with Drp1 and hFis1. MIEF1 and MIEF2, however, also differ in certain aspects. MIEF1 and MIEF2 are differentially expressed in human tissues during development. When overexpressed, MIEF2 exerts a stronger fusion-promoting effect than MIEF1, and in line with this, hFis1 and Mff can only partially revert the MIEF2-induced fusion phenotype, whereas MIEF1-induced fusion is reverted to a larger extent by hFis1 and Mff. MIEF2 forms high molecular weight oligomers, while MIEF1 is largely present as a dimer. Furthermore, MIEF1 and MIEF2 use distinct domains for oligomerization: in MIEF1, the region from amino acid residues 109–154 is required, whereas oligomerization of MIEF2 depends on amino acid residues 1 to 49, i.e. the N-terminal end. We also show that oligomerization of MIEF1 is not required for its mitochondrial localization and interaction with Drp1. In conclusion, our data suggest that the mitochondrial regulators MIEF1 and MIEF2 exert partially distinct functions in mitochondrial dynamics. - Highlights: • MIEF1 and MIEF2 recruit Drp1 to mitochondria and cause mitochondrial fusion. • MIEF2, like MIEF1, can interact with Drp1 and hFis1. • MIEF1 and MIEF2 are differentially expressed in human tissues during development. • MIEF2 exerts a stronger fusion-promoting effect than MIEF1. • MIEF2 can form oligomers, while MIEF1 is largely present as a dimer.« less

Multithreaded Model for Dynamic Load Balancing Parallel Adaptive PDE Computations

NASA Technical Reports Server (NTRS)

Chrisochoides, Nikos

1995-01-01

We present a multithreaded model for the dynamic load-balancing of numerical, adaptive computations required for the solution of Partial Differential Equations (PDE's) on multiprocessors. Multithreading is used as a means of exploring concurrency in the processor level in order to tolerate synchronization costs inherent to traditional (non-threaded) parallel adaptive PDE solvers. Our preliminary analysis for parallel, adaptive PDE solvers indicates that multithreading can be used an a mechanism to mask overheads required for the dynamic balancing of processor workloads with computations required for the actual numerical solution of the PDE's. Also, multithreading can simplify the implementation of dynamic load-balancing algorithms, a task that is very difficult for traditional data parallel adaptive PDE computations. Unfortunately, multithreading does not always simplify program complexity, often makes code re-usability not an easy task, and increases software complexity.

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

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).

Modeling and vibration control of the flapping-wing robotic aircraft with output constraint

NASA Astrophysics Data System (ADS)

He, Wei; Mu, Xinxing; Chen, Yunan; He, Xiuyu; Yu, Yao

2018-06-01

In this paper, we propose the boundary control for undesired vibrations suppression with output constraint of the flapping-wing robotic aircraft (FWRA). We also present the dynamics of the flexible wing of FWRA with governing equations and boundary conditions, which are partial differential equations (PDEs) and ordinary differential equations (ODEs), respectively. An energy-based barrier Lyapunov function is introduced to analyze the system stability and prevent violation of output constraint. With the effect of the proposed boundary controller, distributed states of the system remain in the constrained spaces. Then the IBLF-based boundary controls are proposed to assess the stability of the FWRA in the presence of output constraint.

Dynamic grid refinement for partial differential equations on parallel computers

NASA Technical Reports Server (NTRS)

Mccormick, S.; Quinlan, D.

1989-01-01

The fast adaptive composite grid method (FAC) is an algorithm that uses various levels of uniform grids to provide adaptive resolution and fast solution of PDEs. An asynchronous version of FAC, called AFAC, that completely eliminates the bottleneck to parallelism is presented. This paper describes the advantage that this algorithm has in adaptive refinement for moving singularities on multiprocessor computers. This work is applicable to the parallel solution of two- and three-dimensional shock tracking problems.

Historical evolution of vortex-lattice methods

NASA Technical Reports Server (NTRS)

Deyoung, J.

1976-01-01

A review of the beginning and some orientation of the vortex-lattice method were given. The historical course of this method was followed in conjunction with its field of computational fluid dynamics, spanning the period from L.F. Richardson's paper in 1910 to 1975. The following landmarks were pointed out: numerical analysis of partial differential equations, lifting-line theory, finite-difference method, 1/4-3/4 rule, block relaxation technique, application of electronic computers, and advanced panel methods.

Nonlinear ring resonator: spatial pattern generation

NASA Astrophysics Data System (ADS)

Ivanov, Vladimir Y.; Lachinova, Svetlana L.; Irochnikov, Nikita G.

2000-03-01

We consider theoretically spatial pattern formation processes in a unidirectional ring cavity with thin layer of Kerr-type nonlinear medium. Our method is based on studying of two coupled equations. The first is a partial differential equation for temporal dynamics of phase modulation of light wave in the medium. It describes nonlinear interaction in the Kerr-type lice. The second is a free propagation equation for the intracavity field complex amplitude. It involves diffraction effects of light wave in the cavity.

A computer program for the geometrically nonlinear static and dynamic analysis of arbitrarily loaded shells of revolution, theory and users manual

NASA Technical Reports Server (NTRS)

Ball, R. E.

1972-01-01

A digital computer program known as SATANS (static and transient analysis, nonlinear, shells) for the geometrically nonlinear static and dynamic response of arbitrarily loaded shells of revolution is presented. Instructions for the preparation of the input data cards and other information necessary for the operation of the program are described in detail and two sample problems are included. The governing partial differential equations are based upon Sanders' nonlinear thin shell theory for the conditions of small strains and moderately small rotations. The governing equations are reduced to uncoupled sets of four linear, second order, partial differential equations in the meridional and time coordinates by expanding the dependent variables in a Fourier sine or cosine series in the circumferential coordinate and treating the nonlinear modal coupling terms as pseudo loads. The derivatives with respect to the meridional coordinate are approximated by central finite differences, and the displacement accelerations are approximated by the implicit Houbolt backward difference scheme with a constant time interval. The boundaries of the shell may be closed, free, fixed, or elastically restrained. The program is coded in the FORTRAN 4 language and is dimensioned to allow a maximum of 10 arbitrary Fourier harmonics and a maximum product of the total number of meridional stations and the total number of Fourier harmonics of 200. The program requires 155,000 bytes of core storage.

Numerical studies of the surface tension effect of cryogenic liquid helium

NASA Technical Reports Server (NTRS)

Hung, R. J.

1994-01-01

The generalized mathematical formulation of sloshing dynamics for partially filled liquid of cryogenic superfluid helium II in dewar containers driven by both the gravity gradient and jitter accelerations applicable to scientific spacecraft which is eligible to carry out spinning motion and/or slew motion for the purpose of performing scientific observation during the normal spacecraft operation is investigated. An example is given with Gravity Probe-B (GP-B) spacecraft which is responsible for the sloshing dynamics. The jitter accelerations include slew motion, spinning motion, atmospheric drag on the spacecraft, spacecraft attitude motions arising from machinery vibrations, thruster firing, pointing control of spacecraft, crew motion, etc. Explicit mathematical expressions to cover these forces acting on the spacecraft fluid systems are derived. The numerical computation of sloshing dynamics has been based on the non-inertia frame spacecraft bound coordinate, and solve time-dependent, three-dimensional formulations of partial differential equations subject to initial and boundary conditions. The explicit mathematical expressions of boundary conditions to cover capillary force effect on the liquid vapor interface in microgravity environments are also derived. The formulations of fluid moment and angular moment fluctuations in fluid profiles induced by the sloshing dynamics, together with fluid stress and moment fluctuations exerted on the spacecraft dewar containers, have been derived.

A tutorial on dynamical systems concepts applied to Lagrangian transport in oceanic flows defined as finite time data sets: Theoretical and computational issues

NASA Astrophysics Data System (ADS)

Mancho, Ana M.; Small, Des; Wiggins, Stephen

2006-12-01

In the past 15 years the framework and ideas from dynamical systems theory have been applied to a variety of transport and mixing problems in oceanic flows. The motivation for this approach comes directly from advances in observational capabilities in oceanography (e.g., drifter deployments, remote sensing capabilities, satellite imagery, etc.) which reveal space-time structures that are highly suggestive of the structures one visualizes in the global, geometrical study of dynamical systems theory. In this tutorial, we motivate this approach by showing the relationship between fluid transport in two-dimensional time-periodic incompressible flows and the geometrical structures that exist for two-dimensional area-preserving maps, such as hyperbolic periodic orbits, their stable and unstable manifolds and KAM (Kolmogorov-Arnold-Moser) tori. This serves to set the stage for the attempt to “transfer” this approach to more realistic flows modelling the ocean. However, in order to accomplish this several difficulties must be overcome. The first difficulty that confronts us that any attempt to carry out a dynamical systems approach to transport requires us to obtain the appropriate “dynamical system”, which is the velocity field describing the fluid flow. In general, adequate model velocity fields are obtained by numerical solution of appropriate partial differential equations describing the dynamical evolution of the velocity field. Numerical solution of the partial differential equations can only be done for a finite time interval, and since the ocean is generally not time-periodic, this leads to a new type of dynamical system: a finite-time, aperiodically time-dependent velocity field defined as a data set on a space-time grid. The global, geometrical analysis of transport in such dynamical systems requires both new concepts and new analytical and computational tools, as well as the necessity to discard some of the standard ideas and results from dynamical systems theory. The purpose of this tutorial is to describe these new concepts and analytical tools first using simple dynamical systems where quantities can be computed exactly. We then discuss their computational implications and implementation in the context of a model geophysical flow: a turbulent wind-driven double-gyre in the quasigeostrophic approximation.

Mathematical Methods for Physics and Engineering Third Edition Paperback Set

NASA Astrophysics Data System (ADS)

Riley, Ken F.; Hobson, Mike P.; Bence, Stephen J.

2006-06-01

Prefaces; 1. Preliminary algebra; 2. Preliminary calculus; 3. Complex numbers and hyperbolic functions; 4. Series and limits; 5. Partial differentiation; 6. Multiple integrals; 7. Vector algebra; 8. Matrices and vector spaces; 9. Normal modes; 10. Vector calculus; 11. Line, surface and volume integrals; 12. Fourier series; 13. Integral transforms; 14. First-order ordinary differential equations; 15. Higher-order ordinary differential equations; 16. Series solutions of ordinary differential equations; 17. Eigenfunction methods for differential equations; 18. Special functions; 19. Quantum operators; 20. Partial differential equations: general and particular; 21. Partial differential equations: separation of variables; 22. Calculus of variations; 23. Integral equations; 24. Complex variables; 25. Application of complex variables; 26. Tensors; 27. Numerical methods; 28. Group theory; 29. Representation theory; 30. Probability; 31. Statistics; Index.

Superfluid helium sloshing dynamics induced oscillations and fluctuations of angular momentum, force and moment actuated on spacecraft driven by gravity gradient or jitter acceleration associated with slew motion

NASA Technical Reports Server (NTRS)

Hung, R. J.

1994-01-01

The generalized mathematical formulation of sloshing dynamics for partially filled liquid of cryogenic superfluid helium II in dewar containers driven by the gravity gradient and jitter accelerations associated with slew motion for the purpose to perform scientific observation during the normal spacecraft operation are investigated. An example is given with the Advanced X-Ray Astrophysics Facility-Spectroscopy (AXAF-S) for slew motion which is responsible for the sloshing dynamics. The jitter accelerations include slew motion, spinning motion, atmospheric drag on the spacecraft, spacecraft attitude motions arising from machinery vibrations, thruster firing, pointing control of spacecraft, crew motion, etc. Explicit mathematical expressions to cover these forces acting on the spacecraft fluid systems are derived. The numerical computation of sloshing dynamics is based on the non-inertia frame spacecraft bound coordinate, and solve time-dependent, three-dimensional formulations of partial differential equations subject to initial and boundary conditions. The explicit mathematical expressions of boundary conditions to cover capillary force effect on the liquid-vapor interface in microgravity environments are also derived. The formulations of fluid moment and angular moment fluctuations in fluid profiles induced by the sloshing dynamics, together with fluid stress and moment fluctuations exerted on the spacecraft dewar containers have also been derived. Examples are also given for cases applicable to the AXAF-S spacecraft sloshing dynamics associated with slew motion.

Spatial complexity of solutions of higher order partial differential equations

NASA Astrophysics Data System (ADS)

Kukavica, Igor

2004-03-01

We address spatial oscillation properties of solutions of higher order parabolic partial differential equations. In the case of the Kuramoto-Sivashinsky equation ut + uxxxx + uxx + u ux = 0, we prove that for solutions u on the global attractor, the quantity card {x epsi [0, L]:u(x, t) = lgr}, where L > 0 is the spatial period, can be bounded by a polynomial function of L for all \\lambda\\in{\\Bbb R} . A similar property is proven for a general higher order partial differential equation u_t+(-1)^{s}\\partial_x^{2s}u+ \\sum_{k=0}^{2s-1}v_k(x,t)\\partial_x^k u =0 .

A physical approach to the numerical treatment of boundaries in gas dynamics

NASA Technical Reports Server (NTRS)

Moretti, G.

1981-01-01

Two types of boundaries are considered: rigid walls, and artificial (open) boundaries which were arbitrarily drawn somewhere across a wider flow field. A set of partial differential equations (typically, the Euler equations) has an infinite number of solutions, each one defined by a set of initial and boundary conditions. The initial conditions remaining the same, any change in the boundary conditions will produce a new solution. To pose the problem well, a necessary and sufficient number of boundary conditions are prescribed.

Automating the parallel processing of fluid and structural dynamics calculations

NASA Technical Reports Server (NTRS)

Arpasi, Dale J.; Cole, Gary L.

1987-01-01

The NASA Lewis Research Center is actively involved in the development of expert system technology to assist users in applying parallel processing to computational fluid and structural dynamic analysis. The goal of this effort is to eliminate the necessity for the physical scientist to become a computer scientist in order to effectively use the computer as a research tool. Programming and operating software utilities have previously been developed to solve systems of ordinary nonlinear differential equations on parallel scalar processors. Current efforts are aimed at extending these capabilities to systems of partial differential equations, that describe the complex behavior of fluids and structures within aerospace propulsion systems. This paper presents some important considerations in the redesign, in particular, the need for algorithms and software utilities that can automatically identify data flow patterns in the application program and partition and allocate calculations to the parallel processors. A library-oriented multiprocessing concept for integrating the hardware and software functions is described.

Collective phase description of oscillatory convection

NASA Astrophysics Data System (ADS)

Kawamura, Yoji; Nakao, Hiroya

2013-12-01

We formulate a theory for the collective phase description of oscillatory convection in Hele-Shaw cells. It enables us to describe the dynamics of the oscillatory convection by a single degree of freedom which we call the collective phase. The theory can be considered as a phase reduction method for limit-cycle solutions in infinite-dimensional dynamical systems, namely, stable time-periodic solutions to partial differential equations, representing the oscillatory convection. We derive the phase sensitivity function, which quantifies the phase response of the oscillatory convection to weak perturbations applied at each spatial point, and analyze the phase synchronization between two weakly coupled Hele-Shaw cells exhibiting oscillatory convection on the basis of the derived phase equations.

On the Solution of Elliptic Partial Differential Equations on Regions with Corners

DTIC Science & Technology

2015-07-09

In this report we investigate the solution of boundary value problems on polygonal domains for elliptic partial differential equations . We observe...that when the problems are formulated as the boundary integral equations of classical potential theory, the solutions are representable by series of...efficient numerical algorithms. The results are illustrated by a number of numerical examples. On the solution of elliptic partial differential equations on

State-of-charge estimation in lithium-ion batteries: A particle filter approach

NASA Astrophysics Data System (ADS)

Tulsyan, Aditya; Tsai, Yiting; Gopaluni, R. Bhushan; Braatz, Richard D.

2016-11-01

The dynamics of lithium-ion batteries are complex and are often approximated by models consisting of partial differential equations (PDEs) relating the internal ionic concentrations and potentials. The Pseudo two-dimensional model (P2D) is one model that performs sufficiently accurately under various operating conditions and battery chemistries. Despite its widespread use for prediction, this model is too complex for standard estimation and control applications. This article presents an original algorithm for state-of-charge estimation using the P2D model. Partial differential equations are discretized using implicit stable algorithms and reformulated into a nonlinear state-space model. This discrete, high-dimensional model (consisting of tens to hundreds of states) contains implicit, nonlinear algebraic equations. The uncertainty in the model is characterized by additive Gaussian noise. By exploiting the special structure of the pseudo two-dimensional model, a novel particle filter algorithm that sweeps in time and spatial coordinates independently is developed. This algorithm circumvents the degeneracy problems associated with high-dimensional state estimation and avoids the repetitive solution of implicit equations by defining a 'tether' particle. The approach is illustrated through extensive simulations.

The solids-flux theory--confirmation and extension by using partial differential equations.

PubMed

Diehl, Stefan

2008-12-01

The solids-flux theory has been used for half a century as a tool for estimating concentration and fluxes in the design and operation of secondary settling tanks during stationary conditions. The flux theory means that the conservation of mass is used in one dimension together with the batch-settling flux function according to the Kynch assumption. The flux theory results correspond to stationary solutions of a partial differential equation, a conservation law, with discontinuous coefficients modelling the continuous-sedimentation process in one dimension. The mathematical analysis of such an equation is intricate, partly since it cannot be interpreted in the classical sense. Recent results, however, make it possible to partly confirm and extend the previous flux theory statements, partly draw new conclusions also on the dynamic behaviour and the possibilities and limitations for control. We use here a single example of an ideal settling tank and a given batch-settling flux in a whole series of calculations. The mathematical results are adapted towards the application and many of them are conveniently presented in terms of operating charts.

Towards information-optimal simulation of partial differential equations.

PubMed

Leike, Reimar H; Enßlin, Torsten A

2018-03-01

Most simulation schemes for partial differential equations (PDEs) focus on minimizing a simple error norm of a discretized version of a field. This paper takes a fundamentally different approach; the discretized field is interpreted as data providing information about a real physical field that is unknown. This information is sought to be conserved by the scheme as the field evolves in time. Such an information theoretic approach to simulation was pursued before by information field dynamics (IFD). In this paper we work out the theory of IFD for nonlinear PDEs in a noiseless Gaussian approximation. The result is an action that can be minimized to obtain an information-optimal simulation scheme. It can be brought into a closed form using field operators to calculate the appearing Gaussian integrals. The resulting simulation schemes are tested numerically in two instances for the Burgers equation. Their accuracy surpasses finite-difference schemes on the same resolution. The IFD scheme, however, has to be correctly informed on the subgrid correlation structure. In certain limiting cases we recover well-known simulation schemes like spectral Fourier-Galerkin methods. We discuss implications of the approximations made.

Organization of the cytokeratin network in an epithelial cell.

PubMed

Portet, Stéphanie; Arino, Ovide; Vassy, Jany; Schoëvaërt, Damien

2003-08-07

The cytoskeleton is a dynamic three-dimensional structure mainly located in the cytoplasm. It is involved in many cell functions such as mechanical signal transduction and maintenance of cell integrity. Among the three cytoskeletal components, intermediate filaments (the cytokeratin in epithelial cells) are the best candidates for this mechanical role. A model of the establishment of the cytokeratin network of an epithelial cell is proposed to study the dependence of its structural organization on extracellular mechanical environment. To implicitly describe the latter and its effects on the intracellular domain, we use mechanically regulated protein synthesis. Our model is a hybrid of a partial differential equation of parabolic type, governing the evolution of the concentration of cytokeratin, and a set of stochastic differential equations describing the dynamics of filaments. Each filament is described by a stochastic differential equation that reflects both the local interactions with the environment and the non-local interactions via the past history of the filament. A three-dimensional simulation model is derived from this mathematical model. This simulation model is then used to obtain examples of cytokeratin network architectures under given mechanical conditions, and to study the influence of several parameters.

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.

Student Solution Manual for Mathematical Methods for Physics and Engineering Third Edition

NASA Astrophysics Data System (ADS)

Riley, K. F.; Hobson, M. P.

2006-03-01

Preface; 1. Preliminary algebra; 2. Preliminary calculus; 3. Complex numbers and hyperbolic functions; 4. Series and limits; 5. Partial differentiation; 6. Multiple integrals; 7. Vector algebra; 8. Matrices and vector spaces; 9. Normal modes; 10. Vector calculus; 11. Line, surface and volume integrals; 12. Fourier series; 13. Integral transforms; 14. First-order ordinary differential equations; 15. Higher-order ordinary differential equations; 16. Series solutions of ordinary differential equations; 17. Eigenfunction methods for differential equations; 18. Special functions; 19. Quantum operators; 20. Partial differential equations: general and particular; 21. Partial differential equations: separation of variables; 22. Calculus of variations; 23. Integral equations; 24. Complex variables; 25. Application of complex variables; 26. Tensors; 27. Numerical methods; 28. Group theory; 29. Representation theory; 30. Probability; 31. Statistics.

Thermal buoyancy on magneto hydrodynamic flow over a vertical saturated porous surface with viscous dissipation

NASA Astrophysics Data System (ADS)

Nirmala, P. H.; Saila Kumari, A.; Raju, C. S. K.

2018-04-01

In the present article, we studied the magnetohydro dynamic flow induced heat transfer from vertical surface embedded in a saturated porous medium in the presence of viscous dissipation. Appropriate similarity transformations are used to transmute the non-linear governing partial differential equations to non-linear ODE. To solve these ordinary differential equations (ODE) we used the well-known integral method of Von Karman type. A comparison has been done and originates to be in suitable agreement with the previous published results. The tabulated and graphical results are given to consider the physical nature of the problem. From this results we found that the magnetic field parameter depreciate the velocity profiles and improves the heat transfer rate of the flow.

Boundary control for a constrained two-link rigid-flexible manipulator with prescribed performance

NASA Astrophysics Data System (ADS)

Cao, Fangfei; Liu, Jinkun

2018-05-01

In this paper, we consider a boundary control problem for a constrained two-link rigid-flexible manipulator. The nonlinear system is described by hybrid ordinary differential equation-partial differential equation (ODE-PDE) dynamic model. Based on the coupled ODE-PDE model, boundary control is proposed to regulate the joint positions and eliminate the elastic vibration simultaneously. With the help of prescribed performance functions, the tracking error can converge to an arbitrarily small residual set and the convergence rate is no less than a certain pre-specified value. Asymptotic stability of the closed-loop system is rigorously proved by the LaSalle's Invariance Principle extended to infinite-dimensional system. Numerical simulations are provided to demonstrate the effectiveness of the proposed controller.

Convergence of excitatory and inhibitory hair cell transmitters shapes vestibular afferent responses.

PubMed

Holstein, Gay R; Rabbitt, Richard D; Martinelli, Giorgio P; Friedrich, Victor L; Boyle, Richard D; Highstein, Stephen M

2004-11-02

The vestibular semicircular canals respond to angular acceleration that is integrated to angular velocity by the biofluid mechanics of the canals and is the primary origin of afferent responses encoding velocity. Surprisingly, some afferents actually report angular acceleration. Our data indicate that hair-cell/afferent synapses introduce a mathematical derivative in these afferents that partially cancels the biomechanical integration and results in discharge rates encoding angular acceleration. We examined the role of convergent synaptic inputs from hair cells to this mathematical differentiation. A significant reduction in the order of the differentiation was observed for low-frequency stimuli after gamma-aminobutyric acid type B receptor antagonist administration. Results demonstrate that gamma-aminobutyric acid participates in shaping the temporal dynamics of afferent responses.

Model Predictive Optimal Control of a Time-Delay Distributed-Parameter Systems

NASA Technical Reports Server (NTRS)

Nguyen, Nhan

2006-01-01

This paper presents an optimal control method for a class of distributed-parameter systems governed by first order, quasilinear hyperbolic partial differential equations that arise in many physical systems. Such systems are characterized by time delays since information is transported from one state to another by wave propagation. A general closed-loop hyperbolic transport model is controlled by a boundary control embedded in a periodic boundary condition. The boundary control is subject to a nonlinear differential equation constraint that models actuator dynamics of the system. The hyperbolic equation is thus coupled with the ordinary differential equation via the boundary condition. Optimality of this coupled system is investigated using variational principles to seek an adjoint formulation of the optimal control problem. The results are then applied to implement a model predictive control design for a wind tunnel to eliminate a transport delay effect that causes a poor Mach number regulation.

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.

Local bifurcations in differential equations with state-dependent delay.

PubMed

Sieber, Jan

2017-11-01

A common task when analysing dynamical systems is the determination of normal forms near local bifurcations of equilibria. As most of these normal forms have been classified and analysed, finding which particular class of normal form one encounters in a numerical bifurcation study guides follow-up computations. This paper builds on normal form algorithms for equilibria of delay differential equations with constant delay that were developed and implemented in DDE-Biftool recently. We show how one can extend these methods to delay-differential equations with state-dependent delay (sd-DDEs). Since higher degrees of regularity of local center manifolds are still open for sd-DDEs, we give an independent (still only partial) argument which phenomena from the truncated normal must persist in the full sd-DDE. In particular, we show that all invariant manifolds with a sufficient degree of normal hyperbolicity predicted by the normal form exist also in the full sd-DDE.

Clinical assessment of cerebrospinal fluid dynamics in hydrocephalus. Guide to interpretation based on observational study.

PubMed

Weerakkody, R A; Czosnyka, M; Schuhmann, M U; Schmidt, E; Keong, N; Santarius, T; Pickard, J D; Czosnyka, Z

2011-08-01

The term hydrocephalus encompasses a range of disorders characterised by clinical symptoms, abnormal brain imaging and derangement of cerebrospinal fluid (CSF) dynamics. The ability to elucidate which patients would benefit from CSF diversion (a shunt or third ventriculostomy) is often unclear. Similar difficulties are often encountered in shunted patients to predict the scope for improvement by shunt re-adjustment or revision. In this study we aimed to update our knowledge of how key quantitative parameters describing CSF dynamics may be used in diagnosis of shunt-responsive hydrocephalus and in the assessment of shunt function. A number of quantitative parameters [including resistance to CSF outflow (Rcsf), pulse amplitude of intracranial pressure waveform (AMP), RAP index and slow vasogenic waves] were studies in 1423 patients with 2665 CSF infusion tests and 305 overnight intracranial pressure (ICP)-monitoring sessions over a 17 year period. We demonstrate our observations for typical values of Pb, Rcsf, AMP, slow vasogenic waves derived from infusion studies or overnight ICP monitoring in differentiating atrophy from shunt-responsive normal pressure hydrocephalus or acute hydrocephalus. From the same variables tested on shunted patients we demonstrate a standardised approach to help differentiate a properly-functioning shunt from underdrainage or overdrainage. Quantitative variables derived from CSF dynamics allow differentiation between clinically overlapping entities such as shunt-responsive normal pressure hydrocephalus and brain atrophy (not shunt responsive) as well as allowing the detection of shunt malfunction (partial or complete blockage) or overdrainage. This observational study is intended to serve as an update for our understanding of quantitative testing of CSF dynamics. © 2011 John Wiley & Sons A/S.

The coupled nonlinear dynamics of a lift system

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

Crespo, Rafael Sánchez, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk; Kaczmarczyk, Stefan, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk; Picton, Phil, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk

2014-12-10

Coupled lateral and longitudinal vibrations of suspension and compensating ropes in a high-rise lift system are often induced by the building motions due to wind or seismic excitations. When the frequencies of the building become near the natural frequencies of the ropes, large resonance motions of the system may result. This leads to adverse coupled dynamic phenomena involving nonplanar motions of the ropes, impact loads between the ropes and the shaft walls, as well as vertical vibrations of the car, counterweight and compensating sheave. Such an adverse dynamic behaviour of the system endangers the safety of the installation. This papermore » presents two mathematical models describing the nonlinear responses of a suspension/ compensating rope system coupled with the elevator car / compensating sheave motions. The models accommodate the nonlinear couplings between the lateral and longitudinal modes, with and without longitudinal inertia of the ropes. The partial differential nonlinear equations of motion are derived using Hamilton Principle. Then, the Galerkin method is used to discretise the equations of motion and to develop a nonlinear ordinary differential equation model. Approximate numerical solutions are determined and the behaviour of the system is analysed.« less

An information-theoretic approach to assess practical identifiability of parametric dynamical systems.

PubMed

Pant, Sanjay; Lombardi, Damiano

2015-10-01

A new approach for assessing parameter identifiability of dynamical systems in a Bayesian setting is presented. The concept of Shannon entropy is employed to measure the inherent uncertainty in the parameters. The expected reduction in this uncertainty is seen as the amount of information one expects to gain about the parameters due to the availability of noisy measurements of the dynamical system. Such expected information gain is interpreted in terms of the variance of a hypothetical measurement device that can measure the parameters directly, and is related to practical identifiability of the parameters. If the individual parameters are unidentifiable, correlation between parameter combinations is assessed through conditional mutual information to determine which sets of parameters can be identified together. The information theoretic quantities of entropy and information are evaluated numerically through a combination of Monte Carlo and k-nearest neighbour methods in a non-parametric fashion. Unlike many methods to evaluate identifiability proposed in the literature, the proposed approach takes the measurement-noise into account and is not restricted to any particular noise-structure. Whilst computationally intensive for large dynamical systems, it is easily parallelisable and is non-intrusive as it does not necessitate re-writing of the numerical solvers of the dynamical system. The application of such an approach is presented for a variety of dynamical systems--ranging from systems governed by ordinary differential equations to partial differential equations--and, where possible, validated against results previously published in the literature. Copyright © 2015 Elsevier Inc. All rights reserved.

Solar Prominence Fine Structure and Dynamics

NASA Astrophysics Data System (ADS)

Berger, Thomas

2014-01-01

We review recent observational and theoretical results on the fine structure and dynamics of solar prominences, beginning with an overview of prominence classifications, the proposal of possible new ``funnel prominence'' classification, and a discussion of the recent ``solar tornado'' findings. We then focus on quiescent prominences to review formation, down-flow dynamics, and the ``prominence bubble'' phenomena. We show new observations of the prominence bubble Rayleigh-Taylor instability triggered by a Kelvin-Helmholtz shear flow instability occurring along the bubble boundary. Finally we review recent studies on plasma composition of bubbles, emphasizing that differential emission measure (DEM) analysis offers a more quantitative analysis than photometric comparisons. In conclusion, we discuss the relation of prominences to coronal magnetic flux ropes, proposing that prominences can be understood as partially ionized condensations of plasma forming the return flow of a general magneto-thermal convection in the corona.

Effects of thermal noise on the transitional dynamics of an inextensible elastic filament in stagnation flow.

PubMed

Deng, Mingge; Grinberg, Leopold; Caswell, Bruce; Karniadakis, George Em

2015-06-28

We investigate the dynamics of a single inextensible elastic filament subject to anisotropic friction in a viscous stagnation-point flow, by employing both a continuum model represented by Langevin type stochastic partial differential equations (SPDEs) and a dissipative particle dynamics (DPD) method. Unlike previous works, the filament is free to rotate and the tension along the filament is determined by the local inextensible constraint. The kinematics of the filament is recorded and studied with normal modes analysis. The results show that the filament displays an instability induced by negative tension, which is analogous to Euler buckling of a beam. Symmetry breaking of normal modes dynamics and stretch-coil transitions are observed above the threshold of the buckling instability point. Furthermore, both temporal and spatial noise are amplified resulting from the interaction of thermal fluctuations and nonlinear filament dynamics. Specifically, the spatial noise is amplified with even normal modes being excited due to symmetry breaking, while the temporal noise is amplified with increasing time correlation length and variance.

PDEMOD: Software for control/structures optimization

NASA Technical Reports Server (NTRS)

Taylor, Lawrence W., Jr.; Zimmerman, David

1991-01-01

Because of the possibility of adverse interaction between the control system and the structural dynamics of large, flexible spacecraft, great care must be taken to ensure stability and system performance. Because of the high cost of insertion of mass into low earth orbit, it is prudent to optimize the roles of structure and control systems simultaneously. Because of the difficulty and the computational burden in modeling and analyzing the control structure system dynamics, the total problem is often split and treated iteratively. It would aid design if the control structure system dynamics could be represented in a single system of equations. With the use of the software PDEMOD (Partial Differential Equation Model), it is now possible to optimize structure and control systems simultaneously. The distributed parameter modeling approach enables embedding the control system dynamics into the same equations for the structural dynamics model. By doing this, the current difficulties involved in model order reduction are avoided. The NASA Mini-MAST truss is used an an example for studying integrated control structure design.

Discontinuous Galerkin finite element method for solving population density functions of cortical pyramidal and thalamic neuronal populations.

PubMed

Huang, Chih-Hsu; Lin, Chou-Ching K; Ju, Ming-Shaung

2015-02-01

Compared with the Monte Carlo method, the population density method is efficient for modeling collective dynamics of neuronal populations in human brain. In this method, a population density function describes the probabilistic distribution of states of all neurons in the population and it is governed by a hyperbolic partial differential equation. In the past, the problem was mainly solved by using the finite difference method. In a previous study, a continuous Galerkin finite element method was found better than the finite difference method for solving the hyperbolic partial differential equation; however, the population density function often has discontinuity and both methods suffer from a numerical stability problem. The goal of this study is to improve the numerical stability of the solution using discontinuous Galerkin finite element method. To test the performance of the new approach, interaction of a population of cortical pyramidal neurons and a population of thalamic neurons was simulated. The numerical results showed good agreement between results of discontinuous Galerkin finite element and Monte Carlo methods. The convergence and accuracy of the solutions are excellent. The numerical stability problem could be resolved using the discontinuous Galerkin finite element method which has total-variation-diminishing property. The efficient approach will be employed to simulate the electroencephalogram or dynamics of thalamocortical network which involves three populations, namely, thalamic reticular neurons, thalamocortical neurons and cortical pyramidal neurons. Copyright © 2014 Elsevier Ltd. All rights reserved.

Sonographic differentiation of digital tendon rupture from adhesive scarring after primary surgical repair.

PubMed

Budovec, Joseph J; Sudakoff, Gary S; Dzwierzynski, William W; Matloub, Hani S; Sanger, James R

2006-04-01

After the surgical repair of finger tendons finger range of motion may be limited by tendon rupture or adhesive scarring. Differentiating tendon rupture from adhesive scarring may be difficult clinically. Digital tendon sonography allows the evaluation of tendon integrity in a dynamic setting. Our objective was to determine if sonography could differentiate tendon rupture from adhesive scarring in patients who have had primary tendon repair. A retrospective review was performed of the radiographic, clinical, and surgical records of patients referred for finger sonography over a 2-year period. Twenty-eight digits in 21 patients were evaluated for finger tendon disruption after primary surgical repair. The diagnosis of complete tendon rupture was made when 1 or more of the following was identified: a gap separating the proximal and distal tendon margins, visualization of only the proximal tendon margin, or visualization of only the distal tendon margin. Adhesive scarring was diagnosed if the tendon appeared intact with abnormal peritendinous soft tissue abutting or partially encasing the tendon, with synovial sheath thickening, or with restricted tendon motion during dynamic evaluation. Sonography correctly identified tendon rupture or adhesive scarring in 27 of 28 digits with 1 false-positive case (sensitivity, 100%; specificity, 93%; positive-predictive value, 93%; negative-predictive value, 100%; accuracy, 96%). Sonography is an accurate modality for differentiating tendon rupture from adhesive scarring in patients with prior surgical tendon repair. Diagnostic, Level I.

Differential morphology and image processing.

PubMed

Maragos, P

1996-01-01

Image processing via mathematical morphology has traditionally used geometry to intuitively understand morphological signal operators and set or lattice algebra to analyze them in the space domain. We provide a unified view and analytic tools for morphological image processing that is based on ideas from differential calculus and dynamical systems. This includes ideas on using partial differential or difference equations (PDEs) to model distance propagation or nonlinear multiscale processes in images. We briefly review some nonlinear difference equations that implement discrete distance transforms and relate them to numerical solutions of the eikonal equation of optics. We also review some nonlinear PDEs that model the evolution of multiscale morphological operators and use morphological derivatives. Among the new ideas presented, we develop some general 2-D max/min-sum difference equations that model the space dynamics of 2-D morphological systems (including the distance computations) and some nonlinear signal transforms, called slope transforms, that can analyze these systems in a transform domain in ways conceptually similar to the application of Fourier transforms to linear systems. Thus, distance transforms are shown to be bandpass slope filters. We view the analysis of the multiscale morphological PDEs and of the eikonal PDE solved via weighted distance transforms as a unified area in nonlinear image processing, which we call differential morphology, and briefly discuss its potential applications to image processing and computer vision.

The nonlinear modified equation approach to analyzing finite difference schemes

NASA Technical Reports Server (NTRS)

Klopfer, G. H.; Mcrae, D. S.

1981-01-01

The nonlinear modified equation approach is taken in this paper to analyze the generalized Lax-Wendroff explicit scheme approximation to the unsteady one- and two-dimensional equations of gas dynamics. Three important applications of the method are demonstrated. The nonlinear modified equation analysis is used to (1) generate higher order accurate schemes, (2) obtain more accurate estimates of the discretization error for nonlinear systems of partial differential equations, and (3) generate an adaptive mesh procedure for the unsteady gas dynamic equations. Results are obtained for all three areas. For the adaptive mesh procedure, mesh point requirements for equal resolution of discontinuities were reduced by a factor of five for a 1-D shock tube problem solved by the explicit MacCormack scheme.

Collective phase description of oscillatory convection

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

Kawamura, Yoji, E-mail: ykawamura@jamstec.go.jp; Nakao, Hiroya

We formulate a theory for the collective phase description of oscillatory convection in Hele-Shaw cells. It enables us to describe the dynamics of the oscillatory convection by a single degree of freedom which we call the collective phase. The theory can be considered as a phase reduction method for limit-cycle solutions in infinite-dimensional dynamical systems, namely, stable time-periodic solutions to partial differential equations, representing the oscillatory convection. We derive the phase sensitivity function, which quantifies the phase response of the oscillatory convection to weak perturbations applied at each spatial point, and analyze the phase synchronization between two weakly coupled Hele-Shawmore » cells exhibiting oscillatory convection on the basis of the derived phase equations.« less

Why interdisciplinary research enriches the study of crime. Comment on "Statistical physics of crime: A review" by M.R. D'Orsogna and M. Perc

NASA Astrophysics Data System (ADS)

Donnay, Karsten

2015-03-01

The past several years have seen a rapidly growing interest in the use of advanced quantitative methodologies and formalisms adapted from the natural sciences to study a broad range of social phenomena. The research field of computational social science [1,2], for example, uses digital artifacts of human online activity to cast a new light on social dynamics. Similarly, the studies reviewed by D'Orsogna and Perc showcase a diverse set of advanced quantitative techniques to study the dynamics of crime. Methods used range from partial differential equations and self-exciting point processes to agent-based models, evolutionary game theory and network science [3].

Flow Applications of the Least Squares Finite Element Method

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan

1998-01-01

The main thrust of the effort has been towards the development, analysis and implementation of the least-squares finite element method (LSFEM) for fluid dynamics and electromagnetics applications. In the past year, there were four major accomplishments: 1) special treatments in computational fluid dynamics and computational electromagnetics, such as upwinding, numerical dissipation, staggered grid, non-equal order elements, operator splitting and preconditioning, edge elements, and vector potential are unnecessary; 2) the analysis of the LSFEM for most partial differential equations can be based on the bounded inverse theorem; 3) the finite difference and finite volume algorithms solve only two Maxwell equations and ignore the divergence equations; and 4) the first numerical simulation of three-dimensional Marangoni-Benard convection was performed using the LSFEM.

Construction and accuracy of partial differential equation approximations to the chemical master equation.

PubMed

Grima, Ramon

2011-11-01

The mesoscopic description of chemical kinetics, the chemical master equation, can be exactly solved in only a few simple cases. The analytical intractability stems from the discrete character of the equation, and hence considerable effort has been invested in the development of Fokker-Planck equations, second-order partial differential equation approximations to the master equation. We here consider two different types of higher-order partial differential approximations, one derived from the system-size expansion and the other from the Kramers-Moyal expansion, and derive the accuracy of their predictions for chemical reactive networks composed of arbitrary numbers of unimolecular and bimolecular reactions. In particular, we show that the partial differential equation approximation of order Q from the Kramers-Moyal expansion leads to estimates of the mean number of molecules accurate to order Ω(-(2Q-3)/2), of the variance of the fluctuations in the number of molecules accurate to order Ω(-(2Q-5)/2), and of skewness accurate to order Ω(-(Q-2)). We also show that for large Q, the accuracy in the estimates can be matched only by a partial differential equation approximation from the system-size expansion of approximate order 2Q. Hence, we conclude that partial differential approximations based on the Kramers-Moyal expansion generally lead to considerably more accurate estimates in the mean, variance, and skewness than approximations of the same order derived from the system-size expansion.

Analysis of wavelet technology for NASA applications

NASA Technical Reports Server (NTRS)

Wells, R. O., Jr.

1994-01-01

The purpose of this grant was to introduce a broad group of NASA researchers and administrators to wavelet technology and to determine its future role in research and development at NASA JSC. The activities of several briefings held between NASA JSC scientists and Rice University researchers are discussed. An attached paper, 'Recent Advances in Wavelet Technology', summarizes some aspects of these briefings. Two proposals submitted to NASA reflect the primary areas of common interest. They are image analysis and numerical solutions of partial differential equations arising in computational fluid dynamics and structural mechanics.

Kinetics of the electric double layer formation modelled by the finite difference method

NASA Astrophysics Data System (ADS)

Valent, Ivan

2017-11-01

Dynamics of the elctric double layer formation in 100 mM NaCl solution for sudden potentail steps of 10 and 20 mV was simulated using the Poisson-Nernst-Planck theory and VLUGR2 solver for partial differential equations. The used approach was verified by comparing the obtained steady-state solution with the available exact solution. The simulations allowed for detailed analysis of the relaxation processes of the individual ions and the electric potential. Some computational aspects of the problem were discussed.

Three-dimensional analytic model of the magnetic field for the Chalk River Superconducting Cyclotron

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

Davies, W.G.; Lee-Whiting, G.E.; Douglas, S.R.

1994-07-01

A three-dimensional analytic model of the magnetic field for the TASCC cyclotron that satisfies Maxwell`s equations exactly has been constructed for use with the new differential-algebra orbit-dynamics code. The model includes: (1) the superconducting coils; (2) the saturated iron poles; (3) the partially saturated yoke; (4) the saturated-iron trim rods. Lines of dipole density along the edges of the hills account for the non-uniformities and edge effects and along with three yoke constants constitute the only free parameters.

Stepwise Analysis of Differential Item Functioning Based on Multiple-Group Partial Credit Model.

ERIC Educational Resources Information Center

Muraki, Eiji

1999-01-01

Extended an Item Response Theory (IRT) method for detection of differential item functioning to the partial credit model and applied the method to simulated data using a stepwise procedure. Then applied the stepwise DIF analysis based on the multiple-group partial credit model to writing trend data from the National Assessment of Educational…

Automatic code generation in SPARK: Applications of computer algebra and compiler-compilers

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

Nataf, J.M.; Winkelmann, F.

We show how computer algebra and compiler-compilers are used for automatic code generation in the Simulation Problem Analysis and Research Kernel (SPARK), an object oriented environment for modeling complex physical systems that can be described by differential-algebraic equations. After a brief overview of SPARK, we describe the use of computer algebra in SPARK's symbolic interface, which generates solution code for equations that are entered in symbolic form. We also describe how the Lex/Yacc compiler-compiler is used to achieve important extensions to the SPARK simulation language, including parametrized macro objects and steady-state resetting of a dynamic simulation. The application of thesemore » methods to solving the partial differential equations for two-dimensional heat flow is illustrated.« less

Automatic code generation in SPARK: Applications of computer algebra and compiler-compilers

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

Nataf, J.M.; Winkelmann, F.

We show how computer algebra and compiler-compilers are used for automatic code generation in the Simulation Problem Analysis and Research Kernel (SPARK), an object oriented environment for modeling complex physical systems that can be described by differential-algebraic equations. After a brief overview of SPARK, we describe the use of computer algebra in SPARK`s symbolic interface, which generates solution code for equations that are entered in symbolic form. We also describe how the Lex/Yacc compiler-compiler is used to achieve important extensions to the SPARK simulation language, including parametrized macro objects and steady-state resetting of a dynamic simulation. The application of thesemore » methods to solving the partial differential equations for two-dimensional heat flow is illustrated.« less

A simple spatiotemporal rabies model for skunk and bat interaction in northeast Texas.

PubMed

Borchering, Rebecca K; Liu, Hao; Steinhaus, Mara C; Gardner, Carl L; Kuang, Yang

2012-12-07

We formulate a simple partial differential equation model in an effort to qualitatively reproduce the spread dynamics and spatial pattern of rabies in northeast Texas with overlapping reservoir species (skunks and bats). Most existing models ignore reservoir species or model them with patchy models by ordinary differential equations. In our model, we incorporate interspecies rabies infection in addition to rabid population random movement. We apply this model to the confirmed case data from northeast Texas with most parameter values obtained or computed from the literature. Results of simulations using both our skunk-only model and our skunk and bat model demonstrate that the model with overlapping reservoir species more accurately reproduces the progression of rabies spread in northeast Texas. Copyright © 2012 Elsevier Ltd. All rights reserved.

Study of Falling Roof Vibrations in a Production Face at Roof Support Resistance in the Form of Concentrated Force

NASA Astrophysics Data System (ADS)

Buyalich, G. D.; Buyalich, K. G.; Umrikhina, V. Yu

2016-08-01

One of the main reasons of roof support failures in production faces is mismatch of their parameters and parameters of dynamic impact on the metal structure from the falling roof during its secondary convergences. To assess the parameters of vibrational interaction of roof support with the roof, it was suggested to use computational models of forces application and a partial differential equation of fourth order describing this process, its numerical solution allowed to assess frequency, amplitude and speed of roof strata movement depending on physical and mechanical properties of the roof strata as well as on load bearing and geometry parameters of the roof support. To simplify solving of the differential equation, roof support response was taken as the concentrated force.

Chaotic dynamics of flexible Euler-Bernoulli beams

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

Awrejcewicz, J., E-mail: awrejcew@p.lodz.pl; Krysko, A. V., E-mail: anton.krysko@gmail.com; Kutepov, I. E., E-mail: iekutepov@gmail.com

2013-12-15

Mathematical modeling and analysis of spatio-temporal chaotic dynamics of flexible simple and curved Euler-Bernoulli beams are carried out. The Kármán-type geometric non-linearity is considered. Algorithms reducing partial differential equations which govern the dynamics of studied objects and associated boundary value problems are reduced to the Cauchy problem through both Finite Difference Method with the approximation of O(c{sup 2}) and Finite Element Method. The obtained Cauchy problem is solved via the fourth and sixth-order Runge-Kutta methods. Validity and reliability of the results are rigorously discussed. Analysis of the chaotic dynamics of flexible Euler-Bernoulli beams for a series of boundary conditions ismore » carried out with the help of the qualitative theory of differential equations. We analyze time histories, phase and modal portraits, autocorrelation functions, the Poincaré and pseudo-Poincaré maps, signs of the first four Lyapunov exponents, as well as the compression factor of the phase volume of an attractor. A novel scenario of transition from periodicity to chaos is obtained, and a transition from chaos to hyper-chaos is illustrated. In particular, we study and explain the phenomenon of transition from symmetric to asymmetric vibrations. Vibration-type charts are given regarding two control parameters: amplitude q{sub 0} and frequency ω{sub p} of the uniformly distributed periodic excitation. Furthermore, we detected and illustrated how the so called temporal-space chaos is developed following the transition from regular to chaotic system dynamics.« less

Coarse-grained forms for equations describing the microscopic motion of particles in a fluid.

PubMed

Das, Shankar P; Yoshimori, Akira

2013-10-01

Exact equations of motion for the microscopically defined collective density ρ(x,t) and the momentum density ĝ(x,t) of a fluid have been obtained in the past starting from the corresponding Langevin equations representing the dynamics of the fluid particles. In the present work we average these exact equations of microscopic dynamics over the local equilibrium distribution to obtain stochastic partial differential equations for the coarse-grained densities with smooth spatial and temporal dependence. In particular, we consider Dean's exact balance equation for the microscopic density of a system of interacting Brownian particles to obtain the basic equation of the dynamic density functional theory with noise. Our analysis demonstrates that on thermal averaging the dependence of the exact equations on the bare interaction potential is converted to dependence on the corresponding thermodynamic direct correlation functions in the coarse-grained equations.

A model of partial differential equations for HIV propagation in lymph nodes

NASA Astrophysics Data System (ADS)

Marinho, E. B. S.; Bacelar, F. S.; Andrade, R. F. S.

2012-01-01

A system of partial differential equations is used to model the dissemination of the Human Immunodeficiency Virus (HIV) in CD4+T cells within lymph nodes. Besides diffusion terms, the model also includes a time-delay dependence to describe the time lag required by the immunologic system to provide defenses to new virus strains. The resulting dynamics strongly depends on the properties of the invariant sets of the model, consisting of three fixed points related to the time independent and spatial homogeneous tissue configurations in healthy and infected states. A region in the parameter space is considered, for which the time dependence of the space averaged model variables follows the clinical pattern reported for infected patients: a short scale primary infection, followed by a long latency period of almost complete recovery and third phase characterized by damped oscillations around a value with large HIV counting. Depending on the value of the diffusion coefficient, the latency time increases with respect to that one obtained for the space homogeneous version of the model. It is found that same initial conditions lead to quite different spatial patterns, which depend strongly on the latency interval.

The dynamics of a forced coupled network of active elements

NASA Astrophysics Data System (ADS)

Parks, Helen F.; Ermentrout, Bard; Rubin, Jonathan E.

2011-03-01

This paper presents the derivation and analysis of mathematical models motivated by the experimental induction of contour phosphenes in the retina. First, a spatially discrete chain of periodically forced coupled oscillators is considered via reduction to a chain of scalar phase equations. Each isolated oscillator locks in a 1:2 manner with the forcing so that there is intrinsic bistability, with activity peaking on either the odd or even cycles of the forcing. If half the chain is started on the odd cycle and half on the even cycle (“split state”), then with sufficiently strong coupling, a wave can be produced that can travel in either direction due to symmetry. Numerical and analytic methods are employed to determine the size of coupling necessary for the split state solution to destabilize such that waves appear. Taking a continuum limit, we reduce the chain to a partial differential equation. We use a Melnikov function to compute, to leading order, the speed of the traveling wave solution to the partial differential equation as a function of the form of coupling and the forcing parameters and compare our result to the numerically computed discrete and continuum wave speeds.

Dynamical modeling and free vibration analysis of spinning pipes conveying fluid with axial deployment

NASA Astrophysics Data System (ADS)

Liang, Feng; Yang, Xiao-Dong; Zhang, Wei; Qian, Ying-Jing

2018-03-01

In this paper, a dynamical model of simply-supported spinning pipes conveying fluid with axial deployment is proposed and the transverse free vibration and stability for such a doubly gyroscopic system involving time-dependent parameters are investigated. The partial differential equations of motion are derived by the extended Hamilton principle and then truncated by the Galerkin technique. The time-variant frequencies, mode shapes and responses to initial conditions are comprehensively investigated to reveal the dynamical essence of the system. It is indicated that the qualitative stability evolution of the system mainly depends on the effect of fluid-structure interaction (FSI), while the spinning motion will enhance the pipe rigidity and eliminate the buckling instability. The dynamical evolution of a retracting pipe is almost inverse to that of the deploying one. The pipe possesses different mode configurations of spatial curves as the pipe length increases and some modal and response characteristics of the present system are found rather distinct from those of deploying cantilevered structures.

The dynamic generalization of the Eshelby inclusion problem and its static limit

PubMed Central

2016-01-01

The dynamic generalization of the celebrated Eshelby inclusion with transformation strain is the (subsonically) self-similarly expanding ellipsoidal inclusion starting from the zero dimension. The solution of the governing system of partial differential equations was obtained recently by Ni & Markenscoff (In press. J. Mech. Phys. Solids (doi:10.1016/j.jmps.2016.02.025)) on the basis of the Radon transformation, while here an alternative method is presented. In the self-similarly expanding motion, the Eshelby property of constant constrained strain is valid in the interior domain of the expanding ellipsoid where the particle velocity vanishes (lacuna). The dynamic Eshelby tensor is obtained in integral form. From it, the static Eshelby tensor is obtained by a limiting procedure, as the axes' expansion velocities tend to zero and time to infinity, while their product is equal to the length of the static axis. This makes the Eshelby problem the limit of its dynamic generalization. PMID:27493574

Charge modeling of ionic polymer-metal composites for dynamic curvature sensing

NASA Astrophysics Data System (ADS)

Bahramzadeh, Yousef; Shahinpoor, Mohsen

2011-04-01

A curvature sensor based on Ionic Polymer-Metal Composite (IPMC) is proposed and characterized for sensing of curvature variation in structures such as inflatable space structures in which using low power and flexible curvature sensor is of high importance for dynamic monitoring of shape at desired points. The linearity of output signal of sensor for calibration, effect of deflection rate at low frequencies and the phase delay between the output signal and the input deformation of IPMC curvature sensor is investigated. An analytical chemo-electro-mechanical model for charge dynamic of IPMC sensor is presented based on Nernst-Planck partial differential equation which can be used to explain the phenomena observed in experiments. The rate dependency of output signal and phase delay between the applied deformation and sensor signal is studied using the proposed model. The model provides a background for predicting the general characteristics of IPMC sensor. It is shown that IPMC sensor exhibits good linearity, sensitivity, and repeatability for dynamic curvature sensing of inflatable structures.

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.

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.

Probabilistic density function method for nonlinear dynamical systems driven by colored noise.

PubMed

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 integrodifferential 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 (LED) closure. In contrast to the classical LED closure, the proposed closure accounts for advective transport of the PDF in the approximate temporal deconvolution of the integrodifferential equation. In addition, we introduce the generalized local linearization approximation for deriving a computable PDF equation in the form of a second-order partial differential equation. We demonstrate that the proposed closure and localization accurately describe the dynamics of the PDF in phase space for systems driven by noise with arbitrary autocorrelation time. We apply the proposed PDF method to analyze a set of Kramers equations driven by exponentially autocorrelated Gaussian colored noise to study nonlinear oscillators and the dynamics and stability of a power grid. Numerical experiments show the PDF method is accurate when the noise autocorrelation time is either much shorter or longer than the system's relaxation time, while the accuracy decreases as the ratio of the two timescales approaches unity. Similarly, the PDF method accuracy decreases with increasing standard deviation of the noise.

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.

Mathematical Modelling of Continuous Biotechnological Processes

ERIC Educational Resources Information Center

Pencheva, T.; Hristozov, I.; Shannon, A. G.

2003-01-01

Biotechnological processes (BTP) are characterized by a complicated structure of organization and interdependent characteristics. Partial differential equations or systems of partial differential equations are used for their behavioural description as objects with distributed parameters. Modelling of substrate without regard to dispersion…

Fault Tolerant Optimal Control.

DTIC Science & Technology

1982-08-01

subsystem is modelled by deterministic or stochastic finite-dimensional vector differential or difference equations. The parameters of these equations...is no partial differential equation that must be solved. Thus we can sidestep the inability to solve the Bellman equation for control problems with x...transition models and cost functionals can be reduced to the search for solutions of nonlinear partial differential equations using ’verification

Differential geometry techniques for sets of nonlinear partial differential equations

NASA Technical Reports Server (NTRS)

Estabrook, Frank B.

1990-01-01

An attempt is made to show that the Cartan theory of partial differential equations can be a useful technique for applied mathematics. Techniques for finding consistent subfamilies of solutions that are generically rich and well-posed and for introducing potentials or other usefully consistent auxiliary fields are introduced. An extended sample calculation involving the Korteweg-de Vries equation is given.

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

PubMed

Güner, Özkan; Cevikel, Adem C

2014-01-01

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

Algebraic and geometric structures of analytic partial differential equations

NASA Astrophysics Data System (ADS)

Kaptsov, O. V.

2016-11-01

We study the problem of the compatibility of nonlinear partial differential equations. We introduce the algebra of convergent power series, the module of derivations of this algebra, and the module of Pfaffian forms. Systems of differential equations are given by power series in the space of infinite jets. We develop a technique for studying the compatibility of differential systems analogous to the Gröbner bases. Using certain assumptions, we prove that compatible systems generate infinite manifolds.

Differential association of family subsystem negativity on siblings' maladjustment: using behavior genetic methods to test process theory.

PubMed

Feinberg, Mark E; Reiss, David; Neiderhiser, Jenae M; Hetherington, E Mavis

2005-12-01

This study investigated the family context of adolescent sibling similarity and differentiation in maladjustment (antisocial behavior and depression) by examining negativity in different subsystems. Two hypotheses were proposed: (1) Parental and sibling negativity tends to diffuse through the family system, especially because of the high level of reciprocity in sibling relationships, leading to sibling similarity; and (2) interparental (coparenting) conflict disrupts cohesive functioning and thereby motivates and facilitates sibling differentiation and niche picking. To control for the effects of similar genes between siblings, the authors used behavioral genetic models with a genetically informed sample of 720 two-parent families, each with at least 2 adolescent siblings. Results for the differences in shared environmental influences across groups high and low in each of the domains of family negativity provided partial support for the hypotheses. The results further understanding of influences on individual differences and support a theory of how parent-child and interparental relationships intersect with sibling relationship dynamics. Copyright 2006 APA, all rights reserved).

Optimal control of coupled parabolic-hyperbolic non-autonomous PDEs: infinite-dimensional state-space approach

NASA Astrophysics Data System (ADS)

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

2018-04-01

This paper deals with the design of an optimal state-feedback linear-quadratic (LQ) controller for a system of coupled parabolic-hypebolic non-autonomous partial differential equations (PDEs). The infinite-dimensional state space representation and the corresponding operator Riccati differential equation are used to solve the control problem. Dynamical properties of the coupled system of interest are analysed to guarantee the existence and uniqueness of the solution of the LQ-optimal control problem and also to guarantee the exponential stability of the closed-loop system. Thanks to the eigenvalues and eigenfunctions of the parabolic operator and also the fact that the hyperbolic-associated operator Riccati differential equation can be converted to a scalar Riccati PDE, an algorithm to solve the LQ control problem has been presented. 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 non-linear model. Numerical simulations are performed to show the controller performances.

Causal dissipation for the relativistic dynamics of ideal gases

NASA Astrophysics Data System (ADS)

Freistühler, Heinrich; Temple, Blake

2017-05-01

We derive a general class of relativistic dissipation tensors by requiring that, combined with the relativistic Euler equations, they form a second-order system of partial differential equations which is symmetric hyperbolic in a second-order sense when written in the natural Godunov variables that make the Euler equations symmetric hyperbolic in the first-order sense. We show that this class contains a unique element representing a causal formulation of relativistic dissipative fluid dynamics which (i) is equivalent to the classical descriptions by Eckart and Landau to first order in the coefficients of viscosity and heat conduction and (ii) has its signal speeds bounded sharply by the speed of light. Based on these properties, we propose this system as a natural candidate for the relativistic counterpart of the classical Navier-Stokes equations.

Domain decomposition for aerodynamic and aeroacoustic analyses, and optimization

NASA Technical Reports Server (NTRS)

Baysal, Oktay

1995-01-01

The overarching theme was the domain decomposition, which intended to improve the numerical solution technique for the partial differential equations at hand; in the present study, those that governed either the fluid flow, or the aeroacoustic wave propagation, or the sensitivity analysis for a gradient-based optimization. The role of the domain decomposition extended beyond the original impetus of discretizing geometrical complex regions or writing modular software for distributed-hardware computers. It induced function-space decompositions and operator decompositions that offered the valuable property of near independence of operator evaluation tasks. The objectives have gravitated about the extensions and implementations of either the previously developed or concurrently being developed methodologies: (1) aerodynamic sensitivity analysis with domain decomposition (SADD); (2) computational aeroacoustics of cavities; and (3) dynamic, multibody computational fluid dynamics using unstructured meshes.

Nonlinear model of a rotating hub-beams structure: Equations of motion

NASA Astrophysics Data System (ADS)

Warminski, Jerzy

2018-01-01

Dynamics of a rotating structure composed of a rigid hub and flexible beams is presented in the paper. A nonlinear model of a beam takes into account bending, extension and nonlinear curvature. The influence of geometric nonlinearity and nonconstant angular velocity on dynamics of the rotating structure is presented. The exact equations of motion and associated boundary conditions are derived on the basis of the Hamilton's principle. The simplification of the exact nonlinear mathematical model is proposed taking into account the second order approximation. The reduced partial differential equations of motion together with associated boundary conditions can be used to study natural or forced vibrations of a rotating structure considering constant or nonconstant angular speed of a rigid hub and an arbitrary number of flexible blades.

Geometrical shock dynamics, formation of singularities and topological bifurcations of converging shock fronts

NASA Astrophysics Data System (ADS)

Suramlishvili, Nugzar; Eggers, Jens; Fontelos, Marco

2014-11-01

We are concerned with singularities of the shock fronts of converging perturbed shock waves. Our considerations are based on Whitham's theory of geometrical shock dynamics. The recently developed method of local analysis is applied in order to determine generic singularities. In this case the solutions of partial differential equations describing the geometry of the shock fronts are presented as families of smooth maps with state variables and the set of control parameters dependent on Mach number, time and initial conditions. The space of control parameters of the singularities is analysed, the unfoldings describing the deformations of the canonical germs of shock front singularities are found and corresponding bifurcation diagrams are constructed. Research is supported by the Leverhulme Trust, Grant Number RPG-2012-568.

Numerical simulation of coupled electrochemical and transport processes in battery systems

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

Liaw, B.Y.; Gu, W.B.; Wang, C.Y.

1997-12-31

Advanced numerical modeling to simulate dynamic battery performance characteristics for several types of advanced batteries is being conducted using computational fluid dynamics (CFD) techniques. The CFD techniques provide efficient algorithms to solve a large set of highly nonlinear partial differential equations that represent the complex battery behavior governed by coupled electrochemical reactions and transport processes. The authors have recently successfully applied such techniques to model advanced lead-acid, Ni-Cd and Ni-MH cells. In this paper, the authors briefly discuss how the governing equations were numerically implemented, show some preliminary modeling results, and compare them with other modeling or experimental data reportedmore » in the literature. The authors describe the advantages and implications of using the CFD techniques and their capabilities in future battery applications.« less

Causal dissipation for the relativistic dynamics of ideal gases

PubMed Central

2017-01-01

We derive a general class of relativistic dissipation tensors by requiring that, combined with the relativistic Euler equations, they form a second-order system of partial differential equations which is symmetric hyperbolic in a second-order sense when written in the natural Godunov variables that make the Euler equations symmetric hyperbolic in the first-order sense. We show that this class contains a unique element representing a causal formulation of relativistic dissipative fluid dynamics which (i) is equivalent to the classical descriptions by Eckart and Landau to first order in the coefficients of viscosity and heat conduction and (ii) has its signal speeds bounded sharply by the speed of light. Based on these properties, we propose this system as a natural candidate for the relativistic counterpart of the classical Navier–Stokes equations. PMID:28588397

Causal dissipation for the relativistic dynamics of ideal gases.

PubMed

Freistühler, Heinrich; Temple, Blake

2017-05-01

We derive a general class of relativistic dissipation tensors by requiring that, combined with the relativistic Euler equations, they form a second-order system of partial differential equations which is symmetric hyperbolic in a second-order sense when written in the natural Godunov variables that make the Euler equations symmetric hyperbolic in the first-order sense. We show that this class contains a unique element representing a causal formulation of relativistic dissipative fluid dynamics which (i) is equivalent to the classical descriptions by Eckart and Landau to first order in the coefficients of viscosity and heat conduction and (ii) has its signal speeds bounded sharply by the speed of light. Based on these properties, we propose this system as a natural candidate for the relativistic counterpart of the classical Navier-Stokes equations.

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.

Effects of Thermal Noise on the Transitional Dynamics of an Inextensible Elastic Filament in Stagnation Flow

PubMed Central

Deng, Mingge; Grinberg, Leopold; Caswell, Bruce

2015-01-01

We investigate the dynamics of a single inextensible elastic filament subject to anisotropic friction in a viscous stagnation-point flow, by employing both a continuum model represented by Langevin type stochastic partial differential equations (SPDEs) and a Dissipative Particle Dynamics (DPD) method. Unlike previous works1, the filament is free to rotate and the tension along the filament is determined by the local inextensible constraint. The kinematics of the filament is recorded and studied with normal modes analysis. The results show that the filament displays an instability induced by negative tension, which is analogous to Euler buckling of a beam. Symmetry breaking of normal modes dynamics and stretch-coil transitions are observed above the threshold of the buckling instability point. Furthermore, both temporal and spatial noise are amplified resulting from the interaction of thermal fluctuations and nonlinear filament dynamics. Specifically, the spatial noise is amplified with even normal modes being excited due to symmetry breaking, while the temporal noise is amplified with increasing time correlation length and variance. PMID:26023834

Preface of the "Symposium on Mathematical Models and Methods to investigate Heterogeneity in Cell and Cell Population Biology"

NASA Astrophysics Data System (ADS)

Clairambault, Jean

2016-06-01

This session investigates hot topics related to mathematical representations of cell and cell population dynamics in biology and medicine, in particular, but not only, with applications to cancer. Methods in mathematical modelling and analysis, and in statistical inference using single-cell and cell population data, should contribute to focus this session on heterogeneity in cell populations. Among other methods are proposed: a) Intracellular protein dynamics and gene regulatory networks using ordinary/partial/delay differential equations (ODEs, PDEs, DDEs); b) Representation of cell population dynamics using agent-based models (ABMs) and/or PDEs; c) Hybrid models and multiscale models to integrate single-cell dynamics into cell population behaviour; d) Structured cell population dynamics and asymptotic evolution w.r.t. relevant traits; e) Heterogeneity in cancer cell populations: origin, evolution, phylogeny and methods of reconstruction; f) Drug resistance as an evolutionary phenotype: predicting and overcoming it in therapeutics; g) Theoretical therapeutic optimisation of combined drug treatments in cancer cell populations and in populations of other organisms, such as bacteria.

Time-varying nonlinear dynamics of a deploying piezoelectric laminated composite plate under aerodynamic force

NASA Astrophysics Data System (ADS)

Lu, S. F.; Zhang, W.; Song, X. J.

2017-09-01

Using Reddy's high-order shear theory for laminated plates and Hamilton's principle, a nonlinear partial differential equation for the dynamics of a deploying cantilevered piezoelectric laminated composite plate, under the combined action of aerodynamic load and piezoelectric excitation, is introduced. Two-degree of freedom (DOF) nonlinear dynamic models for the time-varying coefficients describing the transverse vibration of the deploying laminate under the combined actions of a first-order aerodynamic force and piezoelectric excitation were obtained by selecting a suitable time-dependent modal function satisfying the displacement boundary conditions and applying second-order discretization using the Galerkin method. Using a numerical method, the time history curves of the deploying laminate were obtained, and its nonlinear dynamic characteristics, including extension speed and different piezoelectric excitations, were studied. The results suggest that the piezoelectric excitation has a clear effect on the change of the nonlinear dynamic characteristics of such piezoelectric laminated composite plates. The nonlinear vibration of the deploying cantilevered laminate can be effectively suppressed by choosing a suitable voltage and polarity.

Impact analyses for negative flexural responses (hogging) in railway prestressed concrete sleepers

NASA Astrophysics Data System (ADS)

Kaewunruen, S.; Ishida, T.; Remennikov, AM

2016-09-01

By nature, ballast interacts with railway concrete sleepers in order to provide bearing support to track system. Most train-track dynamic models do not consider the degradation of ballast over time. In fact, the ballast degradation causes differential settlement and impact forces acting on partial and unsupported tracks. Furthermore, localised ballast breakages underneath railseat increase the likelihood of centrebound cracks in concrete sleepers due to the unbalanced support under sleepers. This paper presents a dynamic finite element model of a standard-gauge concrete sleeper in a track system, taking into account the tensionless nature of ballast support. The finite element model was calibrated using static and dynamic responses in the past. In this paper, the effects of centre-bound ballast support on the impact behaviours of sleepers are highlighted. In addition, it is the first to demonstrate the dynamic effects of sleeper length on the dynamic design deficiency in concrete sleepers. The outcome of this study will benefit the rail maintenance criteria of track resurfacing in order to restore ballast profile and appropriate sleeper/ballast interaction.

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.

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.

Le Chatelier Principle for Out-of-Equilibrium and Boundary-Driven Systems: Application to Dynamical Phase Transitions.

PubMed

Shpielberg, O; Akkermans, E

2016-06-17

A stability analysis is presented for boundary-driven and out-of-equilibrium systems in the framework of the hydrodynamic macroscopic fluctuation theory. A Hamiltonian description is proposed which allows us to thermodynamically interpret the additivity principle. A necessary and sufficient condition for the validity of the additivity principle is obtained as an extension of the Le Chatelier principle. These stability conditions result from a diagonal quadratic form obtained using the cumulant generating function. This approach allows us to provide a proof for the stability of the weakly asymmetric exclusion process and to reduce the search for stability to the solution of two coupled linear ordinary differential equations instead of nonlinear partial differential equations. Additional potential applications of these results are discussed in the realm of classical and quantum systems.

Le Chatelier Principle for Out-of-Equilibrium and Boundary-Driven Systems: Application to Dynamical Phase Transitions

NASA Astrophysics Data System (ADS)

Shpielberg, O.; Akkermans, E.

2016-06-01

A stability analysis is presented for boundary-driven and out-of-equilibrium systems in the framework of the hydrodynamic macroscopic fluctuation theory. A Hamiltonian description is proposed which allows us to thermodynamically interpret the additivity principle. A necessary and sufficient condition for the validity of the additivity principle is obtained as an extension of the Le Chatelier principle. These stability conditions result from a diagonal quadratic form obtained using the cumulant generating function. This approach allows us to provide a proof for the stability of the weakly asymmetric exclusion process and to reduce the search for stability to the solution of two coupled linear ordinary differential equations instead of nonlinear partial differential equations. Additional potential applications of these results are discussed in the realm of classical and quantum systems.

Finite-time H∞ filtering for non-linear stochastic systems

NASA Astrophysics Data System (ADS)

Hou, Mingzhe; Deng, Zongquan; Duan, Guangren

2016-09-01

This paper describes the robust H∞ filtering analysis and the synthesis of general non-linear stochastic systems with finite settling time. We assume that the system dynamic is modelled by Itô-type stochastic differential equations of which the state and the measurement are corrupted by state-dependent noises and exogenous disturbances. A sufficient condition for non-linear stochastic systems to have the finite-time H∞ performance with gain less than or equal to a prescribed positive number is established in terms of a certain Hamilton-Jacobi inequality. Based on this result, the existence of a finite-time H∞ filter is given for the general non-linear stochastic system by a second-order non-linear partial differential inequality, and the filter can be obtained by solving this inequality. The effectiveness of the obtained result is illustrated by a numerical example.

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.

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.

A Procedure to Construct Exact Solutions of Nonlinear Fractional Differential Equations

PubMed Central

Güner, Özkan; Cevikel, Adem C.

2014-01-01

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

On implicit abstract neutral nonlinear differential equations

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

Hernández, Eduardo, E-mail: lalohm@ffclrp.usp.br; O’Regan, Donal, E-mail: donal.oregan@nuigalway.ie

2016-04-15

In this paper we continue our developments in Hernández and O’Regan (J Funct Anal 261:3457–3481, 2011) on the existence of solutions for abstract neutral differential equations. In particular we extend the results in Hernández and O’Regan (J Funct Anal 261:3457–3481, 2011) for the case of implicit nonlinear neutral equations and we focus on applications to partial “nonlinear” neutral differential equations. Some applications involving partial neutral differential equations are presented.

Oscillation of certain higher-order neutral partial functional differential equations.

PubMed

Li, Wei Nian; Sheng, Weihong

2016-01-01

In this paper, we study the oscillation of certain higher-order neutral partial functional differential equations with the Robin boundary conditions. Some oscillation criteria are established. Two examples are given to illustrate the main results in the end of this paper.

Functional requirements of a mathematical model of the heart.

PubMed

Palladino, Joseph L; Noordergraaf, Abraham

2009-01-01

Functional descriptions of the heart, especially the left ventricle, are often based on the measured variables pressure and ventricular outflow, embodied as a time-varying elastance. The fundamental difficulty of describing the mechanical properties of the heart with a time-varying elastance function that is set a priori is described. As an alternative, a new functional model of the heart is presented, which characterizes the ventricle's contractile state with parameters, rather than variables. Each chamber is treated as a pressure generator that is time and volume dependent. The heart's complex dynamics develop from a single equation based on the formation and relaxation of crossbridge bonds. This equation permits the calculation of ventricular elastance via E(v) = partial differentialp(v)/ partial differentialV(v). This heart model is defined independently from load properties, and ventricular elastance is dynamic and reflects changing numbers of crossbridge bonds. In this paper, the functionality of this new heart model is presented via computed work loops that demonstrate the Frank-Starling mechanism and the effects of preload, the effects of afterload, inotropic changes, and varied heart rate, as well as the interdependence of these effects. Results suggest the origin of the equivalent of Hill's force-velocity relation in the ventricle.

Numerical analysis of the effect of T-tubule location on calcium transient in ventricular myocytes.

PubMed

George, Uduak Z; Wang, Jun; Yu, Zeyun

2014-01-01

Intracellular calcium (Ca2+) signaling in cardiac myocytes is vital for proper functioning of the heart. Understanding the intracellular Ca2+ dynamics would give an insight into the functions of normal and diseased hearts. In the current study, spatiotemporal Ca2+ dynamics is investigated in ventricular myocytes by considering Ca2+ release and re-uptake via sarcolemma and transverse tubules (T-tubules), Ca2+ diffusion and buffering in the cytosol, and the blockade of Ca2+ activities associated with the sarcoplasmic reticulum. This study is carried out using a three dimensional (3D) geometric model of a branch of T-tubule extracted from the electron microscopy (EM) images of a partial ventricular myocyte. Mathematical modeling is done by using a system of partial differential equations involving Ca2+, buffers, and membrane channels. Numerical simulation results suggest that a lack of T-tubule structure at the vicinity of the cell surface could increase the peak time of Ca2+ concentration in myocytes. The results also show that T-tubules and mobile buffers play an important role in the regulation of Ca2+ transient in ventricular myocytes.

Reversible effects of oxygen partial pressure on genes associated with placental angiogenesis and differentiation in primary-term cytotrophoblast cell culture.

PubMed

Debiève, F; Depoix, C; Gruson, D; Hubinont, C

2013-09-01

Timely regulated changes in oxygen partial pressure are important for placental formation. Disturbances could be responsible for pregnancy-related diseases like preeclampsia and intrauterine growth restriction. We aimed to (i) determine the effect of oxygen partial pressure on cytotrophoblast differentiation; (ii) measure mRNA expression and protein secretion from genes associated with placental angiogenesis; and (iii) determine the reversibility of these effects at different oxygen partial pressures. Term cytotrophoblasts were incubated at 21% and 2.5% O2 for 96 hr, or were switched between the two oxygen concentrations after 48 hr. Real-time PCR and enzyme-linked immunosorbent assays (ELISAs) were used to evaluate cell fusion and differentiation, measuring transcript levels for those genes involved in cell fusion and placental angiogenesis, including VEGF, PlGF, VEGFR1, sVEGFR1, sENG, INHA, and GCM1. Cytotrophoblasts underwent fusion and differentiation in 2.5% O2 . PlGF expression was inhibited while sVEGFR1 expression increased. VEGF and sENG mRNA expressions increased in 2.5% compared to 21% O2 , but no protein was detected in the cell supernatants. Finally, GCM1 mRNA expression increased during trophoblast differentiation at 21% O2 , but was inhibited at 2.5% O2 . These mRNA expression effects were reversed by returning the cells to 21% O2 . Thus, low-oxygen partial pressure does not inhibit term-cytotrophoblast cell fusion and differentiation in vitro. Lowering the oxygen partial pressure from 21% to 2.5% caused normal-term trophoblasts to reversibly modify their expression of genes associated with placental angiogenesis. This suggests that modifications observed in pregnancy diseases such as preeclampsia or growth retardation are probably due to an extrinsic effect on trophoblasts. Copyright © 2013 Wiley Periodicals, Inc.

Lattice Boltzmann model for high-order nonlinear partial differential equations

NASA Astrophysics Data System (ADS)

Chai, Zhenhua; He, Nanzhong; Guo, Zhaoli; Shi, Baochang

2018-01-01

In this paper, a general lattice Boltzmann (LB) model is proposed for the high-order nonlinear partial differential equation with the form ∂tϕ +∑k=1mαk∂xkΠk(ϕ ) =0 (1 ≤k ≤m ≤6 ), αk are constant coefficients, Πk(ϕ ) are some known differential functions of ϕ . As some special cases of the high-order nonlinear partial differential equation, the classical (m)KdV equation, KdV-Burgers equation, K (n ,n ) -Burgers equation, Kuramoto-Sivashinsky equation, and Kawahara equation can be solved by the present LB model. Compared to the available LB models, the most distinct characteristic of the present model is to introduce some suitable auxiliary moments such that the correct moments of equilibrium distribution function can be achieved. In addition, we also conducted a detailed Chapman-Enskog analysis, and found that the high-order nonlinear partial differential equation can be correctly recovered from the proposed LB model. Finally, a large number of simulations are performed, and it is found that the numerical results agree with the analytical solutions, and usually the present model is also more accurate than the existing LB models [H. Lai and C. Ma, Sci. China Ser. G 52, 1053 (2009), 10.1007/s11433-009-0149-3; H. Lai and C. Ma, Phys. A (Amsterdam) 388, 1405 (2009), 10.1016/j.physa.2009.01.005] for high-order nonlinear partial differential equations.

Lattice Boltzmann model for high-order nonlinear partial differential equations.

PubMed

Chai, Zhenhua; He, Nanzhong; Guo, Zhaoli; Shi, Baochang

2018-01-01

In this paper, a general lattice Boltzmann (LB) model is proposed for the high-order nonlinear partial differential equation with the form ∂_{t}ϕ+∑_{k=1}^{m}α_{k}∂_{x}^{k}Π_{k}(ϕ)=0 (1≤k≤m≤6), α_{k} are constant coefficients, Π_{k}(ϕ) are some known differential functions of ϕ. As some special cases of the high-order nonlinear partial differential equation, the classical (m)KdV equation, KdV-Burgers equation, K(n,n)-Burgers equation, Kuramoto-Sivashinsky equation, and Kawahara equation can be solved by the present LB model. Compared to the available LB models, the most distinct characteristic of the present model is to introduce some suitable auxiliary moments such that the correct moments of equilibrium distribution function can be achieved. In addition, we also conducted a detailed Chapman-Enskog analysis, and found that the high-order nonlinear partial differential equation can be correctly recovered from the proposed LB model. Finally, a large number of simulations are performed, and it is found that the numerical results agree with the analytical solutions, and usually the present model is also more accurate than the existing LB models [H. Lai and C. Ma, Sci. China Ser. G 52, 1053 (2009)1672-179910.1007/s11433-009-0149-3; H. Lai and C. Ma, Phys. A (Amsterdam) 388, 1405 (2009)PHYADX0378-437110.1016/j.physa.2009.01.005] for high-order nonlinear partial differential equations.

Topographic Effects on Geologic Mass Movements

NASA Technical Reports Server (NTRS)

Baloga, Stephen M.; Frey, Herbert (Technical Monitor)

2000-01-01

This report describes research directed toward understanding the response of volcanic lahars and lava flows to changes in the topography along the path of the flow. We have used a variety of steady-state and time-dependent models of lahars and lava flows to calculate the changes in flow dynamics due to variable topography. These models are based on first-order partial differential equations for the local conservation of volume. A global volume conservation requirement is also imposed to determine the extent of the flow as a function of time and the advance rate. Simulated DEMs have been used in this report.

Optimal control of first order distributed systems. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Johnson, T. L.

1972-01-01

The problem of characterizing optimal controls for a class of distributed-parameter systems is considered. The system dynamics are characterized mathematically by a finite number of coupled partial differential equations involving first-order time and space derivatives of the state variables, which are constrained at the boundary by a finite number of algebraic relations. Multiple control inputs, extending over the entire spatial region occupied by the system ("distributed controls') are to be designed so that the response of the system is optimal. A major example involving boundary control of an unstable low-density plasma is developed from physical laws.

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.

Lyapunov exponents for infinite dimensional dynamical systems

NASA Technical Reports Server (NTRS)

Mhuiris, Nessan Mac Giolla

1987-01-01

Classically it was held that solutions to deterministic partial differential equations (i.e., ones with smooth coefficients and boundary data) could become random only through one mechanism, namely by the activation of more and more of the infinite number of degrees of freedom that are available to such a system. It is only recently that researchers have come to suspect that many infinite dimensional nonlinear systems may in fact possess finite dimensional chaotic attractors. Lyapunov exponents provide a tool for probing the nature of these attractors. This paper examines how these exponents might be measured for infinite dimensional systems.

Entropy and convexity for nonlinear partial differential equations

PubMed Central

Ball, John M.; Chen, Gui-Qiang G.

2013-01-01

Partial differential equations are ubiquitous in almost all applications of mathematics, where they provide a natural mathematical description of many phenomena involving change in physical, chemical, biological and social processes. The concept of entropy originated in thermodynamics and statistical physics during the nineteenth century to describe the heat exchanges that occur in the thermal processes in a thermodynamic system, while the original notion of convexity is for sets and functions in mathematics. Since then, entropy and convexity have become two of the most important concepts in mathematics. In particular, nonlinear methods via entropy and convexity have been playing an increasingly important role in the analysis of nonlinear partial differential equations in recent decades. This opening article of the Theme Issue is intended to provide an introduction to entropy, convexity and related nonlinear methods for the analysis of nonlinear partial differential equations. We also provide a brief discussion about the content and contributions of the papers that make up this Theme Issue. PMID:24249768

Oxidation Behavior of Carbon Fiber-Reinforced Composites

NASA Technical Reports Server (NTRS)

Sullivan, Roy M.

2008-01-01

OXIMAP is a numerical (FEA-based) solution tool capable of calculating the carbon fiber and fiber coating oxidation patterns within any arbitrarily shaped carbon silicon carbide composite structure as a function of time, temperature, and the environmental oxygen partial pressure. The mathematical formulation is derived from the mechanics of the flow of ideal gases through a chemically reacting, porous solid. The result of the formulation is a set of two coupled, non-linear differential equations written in terms of the oxidant and oxide partial pressures. The differential equations are solved simultaneously to obtain the partial vapor pressures of the oxidant and oxides as a function of the spatial location and time. The local rate of carbon oxidation is determined at each time step using the map of the local oxidant partial vapor pressure along with the Arrhenius rate equation. The non-linear differential equations are cast into matrix equations by applying the Bubnov-Galerkin weighted residual finite element method, allowing for the solution of the differential equations numerically.

Entropy and convexity for nonlinear partial differential equations.

PubMed

Ball, John M; Chen, Gui-Qiang G

2013-12-28

Partial differential equations are ubiquitous in almost all applications of mathematics, where they provide a natural mathematical description of many phenomena involving change in physical, chemical, biological and social processes. The concept of entropy originated in thermodynamics and statistical physics during the nineteenth century to describe the heat exchanges that occur in the thermal processes in a thermodynamic system, while the original notion of convexity is for sets and functions in mathematics. Since then, entropy and convexity have become two of the most important concepts in mathematics. In particular, nonlinear methods via entropy and convexity have been playing an increasingly important role in the analysis of nonlinear partial differential equations in recent decades. This opening article of the Theme Issue is intended to provide an introduction to entropy, convexity and related nonlinear methods for the analysis of nonlinear partial differential equations. We also provide a brief discussion about the content and contributions of the papers that make up this Theme Issue.

Differential phase measurements of D-region partial reflections

NASA Technical Reports Server (NTRS)

Wiersma, D. J.; Sechrist, C. F., Jr.

1972-01-01

Differential phase partial reflection measurements were used to deduce D region electron density profiles. The phase difference was measured by taking sums and differences of amplitudes received on an array of crossed dipoles. The reflection model used was derived from Fresnel reflection theory. Seven profiles obtained over the period from 13 October 1971 to 5 November 1971 are presented, along with the results from simultaneous measurements of differential absorption. Some possible sources of error and error propagation are discussed. A collision frequency profile was deduced from the electron concentration calculated from differential phase and differential absorption.

An analytical model of stand dynamics as a function of tree growth, mortality and recruitment: the shade tolerance-stand structure hypothesis revisited.

PubMed

Zavala, Miguel A; Angulo, Oscar; Bravo de la Parra, Rafael; López-Marcos, Juan C

2007-02-07

Light competition and interspecific differences in shade tolerance are considered key determinants of forest stand structure and dynamics. Specifically two main stand diameter distribution types as a function of shade tolerance have been proposed based on empirical observations. All-aged stands of shade tolerant species tend to have steeply descending, monotonic diameter distributions (inverse J-shaped curves). Shade intolerant species in contrast typically exhibit normal (unimodal) tree diameter distributions due to high mortality rates of smaller suppressed trees. In this study we explore the generality of this hypothesis which implies a causal relationship between light competition or shade tolerance and stand structure. For this purpose we formulate a partial differential equation system of stand dynamics as a function of individual tree growth, recruitment and mortality which allows us to explore possible individual-based mechanisms--e.g. light competition-underlying observed patterns of stand structure--e.g. unimodal or inverse J-shaped equilibrium diameter curves. We find that contrary to expectations interspecific differences in growth patterns can result alone in any of the two diameter distributions types observed in the field. In particular, slow growing species can present unimodal equilibrium curves even in the absence of light competition. Moreover, light competition and shade intolerance evaluated both at the tree growth and mortality stages did not have a significant impact on stand structure that tended to converge systematically towards an inverse J-shaped curves for most tree growth scenarios. Realistic transient stand dynamics for even aged stands of shade intolerant species (unimodal curves) were only obtained when recruitment was completely suppressed, providing further evidence on the critical role played by juvenile stages of tree development (e.g. the sampling stage) on final forest structure and composition. The results also point out the relevance of partial differential equations systems as a tool for exploring the individual-level mechanisms underpinning forest structure, particularly in relation to more complex forest simulation models that are more difficult to analyze and to interpret from a biological point of view.

Parameter estimation with bio-inspired meta-heuristic optimization: modeling the dynamics of endocytosis.

PubMed

Tashkova, Katerina; Korošec, Peter; Silc, Jurij; Todorovski, Ljupčo; Džeroski, Sašo

2011-10-11

We address the task of parameter estimation in models of the dynamics of biological systems based on ordinary differential equations (ODEs) from measured data, where the models are typically non-linear and have many parameters, the measurements are imperfect due to noise, and the studied system can often be only partially observed. A representative task is to estimate the parameters in a model of the dynamics of endocytosis, i.e., endosome maturation, reflected in a cut-out switch transition between the Rab5 and Rab7 domain protein concentrations, from experimental measurements of these concentrations. The general parameter estimation task and the specific instance considered here are challenging optimization problems, calling for the use of advanced meta-heuristic optimization methods, such as evolutionary or swarm-based methods. We apply three global-search meta-heuristic algorithms for numerical optimization, i.e., differential ant-stigmergy algorithm (DASA), particle-swarm optimization (PSO), and differential evolution (DE), as well as a local-search derivative-based algorithm 717 (A717) to the task of estimating parameters in ODEs. We evaluate their performance on the considered representative task along a number of metrics, including the quality of reconstructing the system output and the complete dynamics, as well as the speed of convergence, both on real-experimental data and on artificial pseudo-experimental data with varying amounts of noise. We compare the four optimization methods under a range of observation scenarios, where data of different completeness and accuracy of interpretation are given as input. Overall, the global meta-heuristic methods (DASA, PSO, and DE) clearly and significantly outperform the local derivative-based method (A717). Among the three meta-heuristics, differential evolution (DE) performs best in terms of the objective function, i.e., reconstructing the output, and in terms of convergence. These results hold for both real and artificial data, for all observability scenarios considered, and for all amounts of noise added to the artificial data. In sum, the meta-heuristic methods considered are suitable for estimating the parameters in the ODE model of the dynamics of endocytosis under a range of conditions: With the model and conditions being representative of parameter estimation tasks in ODE models of biochemical systems, our results clearly highlight the promise of bio-inspired meta-heuristic methods for parameter estimation in dynamic system models within system biology.

Parameter estimation with bio-inspired meta-heuristic optimization: modeling the dynamics of endocytosis

PubMed Central

2011-01-01

Background We address the task of parameter estimation in models of the dynamics of biological systems based on ordinary differential equations (ODEs) from measured data, where the models are typically non-linear and have many parameters, the measurements are imperfect due to noise, and the studied system can often be only partially observed. A representative task is to estimate the parameters in a model of the dynamics of endocytosis, i.e., endosome maturation, reflected in a cut-out switch transition between the Rab5 and Rab7 domain protein concentrations, from experimental measurements of these concentrations. The general parameter estimation task and the specific instance considered here are challenging optimization problems, calling for the use of advanced meta-heuristic optimization methods, such as evolutionary or swarm-based methods. Results We apply three global-search meta-heuristic algorithms for numerical optimization, i.e., differential ant-stigmergy algorithm (DASA), particle-swarm optimization (PSO), and differential evolution (DE), as well as a local-search derivative-based algorithm 717 (A717) to the task of estimating parameters in ODEs. We evaluate their performance on the considered representative task along a number of metrics, including the quality of reconstructing the system output and the complete dynamics, as well as the speed of convergence, both on real-experimental data and on artificial pseudo-experimental data with varying amounts of noise. We compare the four optimization methods under a range of observation scenarios, where data of different completeness and accuracy of interpretation are given as input. Conclusions Overall, the global meta-heuristic methods (DASA, PSO, and DE) clearly and significantly outperform the local derivative-based method (A717). Among the three meta-heuristics, differential evolution (DE) performs best in terms of the objective function, i.e., reconstructing the output, and in terms of convergence. These results hold for both real and artificial data, for all observability scenarios considered, and for all amounts of noise added to the artificial data. In sum, the meta-heuristic methods considered are suitable for estimating the parameters in the ODE model of the dynamics of endocytosis under a range of conditions: With the model and conditions being representative of parameter estimation tasks in ODE models of biochemical systems, our results clearly highlight the promise of bio-inspired meta-heuristic methods for parameter estimation in dynamic system models within system biology. PMID:21989196

A boundary value approach for solving three-dimensional elliptic and hyperbolic partial differential equations.

PubMed

Biala, T A; Jator, S N

2015-01-01

In this article, the boundary value method is applied to solve three dimensional elliptic and hyperbolic partial differential equations. The partial derivatives with respect to two of the spatial variables (y, z) are discretized using finite difference approximations to obtain a large system of ordinary differential equations (ODEs) in the third spatial variable (x). Using interpolation and collocation techniques, a continuous scheme is developed and used to obtain discrete methods which are applied via the Block unification approach to obtain approximations to the resulting large system of ODEs. Several test problems are investigated to elucidate the solution process.

Direct modeling for computational fluid dynamics

NASA Astrophysics Data System (ADS)

Xu, Kun

2015-06-01

All fluid dynamic equations are valid under their modeling scales, such as the particle mean free path and mean collision time scale of the Boltzmann equation and the hydrodynamic scale of the Navier-Stokes (NS) equations. The current computational fluid dynamics (CFD) focuses on the numerical solution of partial differential equations (PDEs), and its aim is to get the accurate solution of these governing equations. Under such a CFD practice, it is hard to develop a unified scheme that covers flow physics from kinetic to hydrodynamic scales continuously because there is no such governing equation which could make a smooth transition from the Boltzmann to the NS modeling. The study of fluid dynamics needs to go beyond the traditional numerical partial differential equations. The emerging engineering applications, such as air-vehicle design for near-space flight and flow and heat transfer in micro-devices, do require further expansion of the concept of gas dynamics to a larger domain of physical reality, rather than the traditional distinguishable governing equations. At the current stage, the non-equilibrium flow physics has not yet been well explored or clearly understood due to the lack of appropriate tools. Unfortunately, under the current numerical PDE approach, it is hard to develop such a meaningful tool due to the absence of valid PDEs. In order to construct multiscale and multiphysics simulation methods similar to the modeling process of constructing the Boltzmann or the NS governing equations, the development of a numerical algorithm should be based on the first principle of physical modeling. In this paper, instead of following the traditional numerical PDE path, we introduce direct modeling as a principle for CFD algorithm development. Since all computations are conducted in a discretized space with limited cell resolution, the flow physics to be modeled has to be done in the mesh size and time step scales. Here, the CFD is more or less a direct construction of discrete numerical evolution equations, where the mesh size and time step will play dynamic roles in the modeling process. With the variation of the ratio between mesh size and local particle mean free path, the scheme will capture flow physics from the kinetic particle transport and collision to the hydrodynamic wave propagation. Based on the direct modeling, a continuous dynamics of flow motion will be captured in the unified gas-kinetic scheme. This scheme can be faithfully used to study the unexplored non-equilibrium flow physics in the transition regime.

Muscle activation described with a differential equation model for large ensembles of locally coupled molecular motors.

PubMed

Walcott, Sam

2014-10-01

Molecular motors, by turning chemical energy into mechanical work, are responsible for active cellular processes. Often groups of these motors work together to perform their biological role. Motors in an ensemble are coupled and exhibit complex emergent behavior. Although large motor ensembles can be modeled with partial differential equations (PDEs) by assuming that molecules function independently of their neighbors, this assumption is violated when motors are coupled locally. It is therefore unclear how to describe the ensemble behavior of the locally coupled motors responsible for biological processes such as calcium-dependent skeletal muscle activation. Here we develop a theory to describe locally coupled motor ensembles and apply the theory to skeletal muscle activation. The central idea is that a muscle filament can be divided into two phases: an active and an inactive phase. Dynamic changes in the relative size of these phases are described by a set of linear ordinary differential equations (ODEs). As the dynamics of the active phase are described by PDEs, muscle activation is governed by a set of coupled ODEs and PDEs, building on previous PDE models. With comparison to Monte Carlo simulations, we demonstrate that the theory captures the behavior of locally coupled ensembles. The theory also plausibly describes and predicts muscle experiments from molecular to whole muscle scales, suggesting that a micro- to macroscale muscle model is within reach.

Dynamic Decision Making under Uncertainty and Partial Information

DTIC Science & Technology

2017-01-30

order to address these problems, we investigated efficient computational methodologies for dynamic decision making under uncertainty and partial...information. In the course of this research, we developed and studied efficient simulation-based methodologies for dynamic decision making under...uncertainty and partial information; (ii) studied the application of these decision making models and methodologies to practical problems, such as those

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.

Modeling biological gradient formation: combining partial differential equations and Petri nets.

PubMed

Bertens, Laura M F; Kleijn, Jetty; Hille, Sander C; Heiner, Monika; Koutny, Maciej; Verbeek, Fons J

2016-01-01

Both Petri nets and differential equations are important modeling tools for biological processes. In this paper we demonstrate how these two modeling techniques can be combined to describe biological gradient formation. Parameters derived from partial differential equation describing the process of gradient formation are incorporated in an abstract Petri net model. The quantitative aspects of the resulting model are validated through a case study of gradient formation in the fruit fly.

Evolution and End Point of the Black String Instability: Large D Solution.

PubMed

Emparan, Roberto; Suzuki, Ryotaku; Tanabe, Kentaro

2015-08-28

We derive a simple set of nonlinear, (1+1)-dimensional partial differential equations that describe the dynamical evolution of black strings and branes to leading order in the expansion in the inverse of the number of dimensions D. These equations are easily solved numerically. Their solution shows that thin enough black strings are unstable to developing inhomogeneities along their length, and at late times they asymptote to stable nonuniform black strings. This proves an earlier conjecture about the end point of the instability of black strings in a large enough number of dimensions. If the initial black string is very thin, the final configuration is highly nonuniform and resembles a periodic array of localized black holes joined by short necks. We also present the equations that describe the nonlinear dynamics of anti-de Sitter black branes at large D.

Initial value formulation of dynamical Chern-Simons gravity

NASA Astrophysics Data System (ADS)

Delsate, Térence; Hilditch, David; Witek, Helvi

2015-01-01

We derive an initial value formulation for dynamical Chern-Simons gravity, a modification of general relativity involving parity-violating higher derivative terms. We investigate the structure of the resulting system of partial differential equations thinking about linearization around arbitrary backgrounds. This type of consideration is necessary if we are to establish well-posedness of the Cauchy problem. Treating the field equations as an effective field theory we find that weak necessary conditions for hyperbolicity are satisfied. For the full field equations we find that there are states from which subsequent evolution is not determined. Generically the evolution system closes, but is not hyperbolic in any sense that requires a first order pseudodifferential reduction. In a cursory mode analysis we find that the equations of motion contain terms that may cause ill-posedness of the initial value problem.

An Inverse Problem for a Class of Conditional Probability Measure-Dependent Evolution Equations

PubMed Central

Mirzaev, Inom; Byrne, Erin C.; Bortz, David M.

2016-01-01

We investigate the inverse problem of identifying a conditional probability measure in measure-dependent evolution equations arising in size-structured population modeling. We formulate the inverse problem as a least squares problem for the probability measure estimation. Using the Prohorov metric framework, we prove existence and consistency of the least squares estimates and outline a discretization scheme for approximating a conditional probability measure. For this scheme, we prove general method stability. The work is motivated by Partial Differential Equation (PDE) models of flocculation for which the shape of the post-fragmentation conditional probability measure greatly impacts the solution dynamics. To illustrate our methodology, we apply the theory to a particular PDE model that arises in the study of population dynamics for flocculating bacterial aggregates in suspension, and provide numerical evidence for the utility of the approach. PMID:28316360

Boundary Control of Linear Uncertain 1-D Parabolic PDE Using Approximate Dynamic Programming.

PubMed

Talaei, Behzad; Jagannathan, Sarangapani; Singler, John

2018-04-01

This paper develops a near optimal boundary control method for distributed parameter systems governed by uncertain linear 1-D parabolic partial differential equations (PDE) by using approximate dynamic programming. A quadratic surface integral is proposed to express the optimal cost functional for the infinite-dimensional state space. Accordingly, the Hamilton-Jacobi-Bellman (HJB) equation is formulated in the infinite-dimensional domain without using any model reduction. Subsequently, a neural network identifier is developed to estimate the unknown spatially varying coefficient in PDE dynamics. Novel tuning law is proposed to guarantee the boundedness of identifier approximation error in the PDE domain. A radial basis network (RBN) is subsequently proposed to generate an approximate solution for the optimal surface kernel function online. The tuning law for near optimal RBN weights is created, such that the HJB equation error is minimized while the dynamics are identified and closed-loop system remains stable. Ultimate boundedness (UB) of the closed-loop system is verified by using the Lyapunov theory. The performance of the proposed controller is successfully confirmed by simulation on an unstable diffusion-reaction process.

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.

Impaired recognition of body expressions in the behavioral variant of frontotemporal dementia.

PubMed

Van den Stock, Jan; De Winter, François-Laurent; de Gelder, Beatrice; Rangarajan, Janaki Raman; Cypers, Gert; Maes, Frederik; Sunaert, Stefan; Goffin, Karolien; Vandenberghe, Rik; Vandenbulcke, Mathieu

2015-08-01

Progressive deterioration of social cognition and emotion processing are core symptoms of the behavioral variant of frontotemporal dementia (bvFTD). Here we investigate whether bvFTD is also associated with impaired recognition of static (Experiment 1) and dynamic (Experiment 2) bodily expressions. In addition, we compared body expression processing with processing of static (Experiment 3) and dynamic (Experiment 4) facial expressions, as well as with face identity processing (Experiment 5). The results reveal that bvFTD is associated with impaired recognition of static and dynamic bodily and facial expressions, while identity processing was intact. No differential impairments were observed regarding motion (static vs. dynamic) or category (body vs. face). Within the bvFTD group, we observed a significant partial correlation between body and face expression recognition, when controlling for performance on the identity task. Voxel-Based Morphometry (VBM) analysis revealed that body emotion recognition was positively associated with gray matter volume in a region of the inferior frontal gyrus (pars orbitalis/triangularis). The results are in line with a supramodal emotion recognition deficit in bvFTD. Copyright © 2015 Elsevier Ltd. All rights reserved.

Oligopolies with contingent workforce and unemployment insurance systems

NASA Astrophysics Data System (ADS)

Matsumoto, Akio; Merlone, Ugo; Szidarovszky, Ferenc

2015-10-01

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

Dynamic correlation effects in fully differential cross sections for 75-keV proton-impact ionization of helium

NASA Astrophysics Data System (ADS)

Niu, Xiaojie; Sun, Shiyan; Wang, Fujun; Jia, Xiangfu

2017-08-01

The effect of final-state dynamic correlation is investigated for helium single ionization by 75-keV proton impact analyzing fully differential cross sections (FDCS). The final state is represented by a continuum correlated wave (CCW-PT) function which accounts for the interaction between the projectile and the residual target ion (PT interaction). This continuum correlated wave function partially includes the correlation of electron-projectile and electron-target relative motion as coupling terms of the wave equation. The transition matrix is evaluated using the CCW-PT function and the Born initial state. The analytical expression of the transition matrix has been obtained. We have shown that this series is strongly convergent and analyzed the contribution of their different terms to the FDCS within the perturbation method. Illustrative computations are performed in the scattering plane and in the perpendicular plane. Both the correlation effects and the PT interaction are checked by the preset calculations. Our results are compared with absolute experimental data as well as other theoretical models. We have shown that the dynamic correlation plays an important role in the single ionization of atoms by proton impact at intermediate projectile energies, especially at large transverse momentum transfer. While overall agreement between theory and the experimental data is encouraging, detailed agreement is lacking. The need for more theoretical and experimental work is emphasized.

The Statistical Mechanics of Ideal Homogeneous Turbulence

NASA Technical Reports Server (NTRS)

Shebalin, John V.

2002-01-01

Plasmas, such as those found in the space environment or in plasma confinement devices, are often modeled as electrically conducting fluids. When fluids and plasmas are energetically stirred, regions of highly nonlinear, chaotic behavior known as turbulence arise. Understanding the fundamental nature of turbulence is a long-standing theoretical challenge. The present work describes a statistical theory concerning a certain class of nonlinear, finite dimensional, dynamical models of turbulence. These models arise when the partial differential equations describing incompressible, ideal (i.e., nondissipative) homogeneous fluid and magnetofluid (i.e., plasma) turbulence are Fourier transformed into a very large set of ordinary differential equations. These equations define a divergenceless flow in a high-dimensional phase space, which allows for the existence of a Liouville theorem, guaranteeing a distribution function based on constants of the motion (integral invariants). The novelty of these particular dynamical systems is that there are integral invariants other than the energy, and that some of these invariants behave like pseudoscalars under two of the discrete symmetry transformations of physics, parity, and charge conjugation. In this work the 'rugged invariants' of ideal homogeneous turbulence are shown to be the only significant scalar and pseudoscalar invariants. The discovery that pseudoscalar invariants cause symmetries of the original equations to be dynamically broken and induce a nonergodic structure on the associated phase space is the primary result presented here. Applicability of this result to dissipative turbulence is also discussed.

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

Dynamic optimization of open-loop input signals for ramp-up current profiles in tokamak plasmas

NASA Astrophysics Data System (ADS)

Ren, Zhigang; Xu, Chao; Lin, Qun; Loxton, Ryan; Teo, Kok Lay

2016-03-01

Establishing a good current spatial profile in tokamak fusion reactors is crucial to effective steady-state operation. The evolution of the current spatial profile is related to the evolution of the poloidal magnetic flux, which can be modeled in the normalized cylindrical coordinates using a parabolic partial differential equation (PDE) called the magnetic diffusion equation. In this paper, we consider the dynamic optimization problem of attaining the best possible current spatial profile during the ramp-up phase of the tokamak. We first use the Galerkin method to obtain a finite-dimensional ordinary differential equation (ODE) model based on the original magnetic diffusion PDE. Then, we combine the control parameterization method with a novel time-scaling transformation to obtain an approximate optimal parameter selection problem, which can be solved using gradient-based optimization techniques such as sequential quadratic programming (SQP). This control parameterization approach involves approximating the tokamak input signals by piecewise-linear functions whose slopes and break-points are decision variables to be optimized. We show that the gradient of the objective function with respect to the decision variables can be computed by solving an auxiliary dynamic system governing the state sensitivity matrix. Finally, we conclude the paper with simulation results for an example problem based on experimental data from the DIII-D tokamak in San Diego, California.

Stability analysis of coupled torsional vibration and pressure in oilwell drillstring system

NASA Astrophysics Data System (ADS)

Toumi, S.; Beji, L.; Mlayeh, R.; Abichou, A.

2018-01-01

To address security issues in oilwell drillstring system, the drilling operation handling which is in generally not autonomous but ensured by an operator may be drill bit destructive or fatal for the machine. To control of stick-slip phenomenon, the drillstring control at the right speed taking only the drillstring vibration is not sufficient as the mud dynamics and the pressure change around the drill pipes cannot be neglected. A coupled torsional vibration and pressure model is presented, and the well-posedness problem is addressed. As a Partial Differential Equation-Ordinary Differential Equation (PDE-ODE) coupled system, and in order to maintain a non destructive downhole pressure, we investigate the control stability with and without the damping term in the wave PDE. In terms of, the torsional variable, the downhole pressure, and the annulus pressure, the coupled system equilibrium is shown to be exponentially stable.

Conference on Complex Turbulent Flows: Comparison of Computation and Experiment, Stanford University, Stanford, CA, September 14-18, 1981, Proceedings. Volume 2 - Taxonomies, reporters' summaries, evaluation, and conclusions

NASA Technical Reports Server (NTRS)

Kline, S. J. (Editor); Cantwell, B. J. (Editor); Lilley, G. M.

1982-01-01

Computational techniques for simulating turbulent flows were explored, together with the results of experimental investigations. Particular attention was devoted to the possibility of defining a universal closure model, applicable for all turbulence situations; however, conclusions were drawn that zonal models, describing localized structures, were the most promising techniques to date. The taxonomy of turbulent flows was summarized, as were algebraic, differential, integral, and partial differential methods for numerical depiction of turbulent flows. Numerous comparisons of theoretically predicted and experimentally obtained data for wall pressure distributions, velocity profiles, turbulent kinetic energy profiles, Reynolds shear stress profiles, and flows around transonic airfoils were presented. Simplifying techniques for reducing the necessary computational time for modeling complex flowfields were surveyed, together with the industrial requirements and applications of computational fluid dynamics techniques.

A multiphase model for chemically- and mechanically- induced cell differentiation in a hollow fibre membrane bioreactor: minimising growth factor consumption.

PubMed

Pearson, Natalie C; Oliver, James M; Shipley, Rebecca J; Waters, Sarah L

2016-06-01

We present a simplified two-dimensional model of fluid flow, solute transport, and cell distribution in a hollow fibre membrane bioreactor. We consider two cell populations, one undifferentiated and one differentiated, with differentiation stimulated either by growth factor alone, or by both growth factor and fluid shear stress. Two experimental configurations are considered, a 3-layer model in which the cells are seeded in a scaffold throughout the extracapillary space (ECS), and a 4-layer model in which the cell-scaffold construct occupies a layer surrounding the outside of the hollow fibre, only partially filling the ECS. Above this is a region of free-flowing fluid, referred to as the upper fluid layer. Following previous models by the authors (Pearson et al. in Math Med Biol, 2013, Biomech Model Mechanbiol 1-16, 2014a, we employ porous mixture theory to model the dynamics of, and interactions between, the cells, scaffold, and fluid in the cell-scaffold construct. We use this model to determine operating conditions (experiment end time, growth factor inlet concentration, and inlet fluid fluxes) which result in a required percentage of differentiated cells, as well as maximising the differentiated cell yield and minimising the consumption of expensive growth factor.

Testing for Differential Item Functioning with Measures of Partial Association

ERIC Educational Resources Information Center

Woods, Carol M.

2009-01-01

Differential item functioning (DIF) occurs when an item on a test or questionnaire has different measurement properties for one group of people versus another, irrespective of mean differences on the construct. There are many methods available for DIF assessment. The present article is focused on indices of partial association. A family of average…

THREE-POINT BACKWARD FINITE DIFFERENCE METHOD FOR SOLVING A SYSTEM OF MIXED HYPERBOLIC-PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS. (R825549C019)

EPA Science Inventory

A three-point backward finite-difference method has been derived for a system of mixed hyperbolic_¯¯parabolic (convection_¯¯diffusion) partial differential equations (mixed PDEs). The method resorts to the three-point backward differenci...

Magnetic Evidence for a Partially Differentiated Carbonaceous Chondrite Parent Body and Possible Implications for Asteroid 21 Lutetia

NASA Astrophysics Data System (ADS)

Weiss, Benjamin; Carporzen, L.; Elkins-Tanton, L.; Shuster, D. L.; Ebel, D. S.; Gattacceca, J.; Binzel, R. P.

2010-10-01

The origin of remanent magnetization in the CV carbonaceous chondrite Allende has been a longstanding mystery. The possibility of a core dynamo like that known for achondrite parent bodies has been discounted because chondrite parent bodies are assumed to be undifferentiated. Here we report that Allende's magnetization was acquired over several million years (Ma) during metasomatism on the parent planetesimal in a > 20 microtesla field 8-9 Ma after solar system formation. This field was present too recently and directionally stable for too long to have been the generated by the protoplanetary disk or young Sun. The field intensity is in the range expected for planetesimal core dynamos (Weiss et al. 2010), suggesting that CV chondrites are derived from the outer, unmelted layer of a partially differentiated body with a convecting metallic core (Elkins-Tanton et al. 2010). This suggests that asteroids with differentiated interiors could be present today but masked under chondritic surfaces. In fact, CV chondrites are spectrally similar to many members of the Eos asteroid family whose spectral diversity has been interpreted as evidence for a partially differentiated parent asteroid (Mothe-Diniz et al. 2008). CV chondrite spectral and polarimetric data also resemble those of asteroid 21 Lutetia (e.g., Belskaya et al. 2010), recently encountered by the Rosetta spacecraft. Ground-based measurements of Lutetia indicate a high density of 2.4-5.1 g cm-3 (Drummond et al. 2010), while radar data seem to rule out a metallic surface composition (Shepard et al. 2008). If Rosetta spacecraft measurements confirm a high density and a CV-like surface composition for Lutetia, then we propose Lutetia may be an example of a partially differentiated carbonaceous chondrite parent body. Regardless, the very existence of primitive achondrites, which contain evidence of both relict chondrules and partial melting, are prima facie evidence for the formation of partially differentiated bodies.

Bayesian Inference of High-Dimensional Dynamical Ocean Models

NASA Astrophysics Data System (ADS)

Lin, J.; Lermusiaux, P. F. J.; Lolla, S. V. T.; Gupta, A.; Haley, P. J., Jr.

2015-12-01

This presentation addresses a holistic set of challenges in high-dimension ocean Bayesian nonlinear estimation: i) predict the probability distribution functions (pdfs) of large nonlinear dynamical systems using stochastic partial differential equations (PDEs); ii) assimilate data using Bayes' law with these pdfs; iii) predict the future data that optimally reduce uncertainties; and (iv) rank the known and learn the new model formulations themselves. Overall, we allow the joint inference of the state, equations, geometry, boundary conditions and initial conditions of dynamical models. Examples are provided for time-dependent fluid and ocean flows, including cavity, double-gyre and Strait flows with jets and eddies. The Bayesian model inference, based on limited observations, is illustrated first by the estimation of obstacle shapes and positions in fluid flows. Next, the Bayesian inference of biogeochemical reaction equations and of their states and parameters is presented, illustrating how PDE-based machine learning can rigorously guide the selection and discovery of complex ecosystem models. Finally, the inference of multiscale bottom gravity current dynamics is illustrated, motivated in part by classic overflows and dense water formation sites and their relevance to climate monitoring and dynamics. This is joint work with our MSEAS group at MIT.

Nonlinear dynamic simulation of single- and multi-spool core engines

NASA Technical Reports Server (NTRS)

Schobeiri, T.; Lippke, C.; Abouelkheir, M.

1993-01-01

In this paper a new computational method for accurate simulation of the nonlinear dynamic behavior of single- and multi-spool core engines, turbofan engines, and power generation gas turbine engines is presented. In order to perform the simulation, a modularly structured computer code has been developed which includes individual mathematical modules representing various engine components. The generic structure of the code enables the dynamic simulation of arbitrary engine configurations ranging from single-spool thrust generation to multi-spool thrust/power generation engines under adverse dynamic operating conditions. For precise simulation of turbine and compressor components, row-by-row calculation procedures were implemented that account for the specific turbine and compressor cascade and blade geometry and characteristics. The dynamic behavior of the subject engine is calculated by solving a number of systems of partial differential equations, which describe the unsteady behavior of the individual components. In order to ensure the capability, accuracy, robustness, and reliability of the code, comprehensive critical performance assessment and validation tests were performed. As representatives, three different transient cases with single- and multi-spool thrust and power generation engines were simulated. The transient cases range from operating with a prescribed fuel schedule, to extreme load changes, to generator and turbine shut down.

Differential Curing In Fiber/Resin Laminates

NASA Technical Reports Server (NTRS)

Webster, Charles N.

1989-01-01

Modified layup schedule counteracts tendency toward delamination. Improved manufacturing process resembles conventional process, except prepregs partially cured laid on mold in sequence in degree of partial cure decreases from mold side to bag side. Degree of partial cure of each layer at time of layup selected by controlling storage and partial-curing temperatures of prepreg according to Arrhenius equation for rate of gel of resin as function of temperature and time from moment of mixing. Differential advancement of cure in layers made large enough to offset effect of advance bag-side heating in oven or autoclave. Technique helps prevent entrapment of volatile materials during manufacturing of fiber/resin laminates.

Liquid spreading under partial wetting conditions

NASA Astrophysics Data System (ADS)

Chen, M.; Pahlavan, A. A.; Cueto-Felgueroso, L.; McKinley, G. H.; Juanes, R.

2013-12-01

Traditional mathematical descriptions of multiphase flow in porous media rely on a multiphase extension of Darcy's law, and lead to nonlinear second-order (advection-diffusion) partial differential equations for fluid saturations. Here, we study horizontal redistribution of immiscible fluids. The traditional Darcy-flow model predicts that the spreading of a finite amount of liquid in a horizontal porous medium never stops; a prediction that is not substantiated by observation. To help guide the development of new models of multiphase flow in porous media [1], we draw an analogy with the flow of thin films. The flow of thin films over flat surfaces has been the subject of much theoretical, experimental and computational research [2]. Under the lubrication approximation, the classical mathematical model for these flows takes the form of a nonlinear fourth-order PDE, where the fourth-order term models the effect of surface tension [3]. This classical model, however, effectively assumes that the film is perfectly wetting to the substrate and, therefore, does not capture the partial wetting regime. Partial wetting is responsible for stopping the spread of a liquid puddle. Here, we present experiments of (large-volume) liquid spreading over a flat horizontal substrate in the partial wetting regime, and characterize the four spreading regimes that we observe. We extend our previous theoretical work of two-phase flow in a capillary tube [4], and develop a macroscopic phase-field modeling of thin-film flows with partial wetting. Our model naturally accounts for the dynamic contact angle at the contact line, and therefore permits modeling thin-film flows without invoking a precursor film, leading to compactly-supported solutions that reproduce the spreading dynamics and the static equilibrium configuration observed in the experiments. We anticipate that this modeling approach will provide a natural mathematical framework to describe spreading and redistribution of immiscible fluids in porous media. [1] L. Cueto-Felgueroso and R. Juanes, Phys. Rev. Lett. 101, 244504 (2008). [2] D. Bonn et al., Rev. Mod. Phys. 81, 739-805 (2009). [3] H. E. Huppert, Nature 300, 427-429 (1982). [4] L. Cueto-Felgueroso and R. Juanes, Phys. Rev. Lett. 108, 144502 (2012).

Flap-lag-torsional dynamics of helicopter rotor blades in forward flight

NASA Technical Reports Server (NTRS)

Crespodasilva, M. R. M.

1986-01-01

A perturbation/numerical methodology to analyze the flap-lead/lag motion of a centrally hinged spring restrained rotor blade that is valid for both hover and for forward flight was developed. The derivation of the nonlinear differential equations of motion and the analysis of the stability of the steady state response of the blade were conducted entirely in a Symbolics 3670 Machine using MACSYMA to perform all the lengthy symbolic manipulations. It also includes generation of the fortran codes and plots of the results. The Floquet theory was also applied to the differential equations of motion in order to compare results with those obtained from the perturbation analysis. The results obtained from the perturbation methodology and from Floquet theory were found to be very close to each other, which demonstrates the usefullness of the perturbation methodology. Another problem under study consisted in the analysis of the influence of higher order terms in the response and stability of a flexible rotor blade in forward flight using Computerized Symbolic Manipulation and a perturbation technique to bypass the Floquet theory. The derivation of the partial differential equations of motion is presented.

Effects of Regularisation Priors and Anatomical Partial Volume Correction on Dynamic PET Data

NASA Astrophysics Data System (ADS)

Caldeira, Liliana L.; Silva, Nuno da; Scheins, Jürgen J.; Gaens, Michaela E.; Shah, N. Jon

2015-08-01

Dynamic PET provides temporal information about the tracer uptake. However, each PET frame has usually low statistics, resulting in noisy images. Furthermore, PET images suffer from partial volume effects. The goal of this study is to understand the effects of prior regularisation on dynamic PET data and subsequent anatomical partial volume correction. The Median Root Prior (MRP) regularisation method was used in this work during reconstruction. The quantification and noise in image-domain and time-domain (time-activity curves) as well as the impact on parametric images is assessed and compared with Ordinary Poisson Ordered Subset Expectation Maximisation (OP-OSEM) reconstruction with and without Gaussian filter. This study shows the improvement in PET images and time-activity curves (TAC) in terms of noise as well as in the parametric images when using prior regularisation in dynamic PET data. Anatomical partial volume correction improves the TAC and consequently, parametric images. Therefore, the use of MRP with anatomical partial volume correction is of interest for dynamic PET studies.

Bioconvection in Second Grade Nanofluid Flow Containing Nanoparticles and Gyrotactic Microorganisms

NASA Astrophysics Data System (ADS)

Khan, Noor Saeed

2018-04-01

The bioconvection in steady second grade nanofluid thin film flow containing nanoparticles and gyrotactic microorganisms is considered using passively controlled nanofluid model boundary conditions. A real-life system evolves under the flow and various taxis. The study is initially proposed in the context of gyrotactic system, which is used as a key element for the description of complex bioconvection patterns and dynamics in such systems. The governing partial differential equations are transformed into a system of ordinary ones through the similarity variables and solved analytically via homotopy analysis method (HAM). The solution is expressed through graphs and illustrated which show the influences of all the parameters.

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.

Regularization of moving boundaries in a laplacian field by a mixed Dirichlet-Neumann boundary condition: exact results.

PubMed

Meulenbroek, Bernard; Ebert, Ute; Schäfer, Lothar

2005-11-04

The dynamics of ionization fronts that generate a conducting body are in the simplest approximation equivalent to viscous fingering without regularization. Going beyond this approximation, we suggest that ionization fronts can be modeled by a mixed Dirichlet-Neumann boundary condition. We derive exact uniformly propagating solutions of this problem in 2D and construct a single partial differential equation governing small perturbations of these solutions. For some parameter value, this equation can be solved analytically, which shows rigorously that the uniformly propagating solution is linearly convectively stable and that the asymptotic relaxation is universal and exponential in time.

Stability of wave processes in a rotating electrically conducting fluid

NASA Astrophysics Data System (ADS)

Peregudin, S. I.; Peregudina, E. S.; Kholodova, S. E.

2018-05-01

The paper puts forward a mathematical model of dynamics of spatial large-scale motions in a rotating layer of electrically conducting incompressible perfect fluid of variable depth with due account of dissipative effects. The resulting boundary-value problem is reduced to a vector system of partial differential equations for any values of the Reynolds number. Theoretical analysis of the so-obtained analytical solution reveals the effect of the magnetic field diffusion on the stability of the wave mode — namely, with the removed external magnetic field, the diffusion of the magnetic field promotes its damping. Besides, a criterion of stability of a wave mode is obtained.

Spatial model for transmission of mosquito-borne diseases

NASA Astrophysics Data System (ADS)

Kon, Cynthia Mui Lian; Labadin, Jane

2015-05-01

In this paper, a generic model which takes into account spatial heterogeneity for the dynamics of mosquito-borne diseases is proposed. The dissemination of the disease is described by a system of reaction-diffusion partial differential equations. Host human and vector mosquito populations are divided into susceptible and infectious classes. Diffusion is considered to occur in all classes of both populations. Susceptible humans are infected when bitten by infectious mosquitoes. Susceptible mosquitoes bite infectious humans and become infected. The biting rate of mosquitoes is considered to be density dependent on the total human population in different locations. The system is solved numerically and results are shown.

Bioconvection in Second Grade Nanofluid Flow Containing Nanoparticles and Gyrotactic Microorganisms

NASA Astrophysics Data System (ADS)

Khan, Noor Saeed

2018-06-01

The bioconvection in steady second grade nanofluid thin film flow containing nanoparticles and gyrotactic microorganisms is considered using passively controlled nanofluid model boundary conditions. A real-life system evolves under the flow and various taxis. The study is initially proposed in the context of gyrotactic system, which is used as a key element for the description of complex bioconvection patterns and dynamics in such systems. The governing partial differential equations are transformed into a system of ordinary ones through the similarity variables and solved analytically via homotopy analysis method (HAM). The solution is expressed through graphs and illustrated which show the influences of all the parameters.

Numerical Modeling of Nonlinear Thermodynamics in SMA Wires

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

Reynolds, D R; Kloucek, P

We present a mathematical model describing the thermodynamic behavior of shape memory alloy wires, as well as a computational technique to solve the resulting system of partial differential equations. The model consists of conservation equations based on a new Helmholtz free energy potential. The computational technique introduces a viscosity-based continuation method, which allows the model to handle dynamic applications where the temporally local behavior of solutions is desired. Computational experiments document that this combination of modeling and solution techniques appropriately predicts the thermally- and stress-induced martensitic phase transitions, as well as the hysteretic behavior and production of latent heat associatedmore » with such materials.« less

Photodynamic therapy influence on anti-cancer immunity

NASA Astrophysics Data System (ADS)

Isaeva, O. G.; Osipov, V. A.

2010-02-01

The system of partial differential equations describing tumor-immune dynamics with angiogenesis taken into account is presented. For spatially homogeneous case, the steady state analysis of the model is carried out. The effects of single photodynamic impact are numerically simulated. In the case of strong immune response we found that the photodynamic therapy (PDT) gives rise to the substantial shrinkage of tumor size which is accompanied by the increase of IL-2 concentration. On the contrary, the photodynamic stimulation of weak immune response is shown to be insufficient to reduce the tumor. These findings indicate the important role of anti-cancer immune response in the long-term tumor control after PDT.

Photodynamic therapy influence on anti-cancer immunity

NASA Astrophysics Data System (ADS)

Isaeva, O. G.; Osipov, V. A.

2009-10-01

The system of partial differential equations describing tumor-immune dynamics with angiogenesis taken into account is presented. For spatially homogeneous case, the steady state analysis of the model is carried out. The effects of single photodynamic impact are numerically simulated. In the case of strong immune response we found that the photodynamic therapy (PDT) gives rise to the substantial shrinkage of tumor size which is accompanied by the increase of IL-2 concentration. On the contrary, the photodynamic stimulation of weak immune response is shown to be insufficient to reduce the tumor. These findings indicate the important role of anti-cancer immune response in the long-term tumor control after PDT.

Finite elements: Theory and application

NASA Technical Reports Server (NTRS)

Dwoyer, D. L. (Editor); Hussaini, M. Y. (Editor); Voigt, R. G. (Editor)

1988-01-01

Recent advances in FEM techniques and applications are discussed in reviews and reports presented at the ICASE/LaRC workshop held in Hampton, VA in July 1986. Topics addressed include FEM approaches for partial differential equations, mixed FEMs, singular FEMs, FEMs for hyperbolic systems, iterative methods for elliptic finite-element equations on general meshes, mathematical aspects of FEMS for incompressible viscous flows, and gradient weighted moving finite elements in two dimensions. Consideration is given to adaptive flux-corrected FEM transport techniques for CFD, mixed and singular finite elements and the field BEM, p and h-p versions of the FEM, transient analysis methods in computational dynamics, and FEMs for integrated flow/thermal/structural analysis.

A homotopy analysis method for the nonlinear partial differential equations arising in engineering

NASA Astrophysics Data System (ADS)

Hariharan, G.

2017-05-01

In this article, we have established the homotopy analysis method (HAM) for solving a few partial differential equations arising in engineering. This technique provides the solutions in rapid convergence series with computable terms for the problems with high degree of nonlinear terms appearing in the governing differential equations. The convergence analysis of the proposed method is also discussed. Finally, we have given some illustrative examples to demonstrate the validity and applicability of the proposed method.

Mathematical modeling and computational prediction of cancer drug resistance.

PubMed

Sun, Xiaoqiang; Hu, Bin

2017-06-23

Diverse forms of resistance to anticancer drugs can lead to the failure of chemotherapy. Drug resistance is one of the most intractable issues for successfully treating cancer in current clinical practice. Effective clinical approaches that could counter drug resistance by restoring the sensitivity of tumors to the targeted agents are urgently needed. As numerous experimental results on resistance mechanisms have been obtained and a mass of high-throughput data has been accumulated, mathematical modeling and computational predictions using systematic and quantitative approaches have become increasingly important, as they can potentially provide deeper insights into resistance mechanisms, generate novel hypotheses or suggest promising treatment strategies for future testing. In this review, we first briefly summarize the current progress of experimentally revealed resistance mechanisms of targeted therapy, including genetic mechanisms, epigenetic mechanisms, posttranslational mechanisms, cellular mechanisms, microenvironmental mechanisms and pharmacokinetic mechanisms. Subsequently, we list several currently available databases and Web-based tools related to drug sensitivity and resistance. Then, we focus primarily on introducing some state-of-the-art computational methods used in drug resistance studies, including mechanism-based mathematical modeling approaches (e.g. molecular dynamics simulation, kinetic model of molecular networks, ordinary differential equation model of cellular dynamics, stochastic model, partial differential equation model, agent-based model, pharmacokinetic-pharmacodynamic model, etc.) and data-driven prediction methods (e.g. omics data-based conventional screening approach for node biomarkers, static network approach for edge biomarkers and module biomarkers, dynamic network approach for dynamic network biomarkers and dynamic module network biomarkers, etc.). Finally, we discuss several further questions and future directions for the use of computational methods for studying drug resistance, including inferring drug-induced signaling networks, multiscale modeling, drug combinations and precision medicine. © The Author 2017. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

Parent Ratings of ADHD Symptoms: Generalized Partial Credit Model Analysis of Differential Item Functioning across Gender

ERIC Educational Resources Information Center

Gomez, Rapson

2012-01-01

Objective: Generalized partial credit model, which is based on item response theory (IRT), was used to test differential item functioning (DIF) for the "Diagnostic and Statistical Manual of Mental Disorders" (4th ed.), inattention (IA), and hyperactivity/impulsivity (HI) symptoms across boys and girls. Method: To accomplish this, parents completed…

An electric-analog simulation of elliptic partial differential equations using finite element theory

USGS Publications Warehouse

Franke, O.L.; Pinder, G.F.; Patten, E.P.

1982-01-01

Elliptic partial differential equations can be solved using the Galerkin-finite element method to generate the approximating algebraic equations, and an electrical network to solve the resulting matrices. Some element configurations require the use of networks containing negative resistances which, while physically realizable, are more expensive and time-consuming to construct. ?? 1982.

Optimal Variational Asymptotic Method for Nonlinear Fractional Partial Differential Equations.

PubMed

Baranwal, Vipul K; Pandey, Ram K; Singh, Om P

2014-01-01

We propose optimal variational asymptotic method to solve time fractional nonlinear partial differential equations. In the proposed method, an arbitrary number of auxiliary parameters γ 0, γ 1, γ 2,… and auxiliary functions H 0(x), H 1(x), H 2(x),… are introduced in the correction functional of the standard variational iteration method. The optimal values of these parameters are obtained by minimizing the square residual error. To test the method, we apply it to solve two important classes of nonlinear partial differential equations: (1) the fractional advection-diffusion equation with nonlinear source term and (2) the fractional Swift-Hohenberg equation. Only few iterations are required to achieve fairly accurate solutions of both the first and second problems.

Isolation of stress responsive Psb A gene from rice (Oryza sativa l.) using differential display.

PubMed

Tyagi, Aruna; Chandra, Arti

2006-08-01

Differential display (DD) experiments were performed on drought-tolerant rice (Oryza sativa L.) genotype N22 to identify both upregulated and downregulated partial cDNAs with respect to moisture stress. DNA polymorphism was detected between drought-stressed and control leaf tissues on the DD gels. A partial cDNA showing differential expression, with respect to moisture stress was isolated from the gel. Northern blotting analysis was performed using this cDNA as a probe and it was observed that mRNA corresponding to this transcript was accumulated to high level in rice leaves under water deficit stress. At the DNA sequence level, the partial cDNA showed homology with psb A gene encoding for Dl protein.

An extinction/reignition dynamic method for turbulent combustion

NASA Astrophysics Data System (ADS)

Knaus, Robert; Pantano, Carlos

2011-11-01

Quasi-randomly distributed locations of high strain in turbulent combustion can cause a nonpremixed or partially premixed flame to develop local regions of extinction called ``flame holes''. The presence and extent of these holes can increase certain pollutants and reduce the amount of fuel burned. Accurately modeling the dynamics of these interacting regions can improve the accuracy of combustion simulations by effectively incorporating finite-rate chemistry effects. In the proposed method, the flame hole state is characterized by a progress variable that nominally exists on the stoichiometric surface. The evolution of this field is governed by a partial-differential equation embedded in the time-dependent two-manifold of the flame surface. This equation includes advection, propagation, and flame hole formation (flame hole healing or collapse is accounted by propagation naturally). We present a computational algorithm that solves this equation by embedding it in the usual three-dimensional space. A piece-wise parabolic WENO scheme combined with a compression algorithm are used to evolve the flame hole progress variable. A key aspect of the method is the extension of the surface data to the three-dimensional space in an efficient manner. We present results of this method applied to canonical turbulent combusting flows where the flame holes interact and describe their statistics.

Strength measurement of optical fibers by bending

NASA Astrophysics Data System (ADS)

Srubshchik, Leonid S.

1999-01-01

A two-point bending technique has been used not only to measure the breaking stress of optical fiber but also to predict its static and dynamic fatigue. The present theory of this test is based on elastica theory of rod. However, within the limits of elastica theory the tensile and shear stresses cannot be determined. In this paper we study dynamic and static problems for optical fiber in the two- point bending test on the base of geometrically exact theory in which rod can suffer flexure, extension, and shear. We obtain the governing partial differential equations taking into account the fact that the lateral motion of the fiber is restrained by the presence of flat parallel plates. We develop the computational methods for solving the initial and equilibrium free-boundary nonlinear planar problems. We derive the formulas for predicting of the tensile strength from strength in the bending and calculate one example.

Modeling nuclear processes by Simulink

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

Rashid, Nahrul Khair Alang Md, E-mail: nahrul@iium.edu.my

2015-04-29

Modelling and simulation are essential parts in the study of dynamic systems behaviours. In nuclear engineering, modelling and simulation are important to assess the expected results of an experiment before the actual experiment is conducted or in the design of nuclear facilities. In education, modelling can give insight into the dynamic of systems and processes. Most nuclear processes can be described by ordinary or partial differential equations. Efforts expended to solve the equations using analytical or numerical solutions consume time and distract attention from the objectives of modelling itself. This paper presents the use of Simulink, a MATLAB toolbox softwaremore » that is widely used in control engineering, as a modelling platform for the study of nuclear processes including nuclear reactor behaviours. Starting from the describing equations, Simulink models for heat transfer, radionuclide decay process, delayed neutrons effect, reactor point kinetic equations with delayed neutron groups, and the effect of temperature feedback are used as examples.« less

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

NASA Astrophysics Data System (ADS)

Daşdemir, A.

2017-08-01

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

Development of a distributed-parameter mathematical model for simulation of cryogenic wind tunnels

NASA Technical Reports Server (NTRS)

Tripp, J. S.

1983-01-01

A one-dimensional distributed-parameter dynamic model of a cryogenic wind tunnel was developed which accounts for internal and external heat transfer, viscous momentum losses, and slotted-test-section dynamics. Boundary conditions imposed by liquid-nitrogen injection, gas venting, and the tunnel fan were included. A time-dependent numerical solution to the resultant set of partial differential equations was obtained on a CDC CYBER 203 vector-processing digital computer at a usable computational rate. Preliminary computational studies were performed by using parameters of the Langley 0.3-Meter Transonic Cryogenic Tunnel. Studies were performed by using parameters from the National Transonic Facility (NTF). The NTF wind-tunnel model was used in the design of control loops for Mach number, total temperature, and total pressure and for determining interactions between the control loops. It was employed in the application of optimal linear-regulator theory and eigenvalue-placement techniques to develop Mach number control laws.

Quasi-Linear Vacancy Dynamics Modeling and Circuit Analysis of the Bipolar Memristor

PubMed Central

Abraham, Isaac

2014-01-01

The quasi-linear transport equation is investigated for modeling the bipolar memory resistor. The solution accommodates vacancy and circuit level perspectives on memristance. For the first time in literature the component resistors that constitute the contemporary dual variable resistor circuit model are quantified using vacancy parameters and derived from a governing partial differential equation. The model describes known memristor dynamics even as it generates new insight about vacancy migration, bottlenecks to switching speed and elucidates subtle relationships between switching resistance range and device parameters. The model is shown to comply with Chua's generalized equations for the memristor. Independent experimental results are used throughout, to validate the insights obtained from the model. The paper concludes by implementing a memristor-capacitor filter and compares its performance to a reference resistor-capacitor filter to demonstrate that the model is usable for practical circuit analysis. PMID:25390634

Mathematical model of susceptibility, resistance, and resilience in the within-host dynamics between a Plasmodium parasite and the immune system.

PubMed

Yan, Yi; Adam, Brian; Galinski, Mary; C Kissinger, Jessica; Moreno, Alberto; Gutierrez, Juan B

2015-12-01

We developed a coupled age-structured partial differential equation model to capture the disease dynamics during blood-stage malaria. The addition of age structure for the parasite population, with respect to previous models, allows us to better characterize the interaction between the malaria parasite and red blood cells during infection. Here we prove that the system we propose is well-posed and there exist at least two global states. We further demonstrate that the numerical simulation of the system coincides with clinically observed outcomes of primary and secondary malaria infection. The well-posedness of this system guarantees that the behavior of the model remains smooth, bounded, and continuously dependent on initial conditions; calibration with clinical data will constrain domains of parameters and variables to physiological ranges. Copyright © 2015 Elsevier Inc. All rights reserved.

Dynamical patterns and regime shifts in the nonlinear model of soil microorganisms growth

NASA Astrophysics Data System (ADS)

Zaitseva, Maria; Vladimirov, Artem; Winter, Anna-Marie; Vasilyeva, Nadezda

2017-04-01

Dynamical model of soil microorganisms growth and turnover is formulated as a system of nonlinear partial differential equations of reaction-diffusion type. We consider spatial distributions of concentrations of several substrates and microorganisms. Biochemical reactions are modelled by chemical kinetic equations. Transport is modelled by simple linear diffusion for all chemical substances, while for microorganisms we use different transport functions, e.g. some of them can actively move along gradient of substrate concentration, while others cannot move. We solve our model in two dimensions, starting from uniform state with small initial perturbations for various parameters and find parameter range, where small initial perturbations grow and evolve. We search for bifurcation points and critical regime shifts in our model and analyze time-space profile and phase portraits of these solutions approaching critical regime shifts in the system, exploring possibility to detect such shifts in advance. This work is supported by NordForsk, project #81513.

Stationary spiral flow in polytropic stellar models

PubMed Central

Pekeris, C. L.

1980-01-01

It is shown that, in addition to the static Emden solution, a self-gravitating polytropic gas has a dynamic option in which there is stationary flow along spiral trajectories wound around the surfaces of concentric tori. The motion is obtained as a solution of a partial differential equation which is satisfied by the meridional stream function, coupled with Poisson's equation and a Bernoulli-type equation for the pressure (density). The pressure is affected by the whole of the Bernoulli term rather than by the centrifugal part only, which acts for a rotating model, and it may be reduced down to zero at the center. The spiral type of flow is illustrated for an incompressible fluid (n = 0), for which an exact solution is obtained. The features of the dynamic constant-density model are discussed as a basis for future comparison with the solution for compressible models. PMID:16592825

Lyapunov modes in extended systems.

PubMed

Yang, Hong-Liu; Radons, Günter

2009-08-28

Hydrodynamic Lyapunov modes, which have recently been observed in many extended systems with translational symmetry, such as hard sphere systems, dynamic XY models or Lennard-Jones fluids, are nowadays regarded as fundamental objects connecting nonlinear dynamics and statistical physics. We review here our recent results on Lyapunov modes in extended system. The solution to one of the puzzles, the appearance of good and 'vague' modes, is presented for the model system of coupled map lattices. The structural properties of these modes are related to the phase space geometry, especially the angles between Oseledec subspaces, and to fluctuations of local Lyapunov exponents. In this context, we report also on the possible appearance of branches splitting in the Lyapunov spectra of diatomic systems, similar to acoustic and optical branches for phonons. The final part is devoted to the hyperbolicity of partial differential equations and the effective degrees of freedom of such infinite-dimensional systems.

Recent advances in mathematical criminology. Comment on "Statistical physics of crime: A review" by M.R. D'Orsogna and M. Perc

NASA Astrophysics Data System (ADS)

Rodríguez, Nancy

2015-03-01

The use of mathematical tools has long proved to be useful in gaining understanding of complex systems in physics [1]. Recently, many researchers have realized that there is an analogy between emerging phenomena in complex social systems and complex physical or biological systems [4,5,12]. This realization has particularly benefited the modeling and understanding of crime, a ubiquitous phenomena that is far from being understood. In fact, when one is interested in the bulk behavior of patterns that emerge from small and seemingly unrelated interactions as well as decisions that occur at the individual level, the mathematical tools that have been developed in statistical physics, game theory, network theory, dynamical systems, and partial differential equations can be useful in shedding light into the dynamics of these patterns [2-4,6,12].

Quasi-linear vacancy dynamics modeling and circuit analysis of the bipolar memristor.

PubMed

Abraham, Isaac

2014-01-01

The quasi-linear transport equation is investigated for modeling the bipolar memory resistor. The solution accommodates vacancy and circuit level perspectives on memristance. For the first time in literature the component resistors that constitute the contemporary dual variable resistor circuit model are quantified using vacancy parameters and derived from a governing partial differential equation. The model describes known memristor dynamics even as it generates new insight about vacancy migration, bottlenecks to switching speed and elucidates subtle relationships between switching resistance range and device parameters. The model is shown to comply with Chua's generalized equations for the memristor. Independent experimental results are used throughout, to validate the insights obtained from the model. The paper concludes by implementing a memristor-capacitor filter and compares its performance to a reference resistor-capacitor filter to demonstrate that the model is usable for practical circuit analysis.

A New Model for the Estimation of Cell Proliferation Dynamics Using CFSE Data

PubMed Central

Banks, H.T.; Sutton, Karyn L.; Thompson, W. Clayton; Bocharov, Gennady; Doumic, Marie; Schenkel, Tim; Argilaguet, Jordi; Giest, Sandra; Peligero, Cristina; Meyerhans, Andreas

2011-01-01

CFSE analysis of a proliferating cell population is a popular tool for the study of cell division and division-linked changes in cell behavior. Recently [13, 43, 45], a partial differential equation (PDE) model to describe lymphocyte dynamics in a CFSE proliferation assay was proposed. We present a significant revision of this model which improves the physiological understanding of several parameters. Namely, the parameter γ used previously as a heuristic explanation for the dilution of CFSE dye by cell division is replaced with a more physical component, cellular autofluorescence. The rate at which label decays is also quantified using a Gompertz decay process. We then demonstrate a revised method of fitting the model to the commonly used histogram representation of the data. It is shown that these improvements result in a model with a strong physiological basis which is fully capable of replicating the behavior observed in the data. PMID:21889510

[Development of New Mathematical Methodology in Air Traffic Control for the Analysis of Hybrid Systems

NASA Technical Reports Server (NTRS)

Hermann, Robert

1997-01-01

The aim of this research is to develop new mathematical methodology for the analysis of hybrid systems of the type involved in Air Traffic Control (ATC) problems. Two directions of investigation were initiated. The first used the methodology of nonlinear generalized functions, whose mathematical foundations were initiated by Colombeau and developed further by Oberguggenberger; it has been extended to apply to ordinary differential. Systems of the type encountered in control in joint work with the PI and M. Oberguggenberger. This involved a 'mixture' of 'continuous' and 'discrete' methodology. ATC clearly involves mixtures of two sorts of mathematical problems: (1) The 'continuous' dynamics of a standard control type described by ordinary differential equations (ODE) of the form: {dx/dt = f(x, u)} and (2) the discrete lattice dynamics involved of cellular automata. Most of the CA literature involves a discretization of a partial differential equation system of the type encountered in physics problems (e.g. fluid and gas problems). Both of these directions requires much thinking and new development of mathematical fundamentals before they may be utilized in the ATC work. Rather than consider CA as 'discretization' of PDE systems, I believe that the ATC applications will require a completely different and new mathematical methodology, a sort of discrete analogue of jet bundles and/or the sheaf-theoretic techniques to topologists. Here too, I have begun work on virtually 'virgin' mathematical ground (at least from an 'applied' point of view) which will require considerable preliminary work.

Dynamic curvature sensing employing ionic-polymer-metal composite sensors

NASA Astrophysics Data System (ADS)

Bahramzadeh, Yousef; Shahinpoor, Mohsen

2011-09-01

A dynamic curvature sensor is presented based on ionic-polymer-metal composite (IPMC) for curvature monitoring of deployable/inflatable dynamic space structures. Monitoring the curvature variation is of high importance in various engineering structures including shape monitoring of deployable/inflatable space structures in which the structural boundaries undergo a dynamic deployment process. The high sensitivity of IPMCs to the applied deformations as well as its flexibility make IPMCs a promising candidate for sensing of dynamic curvature changes. Herein, we explore the dynamic response of an IPMC sensor strip with respect to controlled curvature deformations subjected to different forms of input functions. Using a specially designed experimental setup, the voltage recovery effect, phase delay, and rate dependency of the output voltage signal of an IPMC curvature sensor are analyzed. Experimental results show that the IPMC sensor maintains the linearity, sensitivity, and repeatability required for curvature sensing. Besides, in order to describe the dynamic phenomena such as the rate dependency of the IPMC sensor, a chemo-electro-mechanical model based on the Poisson-Nernst-Planck (PNP) equation for the kinetics of ion diffusion is presented. By solving the governing partial differential equations the frequency response of the IPMC sensor is derived. The physical model is able to describe the dynamic properties of the IPMC sensor and the dependency of the signal on rate of excitations.

Generalized Lie symmetry approach for fractional order systems of differential equations. III

NASA Astrophysics Data System (ADS)

Singla, Komal; Gupta, R. K.

2017-06-01

The generalized Lie symmetry technique is proposed for the derivation of point symmetries for systems of fractional differential equations with an arbitrary number of independent as well as dependent variables. The efficiency of the method is illustrated by its application to three higher dimensional nonlinear systems of fractional order partial differential equations consisting of the (2 + 1)-dimensional asymmetric Nizhnik-Novikov-Veselov system, (3 + 1)-dimensional Burgers system, and (3 + 1)-dimensional Navier-Stokes equations. With the help of derived Lie point symmetries, the corresponding invariant solutions transform each of the considered systems into a system of lower-dimensional fractional partial differential equations.

Solution of some types of differential equations: operational calculus and inverse differential operators.

PubMed

Zhukovsky, K

2014-01-01

We present a general method of operational nature to analyze and obtain solutions for a variety of equations of mathematical physics and related mathematical problems. We construct inverse differential operators and produce operational identities, involving inverse derivatives and families of generalised orthogonal polynomials, such as Hermite and Laguerre polynomial families. We develop the methodology of inverse and exponential operators, employing them for the study of partial differential equations. Advantages of the operational technique, combined with the use of integral transforms, generating functions with exponentials and their integrals, for solving a wide class of partial derivative equations, related to heat, wave, and transport problems, are demonstrated.

Concatenons as the solutions for non-linear partial differential equations

NASA Astrophysics Data System (ADS)

Kudryashov, N. A.; Volkov, A. K.

2017-07-01

New class of solutions for nonlinear partial differential equations is introduced. We call them the concaten solutions. As an example we consider equations for the description of wave processes in the Fermi-Pasta-Ulam mass chain and construct the concatenon solutions for these equation. Stability of the concatenon-type solutions is investigated numerically. Interaction between the concatenon and solitons is discussed.

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.

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

NASA Astrophysics Data System (ADS)

Ding, Xiao-Li; Nieto, Juan J.

2017-11-01

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

The SMS4 cryptographic system design based on dynamic partial self-reconfiguration technology

NASA Astrophysics Data System (ADS)

Wang, Jianxin; Gao, Xianwei; Li, Xiuying; Sui, Meili

2013-03-01

This paper describes SMS4 algorithm by using dynamic partial self-reconfiguration. The design is implemented on Xilinx VirtexII-Pro XC2VP30 FPGA devices. The partial self-reconfiguration encryption/decryption module data throughput is up to 50Mb/s, key expansion and encryption/decryption modules use 1606 and 1570 slices respectively, and the resource utilization ratio of the key expansion by using partial self-reconfiguration technology is less 32.03% and slices are less 757 than the non-reconfiguration technology. SMS4 implementation gets a good balance between high performance and low complexity in area. The theoretical and practical research of dynamic partial self-reconfiguration has a broad space for development and application prospect.

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.

Partial slip effect in the flow of MHD micropolar nanofluid flow due to a rotating disk - A numerical approach

NASA Astrophysics Data System (ADS)

Ramzan, Muhammad; Chung, Jae Dong; Ullah, Naeem

The aim of present exploration is to study the flow of micropolar nanofluid due to a rotating disk in the presence of magnetic field and partial slip condition. The governing coupled partial differential equations are reduced to nonlinear ordinary differential equations using appropriate transformations. The differential equations are solved numerically by using Maple dsolve command with option numeric which utilize Runge-Kutta fourth-fifth order Fehlberg technique. A comparison to previous study is also added to validate the present results. Moreover, behavior of different parameters on velocity, microrotation, temperature and concentration of nanofluid are presented via graphs and tables. It is noted that the slip effect and magnetic field decay the velocity and microrotation or spin component.

The Uniform Convergence of Eigenfunction Expansions of Schrödinger Operator in the Nikolskii Classes {H}_{p}^{\\alpha }(\\bar{\\Omega })

NASA Astrophysics Data System (ADS)

Jamaludin, N. A.; Ahmedov, A.

2017-09-01

Many boundary value problems in the theory of partial differential equations can be solved by separation methods of partial differential equations. When Schrödinger operator is considered then the influence of the singularity of potential on the solution of the partial differential equation is interest of researchers. In this paper the problems of the uniform convergence of the eigenfunction expansions of the functions from corresponding to the Schrödinger operator with the potential from classes of Sobolev are investigated. The spectral function corresponding to the Schrödinger operator is estimated in closed domain. The isomorphism of the Nikolskii classes is applied to prove uniform convergence of eigenfunction expansions of Schrödinger operator in closed domain.

Low-Degree Partial Melting Experiments of CR and H Chondrite Compositions: Implications for Asteroidal Magmatism Recorded in GRA 06128 and GRA 06129 T

NASA Technical Reports Server (NTRS)

Usui, T.; Jones, John H.; Mittlefehldt, D. W.

2010-01-01

Studies of differentiated meteorites have revealed a diversity of differentiation processes on their parental asteroids; these differentiation mechanisms range from whole-scale melting to partial melting without the core formation [e.g., 1]. Recently discovered paired achondrites GRA 06128 and GRA 06129 (hereafter referred to as GRA) represent unique asteroidal magmatic processes. These meteorites are characterized by high abundances of sodic plagioclase and alkali-rich whole-rock compositions, implying that they could originate from a low-degree partial melt from a volatile-rich oxidized asteroid [e.g., 2, 3, 4]. These conditions are consistent with the high abundances of highly siderophile elements, suggesting that their parent asteroid did not segregate a metallic core [2]. In this study, we test the hypothesis that low-degree partial melts of chondritic precursors under oxidizing conditions can explain the whole-rock and mineral chemistry of GRA based on melting experiments of synthesized CR- and H-chondrite compositions.

The application of Legendre-tau approximation to parameter identification for delay and partial differential equations

NASA Technical Reports Server (NTRS)

Ito, K.

1983-01-01

Approximation schemes based on Legendre-tau approximation are developed for application to parameter identification problem for delay and partial differential equations. The tau method is based on representing the approximate solution as a truncated series of orthonormal functions. The characteristic feature of the Legendre-tau approach is that when the solution to a problem is infinitely differentiable, the rate of convergence is faster than any finite power of 1/N; higher accuracy is thus achieved, making the approach suitable for small N.

Temporal expression profiles indicate a primary function for microRNA during the peak of DNA replication after rat partial hepatectomy.

PubMed

Raschzok, Nathanael; Werner, Wiebke; Sallmon, Hannes; Billecke, Nils; Dame, Christof; Neuhaus, Peter; Sauer, Igor M

2011-06-01

The liver has the unique capacity to regenerate after surgical resection. However, the regulation of liver regeneration is not completely understood. Recent reports indicate an essential role for small noncoding microRNAs (miRNAs) in the regulation of hepatic development, carcinogenesis, and early regeneration. We hypothesized that miRNAs are critically involved in all phases of liver regeneration after partial hepatectomy. We performed miRNA microarray analyses after 70% partial hepatectomy in rats under isoflurane anesthesia at different time points (0 h to 5 days) and after sham laparotomy. Putative targets of differentially expressed miRNAs were determined using a bioinformatic approach. Two-dimensional (2D)-PAGE proteomic analyses and protein identification were performed on specimens at 0 and 24 h after resection. The temporal dynamics of liver regeneration were characterized by 5-bromo- 2-deoxyuridine, proliferating cell nuclear antigen, IL-6, and hepatocyte growth factor. We demonstrate that miRNA expression patterns changed during liver regeneration and that these changes were most evident during the peak of DNA replication at 24 h after resection. Expression of 13 miRNAs was significantly reduced 12-48 h after resection (>25% change), out of which downreguation was confirmed in isolated hepatocytes for 6 miRNAs at 24 h, whereas three miRNAs were significantly upregulated. Proteomic analysis revealed 65 upregulated proteins; among them, 23 represent putative targets of the differentially expressed miRNAs. We provide a temporal miRNA expression and proteomic dataset of the regenerating rat liver, which indicates a primary function for miRNA during the peak of DNA replication. These data will assist further functional studies on the role of miRNAs during liver regeneration.

Describing the geographic spread of dengue disease by traveling waves.

PubMed

Maidana, Norberto Aníbal; Yang, Hyun Mo

2008-09-01

Dengue is a human disease transmitted by the mosquito Aedes aegypti. For this reason geographical regions infested by this mosquito species are under the risk of dengue outbreaks. In this work, we propose a mathematical model to study the spatial dissemination of dengue using a system of partial differential reaction-diffusion equations. With respect to the human and mosquito populations, we take into account their respective subclasses of infected and uninfected individuals. The dynamics of the mosquito population considers only two subpopulations: the winged form (mature female mosquitoes), and an aquatic population (comprising eggs, larvae and pupae). We disregard the long-distance movement by transportation facilities, for which reason the diffusion is considered restricted only to the winged form. The human population is considered homogeneously distributed in space, in order to describe localized dengue dissemination during a short period of epidemics. The cross-infection is modeled by the law of mass action. A threshold value as a function of the model's parameters is obtained, which determines the rate of dengue dissemination and the risk of dengue outbreaks. Assuming that an area was previously colonized by the mosquitoes, the rate of disease dissemination is determined as a function of the model's parameters. This rate of dissemination of dengue disease is determined by applying the traveling wave solutions to the corresponding system of partial differential equations.

Partial differential equation methods for stochastic dynamic optimization: an application to wind power generation with energy storage.

PubMed

Johnson, Paul; Howell, Sydney; Duck, Peter

2017-08-13

A mixed financial/physical partial differential equation (PDE) can optimize the joint earnings of a single wind power generator (WPG) and a generic energy storage device (ESD). Physically, the PDE includes constraints on the ESD's capacity, efficiency and maximum speeds of charge and discharge. There is a mean-reverting daily stochastic cycle for WPG power output. Physically, energy can only be produced or delivered at finite rates. All suppliers must commit hourly to a finite rate of delivery C , which is a continuous control variable that is changed hourly. Financially, we assume heavy 'system balancing' penalties in continuous time, for deviations of output rate from the commitment C Also, the electricity spot price follows a mean-reverting stochastic cycle with a strong evening peak, when system balancing penalties also peak. Hence the economic goal of the WPG plus ESD, at each decision point, is to maximize expected net present value (NPV) of all earnings (arbitrage) minus the NPV of all expected system balancing penalties, along all financially/physically feasible future paths through state space. Given the capital costs for the various combinations of the physical parameters, the design and operating rules for a WPG plus ESD in a finite market may be jointly optimizable.This article is part of the themed issue 'Energy management: flexibility, risk and optimization'. © 2017 The Author(s).

Trigonometric Integrals via Partial Fractions

ERIC Educational Resources Information Center

Chen, H.; Fulford, M.

2005-01-01

Parametric differentiation is used to derive the partial fractions decompositions of certain rational functions. Those decompositions enable us to integrate some new combinations of trigonometric functions.

Exp-function method for solving fractional partial differential equations.

PubMed

Zheng, Bin

2013-01-01

We extend the Exp-function method to fractional partial differential equations in the sense of modified Riemann-Liouville derivative based on nonlinear fractional complex transformation. For illustrating the validity of this method, we apply it to the space-time fractional Fokas equation and the nonlinear fractional Sharma-Tasso-Olver (STO) equation. As a result, some new exact solutions for them are successfully established.

A transmission-line model of back-cavity dynamics for in-plane pressure-differential microphones.

PubMed

Kim, Donghwan; Kuntzman, Michael L; Hall, Neal A

2014-11-01

Pressure-differential microphones inspired by the hearing mechanism of a special parasitoid fly have been described previously. The designs employ a beam structure that rotates about two pivots over an enclosed back volume. The back volume is only partially enclosed due to open slits around the perimeter of the beam. The open slits enable incoming sound waves to affect the pressure profile in the microphone's back volume. The goal of this work is to study the net moment applied to pressure-differential microphones by an incoming sound wave, which in-turn requires modeling the acoustic pressure distribution within the back volume. A lumped-element distributed transmission-line model of the back volume is introduced for this purpose. It is discovered that the net applied moment follows a low-pass filter behavior such that, at frequencies below a corner frequency depending on geometrical parameters of the design, the applied moment is unaffected by the open slits. This is in contrast to the high-pass filter behavior introduced by barometric pressure vents in conventional omnidirectional microphones. The model accurately predicts observed curvature in the frequency response of a prototype pressure-differential microphone 2 mm × 1 mm × 0.5 mm in size and employing piezoelectric readout.

Queues on a Dynamically Evolving Graph

NASA Astrophysics Data System (ADS)

Mandjes, Michel; Starreveld, Nicos J.; Bekker, René

2018-04-01

This paper considers a population process on a dynamically evolving graph, which can be alternatively interpreted as a queueing network. The queues are of infinite-server type, entailing that at each node all customers present are served in parallel. The links that connect the queues have the special feature that they are unreliable, in the sense that their status alternates between `up' and `down'. If a link between two nodes is down, with a fixed probability each of the clients attempting to use that link is lost; otherwise the client remains at the origin node and reattempts using the link (and jumps to the destination node when it finds the link restored). For these networks we present the following results: (a) a system of coupled partial differential equations that describes the joint probability generating function corresponding to the queues' time-dependent behavior (and a system of ordinary differential equations for its stationary counterpart), (b) an algorithm to evaluate the (time-dependent and stationary) moments, and procedures to compute user-perceived performance measures which facilitate the quantification of the impact of the links' outages, (c) a diffusion limit for the joint queue length process. We include explicit results for a series relevant special cases, such as tandem networks and symmetric fully connected networks.

Transient response of an active nonlinear sandwich piezolaminated plate

NASA Astrophysics Data System (ADS)

Oveisi, Atta; Nestorović, Tamara

2017-04-01

In this paper, the dynamic modelling and active vibration control of a piezolaminated plate with geometrical nonlinearities are investigated using a semi-analytical approach. For active vibration control purposes, the core orthotropic elastic layer is assumed to be perfectly bonded with two piezo-layers on its top and bottom surfaces which act as sensor and actuator, respectively. In the modelling procedure, the piezo-layers are assumed to be connected via a proportional derivative (PD) feedback control law. Hamilton's principle is employed to acquire the strong form of the dynamic equation in terms of additional higher order strain expressions by means of von Karman strain-displacement correlation. The obtained nonlinear partial differential equation (NPDE) is converted to a system of nonlinear ordinary differential equations (NODEs) by engaging Galerkin method and using the orthogonality of shape functions for the simply supported boundary conditions. Then, the resulting system of NODEs is solved numerically by employing the built-in Mathematica function, "NDSolve". Next, the vibration attenuation performance is evaluated and sensitivity of the closed-loop system is investigated for several control parameters and the external disturbance parameters. The proposed solution in open loop configuration is validated by finite element (FE) package ABAQUS both in the spatial domain and for the time-/frequency-dependent response.

Spatial orientation perception and reflexive eye movements--a perspective, an overview, and some clinical implications

NASA Technical Reports Server (NTRS)

Guedry, F. E.; Paloski, W. F. (Principal Investigator)

1996-01-01

When head motion includes a linear velocity component, eye velocity required to track an earth-fixed target depends upon: a) angular and linear head velocity, b) target distance, and c) direction of gaze relative to the motion trajectory. Recent research indicates that eye movements (LVOR), presumably otolith-mediated, partially compensate for linear velocity in small head excursions on small devices. Canal-mediated eye velocity (AVOR), otolith-mediated eye velocity (LVOR), and Ocular Torsion (OT) can be measured, one by one, on small devices. However, response dynamics that depend upon the ratio of linear to angular velocity in the motion trajectory and on subject orientation relative to the trajectory are present in a centrifuge paradigm. With this paradigm, two 3-min runs yields measures of: LVOR differentially modulated by different subject orientations in the two runs; OT dynamics in four conditions; two directions of "steady-state" OT, and two directions of AVOR. Efficient assessment of the dynamics (and of the underlying central integrative processes) may require a centrifuge radius of 1.0 meters or more. Clinical assessment of the spatial orientation system should include evaluation of central integrative processes that determine the dynamics of these responses.

Convection-diffusion effects in marathon race dynamics

NASA Astrophysics Data System (ADS)

Rodriguez, E.; Espinosa-Paredes, G.; Alvarez-Ramirez, J.

2014-01-01

In the face of the recent terrorist attack event on the 2013 Boston Marathon, the increasing participation of recreational runners in large marathon races has imposed important logistical and safety issues for organizers and city authorities. An accurate understanding of the dynamics of the marathon pack along the race course can provide important insights for improving safety and performance of these events. On the other hand, marathon races can be seen as a model of pedestrian movement under confined conditions. This work used data of the 2011 Chicago Marathon event for modeling the dynamics of the marathon pack from the corral zone to the finish line. By considering the marathon pack as a set of particles moving along the race course, the dynamics are modeled as a convection-diffusion partial differential equation with position-dependent mean velocity and diffusion coefficient. A least-squares problem is posed and solved with optimization techniques for fitting field data from the 2011 Chicago Marathon. It was obtained that the mean pack velocity decreases while the diffusion coefficient increases with distance. This means that the dispersion rate of the initially compact marathon pack increases as the marathon race evolves along the race course.

Pre-impact fall detection system using dynamic threshold and 3D bounding box

NASA Astrophysics Data System (ADS)

Otanasap, Nuth; Boonbrahm, Poonpong

2017-02-01

Fall prevention and detection system have to subjugate many challenges in order to develop an efficient those system. Some of the difficult problems are obtrusion, occlusion and overlay in vision based system. Other associated issues are privacy, cost, noise, computation complexity and definition of threshold values. Estimating human motion using vision based usually involves with partial overlay, caused either by direction of view point between objects or body parts and camera, and these issues have to be taken into consideration. This paper proposes the use of dynamic threshold based and bounding box posture analysis method with multiple Kinect cameras setting for human posture analysis and fall detection. The proposed work only uses two Kinect cameras for acquiring distributed values and differentiating activities between normal and falls. If the peak value of head velocity is greater than the dynamic threshold value, bounding box posture analysis will be used to confirm fall occurrence. Furthermore, information captured by multiple Kinect placed in right angle will address the skeleton overlay problem due to single Kinect. This work contributes on the fusion of multiple Kinect based skeletons, based on dynamic threshold and bounding box posture analysis which is the only research work reported so far.

Noise, chaos, and (ɛ, τ)-entropy per unit time

NASA Astrophysics Data System (ADS)

Gaspard, Pierre; Wang, Xiao-Jing

1993-12-01

The degree of dynamical randomness of different time processes is characterized in terms of the (ε, τ)-entropy per unit time. The (ε, τ)-entropy is the amount of information generated per unit time, at different scales τ of time and ε of the observables. This quantity generalizes the Kolmogorov-Sinai entropy per unit time from deterministic chaotic processes, to stochastic processes such as fluctuations in mesoscopic physico-chemical phenomena or strong turbulence in macroscopic spacetime dynamics. The random processes that are characterized include chaotic systems, Bernoulli and Markov chains, Poisson and birth-and-death processes, Ornstein-Uhlenbeck and Yaglom noises, fractional Brownian motions, different regimes of hydrodynamical turbulence, and the Lorentz-Boltzmann process of nonequilibrium statistical mechanics. We also extend the (ε, τ)-entropy to spacetime processes like cellular automata, Conway's game of life, lattice gas automata, coupled maps, spacetime chaos in partial differential equations, as well as the ideal, the Lorentz, and the hard sphere gases. Through these examples it is demonstrated that the (ε, τ)-entropy provides a unified quantitative measure of dynamical randomness to both chaos and noises, and a method to detect transitions between dynamical states of different degrees of randomness as a parameter of the system is varied.

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.

Effect of evaporative surface cooling on thermographic assessment of burn depth

NASA Technical Reports Server (NTRS)

Anselmo, V. J.; Zawacki, B. E.

1977-01-01

Differences in surface temperature between evaporating and nonevaporating, partial- and full-thickness burn injuries were studied in 20 male, white guinea pigs. Evaporative cooling can disguise the temperature differential of the partial-thickness injury and lead to a false full-thickness diagnosis. A full-thickness burn with blister intact may retain enough heat to result in a false partial-thickness diagnosis. By the fourth postburn day, formation of a dry eschar may allow a surface temperature measurement without the complication of differential evaporation. For earlier use of thermographic information, evaporation effects must be accounted for or eliminated.

Solving Differential Equations in R: Package deSolve

EPA Science Inventory

In this paper we present the R package deSolve to solve initial value problems (IVP) written as ordinary differential equations (ODE), differential algebraic equations (DAE) of index 0 or 1 and partial differential equations (PDE), the latter solved using the method of lines appr...

A higher order numerical method for time fractional partial differential equations with nonsmooth data

NASA Astrophysics Data System (ADS)

Xing, Yanyuan; Yan, Yubin

2018-03-01

Gao et al. [11] (2014) introduced a numerical scheme to approximate the Caputo fractional derivative with the convergence rate O (k 3 - α), 0 < α < 1 by directly approximating the integer-order derivative with some finite difference quotients in the definition of the Caputo fractional derivative, see also Lv and Xu [20] (2016), where k is the time step size. Under the assumption that the solution of the time fractional partial differential equation is sufficiently smooth, Lv and Xu [20] (2016) proved by using energy method that the corresponding numerical method for solving time fractional partial differential equation has the convergence rate O (k 3 - α), 0 < α < 1 uniformly with respect to the time variable t. However, in general the solution of the time fractional partial differential equation has low regularity and in this case the numerical method fails to have the convergence rate O (k 3 - α), 0 < α < 1 uniformly with respect to the time variable t. In this paper, we first obtain a similar approximation scheme to the Riemann-Liouville fractional derivative with the convergence rate O (k 3 - α), 0 < α < 1 as in Gao et al. [11] (2014) by approximating the Hadamard finite-part integral with the piecewise quadratic interpolation polynomials. Based on this scheme, we introduce a time discretization scheme to approximate the time fractional partial differential equation and show by using Laplace transform methods that the time discretization scheme has the convergence rate O (k 3 - α), 0 < α < 1 for any fixed tn > 0 for smooth and nonsmooth data in both homogeneous and inhomogeneous cases. Numerical examples are given to show that the theoretical results are consistent with the numerical results.

Taguchi method for partial differential equations with application in tumor growth.

PubMed

Ilea, M; Turnea, M; Rotariu, M; Arotăriţei, D; Popescu, Marilena

2014-01-01

The growth of tumors is a highly complex process. To describe this process, mathematical models are needed. A variety of partial differential mathematical models for tumor growth have been developed and studied. Most of those models are based on the reaction-diffusion equations and mass conservation law. A variety of modeling strategies have been developed, each focusing on tumor growth. Systems of time-dependent partial differential equations occur in many branches of applied mathematics. The vast majority of mathematical models in tumor growth are formulated in terms of partial differential equations. We propose a mathematical model for the interactions between these three cancer cell populations. The Taguchi methods are widely used by quality engineering scientists to compare the effects of multiple variables, together with their interactions, with a simple and manageable experimental design. In Taguchi's design of experiments, variation is more interesting to study than the average. First, Taguchi methods are utilized to search for the significant factors and the optimal level combination of parameters. Except the three parameters levels, other factors levels other factors levels would not be considered. Second, cutting parameters namely, cutting speed, depth of cut, and feed rate are designed using the Taguchi method. Finally, the adequacy of the developed mathematical model is proved by ANOVA. According to the results of ANOVA, since the percentage contribution of the combined error is as small. Many mathematical models can be quantitatively characterized by partial differential equations. The use of MATLAB and Taguchi method in this article illustrates the important role of informatics in research in mathematical modeling. The study of tumor growth cells is an exciting and important topic in cancer research and will profit considerably from theoretical input. Interpret these results to be a permanent collaboration between math's and medical oncologists.

Modeling Cancer Cell Growth Dynamics In vitro in Response to Antimitotic Drug Treatment

PubMed Central

Lorz, Alexander; Botesteanu, Dana-Adriana; Levy, Doron

2017-01-01

Investigating the role of intrinsic cell heterogeneity emerging from variations in cell-cycle parameters and apoptosis is a crucial step toward better informing drug administration. Antimitotic agents, widely used in chemotherapy, target exclusively proliferative cells and commonly induce a prolonged mitotic arrest followed by cell death via apoptosis. In this paper, we developed a physiologically motivated mathematical framework for describing cancer cell growth dynamics that incorporates the intrinsic heterogeneity in the time individual cells spend in the cell-cycle and apoptosis process. More precisely, our model comprises two age-structured partial differential equations for the proliferative and apoptotic cell compartments and one ordinary differential equation for the quiescent compartment. To reflect the intrinsic cell heterogeneity that governs the growth dynamics, proliferative and apoptotic cells are structured in “age,” i.e., the amount of time remaining to be spent in each respective compartment. In our model, we considered an antimitotic drug whose effect on the cellular dynamics is to induce mitotic arrest, extending the average cell-cycle length. The prolonged mitotic arrest induced by the drug can trigger apoptosis if the time a cell will spend in the cell cycle is greater than the mitotic arrest threshold. We studied the drug’s effect on the long-term cancer cell growth dynamics using different durations of prolonged mitotic arrest induced by the drug. Our numerical simulations suggest that at confluence and in the absence of the drug, quiescence is the long-term asymptotic behavior emerging from the cancer cell growth dynamics. This pattern is maintained in the presence of small increases in the average cell-cycle length. However, intermediate increases in cell-cycle length markedly decrease the total number of cells and can drive the cancer population to extinction. Intriguingly, a large “switch-on/switch-off” increase in the average cell-cycle length maintains an active cell population in the long term, with oscillating numbers of proliferative cells and a relatively constant quiescent cell number. PMID:28913178

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.

Variational principles for stochastic fluid dynamics

PubMed Central

Holm, Darryl D.

2015-01-01

This paper derives stochastic partial differential equations (SPDEs) for fluid dynamics from a stochastic variational principle (SVP). The paper proceeds by taking variations in the SVP to derive stochastic Stratonovich fluid equations; writing their Itô representation; and then investigating the properties of these stochastic fluid models in comparison with each other, and with the corresponding deterministic fluid models. The circulation properties of the stochastic Stratonovich fluid equations are found to closely mimic those of the deterministic ideal fluid models. As with deterministic ideal flows, motion along the stochastic Stratonovich paths also preserves the helicity of the vortex field lines in incompressible stochastic flows. However, these Stratonovich properties are not apparent in the equivalent Itô representation, because they are disguised by the quadratic covariation drift term arising in the Stratonovich to Itô transformation. This term is a geometric generalization of the quadratic covariation drift term already found for scalar densities in Stratonovich's famous 1966 paper. The paper also derives motion equations for two examples of stochastic geophysical fluid dynamics; namely, the Euler–Boussinesq and quasi-geostropic approximations. PMID:27547083

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

An Evaluation of the Scattering Law for Light and Heavy Water in ENDF-6 Format, Based on Experimental Data and Molecular Dynamics

NASA Astrophysics Data System (ADS)

Márquez Damián, J. I.; Granada, J. R.; Malaspina, D. C.

2014-04-01

In this work we present an evaluation in ENDF-6 format of the scattering law for light and heavy water computed using the LEAPR module of NJOY99. The models used in this evaluation are based on experimental data on light water dynamics measured by Novikov, partial structure factors obtained by Soper, and molecular dynamics calculations performed with GROMACS using a reparameterized version of the flexible SPC model by Toukan and Rahman. The models use the Egelstaff-Schofield diffusion equation for translational motion, and a continuous spectrum calculated from the velocity autocorrelation function computed with GROMACS. The scattering law for H in H2O is computed using the incoherent approximation, and the scattering law D and O in D2O are computed using the Sköld approximation for coherent scattering. The calculations show significant improvement over ENDF/B-VI and ENDF/B-VII when compared with measurements of the total cross section, differential scattering experiments and quasi-elastic neutron scattering experiments (QENS).

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

Stoynov, Y.; Dineva, P.

The stress, magnetic and electric field analysis of multifunctional composites, weakened by impermeable cracks, is of fundamental importance for their structural integrity and reliable service performance. The aim is to study dynamic behavior of a plane of functionally graded magnetoelectroelastic composite with more than one crack. The coupled material properties vary exponentially in an arbitrary direction. The plane is subjected to anti-plane mechanical and in-plane electric and magnetic load. The boundary value problem described by the partial differential equations with variable coefficients is reduced to a non-hypersingular traction boundary integral equation based on the appropriate functional transform and frequency-dependent fundamentalmore » solution derived in a closed form by Radon transform. Software code based on the boundary integral equation method (BIEM) is developed, validated and inserted in numerical simulations. The obtained results show the sensitivity of the dynamic stress, magnetic and electric field concentration in the cracked plane to the type and characteristics of the dynamic load, to the location and cracks disposition, to the wave-crack-crack interactions and to the magnitude and direction of the material gradient.« less

Fast methods to numerically integrate the Reynolds equation for gas fluid films

NASA Technical Reports Server (NTRS)

Dimofte, Florin

1992-01-01

The alternating direction implicit (ADI) method is adopted, modified, and applied to the Reynolds equation for thin, gas fluid films. An efficient code is developed to predict both the steady-state and dynamic performance of an aerodynamic journal bearing. An alternative approach is shown for hybrid journal gas bearings by using Liebmann's iterative solution (LIS) for elliptic partial differential equations. The results are compared with known design criteria from experimental data. The developed methods show good accuracy and very short computer running time in comparison with methods based on an inverting of a matrix. The computer codes need a small amount of memory and can be run on either personal computers or on mainframe systems.

Three-dimensional elliptic grid generation technique with application to turbomachinery cascades

NASA Technical Reports Server (NTRS)

Chen, S. C.; Schwab, J. R.

1988-01-01

Described is a numerical method for generating 3-D grids for turbomachinery computational fluid dynamic codes. The basic method is general and involves the solution of a quasi-linear elliptic partial differential equation via pointwise relaxation with a local relaxation factor. It allows specification of the grid point distribution on the boundary surfaces, the grid spacing off the boundary surfaces, and the grid orthogonality at the boundary surfaces. A geometry preprocessor constructs the grid point distributions on the boundary surfaces for general turbomachinery cascades. Representative results are shown for a C-grid and an H-grid for a turbine rotor. Two appendices serve as user's manuals for the basic solver and the geometry preprocessor.

Thermal, dynamic and compositional aspects of the core-forming Earth

NASA Technical Reports Server (NTRS)

Stevenson, D. J.

1985-01-01

Core formation is the most important and singular differentiation event in the history of a terrestrial planet. It almost certainly involved the downward migration of a partially or wholly molten iron alloy through a silicate and oxide mantle, and was contemporaneous with accretion. Several important, unresolved issues which have implications for mantle and core geochemistry, the thermal history of the Earth, and the origin of geomagnetism are addressed: whether the early Earth was molten; whether core formation involved low or high pressure geochemistry, or both; early Earth mantle homogenization; whether equilibration established between core forming material and the mantle through which it migrated; and how much iron is stranded and unable to reach the core.

Connectivity as an alternative to boundary integral equations: Construction of bases

PubMed Central

Herrera, Ismael; Sabina, Federico J.

1978-01-01

In previous papers Herrera developed a theory of connectivity that is applicable to the problem of connecting solutions defined in different regions, which occurs when solving partial differential equations and many problems of mechanics. In this paper we explain how complete connectivity conditions can be used to replace boundary integral equations in many situations. We show that completeness is satisfied not only in steady-state problems such as potential, reduced wave equation and static and quasi-static elasticity, but also in time-dependent problems such as heat and wave equations and dynamical elasticity. A method to obtain bases of connectivity conditions, which are independent of the regions considered, is also presented. PMID:16592522

Galactic civilizations: Population dynamics and interstellar diffusion

NASA Technical Reports Server (NTRS)

Newman, W. I.; Sagan, C.

1978-01-01

The interstellar diffusion of galactic civilizations is reexamined by potential theory; both numerical and analytical solutions are derived for the nonlinear partial differential equations which specify a range of relevant models, drawn from blast wave physics, soil science, and, especially, population biology. An essential feature of these models is that, for all civilizations, population growth must be limited by the carrying capacity of the environment. Dispersal is fundamentally a diffusion process; a density-dependent diffusivity describes interstellar emigration. Two models are considered: the first describing zero population growth (ZPG), and the second which also includes local growth and saturation of a planetary population, and for which an asymptotic traveling wave solution is found.

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.

Series expansion solutions for the multi-term time and space fractional partial differential equations in two- and three-dimensions

NASA Astrophysics Data System (ADS)

Ye, H.; Liu, F.; Turner, I.; Anh, V.; Burrage, K.

2013-09-01

Fractional partial differential equations with more than one fractional derivative in time describe some important physical phenomena, such as the telegraph equation, the power law wave equation, or the Szabo wave equation. In this paper, we consider two- and three-dimensional multi-term time and space fractional partial differential equations. The multi-term time-fractional derivative is defined in the Caputo sense, whose order belongs to the interval (1,2],(2,3],(3,4] or (0, m], and the space-fractional derivative is referred to as the fractional Laplacian form. We derive series expansion solutions based on a spectral representation of the Laplacian operator on a bounded region. Some applications are given for the two- and three-dimensional telegraph equation, power law wave equation and Szabo wave equation.

Shift-connected SIMD array architectures for digital optical computing systems, with algorithms for numerical transforms and partial differential equations

NASA Astrophysics Data System (ADS)

Drabik, Timothy J.; Lee, Sing H.

1986-11-01

The intrinsic parallelism characteristics of easily realizable optical SIMD arrays prompt their present consideration in the implementation of highly structured algorithms for the numerical solution of multidimensional partial differential equations and the computation of fast numerical transforms. Attention is given to a system, comprising several spatial light modulators (SLMs), an optical read/write memory, and a functional block, which performs simple, space-invariant shifts on images with sufficient flexibility to implement the fastest known methods for partial differential equations as well as a wide variety of numerical transforms in two or more dimensions. Either fixed or floating-point arithmetic may be used. A performance projection of more than 1 billion floating point operations/sec using SLMs with 1000 x 1000-resolution and operating at 1-MHz frame rates is made.

In silico ordinary differential equation/partial differential equation hemodialysis model estimates methadone removal during dialysis.

PubMed

Linares, Oscar A; Schiesser, William E; Fudin, Jeffrey; Pham, Thien C; Bettinger, Jeffrey J; Mathew, Roy O; Daly, Annemarie L

2015-01-01

There is a need to have a model to study methadone's losses during hemodialysis to provide informed methadone dose recommendations for the practitioner. To build a one-dimensional (1-D), hollow-fiber geometry, ordinary differential equation (ODE) and partial differential equation (PDE) countercurrent hemodialyzer model (ODE/PDE model). We conducted a cross-sectional study in silico that evaluated eleven hemodialysis patients. Patients received a ceiling dose of methadone hydrochloride 30 mg/day. Outcome measures included: the total amount of methadone removed during dialysis; methadone's overall intradialytic mass transfer rate coefficient, km ; and, methadone's removal rate, j ME. Each metric was measured at dialysate flow rates of 250 mL/min and 800 mL/min. The ODE/PDE model revealed a significant increase in the change of methadone's mass transfer with increased dialysate flow rate, %Δkm =18.56, P=0.02, N=11. The total amount of methadone mass transferred across the dialyzer membrane with high dialysate flow rate significantly increased (0.042±0.016 versus 0.052±0.019 mg/kg, P=0.02, N=11). This was accompanied by a small significant increase in methadone's mass transfer rate (0.113±0.002 versus 0.014±0.002 mg/kg/h, P=0.02, N=11). The ODE/PDE model accurately predicted methadone's removal during dialysis. The absolute value of the prediction errors for methadone's extraction and throughput were less than 2%. ODE/PDE modeling of methadone's hemodialysis is a new approach to study methadone's removal, in particular, and opioid removal, in general, in patients with end-stage renal disease on hemodialysis. ODE/PDE modeling accurately quantified the fundamental phenomena of methadone's mass transfer during hemodialysis. This methodology may lead to development of optimally designed intradialytic opioid treatment protocols, and allow dynamic monitoring of outflow plasma opioid concentrations for model predictive control during dialysis in humans.

Rule-based spatial modeling with diffusing, geometrically constrained molecules.

PubMed

Gruenert, Gerd; Ibrahim, Bashar; Lenser, Thorsten; Lohel, Maiko; Hinze, Thomas; Dittrich, Peter

2010-06-07

We suggest a new type of modeling approach for the coarse grained, particle-based spatial simulation of combinatorially complex chemical reaction systems. In our approach molecules possess a location in the reactor as well as an orientation and geometry, while the reactions are carried out according to a list of implicitly specified reaction rules. Because the reaction rules can contain patterns for molecules, a combinatorially complex or even infinitely sized reaction network can be defined. For our implementation (based on LAMMPS), we have chosen an already existing formalism (BioNetGen) for the implicit specification of the reaction network. This compatibility allows to import existing models easily, i.e., only additional geometry data files have to be provided. Our simulations show that the obtained dynamics can be fundamentally different from those simulations that use classical reaction-diffusion approaches like Partial Differential Equations or Gillespie-type spatial stochastic simulation. We show, for example, that the combination of combinatorial complexity and geometric effects leads to the emergence of complex self-assemblies and transportation phenomena happening faster than diffusion (using a model of molecular walkers on microtubules). When the mentioned classical simulation approaches are applied, these aspects of modeled systems cannot be observed without very special treatment. Further more, we show that the geometric information can even change the organizational structure of the reaction system. That is, a set of chemical species that can in principle form a stationary state in a Differential Equation formalism, is potentially unstable when geometry is considered, and vice versa. We conclude that our approach provides a new general framework filling a gap in between approaches with no or rigid spatial representation like Partial Differential Equations and specialized coarse-grained spatial simulation systems like those for DNA or virus capsid self-assembly.

Rule-based spatial modeling with diffusing, geometrically constrained molecules

PubMed Central

2010-01-01

Background We suggest a new type of modeling approach for the coarse grained, particle-based spatial simulation of combinatorially complex chemical reaction systems. In our approach molecules possess a location in the reactor as well as an orientation and geometry, while the reactions are carried out according to a list of implicitly specified reaction rules. Because the reaction rules can contain patterns for molecules, a combinatorially complex or even infinitely sized reaction network can be defined. For our implementation (based on LAMMPS), we have chosen an already existing formalism (BioNetGen) for the implicit specification of the reaction network. This compatibility allows to import existing models easily, i.e., only additional geometry data files have to be provided. Results Our simulations show that the obtained dynamics can be fundamentally different from those simulations that use classical reaction-diffusion approaches like Partial Differential Equations or Gillespie-type spatial stochastic simulation. We show, for example, that the combination of combinatorial complexity and geometric effects leads to the emergence of complex self-assemblies and transportation phenomena happening faster than diffusion (using a model of molecular walkers on microtubules). When the mentioned classical simulation approaches are applied, these aspects of modeled systems cannot be observed without very special treatment. Further more, we show that the geometric information can even change the organizational structure of the reaction system. That is, a set of chemical species that can in principle form a stationary state in a Differential Equation formalism, is potentially unstable when geometry is considered, and vice versa. Conclusions We conclude that our approach provides a new general framework filling a gap in between approaches with no or rigid spatial representation like Partial Differential Equations and specialized coarse-grained spatial simulation systems like those for DNA or virus capsid self-assembly. PMID:20529264

Dynamic coupling of subsurface and seepage flows solved within a regularized partition formulation

NASA Astrophysics Data System (ADS)

Marçais, J.; de Dreuzy, J.-R.; Erhel, J.

2017-11-01

Hillslope response to precipitations is characterized by sharp transitions from purely subsurface flow dynamics to simultaneous surface and subsurface flows. Locally, the transition between these two regimes is triggered by soil saturation. Here we develop an integrative approach to simultaneously solve the subsurface flow, locate the potential fully saturated areas and deduce the generated saturation excess overland flow. This approach combines the different dynamics and transitions in a single partition formulation using discontinuous functions. We propose to regularize the system of partial differential equations and to use classic spatial and temporal discretization schemes. We illustrate our methodology on the 1D hillslope storage Boussinesq equations (Troch et al., 2003). We first validate the numerical scheme on previous numerical experiments without saturation excess overland flow. Then we apply our model to a test case with dynamic transitions from purely subsurface flow dynamics to simultaneous surface and subsurface flows. Our results show that discretization respects mass balance both locally and globally, converges when the mesh or time step are refined. Moreover the regularization parameter can be taken small enough to ensure accuracy without suffering of numerical artefacts. Applied to some hundreds of realistic hillslope cases taken from Western side of France (Brittany), the developed method appears to be robust and efficient.

Dynamic Proteomic Analysis of Pancreatic Mesenchyme Reveals Novel Factors That Enhance Human Embryonic Stem Cell to Pancreatic Cell Differentiation.

PubMed

Russ, Holger A; Landsman, Limor; Moss, Christopher L; Higdon, Roger; Greer, Renee L; Kaihara, Kelly; Salamon, Randy; Kolker, Eugene; Hebrok, Matthias

2016-01-01

Current approaches in human embryonic stem cell (hESC) to pancreatic beta cell differentiation have largely been based on knowledge gained from developmental studies of the epithelial pancreas, while the potential roles of other supporting tissue compartments have not been fully explored. One such tissue is the pancreatic mesenchyme that supports epithelial organogenesis throughout embryogenesis. We hypothesized that detailed characterization of the pancreatic mesenchyme might result in the identification of novel factors not used in current differentiation protocols. Supplementing existing hESC differentiation conditions with such factors might create a more comprehensive simulation of normal development in cell culture. To validate our hypothesis, we took advantage of a novel transgenic mouse model to isolate the pancreatic mesenchyme at distinct embryonic and postnatal stages for subsequent proteomic analysis. Refined sample preparation and analysis conditions across four embryonic and prenatal time points resulted in the identification of 21,498 peptides with high-confidence mapping to 1,502 proteins. Expression analysis of pancreata confirmed the presence of three potentially important factors in cell differentiation: Galectin-1 (LGALS1), Neuroplastin (NPTN), and the Laminin α-2 subunit (LAMA2). Two of the three factors (LGALS1 and LAMA2) increased expression of pancreatic progenitor transcript levels in a published hESC to beta cell differentiation protocol. In addition, LAMA2 partially blocks cell culture induced beta cell dedifferentiation. Summarily, we provide evidence that proteomic analysis of supporting tissues such as the pancreatic mesenchyme allows for the identification of potentially important factors guiding hESC to pancreas differentiation.

Dynamic Proteomic Analysis of Pancreatic Mesenchyme Reveals Novel Factors That Enhance Human Embryonic Stem Cell to Pancreatic Cell Differentiation

PubMed Central

Russ, Holger A.; Landsman, Limor; Moss, Christopher L.; Higdon, Roger; Greer, Renee L.; Kaihara, Kelly; Salamon, Randy; Kolker, Eugene; Hebrok, Matthias

2016-01-01

Current approaches in human embryonic stem cell (hESC) to pancreatic beta cell differentiation have largely been based on knowledge gained from developmental studies of the epithelial pancreas, while the potential roles of other supporting tissue compartments have not been fully explored. One such tissue is the pancreatic mesenchyme that supports epithelial organogenesis throughout embryogenesis. We hypothesized that detailed characterization of the pancreatic mesenchyme might result in the identification of novel factors not used in current differentiation protocols. Supplementing existing hESC differentiation conditions with such factors might create a more comprehensive simulation of normal development in cell culture. To validate our hypothesis, we took advantage of a novel transgenic mouse model to isolate the pancreatic mesenchyme at distinct embryonic and postnatal stages for subsequent proteomic analysis. Refined sample preparation and analysis conditions across four embryonic and prenatal time points resulted in the identification of 21,498 peptides with high-confidence mapping to 1,502 proteins. Expression analysis of pancreata confirmed the presence of three potentially important factors in cell differentiation: Galectin-1 (LGALS1), Neuroplastin (NPTN), and the Laminin α-2 subunit (LAMA2). Two of the three factors (LGALS1 and LAMA2) increased expression of pancreatic progenitor transcript levels in a published hESC to beta cell differentiation protocol. In addition, LAMA2 partially blocks cell culture induced beta cell dedifferentiation. Summarily, we provide evidence that proteomic analysis of supporting tissues such as the pancreatic mesenchyme allows for the identification of potentially important factors guiding hESC to pancreas differentiation. PMID:26681951

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.

Geometric properties of commutative subalgebras of partial differential operators

NASA Astrophysics Data System (ADS)

Zheglov, A. B.; Kurke, H.

2015-05-01

We investigate further algebro-geometric properties of commutative rings of partial differential operators, continuing our research started in previous articles. In particular, we start to explore the simplest and also certain known examples of quantum algebraically completely integrable systems from the point of view of a recent generalization of Sato's theory, developed by the first author. We give a complete characterization of the spectral data for a class of 'trivial' commutative algebras and strengthen geometric properties known earlier for a class of known examples. We also define a kind of restriction map from the moduli space of coherent sheaves with fixed Hilbert polynomial on a surface to an analogous moduli space on a divisor (both the surface and the divisor are part of the spectral data). We give several explicit examples of spectral data and corresponding algebras of commuting (completed) operators, producing as a by-product interesting examples of surfaces that are not isomorphic to spectral surfaces of any (maximal) commutative ring of partial differential operators of rank one. Finally, we prove that any commutative ring of partial differential operators whose normalization is isomorphic to the ring of polynomials k \\lbrack u,t \\rbrack is a Darboux transformation of a ring of operators with constant coefficients. Bibliography: 39 titles.

Flap-lag-torsional dynamic modelling of rotor blades in hover and in forward flight, including the effect of cubic nonlinearities

NASA Technical Reports Server (NTRS)

Crespodasilva, M. R. M.

1981-01-01

The differential equations of motion, and boundary conditions, describing the flap-lead/lag-torsional motion of a flexible rotor blade with a precone angle and a variable pitch angle, which incorporates a pretwist, are derived via Hamilton's principle. The meaning of inextensionality is discussed. The equations are reduced to a set of three integro partial differential equations by elimination of the extension variable. The generalized aerodynamic forces are modelled using Greenberg's extension of Theodorsen's strip theory. The equations of motion are systematically expanded into polynomial nonlinearities with the objective of retaining all terms up to third degree. The blade is modeled as a long, slender, of isotropic Hookean materials. Offsets from the blade's elastic axis through its shear center and the axes for the mass, area and aerodynamic centers, radial nonuniformaties of the blade's stiffnesses and cross section properties are considered and the effect of warp of the cross section is included in the formulation.

Partial replacement of animal fat by oleogels structured with monoglycerides and phytosterols in frankfurter sausages.

PubMed

Kouzounis, Dimitrios; Lazaridou, Athina; Katsanidis, Eugenios

2017-08-01

Sunflower oil was structured with monoglycerides and phytosterols. The properties of the oleogels were studied by optical microscopy, large deformation mechanical measurements, dynamic rheometry and differential scanning calorimetry. The interaction between monoglycerides and phytosterols resulted in stronger oleogel networks with a differentiated crystalline structure, increased hardness and gel strength, increased storage modulus (G') values and decreased melting temperatures compared to monoglycerides oleogels. The oleogel structured with 15:5 monoglycerides to phytosterols weight ratio was selected to replace 50% of the pork backfat in frankfurter sausages. The control treatment (FSS1) presented higher values of hardness, brittleness, gumminess and chewiness than the oleogel-substituted samples (FSS2), whereas cohesiveness and elasticity did not present any differences. Instrumental color measurements indicated that FSS1 samples had higher a*, lower L* and similar b* values compared to FSS2. No differences were detected in the oxidation levels and sensory evaluation revealed similar overall liking for the two treatments. Copyright © 2017 Elsevier Ltd. All rights reserved.

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.

Robustness of Quadratic Hedging Strategies in Finance via Backward Stochastic Differential Equations with Jumps

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

Di Nunno, Giulia, E-mail: giulian@math.uio.no; Khedher, Asma, E-mail: asma.khedher@tum.de; Vanmaele, Michèle, E-mail: michele.vanmaele@ugent.be

We consider a backward stochastic differential equation with jumps (BSDEJ) which is driven by a Brownian motion and a Poisson random measure. We present two candidate-approximations to this BSDEJ and we prove that the solution of each candidate-approximation converges to the solution of the original BSDEJ in a space which we specify. We use this result to investigate in further detail the consequences of the choice of the model to (partial) hedging in incomplete markets in finance. As an application, we consider models in which the small variations in the price dynamics are modeled with a Poisson random measure withmore » infinite activity and models in which these small variations are modeled with a Brownian motion or are cut off. Using the convergence results on BSDEJs, we show that quadratic hedging strategies are robust towards the approximation of the market prices and we derive an estimation of the model risk.« less

Rapid Airplane Parametric Input Design(RAPID)

NASA Technical Reports Server (NTRS)

Smith, Robert E.; Bloor, Malcolm I. G.; Wilson, Michael J.; Thomas, Almuttil M.

2004-01-01

An efficient methodology is presented for defining a class of airplane configurations. Inclusive in this definition are surface grids, volume grids, and grid sensitivity. A small set of design parameters and grid control parameters govern the process. The general airplane configuration has wing, fuselage, vertical tail, horizontal tail, and canard components. The wing, tail, and canard components are manifested by solving a fourth-order partial differential equation subject to Dirichlet and Neumann boundary conditions. The design variables are incorporated into the boundary conditions, and the solution is expressed as a Fourier series. The fuselage has circular cross section, and the radius is an algebraic function of four design parameters and an independent computational variable. Volume grids are obtained through an application of the Control Point Form method. Grid sensitivity is obtained by applying the automatic differentiation precompiler ADIFOR to software for the grid generation. The computed surface grids, volume grids, and sensitivity derivatives are suitable for a wide range of Computational Fluid Dynamics simulation and configuration optimizations.

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

Aeroelastic Analysis of Helicopter Rotor Blades Incorporating Anisotropic Piezoelectric Twist Actuation

NASA Technical Reports Server (NTRS)

Wilkie, W. Keats; Belvin, W. Keith; Park, K. C.

1996-01-01

A simple aeroelastic analysis of a helicopter rotor blade incorporating embedded piezoelectric fiber composite, interdigitated electrode blade twist actuators is described. The analysis consists of a linear torsion and flapwise bending model coupled with a nonlinear ONERA based unsteady aerodynamics model. A modified Galerkin procedure is performed upon the rotor blade partial differential equations of motion to develop a system of ordinary differential equations suitable for dynamics simulation using numerical integration. The twist actuation responses for three conceptual fullscale blade designs with realistic constraints on blade mass are numerically evaluated using the analysis. Numerical results indicate that useful amplitudes of nonresonant elastic twist, on the order of one to two degrees, are achievable under one-g hovering flight conditions for interdigitated electrode poling configurations. Twist actuation for the interdigitated electrode blades is also compared with the twist actuation of a conventionally poled piezoelectric fiber composite blade. Elastic twist produced using the interdigitated electrode actuators was found to be four to five times larger than that obtained with the conventionally poled actuators.

An efficient and guaranteed stable numerical method for continuous modeling of infiltration and redistribution with a shallow dynamic water table

NASA Astrophysics Data System (ADS)

Lai, Wencong; Ogden, Fred L.; Steinke, Robert C.; Talbot, Cary A.

2015-03-01

We have developed a one-dimensional numerical method to simulate infiltration and redistribution in the presence of a shallow dynamic water table. This method builds upon the Green-Ampt infiltration with Redistribution (GAR) model and incorporates features from the Talbot-Ogden (T-O) infiltration and redistribution method in a discretized moisture content domain. The redistribution scheme is more physically meaningful than the capillary weighted redistribution scheme in the T-O method. Groundwater dynamics are considered in this new method instead of hydrostatic groundwater front. It is also computationally more efficient than the T-O method. Motion of water in the vadose zone due to infiltration, redistribution, and interactions with capillary groundwater are described by ordinary differential equations. Numerical solutions to these equations are computationally less expensive than solutions of the highly nonlinear Richards' (1931) partial differential equation. We present results from numerical tests on 11 soil types using multiple rain pulses with different boundary conditions, with and without a shallow water table and compare against the numerical solution of Richards' equation (RE). Results from the new method are in satisfactory agreement with RE solutions in term of ponding time, deponding time, infiltration rate, and cumulative infiltrated depth. The new method, which we call "GARTO" can be used as an alternative to the RE for 1-D coupled surface and groundwater models in general situations with homogeneous soils with dynamic water table. The GARTO method represents a significant advance in simulating groundwater surface water interactions because it very closely matches the RE solution while being computationally efficient, with guaranteed mass conservation, and no stability limitations that can affect RE solvers in the case of a near-surface water table.

7 CFR 1000.76 - Payments by a handler operating a partially regulated distributing plant.

Code of Federal Regulations, 2010 CFR

2010-01-01

..., compute a Class I differential price by subtracting Class III price from the current month's Class I price... by which the Class I differential price exceeds the producer price differential, both prices to be... Class I differential price nor the adjusted producer price differential shall be less than zero; (3) For...

Graded activation and free energy landscapes of a muscarinic G-protein-coupled receptor.

PubMed

Miao, Yinglong; McCammon, J Andrew

2016-10-25

G-protein-coupled receptors (GPCRs) recognize ligands of widely different efficacies, from inverse to partial and full agonists, which transduce cellular signals at differentiated levels. However, the mechanism of such graded activation remains unclear. Using the Gaussian accelerated molecular dynamics (GaMD) method that enables both unconstrained enhanced sampling and free energy calculation, we have performed extensive GaMD simulations (∼19 μs in total) to investigate structural dynamics of the M 2 muscarinic GPCR that is bound by the full agonist iperoxo (IXO), the partial agonist arecoline (ARC), and the inverse agonist 3-quinuclidinyl-benzilate (QNB), in the presence or absence of the G-protein mimetic nanobody. In the receptor-nanobody complex, IXO binding leads to higher fluctuations in the protein-coupling interface than ARC, especially in the receptor transmembrane helix 5 (TM5), TM6, and TM7 intracellular domains that are essential elements for GPCR activation, but less flexibility in the receptor extracellular region due to stronger binding compared with ARC. Two different binding poses are revealed for ARC in the orthosteric pocket. Removal of the nanobody leads to GPCR deactivation that is characterized by inward movement of the TM6 intracellular end. Distinct low-energy intermediate conformational states are identified for the IXO- and ARC-bound M 2 receptor. Both dissociation and binding of an orthosteric ligand are observed in a single all-atom GPCR simulation in the case of partial agonist ARC binding to the M 2 receptor. This study demonstrates the applicability of GaMD for exploring free energy landscapes of large biomolecules and the simulations provide important insights into the GPCR functional mechanism.

Developmental regulation of MURF ubiquitin ligases and autophagy proteins nbr1, p62/SQSTM1 and LC3 during cardiac myofibril assembly and turnover.

PubMed

Perera, Sue; Holt, Mark R; Mankoo, Baljinder S; Gautel, Mathias

2011-03-01

The striated muscle-specific tripartite motif (TRIM) proteins TRIM63/MURF1, TRIM55/MURF2 and TRIM54/MURF3 can function as ubiquitin E3 ligases in ubiquitin-mediated muscle protein turnover. Despite their well-characterised roles in muscle atrophy, the dynamics of MURF expression in the development and early postnatal adaptation of striated muscle is largely unknown. Here, we show that MURF2 is expressed at the very onset of mouse cardiac differentiation at embryonic day 8.5, and represents a sensitive marker for differentiating myocardium. During cardiac development, expression shifts from the 50 kDa to the 60 kDa A-isoform, which dominates postnatally. In contrast, MURF1 shows strong postnatal upregulation and MURF3 is not significantly expressed before birth. MURF2 expression parallels that of the autophagy-associated proteins LC3, p62/SQSTM1 and nbr1. SiRNA knockdown of MURF2 in neonatal rat cardiomyocytes disrupts posttranslational microtubule modification and myofibril assembly, and is only partly compensated by upregulation of MURF3 but not MURF1. Knockdown of both MURF2 and MURF3 severely disrupts the formation of ordered Z- and M-bands, likely by perturbed tubulin dynamics. These results suggest that ubiquitin-mediated protein turnover and MURF2 in particular play an unrecognised role in the earliest steps of heart muscle differentiation, and that partial complementation of MURF2 deficiency is afforded by MURF3. Copyright © 2010 Elsevier Inc. All rights reserved.

Solution NMR studies provide structural basis for endotoxin pattern recognition by the innate immune receptor CD14

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

Albright, Seth; Chen Bin; Holbrook, Kristen

CD14 functions as a key pattern recognition receptor for a diverse array of Gram-negative and Gram-positive cell-wall components in the host innate immune response by binding to pathogen-associated molecular patterns (PAMPs) at partially overlapping binding site(s). To determine the potential contribution of CD14 residues in this pattern recognition, we have examined using solution NMR spectroscopy, the binding of three different endotoxin ligands, lipopolysaccharide, lipoteichoic acid, and a PGN-derived compound, muramyl dipeptide to a {sup 15}N isotopically labeled 152-residue N-terminal fragment of sCD14 expressed in Pichia pastoris. Mapping of NMR spectral changes upon addition of ligands revealed that the pattern ofmore » residues affected by binding of each ligand is partially similar and partially different. This first direct structural observation of the ability of specific residue combinations of CD14 to differentially affect endotoxin binding may help explain the broad specificity of CD14 in ligand recognition and provide a structural basis for pattern recognition. Another interesting finding from the observed spectral changes is that the mode of binding may be dynamically modulated and could provide a mechanism for binding endotoxins with structural diversity through a common binding site.« less

Thermal evolution of a partially differentiated H chondrite parent body

NASA Astrophysics Data System (ADS)

Abrahams, J. N. H.; Bryson, J. F. J.; Weiss, B. P.; Nimmo, F.

2016-12-01

It has traditionally been assumed that planetesimals either melted entirely or remained completely undifferentiated as they accreted. The unmelted textures and cooling histories of chondrites have been used to argue that these meteorites originated from bodies that never differentiated. However, paleomagnetic measurements indicate that some chondrites (e.g., the H chondrite Portales Valley and several CV chondrites) were magnetized by a core dynamo magnetic field, implying that their parent bodies were partially differentiated. It has been unclear, however, whether planetesimal histories consistent with dynamo production can also be consistent with the diversity of chondrite cooling rates and ages. To address this, we modeled the thermal evolution of the H chondrite parent body, considering a variety of accretion histories and parent body radii. We considered partial differentiation using two-stage accretion involving the initial formation and differentiation of a small body, followed by the later addition of low thermal conductivity chondritic material that remains mostly unmelted. We were able to reproduce the measured thermal evolution of multiple H chondrites for a range of parent body parameters, including initial radii from 70-150 km, chondritic layer thicknesses from 50 km to over 100 km, and second stage accretion times of 2.5-3 Myr after solar system formation. Our predicted rates of core cooling and crystallization are consistent with dynamo generation by compositional convection beginning 60-200 Myr after solar system formation and lasting for at least tens of millions of years. This is consistent with magnetic studies of Portales Valley [Bryson et al., this meeting]. In summary, we find that thermal models of partial differentiation are consistent the radiometric ages, magnetization, and cooling rates of a diversity H chondrites.

Some remarks on the numerical solution of parabolic partial differential equations

NASA Astrophysics Data System (ADS)

Campagna, R.; Cuomo, S.; Leveque, S.; Toraldo, G.; Giannino, F.; Severino, G.

2017-11-01

Numerous environmental/engineering applications relying upon the theory of diffusion phenomena into chaotic environments have recently stimulated the interest toward the numerical solution of parabolic partial differential equations (PDEs). In the present paper, we outline a formulation of the mathematical problem underlying a quite general diffusion mechanism in the natural environments, and we shortly emphasize some remarks concerning the applicability of the (straightforward) finite difference method. An illustration example is also presented.

Study of coupled nonlinear partial differential equations for finding exact analytical solutions.

PubMed

Khan, Kamruzzaman; Akbar, M Ali; Koppelaar, H

2015-07-01

Exact solutions of nonlinear partial differential equations (NPDEs) are obtained via the enhanced (G'/G)-expansion method. The method is subsequently applied to find exact solutions of the Drinfel'd-Sokolov-Wilson (DSW) equation and the (2+1)-dimensional Painlevé integrable Burgers (PIB) equation. The efficiency of this method for finding these exact solutions is demonstrated. The method is effective and applicable for many other NPDEs in mathematical physics.

A convex penalty for switching control of partial differential equations

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

Clason, Christian; Rund, Armin; Kunisch, Karl

2016-01-19

A convex penalty for promoting switching controls for partial differential equations is introduced; such controls consist of an arbitrary number of components of which at most one should be simultaneously active. Using a Moreau–Yosida approximation, a family of approximating problems is obtained that is amenable to solution by a semismooth Newton method. In conclusion, the efficiency of this approach and the structure of the obtained controls are demonstrated by numerical examples.

Numerical methods for large-scale, time-dependent partial differential equations

NASA Technical Reports Server (NTRS)

Turkel, E.

1979-01-01

A survey of numerical methods for time dependent partial differential equations is presented. The emphasis is on practical applications to large scale problems. A discussion of new developments in high order methods and moving grids is given. The importance of boundary conditions is stressed for both internal and external flows. A description of implicit methods is presented including generalizations to multidimensions. Shocks, aerodynamics, meteorology, plasma physics and combustion applications are also briefly described.

Spectral methods for time dependent partial differential equations

NASA Technical Reports Server (NTRS)

Gottlieb, D.; Turkel, E.

1983-01-01

The theory of spectral methods for time dependent partial differential equations is reviewed. When the domain is periodic Fourier methods are presented while for nonperiodic problems both Chebyshev and Legendre methods are discussed. The theory is presented for both hyperbolic and parabolic systems using both Galerkin and collocation procedures. While most of the review considers problems with constant coefficients the extension to nonlinear problems is also discussed. Some results for problems with shocks are presented.

Stability analysis of multigrid acceleration methods for the solution of partial differential equations

NASA Technical Reports Server (NTRS)

Fay, John F.

1990-01-01

A calculation is made of the stability of various relaxation schemes for the numerical solution of partial differential equations. A multigrid acceleration method is introduced, and its effects on stability are explored. A detailed stability analysis of a simple case is carried out and verified by numerical experiment. It is shown that the use of multigrids can speed convergence by several orders of magnitude without adversely affecting stability.

Constructing and predicting solitary pattern solutions for nonlinear time-fractional dispersive partial differential equations

NASA Astrophysics Data System (ADS)

Arqub, Omar Abu; El-Ajou, Ahmad; Momani, Shaher

2015-07-01

Building fractional mathematical models for specific phenomena and developing numerical or analytical solutions for these fractional mathematical models are crucial issues in mathematics, physics, and engineering. In this work, a new analytical technique for constructing and predicting solitary pattern solutions of time-fractional dispersive partial differential equations is proposed based on the generalized Taylor series formula and residual error function. The new approach provides solutions in the form of a rapidly convergent series with easily computable components using symbolic computation software. For method evaluation and validation, the proposed technique was applied to three different models and compared with some of the well-known methods. The resultant simulations clearly demonstrate the superiority and potentiality of the proposed technique in terms of the quality performance and accuracy of substructure preservation in the construct, as well as the prediction of solitary pattern solutions for time-fractional dispersive partial differential equations.

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.

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

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…

Differential Equation Models for Sharp Threshold Dynamics

DTIC Science & Technology

2012-08-01

dynamics, and the Lanchester model of armed conflict, where the loss of a key capability drastically changes dynamics. We derive and demonstrate a step...dynamics using differential equations. 15. SUBJECT TERMS Differential Equations, Markov Population Process, S-I-R Epidemic, Lanchester Model 16...infection, where a detection event drastically changes dynamics, and the Lanchester model of armed conflict, where the loss of a key capability

The effect of various quantum mechanically derived partial atomic charges on the bulk properties of chloride-based ionic liquids

NASA Astrophysics Data System (ADS)

Zolghadr, Amin Reza; Ghatee, Mohammad Hadi; Moosavi, Fatemeh

2016-08-01

Partial atomic charges using various quantum mechanical calculations for [Cnmim]Cl (n = 1, 4) ionic liquids (ILs) are obtained and used for development of molecular dynamics simulation (MD) force fields. The isolated ion pairs are optimized using HF, B3LYP, and MP2 methods for electronic structure with 6-311++G(d,p) basis set. Partial atomic charges are assigned to the atomic center with CHELPG and NBO methods. The effect of these sets of partial charges on the static and dynamic properties of ILs is evaluated by performing a series of MD simulations and comparing the essential thermodynamic properties with the available experimental data and available molecular dynamics simulation results. In contrast to the general trends reported for ionic liquids with BF4, PF6, and iodide anions (in which restrained electrostatic potential (RESP) charges are preferred), partial charges derived by B3LYP-NBO method are relatively good in prediction of the structural, dynamical, and thermodynamic energetic properties of the chloride based ILs.

A Model for the Oxidation of Carbon Silicon Carbide Composite Structures

NASA Technical Reports Server (NTRS)

Sullivan, Roy M.

2004-01-01

A mathematical theory and an accompanying numerical scheme have been developed for predicting the oxidation behavior of carbon silicon carbide (C/SiC) composite structures. The theory is derived from the mechanics of the flow of ideal gases through a porous solid. The result of the theoretical formulation is a set of two coupled nonlinear differential equations written in terms of the oxidant and oxide partial pressures. The differential equations are solved simultaneously to obtain the partial vapor pressures of the oxidant and oxides as a function of the spatial location and time. The local rate of carbon oxidation is determined using the map of the local oxidant partial vapor pressure along with the Arrhenius rate equation. The nonlinear differential equations are cast into matrix equations by applying the Bubnov-Galerkin weighted residual method, allowing for the solution of the differential equations numerically. The numerical method is demonstrated by utilizing the method to model the carbon oxidation and weight loss behavior of C/SiC specimens during thermogravimetric experiments. The numerical method is used to study the physics of carbon oxidation in carbon silicon carbide composites.

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)

Group theoretic approach for solving the problem of diffusion of a drug through a thin membrane

NASA Astrophysics Data System (ADS)

Abd-El-Malek, Mina B.; Kassem, Magda M.; Meky, Mohammed L. M.

2002-03-01

The transformation group theoretic approach is applied to study the diffusion process of a drug through a skin-like membrane which tends to partially absorb the drug. Two cases are considered for the diffusion coefficient. The application of one parameter group reduces the number of independent variables by one, and consequently the partial differential equation governing the diffusion process with the boundary and initial conditions is transformed into an ordinary differential equation with the corresponding conditions. The obtained differential equation is solved numerically using the shooting method, and the results are illustrated graphically and in tables.

Series: Utilization of Differential Equations and Methods for Solving Them in Medical Physics (4).

PubMed

Murase, Kenya

2016-01-01

Partial differential equations are often used in the field of medical physics. In this (final) issue, the methods for solving the partial differential equations were introduced, which include separation of variables, integral transform (Fourier and Fourier-sine transforms), Green's function, and series expansion methods. Some examples were also introduced, in which the integral transform and Green's function methods were applied to solving Pennes' bioheat transfer equation and the Fourier series expansion method was applied to Navier-Stokes equation for analyzing the wall shear stress in blood vessels.Finally, the author hopes that this series will be helpful for people who engage in medical physics.

Quinoa - Adaptive Computational Fluid Dynamics, 0.2

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

Bakosi, Jozsef; Gonzalez, Francisco; Rogers, Brandon

Quinoa is a set of computational tools that enables research and numerical analysis in fluid dynamics. At this time it remains a test-bed to experiment with various algorithms using fully asynchronous runtime systems. Currently, Quinoa consists of the following tools: (1) Walker, a numerical integrator for systems of stochastic differential equations in time. It is a mathematical tool to analyze and design the behavior of stochastic differential equations. It allows the estimation of arbitrary coupled statistics and probability density functions and is currently used for the design of statistical moment approximations for multiple mixing materials in variable-density turbulence. (2) Inciter,more » an overdecomposition-aware finite element field solver for partial differential equations using 3D unstructured grids. Inciter is used to research asynchronous mesh-based algorithms and to experiment with coupling asynchronous to bulk-synchronous parallel code. Two planned new features of Inciter, compared to the previous release (LA-CC-16-015), to be implemented in 2017, are (a) a simple Navier-Stokes solver for ideal single-material compressible gases, and (b) solution-adaptive mesh refinement (AMR), which enables dynamically concentrating compute resources to regions with interesting physics. Using the NS-AMR problem we plan to explore how to scale such high-load-imbalance simulations, representative of large production multiphysics codes, to very large problems on very large computers using an asynchronous runtime system. (3) RNGTest, a test harness to subject random number generators to stringent statistical tests enabling quantitative ranking with respect to their quality and computational cost. (4) UnitTest, a unit test harness, running hundreds of tests per second, capable of testing serial, synchronous, and asynchronous functions. (5) MeshConv, a mesh file converter that can be used to convert 3D tetrahedron meshes from and to either of the following formats: Gmsh, (http://www.geuz.org/gmsh), Netgen, (http://sourceforge.net/apps/mediawiki/netgen-mesher), ExodusII, (http://sourceforge.net/projects/exodusii), HyperMesh, (http://www.altairhyperworks.com/product/HyperMesh).« less

FPGA-based distributed computing microarchitecture for complex physical dynamics investigation.

PubMed

Borgese, Gianluca; Pace, Calogero; Pantano, Pietro; Bilotta, Eleonora

2013-09-01

In this paper, we present a distributed computing system, called DCMARK, aimed at solving partial differential equations at the basis of many investigation fields, such as solid state physics, nuclear physics, and plasma physics. This distributed architecture is based on the cellular neural network paradigm, which allows us to divide the differential equation system solving into many parallel integration operations to be executed by a custom multiprocessor system. We push the number of processors to the limit of one processor for each equation. In order to test the present idea, we choose to implement DCMARK on a single FPGA, designing the single processor in order to minimize its hardware requirements and to obtain a large number of easily interconnected processors. This approach is particularly suited to study the properties of 1-, 2- and 3-D locally interconnected dynamical systems. In order to test the computing platform, we implement a 200 cells, Korteweg-de Vries (KdV) equation solver and perform a comparison between simulations conducted on a high performance PC and on our system. Since our distributed architecture takes a constant computing time to solve the equation system, independently of the number of dynamical elements (cells) of the CNN array, it allows us to reduce the elaboration time more than other similar systems in the literature. To ensure a high level of reconfigurability, we design a compact system on programmable chip managed by a softcore processor, which controls the fast data/control communication between our system and a PC Host. An intuitively graphical user interface allows us to change the calculation parameters and plot the results.

Study of coupled nonlinear partial differential equations for finding exact analytical solutions

PubMed Central

Khan, Kamruzzaman; Akbar, M. Ali; Koppelaar, H.

2015-01-01

Exact solutions of nonlinear partial differential equations (NPDEs) are obtained via the enhanced (G′/G)-expansion method. The method is subsequently applied to find exact solutions of the Drinfel'd–Sokolov–Wilson (DSW) equation and the (2+1)-dimensional Painlevé integrable Burgers (PIB) equation. The efficiency of this method for finding these exact solutions is demonstrated. The method is effective and applicable for many other NPDEs in mathematical physics. PMID:26587256

The use of solution adaptive grids in solving partial differential equations

NASA Technical Reports Server (NTRS)

Anderson, D. A.; Rai, M. M.

1982-01-01

The grid point distribution used in solving a partial differential equation using a numerical method has a substantial influence on the quality of the solution. An adaptive grid which adjusts as the solution changes provides the best results when the number of grid points available for use during the calculation is fixed. Basic concepts used in generating and applying adaptive grids are reviewed in this paper, and examples illustrating applications of these concepts are presented.

Multirate Integration Properties of Waveform Relaxation with Applications to Circuit Simulation and Parallel Computation

DTIC Science & Technology

1985-11-18

Greenberg and K. Sakallah at Digital Equipment Corporation, and C-F. Chen, L Nagel, and P. ,. Subrahmanyam at AT&T Bell Laboratories, both for providing...Circuit Theory McGraw-Hill, 1969. [37] R. Courant and D. Hilbert , Partial Differential Equations, Vol. 2 of Methods of Mathematical Physics...McGraw-Hill, N.Y., 1965. Page 161 [44) R. Courant and D. Hilbert , Partial Differential Equations, Vol. 2 of Methods of Mathematical Physics

A Posteriori Finite Element Bounds for Sensitivity Derivatives of Partial-Differential-Equation Outputs. Revised

NASA Technical Reports Server (NTRS)

Lewis, Robert Michael; Patera, Anthony T.; Peraire, Jaume

1998-01-01

We present a Neumann-subproblem a posteriori finite element procedure for the efficient and accurate calculation of rigorous, 'constant-free' upper and lower bounds for sensitivity derivatives of functionals of the solutions of partial differential equations. The design motivation for sensitivity derivative error control is discussed; the a posteriori finite element procedure is described; the asymptotic bounding properties and computational complexity of the method are summarized; and illustrative numerical results are presented.

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.

Quantitative evaluation method for differentiation of C2C12 myoblasts by ultrasonic microscopy

NASA Astrophysics Data System (ADS)

Takanashi, Kyoichi; Washiya, Mamoru; Ota, Kazuki; Yoshida, Sachiko; Hozumi, Naohiro; Kobayashi, Kazuto

2017-07-01

Cell differentiation was evaluated by ultrasonic microscopy. However, there were some regions that showed a lower acoustic impedance than the culture liquid. It was considered that, in such regions, the cells were not perfectly in contact with the film substrate. Hence, a waveform analysis was performed, and compensated acoustic impedances in such regions were in a reasonable range of values. By the same analysis, the displacements of partially floated cells were also successfully calculated. The elapsed day transitions of the compensated acoustic impedances and displacements were successfully evaluated. In the process of differentiation, actin fibers comprising the cytoskeleton are supposed to loosen in order to induce cellular fusion. In addition, the progress in cell differentiation accompanied by a change into a three-dimensional structure can partially be assessed by the displacement between a cell and a cultured film. Hence, we believe that cell differentiation can be evaluated using an ultrasonic microscope.

A Long-Term Mathematical Model for Mining Industries

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

Achdou, Yves, E-mail: achdou@ljll.univ-paris-diderot.fr; Giraud, Pierre-Noel; Lasry, Jean-Michel

A parcimonious long term model is proposed for a mining industry. Knowing the dynamics of the global reserve, the strategy of each production unit consists of an optimal control problem with two controls, first the flux invested into prospection and the building of new extraction facilities, second the production rate. In turn, the dynamics of the global reserve depends on the individual strategies of the producers, so the models leads to an equilibrium, which is described by low dimensional systems of partial differential equations. The dimensionality depends on the number of technologies that a mining producer can choose. In somemore » cases, the systems may be reduced to a Hamilton–Jacobi equation which is degenerate at the boundary and whose right hand side may blow up at the boundary. A mathematical analysis is supplied. Then numerical simulations for models with one or two technologies are described. In particular, a numerical calibration of the model in order to fit the historical data is carried out.« less

A three-dimensional model of corotating streams in the solar wind. 1: Theoretical foundations

NASA Technical Reports Server (NTRS)

Pizzo, V. J.

1978-01-01

The theoretical and mathematical background pertinent to the study of steady, corotating solar wind structure in all three spatial dimensions (3-D) is discussed. The dynamical evolution of the plasma in interplanetary space (defined as the region beyond roughly 35 solar radii where the flow is supersonic) is approximately described by the nonlinear, single fluid, polytropic (magneto-) hydrodynamic equations. Efficient numerical techniques for solving this complex system of coupled, hyperbolic partial differential equations are outlined. The formulation is inviscid and nonmagnetic, but methods allow for the potential inclusion of both features with only modest modifications. One simple, highly idealized, hydrodynamic model stream is examined to illustrate the fundamental processes involved in the 3-D dynamics of stream evolution. Spatial variations in the rotational stream interaction mechanism were found to produce small nonradial flows on a global scale that lead to the transport of mass, energy, and momentum away from regions of relative compression and into regions of relative rarefaction.

Convolutionless Nakajima-Zwanzig equations for stochastic analysis in nonlinear dynamical systems.

PubMed

Venturi, D; Karniadakis, G E

2014-06-08

Determining the statistical properties of stochastic nonlinear systems is of major interest across many disciplines. Currently, there are no general efficient methods to deal with this challenging problem that involves high dimensionality, low regularity and random frequencies. We propose a framework for stochastic analysis in nonlinear dynamical systems based on goal-oriented probability density function (PDF) methods. The key idea stems from techniques of irreversible statistical mechanics, and it relies on deriving evolution equations for the PDF of quantities of interest, e.g. functionals of the solution to systems of stochastic ordinary and partial differential equations. Such quantities could be low-dimensional objects in infinite dimensional phase spaces. We develop the goal-oriented PDF method in the context of the time-convolutionless Nakajima-Zwanzig-Mori formalism. We address the question of approximation of reduced-order density equations by multi-level coarse graining, perturbation series and operator cumulant resummation. Numerical examples are presented for stochastic resonance and stochastic advection-reaction problems.

A multivariate variational objective analysis-assimilation method. Part 1: Development of the basic model

NASA Technical Reports Server (NTRS)

Achtemeier, Gary L.; Ochs, Harry T., III

1988-01-01

The variational method of undetermined multipliers is used to derive a multivariate model for objective analysis. The model is intended for the assimilation of 3-D fields of rawinsonde height, temperature and wind, and mean level temperature observed by satellite into a dynamically consistent data set. Relative measurement errors are taken into account. The dynamic equations are the two nonlinear horizontal momentum equations, the hydrostatic equation, and an integrated continuity equation. The model Euler-Lagrange equations are eleven linear and/or nonlinear partial differential and/or algebraic equations. A cyclical solution sequence is described. Other model features include a nonlinear terrain-following vertical coordinate that eliminates truncation error in the pressure gradient terms of the horizontal momentum equations and easily accommodates satellite observed mean layer temperatures in the middle and upper troposphere. A projection of the pressure gradient onto equivalent pressure surfaces removes most of the adverse impacts of the lower coordinate surface on the variational adjustment.

General Tricomi-Rassias problem and oblique derivative problem for generalized Chaplygin equations

NASA Astrophysics Data System (ADS)

Wen, Guochun; Chen, Dechang; Cheng, Xiuzhen

2007-09-01

Many authors have discussed the Tricomi problem for some second order equations of mixed type, which has important applications in gas dynamics. In particular, Bers proposed the Tricomi problem for Chaplygin equations in multiply connected domains [L. Bers, Mathematical Aspects of Subsonic and Transonic Gas Dynamics, Wiley, New York, 1958]. And Rassias proposed the exterior Tricomi problem for mixed equations in a doubly connected domain and proved the uniqueness of solutions for the problem [J.M. Rassias, Lecture Notes on Mixed Type Partial Differential Equations, World Scientific, Singapore, 1990]. In the present paper, we discuss the general Tricomi-Rassias problem for generalized Chaplygin equations. This is one general oblique derivative problem that includes the exterior Tricomi problem as a special case. We first give the representation of solutions of the general Tricomi-Rassias problem, and then prove the uniqueness and existence of solutions for the problem by a new method. In this paper, we shall also discuss another general oblique derivative problem for generalized Chaplygin equations.

Planar dynamics of a uniform beam with rigid bodies affixed to the ends

NASA Technical Reports Server (NTRS)

Storch, J.; Gates, S.

1983-01-01

The planar dynamics of a uniform elastic beam subject to a variety of geometric and natural boundary conditions and external excitations were analyzed. The beams are inextensible and capable of small transverse bending deformations only. Classical beam vibration eigenvalue problems for a cantilever with tip mass, a cantilever with tip body and an unconstrained beam with rigid bodies at each are examined. The characteristic equations, eigenfunctions and orthogonality relations for each are derived. The forced vibration of a cantilever with tip body subject to base acceleration is analyzed. The exact solution of the governing nonhomogeneous partial differential equation with time dependent boundary conditions is presented and compared with a Rayleigh-Ritz approximate solution. The arbitrary planar motion of an elastic beam with rigid bodies at the ends is addressed. Equations of motion are derived for two modal expansions of the beam deflection. The motion equations are cast in a first order form suitable for numerical integration. Selected FORTRAN programs are provided.

Tumor evolution in space: the effects of competition colonization tradeoffs on tumor invasion dynamics.

PubMed

Orlando, Paul A; Gatenby, Robert A; Brown, Joel S

2013-01-01

We apply competition colonization tradeoff models to tumor growth and invasion dynamics to explore the hypothesis that varying selection forces will result in predictable phenotypic differences in cells at the tumor invasive front compared to those in the core. Spatially, ecologically, and evolutionarily explicit partial differential equation models of tumor growth confirm that spatial invasion produces selection pressure for motile phenotypes. The effects of the invasive phenotype on normal adjacent tissue determine the patterns of growth and phenotype distribution. If tumor cells do not destroy their environment, colonizer and competitive phenotypes coexist with the former localized at the invasion front and the latter, to the tumor interior. If tumors cells do destroy their environment, then cell motility is strongly selected resulting in accelerated invasion speed with time. Our results suggest that the widely observed genetic heterogeneity within cancers may not be the stochastic effect of random mutations. Rather, it may be the consequence of predictable variations in environmental selection forces and corresponding phenotypic adaptations.

Role of computational fluid dynamics in unsteady aerodynamics for aeroelasticity

NASA Technical Reports Server (NTRS)

Guruswamy, Guru P.; Goorjian, Peter M.

1989-01-01

In the last two decades there have been extensive developments in computational unsteady transonic aerodynamics. Such developments are essential since the transonic regime plays an important role in the design of modern aircraft. Therefore, there has been a large effort to develop computational tools with which to accurately perform flutter analysis at transonic speeds. In the area of Computational Fluid Dynamics (CFD), unsteady transonic aerodynamics are characterized by the feature of modeling the motion of shock waves over aerodynamic bodies, such as wings. This modeling requires the solution of nonlinear partial differential equations. Most advanced codes such as XTRAN3S use the transonic small perturbation equation. Currently, XTRAN3S is being used for generic research in unsteady aerodynamics and aeroelasticity of almost full aircraft configurations. Use of Euler/Navier Stokes equations for simple typical sections has just begun. A brief history of the development of CFD for aeroelastic applications is summarized. The development of unsteady transonic aerodynamics and aeroelasticity are also summarized.

Dynamics of one- and two-dimensional fronts in a bistable equation with time-delayed global feedback: Propagation failure and control mechanisms

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

Boubendir, Yassine; Mendez, Vicenc; Rotstein, Horacio G.

2010-09-15

We study the evolution of fronts in a bistable equation with time-delayed global feedback in the fast reaction and slow diffusion regime. This equation generalizes the Hodgkin-Grafstein and Allen-Cahn equations. We derive a nonlinear equation governing the motion of fronts, which includes a term with delay. In the one-dimensional case this equation is linear. We study the motion of one- and two-dimensional fronts, finding a much richer dynamics than for the previously studied cases (without time-delayed global feedback). We explain the mechanism by which localized fronts created by inhibitory global coupling loose stability in a Hopf bifurcation as the delaymore » time increases. We show that for certain delay times, the prevailing phase is different from that corresponding to the system in the absence of global coupling. Numerical simulations of the partial differential equation are in agreement with the analytical predictions.« less

Tumor Evolution in Space: The Effects of Competition Colonization Tradeoffs on Tumor Invasion Dynamics

PubMed Central

Orlando, Paul A.; Gatenby, Robert A.; Brown, Joel S.

2013-01-01

We apply competition colonization tradeoff models to tumor growth and invasion dynamics to explore the hypothesis that varying selection forces will result in predictable phenotypic differences in cells at the tumor invasive front compared to those in the core. Spatially, ecologically, and evolutionarily explicit partial differential equation models of tumor growth confirm that spatial invasion produces selection pressure for motile phenotypes. The effects of the invasive phenotype on normal adjacent tissue determine the patterns of growth and phenotype distribution. If tumor cells do not destroy their environment, colonizer and competitive phenotypes coexist with the former localized at the invasion front and the latter, to the tumor interior. If tumors cells do destroy their environment, then cell motility is strongly selected resulting in accelerated invasion speed with time. Our results suggest that the widely observed genetic heterogeneity within cancers may not be the stochastic effect of random mutations. Rather, it may be the consequence of predictable variations in environmental selection forces and corresponding phenotypic adaptations. PMID:23508890

Novel Regulation of Ski Protein Stability and Endosomal Sorting by Actin Cytoskeleton Dynamics in Hepatocytes*

PubMed Central

Vázquez-Victorio, Genaro; Caligaris, Cassandre; Del Valle-Espinosa, Eugenio; Sosa-Garrocho, Marcela; González-Arenas, Nelly R.; Reyes-Cruz, Guadalupe; Briones-Orta, Marco A.; Macías-Silva, Marina

2015-01-01

TGF-β-induced antimitotic signals are highly regulated during cell proliferation under normal and pathological conditions, such as liver regeneration and cancer. Up-regulation of the transcriptional cofactors Ski and SnoN during liver regeneration may favor hepatocyte proliferation by inhibiting TGF-β signals. In this study, we found a novel mechanism that regulates Ski protein stability through TGF-β and G protein-coupled receptor (GPCR) signaling. Ski protein is distributed between the nucleus and cytoplasm of normal hepatocytes, and the molecular mechanisms controlling Ski protein stability involve the participation of actin cytoskeleton dynamics. Cytoplasmic Ski is partially associated with actin and localized in cholesterol-rich vesicles. Ski protein stability is decreased by TGF-β/Smads, GPCR/Rho signals, and actin polymerization, whereas GPCR/cAMP signals and actin depolymerization promote Ski protein stability. In conclusion, TGF-β and GPCR signals differentially regulate Ski protein stability and sorting in hepatocytes, and this cross-talk may occur during liver regeneration. PMID:25561741

Phase structure of NJL model with weak renormalization group

NASA Astrophysics Data System (ADS)

Aoki, Ken-Ichi; Kumamoto, Shin-Ichiro; Yamada, Masatoshi

2018-06-01

We analyze the chiral phase structure of the Nambu-Jona-Lasinio model at finite temperature and density by using the functional renormalization group (FRG). The renormalization group (RG) equation for the fermionic effective potential V (σ ; t) is given as a partial differential equation, where σ : = ψ bar ψ and t is a dimensionless RG scale. When the dynamical chiral symmetry breaking (DχSB) occurs at a certain scale tc, V (σ ; t) has singularities originated from the phase transitions, and then one cannot follow RG flows after tc. In this study, we introduce the weak solution method to the RG equation in order to follow the RG flows after the DχSB and to evaluate the dynamical mass and the chiral condensate in low energy scales. It is shown that the weak solution of the RG equation correctly captures vacuum structures and critical phenomena within the pure fermionic system. We show the chiral phase diagram on temperature, chemical potential and the four-Fermi coupling constant.

Convolutionless Nakajima–Zwanzig equations for stochastic analysis in nonlinear dynamical systems

PubMed Central

Venturi, D.; Karniadakis, G. E.

2014-01-01

Determining the statistical properties of stochastic nonlinear systems is of major interest across many disciplines. Currently, there are no general efficient methods to deal with this challenging problem that involves high dimensionality, low regularity and random frequencies. We propose a framework for stochastic analysis in nonlinear dynamical systems based on goal-oriented probability density function (PDF) methods. The key idea stems from techniques of irreversible statistical mechanics, and it relies on deriving evolution equations for the PDF of quantities of interest, e.g. functionals of the solution to systems of stochastic ordinary and partial differential equations. Such quantities could be low-dimensional objects in infinite dimensional phase spaces. We develop the goal-oriented PDF method in the context of the time-convolutionless Nakajima–Zwanzig–Mori formalism. We address the question of approximation of reduced-order density equations by multi-level coarse graining, perturbation series and operator cumulant resummation. Numerical examples are presented for stochastic resonance and stochastic advection–reaction problems. PMID:24910519

A computational proof of concept of a machine-intelligent artificial pancreas using Lyapunov stability and differential game theory.

PubMed

Greenwood, Nigel J C; Gunton, Jenny E

2014-07-01

This study demonstrated the novel application of a "machine-intelligent" mathematical structure, combining differential game theory and Lyapunov-based control theory, to the artificial pancreas to handle dynamic uncertainties. Realistic type 1 diabetes (T1D) models from the literature were combined into a composite system. Using a mixture of "black box" simulations and actual data from diabetic medical histories, realistic sets of diabetic time series were constructed for blood glucose (BG), interstitial fluid glucose, infused insulin, meal estimates, and sometimes plasma insulin assays. The problem of underdetermined parameters was side stepped by applying a variant of a genetic algorithm to partial information, whereby multiple candidate-personalized models were constructed and then rigorously tested using further data. These formed a "dynamic envelope" of trajectories in state space, where each trajectory was generated by a hypothesis on the hidden T1D system dynamics. This dynamic envelope was then culled to a reduced form to cover observed dynamic behavior. A machine-intelligent autonomous algorithm then implemented game theory to construct real-time insulin infusion strategies, based on the flow of these trajectories through state space and their interactions with hypoglycemic or near-hyperglycemic states. This technique was tested on 2 simulated participants over a total of fifty-five 24-hour days, with no hypoglycemic or hyperglycemic events, despite significant uncertainties from using actual diabetic meal histories with 10-minute warnings. In the main case studies, BG was steered within the desired target set for 99.8% of a 16-hour daily assessment period. Tests confirmed algorithm robustness for ±25% carbohydrate error. For over 99% of the overall 55-day simulation period, either formal controller stability was achieved to the desired target or else the trajectory was within the desired target. These results suggest that this is a stable, high-confidence way to generate closed-loop insulin infusion strategies. © 2014 Diabetes Technology Society.

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…

Dynamical properties and extremes of Northern Hemisphere climate fields over the past 60 years

NASA Astrophysics Data System (ADS)

Faranda, Davide; Messori, Gabriele; Alvarez-Castro, M. Carmen; Yiou, Pascal

2017-12-01

Atmospheric dynamics are described by a set of partial differential equations yielding an infinite-dimensional phase space. However, the actual trajectories followed by the system appear to be constrained to a finite-dimensional phase space, i.e. a strange attractor. The dynamical properties of this attractor are difficult to determine due to the complex nature of atmospheric motions. A first step to simplify the problem is to focus on observables which affect - or are linked to phenomena which affect - human welfare and activities, such as sea-level pressure, 2 m temperature, and precipitation frequency. We make use of recent advances in dynamical systems theory to estimate two instantaneous dynamical properties of the above fields for the Northern Hemisphere: local dimension and persistence. We then use these metrics to characterize the seasonality of the different fields and their interplay. We further analyse the large-scale anomaly patterns corresponding to phase-space extremes - namely time steps at which the fields display extremes in their instantaneous dynamical properties. The analysis is based on the NCEP/NCAR reanalysis data, over the period 1948-2013. The results show that (i) despite the high dimensionality of atmospheric dynamics, the Northern Hemisphere sea-level pressure and temperature fields can on average be described by roughly 20 degrees of freedom; (ii) the precipitation field has a higher dimensionality; and (iii) the seasonal forcing modulates the variability of the dynamical indicators and affects the occurrence of phase-space extremes. We further identify a number of robust correlations between the dynamical properties of the different variables.

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

Chiral dynamics of the p wave in K-p and coupled states

NASA Astrophysics Data System (ADS)

Jido, D.; Oset, E.; Ramos, A.

2002-11-01

We perform an evaluation of the p-wave amplitudes of meson-baryon scattering in the strangeness S=-1 sector starting from the lowest order chiral Lagrangians and introducing explicitly the Σ* field with couplings to the meson-baryon states obtained using SU(6) symmetry. The N/D method of unitarization is used, equivalent, in practice, to the use of the Bethe-Salpeter equation with a cutoff. The procedure leaves no freedom for the p-waves once the s-waves are fixed and thus one obtains genuine predictions for the p-wave scattering amplitudes, which are in good agreement with experimental results for differential cross sections, as well as for the width and partial decay widths of the Σ*(1385).

Computational methods for the identification of spatially varying stiffness and damping in beams

NASA Technical Reports Server (NTRS)

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

1986-01-01

A numerical approximation scheme for the estimation of functional parameters in Euler-Bernoulli models for the transverse vibration of flexible beams with tip bodies is developed. The method permits the identification of spatially varying flexural stiffness and Voigt-Kelvin viscoelastic damping coefficients which appear in the hybrid system of ordinary and partial differential equations and boundary conditions describing the dynamics of such structures. An inverse problem is formulated as a least squares fit to data subject to constraints in the form of a vector system of abstract first order evolution equations. Spline-based finite element approximations are used to finite dimensionalize the problem. Theoretical convergence results are given and numerical studies carried out on both conventional (serial) and vector computers are discussed.

LANDSAT imagery of the Venetian Lagoon: A multitemporal analysis

NASA Technical Reports Server (NTRS)

Alberotanza, L.; Zandonella, A. (Principal Investigator)

1980-01-01

The use of LANDSAT multispectral scanner images from 1975 to 1979 to determine pollution dispersion in the central basin of the lagoon under varying tidal conditions is described. Images taken during the late spring and representing both short and long range tidal dynamics were processed for partial haze removal and removal of residual striping. Selected spectral bands were correlated to different types of turbid water. The multitemporal data was calibrated, classified considering sea truth data, and evaluated. The classification differentiated tide diffusion, algae belts, and industrial, agricultural, and urban turbidity distributions. Pollution concentration is derived during the short time interval between inflow and outflow and from the distance between the two lagoon inlets and the industrial zones. Increasing pollution of the lagoon is indicated.

Automated airplane surface generation

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

Smith, R.E.; Cordero, Y.; Jones, W.

1996-12-31

An efficient methodology and software axe presented for defining a class of airplane configurations. A small set of engineering design parameters and grid control parameters govern the process. The general airplane configuration has wing, fuselage, vertical tall, horizontal tail, and canard components. Wing, canard, and tail surface grids axe manifested by solving a fourth-order partial differential equation subject to Dirichlet and Neumann boundary conditions. The design variables are incorporated into the boundary conditions, and the solution is expressed as a Fourier series. The fuselage is described by an algebraic function with four design parameters. The computed surface grids are suitablemore » for a wide range of Computational Fluid Dynamics simulation and configuration optimizations. Both batch and interactive software are discussed for applying the methodology.« less

Numerical algorithms based on Galerkin methods for the modeling of reactive interfaces in photoelectrochemical (PEC) solar cells

NASA Astrophysics Data System (ADS)

Harmon, Michael; Gamba, Irene M.; Ren, Kui

2016-12-01

This work concerns the numerical solution of a coupled system of self-consistent reaction-drift-diffusion-Poisson equations that describes the macroscopic dynamics of charge transport in photoelectrochemical (PEC) solar cells with reactive semiconductor and electrolyte interfaces. We present three numerical algorithms, mainly based on a mixed finite element and a local discontinuous Galerkin method for spatial discretization, with carefully chosen numerical fluxes, and implicit-explicit time stepping techniques, for solving the time-dependent nonlinear systems of partial differential equations. We perform computational simulations under various model parameters to demonstrate the performance of the proposed numerical algorithms as well as the impact of these parameters on the solution to the model.

Distinct functional outputs of PTEN signalling are controlled by dynamic association with β-arrestins

PubMed Central

Lima-Fernandes, Evelyne; Enslen, Hervé; Camand, Emeline; Kotelevets, Larissa; Boularan, Cédric; Achour, Lamia; Benmerah, Alexandre; Gibson, Lucien C D; Baillie, George S; Pitcher, Julie A; Chastre, Eric; Etienne-Manneville, Sandrine; Marullo, Stefano; Scott, Mark G H

2011-01-01

The tumour suppressor PTEN (phosphatase and tensin deleted on chromosome 10) regulates major cellular functions via lipid phosphatase-dependent and -independent mechanisms. Despite its fundamental pathophysiological importance, how PTEN's cellular activity is regulated has only been partially elucidated. We report that the scaffolding proteins β-arrestins (β-arrs) are important regulators of PTEN. Downstream of receptor-activated RhoA/ROCK signalling, β-arrs activate the lipid phosphatase activity of PTEN to negatively regulate Akt and cell proliferation. In contrast, following wound-induced RhoA activation, β-arrs inhibit the lipid phosphatase-independent anti-migratory effects of PTEN. β-arrs can thus differentially control distinct functional outputs of PTEN important for cell proliferation and migration. PMID:21642958

Effects of partial reinforcement and time between reinforced trials on terminal response rate in pigeon autoshaping.

PubMed

Gottlieb, Daniel A

2006-03-01

Partial reinforcement often leads to asymptotically higher rates of responding and number of trials with a response than does continuous reinforcement in pigeon autoshaping. However, comparisons typically involve a partial reinforcement schedule that differs from the continuous reinforcement schedule in both time between reinforced trials and probability of reinforcement. Two experiments examined the relative contributions of these two manipulations to asymptotic response rate. Results suggest that the greater responding previously seen with partial reinforcement is primarily due to differential probability of reinforcement and not differential time between reinforced trials. Further, once established, differences in responding are resistant to a change in stimulus and contingency. Secondary response theories of autoshaped responding (theories that posit additional response-augmenting or response-attenuating mechanisms specific to partial or continuous reinforcement) cannot fully accommodate the current body of data. It is suggested that researchers who study pigeon autoshaping train animals on a common task prior to training them under different conditions.

On the preservation of cooperation in two-strategy games with nonlocal interactions.

PubMed

Aydogmus, Ozgur; Zhou, Wen; Kang, Yun

2017-03-01

Nonlocal interactions such as spatial interaction are ubiquitous in nature and may alter the equilibrium in evolutionary dynamics. Models including nonlocal spatial interactions can provide a further understanding on the preservation and emergence of cooperation in evolutionary dynamics. In this paper, we consider a variety of two-strategy evolutionary spatial games with nonlocal interactions based on an integro-differential replicator equation. By defining the invasion speed and minimal traveling wave speed for the derived model, we study the effects of the payoffs, the selection pressure and the spatial parameter on the preservation of cooperation. One of our most interesting findings is that, for the Prisoners Dilemma games in which the defection is the only evolutionary stable strategy for unstructured populations, analyses on its asymptotic speed of propagation suggest that, in contrast with spatially homogeneous games, the cooperators can invade the habitat under proper conditions. Other two-strategy evolutionary spatial games are also explored. Both our theoretical and numerical studies show that the nonlocal spatial interaction favors diversity in strategies in a population and is able to preserve cooperation in a competing environment. A real data application in a virus mutation study echoes our theoretical observations. In addition, we compare the results of our model to the partial differential equation approach to demonstrate the importance of including non-local interaction component in evolutionary game models. Copyright © 2016 Elsevier Inc. All rights reserved.

Quantitative Analysis of Hepatitis C NS5A Viral Protein Dynamics on the ER Surface.

PubMed

Knodel, Markus M; Nägel, Arne; Reiter, Sebastian; Vogel, Andreas; Targett-Adams, Paul; McLauchlan, John; Herrmann, Eva; Wittum, Gabriel

2018-01-08

Exploring biophysical properties of virus-encoded components and their requirement for virus replication is an exciting new area of interdisciplinary virological research. To date, spatial resolution has only rarely been analyzed in computational/biophysical descriptions of virus replication dynamics. However, it is widely acknowledged that intracellular spatial dependence is a crucial component of virus life cycles. The hepatitis C virus-encoded NS5A protein is an endoplasmatic reticulum (ER)-anchored viral protein and an essential component of the virus replication machinery. Therefore, we simulate NS5A dynamics on realistic reconstructed, curved ER surfaces by means of surface partial differential equations (sPDE) upon unstructured grids. We match the in silico NS5A diffusion constant such that the NS5A sPDE simulation data reproduce experimental NS5A fluorescence recovery after photobleaching (FRAP) time series data. This parameter estimation yields the NS5A diffusion constant. Such parameters are needed for spatial models of HCV dynamics, which we are developing in parallel but remain qualitative at this stage. Thus, our present study likely provides the first quantitative biophysical description of the movement of a viral component. Our spatio-temporal resolved ansatz paves new ways for understanding intricate spatial-defined processes central to specfic aspects of virus life cycles.

Dynamic Characteristics of Micro-Beams Considering the Effect of Flexible Supports

PubMed Central

Zhong, Zuo-Yang; Zhang, Wen-Ming; Meng, Guang

2013-01-01

Normally, the boundaries are assumed to allow small deflections and moments for MEMS beams with flexible supports. The non-ideal boundary conditions have a significant effect on the qualitative dynamical behavior. In this paper, by employing the principle of energy equivalence, rigorous theoretical solutions of the tangential and rotational equivalent stiffness are derived based on the Boussinesq's and Cerruti's displacement equations. The non-dimensional differential partial equation of the motion, as well as coupled boundary conditions, are solved analytically using the method of multiple time scales. The closed-form solution provides a direct insight into the relationship between the boundary conditions and vibration characteristics of the dynamic system, in which resonance frequencies increase with the nonlinear mechanical spring effect but decrease with the effect of flexible supports. The obtained results of frequencies and mode shapes are compared with the cases of ideal boundary conditions, and the differences between them are contrasted on frequency response curves. The influences of the support material property on the equivalent stiffness and resonance frequency shift are also discussed. It is demonstrated that the proposed model with the flexible supports boundary conditions has significant effect on the rigorous quantitative dynamical analysis of the MEMS beams. Moreover, the proposed analytical solutions are in good agreement with those obtained from finite element analyses.

Quantitative Analysis of Hepatitis C NS5A Viral Protein Dynamics on the ER Surface

PubMed Central

Nägel, Arne; Reiter, Sebastian; Vogel, Andreas; McLauchlan, John; Herrmann, Eva; Wittum, Gabriel

2018-01-01

Exploring biophysical properties of virus-encoded components and their requirement for virus replication is an exciting new area of interdisciplinary virological research. To date, spatial resolution has only rarely been analyzed in computational/biophysical descriptions of virus replication dynamics. However, it is widely acknowledged that intracellular spatial dependence is a crucial component of virus life cycles. The hepatitis C virus-encoded NS5A protein is an endoplasmatic reticulum (ER)-anchored viral protein and an essential component of the virus replication machinery. Therefore, we simulate NS5A dynamics on realistic reconstructed, curved ER surfaces by means of surface partial differential equations (sPDE) upon unstructured grids. We match the in silico NS5A diffusion constant such that the NS5A sPDE simulation data reproduce experimental NS5A fluorescence recovery after photobleaching (FRAP) time series data. This parameter estimation yields the NS5A diffusion constant. Such parameters are needed for spatial models of HCV dynamics, which we are developing in parallel but remain qualitative at this stage. Thus, our present study likely provides the first quantitative biophysical description of the movement of a viral component. Our spatio-temporal resolved ansatz paves new ways for understanding intricate spatial-defined processes central to specfic aspects of virus life cycles. PMID:29316722

Column-by-column observation of dislocation motion in CdTe: Dynamic scanning transmission electron microscopy

NASA Astrophysics Data System (ADS)

Li, Chen; Zhang, Yu-Yang; Pennycook, Timothy J.; Wu, Yelong; Lupini, Andrew R.; Paudel, Naba; Pantelides, Sokrates T.; Yan, Yanfa; Pennycook, Stephen J.

2016-10-01

The dynamics of partial dislocations in CdTe have been observed at the atomic scale using aberration-corrected scanning transmission electron microscopy (STEM), allowing the mobility of different dislocations to be directly compared: Cd-core Shockley partial dislocations are more mobile than Te-core partials, and dislocation cores with unpaired columns have higher mobility than those without unpaired columns. The dynamic imaging also provides insight into the process by which the dislocations glide. Dislocations with dangling bonds on unpaired columns are found to be more mobile because the dangling bonds mediate the bond exchanges required for the dislocations to move. Furthermore, a screw dislocation has been resolved to dissociate into a Shockley partial-dislocation pair along two different directions, revealing a way for the screw dislocation to glide in the material. The results show that dynamic STEM imaging has the potential to uncover the details of dislocation motion not easily accessible by other means.

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

A partial differential equation for pseudocontact shift.

PubMed

Charnock, G T P; Kuprov, Ilya

2014-10-07

It is demonstrated that pseudocontact shift (PCS), viewed as a scalar or a tensor field in three dimensions, obeys an elliptic partial differential equation with a source term that depends on the Hessian of the unpaired electron probability density. The equation enables straightforward PCS prediction and analysis in systems with delocalized unpaired electrons, particularly for the nuclei located in their immediate vicinity. It is also shown that the probability density of the unpaired electron may be extracted, using a regularization procedure, from PCS data.

Solution of elliptic partial differential equations by fast Poisson solvers using a local relaxation factor. 2: Two-step method

NASA Technical Reports Server (NTRS)

Chang, S. C.

1986-01-01

A two-step semidirect procedure is developed to accelerate the one-step procedure described in NASA TP-2529. For a set of constant coefficient model problems, the acceleration factor increases from 1 to 2 as the one-step procedure convergence rate decreases from + infinity to 0. It is also shown numerically that the two-step procedure can substantially accelerate the convergence of the numerical solution of many partial differential equations (PDE's) with variable coefficients.

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.

Exact Solutions for the Integrable Sixth-Order Drinfeld-Sokolov-Satsuma-Hirota System by the Analytical Methods.

PubMed

Manafian Heris, Jalil; Lakestani, Mehrdad

2014-01-01

We establish exact solutions including periodic wave and solitary wave solutions for the integrable sixth-order Drinfeld-Sokolov-Satsuma-Hirota system. We employ this system by using a generalized (G'/G)-expansion and the generalized tanh-coth methods. These methods are developed for searching exact travelling wave solutions of nonlinear partial differential equations. It is shown that these methods, with the help of symbolic computation, provide a straightforward and powerful mathematical tool for solving nonlinear partial differential equations.

Parameter estimation problems for distributed systems using a multigrid method

NASA Technical Reports Server (NTRS)

Ta'asan, Shlomo; Dutt, Pravir

1990-01-01

The problem of estimating spatially varying coefficients of partial differential equations is considered from observation of the solution and of the right hand side of the equation. It is assumed that the observations are distributed in the domain and that enough observations are given. A method of discretization and an efficient multigrid method for solving the resulting discrete systems are described. Numerical results are presented for estimation of coefficients in an elliptic and a parabolic partial differential equation.

Explicit finite difference predictor and convex corrector with applications to hyperbolic partial differential equations

NASA Technical Reports Server (NTRS)

Dey, C.; Dey, S. K.

1983-01-01

An explicit finite difference scheme consisting of a predictor and a corrector has been developed and applied to solve some hyperbolic partial differential equations (PDEs). The corrector is a convex-type function which is applied at each time level and at each mesh point. It consists of a parameter which may be estimated such that for larger time steps the algorithm should remain stable and generate a fast speed of convergence to the steady-state solution. Some examples have been given.

Algebraic aspects of evolution partial differential equation arising in the study of constant elasticity of variance model from financial mathematics

NASA Astrophysics Data System (ADS)

Motsepa, Tanki; Aziz, Taha; Fatima, Aeeman; Khalique, Chaudry Masood

2018-03-01

The optimal investment-consumption problem under the constant elasticity of variance (CEV) model is investigated from the perspective of Lie group analysis. The Lie symmetry group of the evolution partial differential equation describing the CEV model is derived. The Lie point symmetries are then used to obtain an exact solution of the governing model satisfying a standard terminal condition. Finally, we construct conservation laws of the underlying equation using the general theorem on conservation laws.

DISCHARGE AND DEPTH BEHIND A PARTIALLY BREACHED DAM.

USGS Publications Warehouse

Chen, Cheng-lung

1987-01-01

The role that the velocity-distribution correction factor plays in the determination of the flood discharge and corresponding flow depth behind a partially breached dam is investigated. Assumption of a uniformly progressive flow for an established dam-break flood in a rectangular channel of infinite extent leads to the formulation of a theoretical relation between the depth and velocity of flow expressed in differential form. Integrating this ordinary differential equation, one can express the velocity in terms of the depth.

Predator-prey-subsidy population dynamics on stepping-stone domains with dispersal delays.

PubMed

Eide, Ragna M; Krause, Andrew L; Fadai, Nabil T; Van Gorder, Robert A

2018-08-14

We examine the role of the travel time of a predator along a spatial network on predator-prey population interactions, where the predator is able to partially or fully sustain itself on a resource subsidy. The impact of access to food resources on the stability and behaviour of the predator-prey-subsidy system is investigated, with a primary focus on how incorporating travel time changes the dynamics. The population interactions are modelled by a system of delay differential equations, where travel time is incorporated as discrete delay in the network diffusion term in order to model time taken to migrate between spatial regions. The model is motivated by the Arctic ecosystem, where the Arctic fox consumes both hunted lemming and scavenged seal carcass. The fox travels out on sea ice, in addition to quadrennially migrating over substantial distances. We model the spatial predator-prey-subsidy dynamics through a "stepping-stone" approach. We find that a temporal delay alone does not push species into extinction, but rather may stabilize or destabilize coexistence equilibria. We are able to show that delay can stabilize quasi-periodic or chaotic dynamics, and conclude that the incorporation of dispersal delay has a regularizing effect on dynamics, suggesting that dispersal delay can be proposed as a solution to the paradox of enrichment. Copyright © 2018 Elsevier Ltd. All rights reserved.

A stochastic-field description of finite-size spiking neural networks

PubMed Central

Longtin, André

2017-01-01

Neural network dynamics are governed by the interaction of spiking neurons. Stochastic aspects of single-neuron dynamics propagate up to the network level and shape the dynamical and informational properties of the population. Mean-field models of population activity disregard the finite-size stochastic fluctuations of network dynamics and thus offer a deterministic description of the system. Here, we derive a stochastic partial differential equation (SPDE) describing the temporal evolution of the finite-size refractory density, which represents the proportion of neurons in a given refractory state at any given time. The population activity—the density of active neurons per unit time—is easily extracted from this refractory density. The SPDE includes finite-size effects through a two-dimensional Gaussian white noise that acts both in time and along the refractory dimension. For an infinite number of neurons the standard mean-field theory is recovered. A discretization of the SPDE along its characteristic curves allows direct simulations of the activity of large but finite spiking networks; this constitutes the main advantage of our approach. Linearizing the SPDE with respect to the deterministic asynchronous state allows the theoretical investigation of finite-size activity fluctuations. In particular, analytical expressions for the power spectrum and autocorrelation of activity fluctuations are obtained. Moreover, our approach can be adapted to incorporate multiple interacting populations and quasi-renewal single-neuron dynamics. PMID:28787447

Dynamical Casimir-Polder force on a partially dressed atom near a conducting wall

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

Messina, Riccardo; Vasile, Ruggero; Passante, Roberto

2010-12-15

We study the time evolution of the Casimir-Polder force acting on a neutral atom in front of a perfectly conducting plate, when the system starts its unitary evolution from a partially dressed state. We solve the Heisenberg equations for both atomic and field quantum operators, exploiting a series expansion with respect to the electric charge and an iterative technique. After discussing the behavior of the time-dependent force on an initially partially dressed atom, we analyze a possible experimental scheme to prepare the partially dressed state and the observability of this new dynamical effect.

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…

Strongly nonlinear parabolic variational inequalities.

PubMed

Browder, F E; Brézis, H

1980-02-01

An existence and uniqueness result is established for a general class of variational inequalities for parabolic partial differential equations of the form partial differentialu/ partial differentialt + A(u) + g(u) = f with g nondecreasing but satisfying no growth condition. The proof is based upon a type of compactness result for solutions of variational inequalities that should find a variety of other applications.

Anomalous diffusion associated with nonlinear fractional derivative fokker-planck-like equation: exact time-dependent solutions

PubMed

Bologna; Tsallis; Grigolini

2000-08-01

We consider the d=1 nonlinear Fokker-Planck-like equation with fractional derivatives ( partial differential/ partial differentialt)P(x,t)=D( partial differential(gamma)/ partial differentialx(gamma))[P(x,t)](nu). Exact time-dependent solutions are found for nu=(2-gamma)/(1+gamma)(-infinity

Differential dynamic microscopy of bidisperse colloidal suspensions.

PubMed

Safari, Mohammad S; Poling-Skutvik, Ryan; Vekilov, Peter G; Conrad, Jacinta C

2017-01-01

Research tasks in microgravity include monitoring the dynamics of constituents of varying size and mobility in processes such as aggregation, phase separation, or self-assembly. We use differential dynamic microscopy, a method readily implemented with equipment available on the International Space Station, to simultaneously resolve the dynamics of particles of radius 50 nm and 1 μm in bidisperse aqueous suspensions. Whereas traditional dynamic light scattering fails to detect a signal from the larger particles at low concentrations, differential dynamic microscopy exhibits enhanced sensitivity in these conditions by accessing smaller wavevectors where scattering from the large particles is stronger. Interference patterns due to scattering from the large particles induce non-monotonic decay of the amplitude of the dynamic correlation function with the wavevector. We show that the position of the resulting minimum contains information on the vertical position of the particles. Together with the simple instrumental requirements, the enhanced sensitivity of differential dynamic microscopy makes it an appealing alternative to dynamic light scattering to characterize samples with complex dynamics.

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.)

Analysis and design of an ultrahigh temperature hydrogen-fueled MHD generator

NASA Technical Reports Server (NTRS)

Moder, Jeffrey P.; Myrabo, Leik N.; Kaminski, Deborah A.

1993-01-01

A coupled gas dynamics/radiative heat transfer analysis of partially ionized hydrogen, in local thermodynamic equilibrium, flowing through an ultrahigh temperature (10,000-20,000 K) magnetohydrodynamic (MHD) generator is performed. Gas dynamics are modeled by a set of quasi-one-dimensional, nonlinear differential equations which account for friction, convective and radiative heat transfer, and the interaction between the ionized gas and applied magnetic field. Radiative heat transfer is modeled using nongray, absorbing-emitting 2D and 3D P-1 approximations which permit an arbitrary variation of the spectral absorption coefficient with frequency. Gas dynamics and radiative heat transfer are coupled through the energy equation and through the temperature- and density-dependent absorption coefficient. The resulting nonlinear elliptic problem is solved by iterative methods. Design of such MHD generators as onboard, open-cycle, electric power supplies for a particular advanced airbreathing propulsion concept produced an efficient and compact 128-MWe generator characterized by an extraction ratio of 35.5 percent, a power density of 10,500 MWe/cu m, and a specific (extracted) energy of 324 MJe/kg of hydrogen. The maximum wall heat flux and total wall heat load were 453 MW/sq m and 62 MW, respectively.

14-3-3 proteins regulate desmosomal adhesion via plakophilins.

PubMed

Rietscher, Katrin; Keil, René; Jordan, Annemarie; Hatzfeld, Mechthild

2018-05-22

Desmosomes are essential for strong intercellular adhesion and are abundant in tissues exposed to mechanical strain. At the same time, desmosomes need to be dynamic to allow for remodeling of epithelia during differentiation or wound healing. Phosphorylation of desmosomal plaque proteins appears to be essential for desmosome dynamics. However, the mechanisms of how context-dependent post-translational modifications regulate desmosome formation, dynamics or stability are incompletely understood. Here, we show that growth factor signaling regulates the phosphorylation-dependent association of plakophilins 1 and 3 (PKP1 and PKP3) with 14-3-3 protein isoforms, and uncover unique and partially antagonistic functions of members of the 14-3-3 family in the regulation of desmosomes. 14-3-3γ associated primarily with cytoplasmic PKP1 phosphorylated at S155 and destabilized intercellular cohesion of keratinocytes by reducing its incorporation into desmosomes. In contrast, 14-3-3σ (also known as stratifin, encoded by SFN ) interacted preferentially with S285-phosphorylated PKP3 to promote its accumulation at tricellular contact sites, leading to stable desmosomes. Taken together, our study identifies a new layer of regulation of intercellular adhesion by 14-3-3 proteins. © 2018. Published by The Company of Biologists Ltd.

A symplectic integration method for elastic filaments

NASA Astrophysics Data System (ADS)

Ladd, Tony; Misra, Gaurav

2009-03-01

Elastic rods are a ubiquitous coarse-grained model of semi-flexible biopolymers such as DNA, actin, and microtubules. The Worm-Like Chain (WLC) is the standard numerical model for semi-flexible polymers, but it is only a linearized approximation to the dynamics of an elastic rod, valid for small deflections; typically the torsional motion is neglected as well. In the standard finite-difference and finite-element formulations of an elastic rod, the continuum equations of motion are discretized in space and time, but it is then difficult to ensure that the Hamiltonian structure of the exact equations is preserved. Here we discretize the Hamiltonian itself, expressed as a line integral over the contour of the filament. This discrete representation of the continuum filament can then be integrated by one of the explicit symplectic integrators frequently used in molecular dynamics. The model systematically approximates the continuum partial differential equations, but has the same level of computational complexity as molecular dynamics and is constraint free. Numerical tests show that the algorithm is much more stable than a finite-difference formulation and can be used for high aspect ratio filaments, such as actin. We present numerical results for the deterministic and stochastic motion of single filaments.

Nonlinear dynamics of contact interaction of a size-dependent plate supported by a size-dependent beam

NASA Astrophysics Data System (ADS)

Awrejcewicz, J.; Krysko, V. A.; Yakovleva, T. V.; Pavlov, S. P.; Krysko, V. A.

2018-05-01

A mathematical model of complex vibrations exhibited by contact dynamics of size-dependent beam-plate constructions was derived by taking the account of constraints between these structural members. The governing equations were yielded by variational principles based on the moment theory of elasticity. The centre of the investigated plate was supported by a beam. The plate and the beam satisfied the Kirchhoff/Euler-Bernoulli hypotheses. The derived partial differential equations (PDEs) were reduced to the Cauchy problems by the Faedo-Galerkin method in higher approximations, whereas the Cauchy problem was solved using a few Runge-Kutta methods. Reliability of results was validated by comparing the solutions obtained by qualitatively different methods. Complex vibrations were investigated with the help of methods of nonlinear dynamics such as vibration signals, phase portraits, Fourier power spectra, wavelet analysis, and estimation of the largest Lyapunov exponents based on the Rosenstein, Kantz, and Wolf methods. The effect of size-dependent parameters of the beam and plate on their contact interaction was investigated. It was detected and illustrated that the first contact between the size-dependent structural members implies chaotic vibrations. In addition, problems of chaotic synchronization between a nanoplate and a nanobeam were addressed.

Monge-Ampére simulation of fourth order PDEs in two dimensions with application to elastic-electrostatic contact problems

NASA Astrophysics Data System (ADS)

DiPietro, Kelsey L.; Lindsay, Alan E.

2017-11-01

We present an efficient moving mesh method for the simulation of fourth order nonlinear partial differential equations (PDEs) in two dimensions using the Parabolic Monge-Ampére (PMA) equation. PMA methods have been successfully applied to the simulation of second order problems, but not on systems with higher order equations which arise in many topical applications. Our main application is the resolution of fine scale behavior in PDEs describing elastic-electrostatic interactions. The PDE system considered has multiple parameter dependent singular solution modalities, including finite time singularities and sharp interface dynamics. We describe how to construct a dynamic mesh algorithm for such problems which incorporates known self similar or boundary layer scalings of the underlying equation to locate and dynamically resolve fine scale solution features in these singular regimes. We find a key step in using the PMA equation for mesh generation in fourth order problems is the adoption of a high order representation of the transformation from the computational to physical mesh. We demonstrate the efficacy of the new method on a variety of examples and establish several new results and conjectures on the nature of self-similar singularity formation in higher order PDEs.

Fundamentals of Geophysical Fluid Dynamics

NASA Astrophysics Data System (ADS)

McWilliams, James C.

2006-07-01

Earth's atmosphere and oceans exhibit complex patterns of fluid motion over a vast range of space and time scales. These patterns combine to establish the climate in response to solar radiation that is inhomogeneously absorbed by the materials comprising air, water, and land. Spontaneous, energetic variability arises from instabilities in the planetary-scale circulations, appearing in many different forms such as waves, jets, vortices, boundary layers, and turbulence. Geophysical fluid dynamics (GFD) is the science of all these types of fluid motion. This textbook is a concise and accessible introduction to GFD for intermediate to advanced students of the physics, chemistry, and/or biology of Earth's fluid environment. The book was developed from the author's many years of teaching a first-year graduate course at the University of California, Los Angeles. Readers are expected to be familiar with physics and mathematics at the level of general dynamics (mechanics) and partial differential equations. Covers the essential GFD required for atmospheric science and oceanography courses Mathematically rigorous, concise coverage of basic theory and applications to both oceans and atmospheres Author is a world expert; this book is based on the course he has taught for many years Exercises are included, with solutions available to instructors from solutions@cambridge.org

Improved Performance in Differentiating Benign from Malignant Sinonasal Tumors Using Diffusion-weighted Combined with Dynamic Contrast-enhanced Magnetic Resonance Imaging

PubMed Central

Wang, Xin-Yan; Yan, Fei; Hao, Hui; Wu, Jian-Xing; Chen, Qing-Hua; Xian, Jun-Fang

2015-01-01

Background: Differentiating benign from malignant sinonsal lesions is essential for treatment planning as well as determining the patient's prognosis, but the differentiation is often difficult in clinical practice. The study aimed to determine whether the combination of diffusion-weighted (DW) and dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) can improve the performance in differentiating benign from malignant sinonasal tumors. Methods: This retrospective study included 197 consecutive patients with sinonasal tumors (116 malignant tumors and 81 benign tumors). All patients underwent both DW and DCE-MRI in a 3-T magnetic resonance scanner. Two different settings of b values (0,700 and 0,1000 s/mm2) and two different strategies of region of interest (ROI) including whole slice (WS) and partial slice (PS) were used to calculate apparent diffusion coefficients (ADCs). A DW parameter with WS ADCsb0,1000 and two DCE-MRI parameters (time intensity curve [TIC] and time to peak enhancement [Tpeak]) were finally combined to use in differentiating the benign from the malignant tumors in this study. Results: The mean ADCs of malignant sinonasal tumors (WS ADCsb0,1000 = 1.084 × 10−3 mm2/s) were significantly lower than those of benign tumors (WS ADCsb0,1000 = 1.617 × 10−3 mm2/s, P < 0.001). The accuracy using WS ADCsb0,1000 alone was 83.7% in differentiating the benign from the malignant tumors (85.3% sensitivity, 81.2% specificity, 86.4% positive predictive value [PPV], and 79.5% negative predictive value [NPV]). The accuracy using DCE with Tpeak and TIC alone was 72.1% (69.1% sensitivity, 74.1% specificity, 77.5% PPV, and 65.1% NPV). Using DW-MRI parameter was superior than using DCE parameters in differentiation between benign and malignant sinonasal tumors (P < 0.001). The accuracy was 87.3% (90.5% sensitivity, 82.7% specificity, 88.2% PPV, and 85.9% NPV) using DW-MRI combined with DCE-MRI, which was superior than that using DCE-MRI alone or using DW-MRI alone (both P < 0.001) in differentiating the benign from the malignant tumors. Conclusions: Diffusion-weighted combined with DCE-MRI can improve imaging performance in differentiating benign from malignant sinonasal tumors, which has the potential to improve diagnostic accuracy and to provide added value in the management for these tumors. PMID:25698188

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

(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.

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).

Accurate spectral solutions for the parabolic and elliptic partial differential equations by the ultraspherical tau method

NASA Astrophysics Data System (ADS)

Doha, E. H.; Abd-Elhameed, W. M.

2005-09-01

We present a double ultraspherical spectral methods that allow the efficient approximate solution for the parabolic partial differential equations in a square subject to the most general inhomogeneous mixed boundary conditions. The differential equations with their boundary and initial conditions are reduced to systems of ordinary differential equations for the time-dependent expansion coefficients. These systems are greatly simplified by using tensor matrix algebra, and are solved by using the step-by-step method. Numerical applications of how to use these methods are described. Numerical results obtained compare favorably with those of the analytical solutions. Accurate double ultraspherical spectral approximations for Poisson's and Helmholtz's equations are also noted. Numerical experiments show that spectral approximation based on Chebyshev polynomials of the first kind is not always better than others based on ultraspherical polynomials.

Isotropic differential phase contrast microscopy for quantitative phase bio-imaging.

PubMed

Chen, Hsi-Hsun; Lin, Yu-Zi; Luo, Yuan

2018-05-16

Quantitative phase imaging (QPI) has been investigated to retrieve optical phase information of an object and applied to biological microscopy and related medical studies. In recent examples, differential phase contrast (DPC) microscopy can recover phase image of thin sample under multi-axis intensity measurements in wide-field scheme. Unlike conventional DPC, based on theoretical approach under partially coherent condition, we propose a new method to achieve isotropic differential phase contrast (iDPC) with high accuracy and stability for phase recovery in simple and high-speed fashion. The iDPC is simply implemented with a partially coherent microscopy and a programmable thin-film transistor (TFT) shield to digitally modulate structured illumination patterns for QPI. In this article, simulation results show consistency of our theoretical approach for iDPC under partial coherence. In addition, we further demonstrate experiments of quantitative phase images of a standard micro-lens array, as well as label-free live human cell samples. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

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.

Auto-Bäcklund transformations for a matrix partial differential equation

NASA Astrophysics Data System (ADS)

Gordoa, P. R.; Pickering, A.

2018-07-01

We derive auto-Bäcklund transformations, analogous to those of the matrix second Painlevé equation, for a matrix partial differential equation. We also then use these auto-Bäcklund transformations to derive matrix equations involving shifts in a discrete variable, a process analogous to the use of the auto-Bäcklund transformations of the matrix second Painlevé equation to derive a discrete matrix first Painlevé equation. The equations thus derived then include amongst other examples a semidiscrete matrix equation which can be considered to be an extension of this discrete matrix first Painlevé equation. The application of this technique to the auto-Bäcklund transformations of the scalar case of our partial differential equation has not been considered before, and so the results obtained here in this scalar case are also new. Other equations obtained here using this technique include a scalar semidiscrete equation which arises in the case of the second Painlevé equation, and which does not seem to have been thus derived previously.

Boundary-fitted curvilinear coordinate systems for solution of partial differential equations on fields containing any number of arbitrary two-dimensional bodies

NASA Technical Reports Server (NTRS)

Thompson, J. F.; Thames, F. C.; Mastin, C. W.

1977-01-01

A method is presented for automatic numerical generation of a general curvilinear coordinate system with coordinate lines coincident with all boundaries of a general multi-connected two-dimensional region containing any number of arbitrarily shaped bodies. No restrictions are placed on the shape of the boundaries, which may even be time-dependent, and the approach is not restricted in principle to two dimensions. With this procedure the numerical solution of a partial differential system may be done on a fixed rectangular field with a square mesh with no interpolation required regardless of the shape of the physical boundaries, regardless of the spacing of the curvilinear coordinate lines in the physical field, and regardless of the movement of the coordinate system in the physical plane. A number of examples of coordinate systems and application thereof to the solution of partial differential equations are given. The FORTRAN computer program and instructions for use are included.

Solving Partial Differential Equations in a data-driven multiprocessor environment

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

Gaudiot, J.L.; Lin, C.M.; Hosseiniyar, M.

1988-12-31

Partial differential equations can be found in a host of engineering and scientific problems. The emergence of new parallel architectures has spurred research in the definition of parallel PDE solvers. Concurrently, highly programmable systems such as data-how architectures have been proposed for the exploitation of large scale parallelism. The implementation of some Partial Differential Equation solvers (such as the Jacobi method) on a tagged token data-flow graph is demonstrated here. Asynchronous methods (chaotic relaxation) are studied and new scheduling approaches (the Token No-Labeling scheme) are introduced in order to support the implementation of the asychronous methods in a data-driven environment.more » New high-level data-flow language program constructs are introduced in order to handle chaotic operations. Finally, the performance of the program graphs is demonstrated by a deterministic simulation of a message passing data-flow multiprocessor. An analysis of the overhead in the data-flow graphs is undertaken to demonstrate the limits of parallel operations in dataflow PDE program graphs.« less

Simulations of pattern dynamics for reaction-diffusion systems via SIMULINK

PubMed Central

2014-01-01

Background Investigation of the nonlinear pattern dynamics of a reaction-diffusion system almost always requires numerical solution of the system’s set of defining differential equations. Traditionally, this would be done by selecting an appropriate differential equation solver from a library of such solvers, then writing computer codes (in a programming language such as C or Matlab) to access the selected solver and display the integrated results as a function of space and time. This “code-based” approach is flexible and powerful, but requires a certain level of programming sophistication. A modern alternative is to use a graphical programming interface such as Simulink to construct a data-flow diagram by assembling and linking appropriate code blocks drawn from a library. The result is a visual representation of the inter-relationships between the state variables whose output can be made completely equivalent to the code-based solution. Results As a tutorial introduction, we first demonstrate application of the Simulink data-flow technique to the classical van der Pol nonlinear oscillator, and compare Matlab and Simulink coding approaches to solving the van der Pol ordinary differential equations. We then show how to introduce space (in one and two dimensions) by solving numerically the partial differential equations for two different reaction-diffusion systems: the well-known Brusselator chemical reactor, and a continuum model for a two-dimensional sheet of human cortex whose neurons are linked by both chemical and electrical (diffusive) synapses. We compare the relative performances of the Matlab and Simulink implementations. Conclusions The pattern simulations by Simulink are in good agreement with theoretical predictions. Compared with traditional coding approaches, the Simulink block-diagram paradigm reduces the time and programming burden required to implement a solution for reaction-diffusion systems of equations. Construction of the block-diagram does not require high-level programming skills, and the graphical interface lends itself to easy modification and use by non-experts. PMID:24725437

Simulations of pattern dynamics for reaction-diffusion systems via SIMULINK.

PubMed

Wang, Kaier; Steyn-Ross, Moira L; Steyn-Ross, D Alistair; Wilson, Marcus T; Sleigh, Jamie W; Shiraishi, Yoichi

2014-04-11

Investigation of the nonlinear pattern dynamics of a reaction-diffusion system almost always requires numerical solution of the system's set of defining differential equations. Traditionally, this would be done by selecting an appropriate differential equation solver from a library of such solvers, then writing computer codes (in a programming language such as C or Matlab) to access the selected solver and display the integrated results as a function of space and time. This "code-based" approach is flexible and powerful, but requires a certain level of programming sophistication. A modern alternative is to use a graphical programming interface such as Simulink to construct a data-flow diagram by assembling and linking appropriate code blocks drawn from a library. The result is a visual representation of the inter-relationships between the state variables whose output can be made completely equivalent to the code-based solution. As a tutorial introduction, we first demonstrate application of the Simulink data-flow technique to the classical van der Pol nonlinear oscillator, and compare Matlab and Simulink coding approaches to solving the van der Pol ordinary differential equations. We then show how to introduce space (in one and two dimensions) by solving numerically the partial differential equations for two different reaction-diffusion systems: the well-known Brusselator chemical reactor, and a continuum model for a two-dimensional sheet of human cortex whose neurons are linked by both chemical and electrical (diffusive) synapses. We compare the relative performances of the Matlab and Simulink implementations. The pattern simulations by Simulink are in good agreement with theoretical predictions. Compared with traditional coding approaches, the Simulink block-diagram paradigm reduces the time and programming burden required to implement a solution for reaction-diffusion systems of equations. Construction of the block-diagram does not require high-level programming skills, and the graphical interface lends itself to easy modification and use by non-experts.

First-principles investigations of equilibrium Ca, Mg, Si and O isotope fractionations between silicate melts and minerals

NASA Astrophysics Data System (ADS)

Qi, Y.; Liu, X.; Kang, J.; He, L.

2017-12-01

Equilibrium isotope fractionation factors are essential for using stable isotope data to study many geosciences processes such as planetary differentiation and mantle evolution. The mass-dependent equilibrium isotope fractionation is primarily controlled by the difference in bond energies triggered by the isotope substitution. With the recent advances in computational capabilities, first-principles calculation has become a reliable tool to investigate equilibrium isotopic fractionations, greatly improving our understanding of the factors controlling isotope fractionations. It is important to understand the isotope fractionation between melts and minerals because magmatism is critical for creating and shaping the Earth. However, because isotope fractionation between melts and minerals is small at high temperature, it is difficult to experimentally calibrate such small signature. Due to the disordered and dynamic character of melts, calculations of equilibrium isotope fractionation of melts are more challenging than that for gaseous molecules or minerals. Here, we apply first-principles molecular dynamics method to calculate equilibrium Ca, Mg, Si, and O isotope fractionations between silicate melts and minerals. Our results show that equilibrium Mg, Si, and O isotope fractionations between olivine and pure Mg2SiO4 melt are close to zero at high temperature (e.g. δ26Mgmelt-ol = 0.03 ± 0.04‰, δ30Simelt-ol = -0.06 ± 0.07‰, δ18Omelt-ol = 0.07‰ ± 0.08 at 1500 K). Equilibrium Ca, Mg, Si, and O isotope fractionations between diopside and basalt melt (67% CaMgSi2O6 + 33% CaAl2Si2O8) are also negligible at high temperature (e.g. δ44/40Camelt-cpx = -0.01 ± 0.02‰, δ26Mgmelt-cpx = -0.05 ± 0.14‰, δ30Simelt-cpx = 0.04 ± 0.04‰, δ18Omelt-cpx = 0.03 ± 0.07‰ at 1500 K). These results are consistent with the observations in natural samples that there is no significant Ca, Mg, Si, and O isotope fractionation during mantle partial melting, demonstrating the reliability of our methods. Thus, our results can be used to understand stable isotope fractionation during partial melting of mantle peridotite or fractional crystallization during magmatic differentiation. The first-principles molecular dynamics method is a promising tool to obtain equilibrium fractionation of more isotope systems for complicate liquids.

Serum-induced neurite retraction in CAD cells--involvement of an ATP-actin retractile system and the lack of microtubule-associated proteins.

PubMed

Chesta, María E; Carbajal, Agustín; Arce, Carlos A; Bisig, Carlos G

2014-11-01

Cultured catecholamine-differentiated cells [which lack the microtubule-associated proteins (MAPs): MAP1B, MAP2, Tau, STOP, and Doublecortin] proliferate in the presence of fetal bovine serum, and, in its absence, cease dividing and generate processes similar to the neurites of normal neurons. The reintroduction of serum induces neurite retraction, and proliferation resumes. The neurite retraction process in catecholamine-differentiated cells was partially characterized in this study. Microtubules in the cells were found to be in a highly dynamic state, and tubulin in the microtubules consisted primarily of the tyrosinated and deacetylated isotypes. Increased levels of acetylated or Δ2-tubulin (which are normally absent) did not prevent serum-induced neurite retraction. Treatment of differentiated cells with lysophosphatidic acid or adenosine deaminase induced neurite retraction. Inhibition of Rho-associated protein kinase, ATP depletion and microfilament disruption each (individually) blocked serum-induced neurite retraction, suggesting that an ATP-dependent actomyosin system underlies the mechanism of neurite retraction. Nocodazole treatment induced neurite retraction, but this effect was blocked by pretreatment with the microtubule-stabilizing drug paclitaxel (Taxol). Paclitaxel did not prevent serum-induced or lysophosphatidic acid-induced retraction, suggesting that integrity of microtubules (despite their dynamic state) is necessary to maintain neurite elongation, and that paclitaxel-induced stabilization alone is not sufficient to resist the retraction force induced by serum. Transfection with green fluorescent protein-Tau conferred resistance to retraction caused by serum. We hypothesize that, in normal neurons (cultured or in vivo), MAPs are necessary not only to stabilize microtubules, but also to establish interactions with other cytoskeletal or membrane components to form a stable structure capable of resisting the retraction force. © 2014 FEBS.

The mechanical and chemical equations of motion of muscle contraction

NASA Astrophysics Data System (ADS)

Shiner, J. S.; Sieniutycz, Stanislaw

1997-11-01

Up to now no formulation of muscle contraction has provided both the chemical kinetic equations for the reactions responsible for the contraction and the mechanical equation of motion for the muscle. This has most likely been due to the lack of general formalisms for nonlinear systems with chemical-nonchemical coupling valid under the far from equilibrium conditions under which muscle operates physiologically. We have recently developed such formalisms and apply them here to the formulation of muscle contraction to obtain both the chemical and the mechanical equations. The standard formulation up to now has yielded only the dynamic equations for the chemical variables and has considered these to be functions of both time and an appropriate mechanical variable. The macroscopically observable quantities were then obtained by averaging over the mechanical variable. When attempting to derive the dynamics equations for both the chemistry and mechanics this choice of variables leads to conflicting results for the mechanical equation of motion when two different general formalisms are applied. The conflict can be resolved by choosing the variables such that both the chemical variables and the mechanical variables are considered to be functions of time alone. This adds one equation to the set of differential equations to be solved but is actually a simplification of the problem, since these equations are ordinary differential equations, not the partial differential equations of the now standard formulation, and since in this choice of variables the variables themselves are the macroscopic observables the procedure of averaging over the mechanical variable is eliminated. Furthermore, the parameters occurring in the equations at this level of description should be accessible to direct experimental determination.

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.

Development of a simulation model for dynamic derailment analysis of high-speed trains

NASA Astrophysics Data System (ADS)

Ling, Liang; Xiao, Xin-Biao; Jin, Xue-Song

2014-12-01

The running safety of high-speed trains has become a major concern of the current railway research with the rapid development of high-speed railways around the world. The basic safety requirement is to prevent the derailment. The root causes of the dynamic derailment of high-speed trains operating in severe environments are not easy to identify using the field tests or laboratory experiments. Numerical simulation using an advanced train-track interaction model is a highly efficient and low-cost approach to investigate the dynamic derailment behavior and mechanism of high-speed trains. This paper presents a three-dimensional dynamic model of a high-speed train coupled with a ballast track for dynamic derailment analysis. The model considers a train composed of multiple vehicles and the nonlinear inter-vehicle connections. The ballast track model consists of rails, fastenings, sleepers, ballasts, and roadbed, which are modeled by Euler beams, nonlinear spring-damper elements, equivalent ballast bodies, and continuous viscoelastic elements, in which the modal superposition method was used to reduce the order of the partial differential equations of Euler beams. The commonly used derailment safety assessment criteria around the world are embedded in the simulation model. The train-track model was then used to investigate the dynamic derailment responses of a high-speed train passing over a buckled track, in which the derailment mechanism and train running posture during the dynamic derailment process were analyzed in detail. The effects of train and track modelling on dynamic derailment analysis were also discussed. The numerical results indicate that the train and track modelling options have a significant effect on the dynamic derailment analysis. The inter-vehicle impacts and the track flexibility and nonlinearity should be considered in the dynamic derailment simulations.

Rotor-to-stator Partial Rubbing and Its Effects on Rotor Dynamic Response

NASA Technical Reports Server (NTRS)

Muszynska, Agnes; Franklin, Wesley D.; Hayashida, Robert D.

1991-01-01

Results from experimental and analytical studies on rotor to stationary element partial rubbings at several locations and their effects on rotor dynamic responses are presented. The mathematical model of a rubbing rotor is given. The computer program provides numerical results which agree with experimentally obtained rotor responses.

Radioecological modelling of Polonium-210 and Caesium-137 in lichen-reindeer-man and top predators.

PubMed

Persson, Bertil R R; Gjelsvik, Runhild; Holm, Elis

2018-06-01

This work deals with analysis and modelling of the radionuclides 210 Pb and 210 Po in the food-chain lichen-reindeer-man in addition to 210 Po and 137 Cs in top predators. By using the methods of Partial Least Square Regression (PLSR) the atmospheric deposition of 210 Pb and 210 Po is predicted at the sample locations. Dynamic modelling of the activity concentration with differential equations is fitted to the sample data. Reindeer lichen consumption, gastrointestinal absorption, organ distribution and elimination is derived from information in the literature. Dynamic modelling of transfer of 210 Pb and 210 Po to reindeer meat, liver and bone from lichen consumption, fitted well with data from Sweden and Finland from 1966 to 1971. The activity concentration of 210 Pb in the skeleton in man is modelled by using the results of studying the kinetics of lead in skeleton and blood in lead-workers after end of occupational exposure. The result of modelling 210 Pb and 210 Po activity in skeleton matched well with concentrations of 210 Pb and 210 Po in teeth from reindeer-breeders and autopsy bone samples in Finland. The results of 210 Po and 137 Cs in different tissues of wolf, wolverine and lynx previously published, are analysed with multivariate data processing methods such as Principal Component Analysis PCA, and modelled with the method of Projection to Latent Structures, PLS, or Partial Least Square Regression PLSR. Copyright © 2017 Elsevier Ltd. All rights reserved.

Black Hole Firewalls and Lorentzian Relativity

NASA Astrophysics Data System (ADS)

Winterberg, Friedwardt

2013-04-01

In a paper published (Z. f. Naturforsch. 56a, 889, 2001) I had shown that the pre-Einstein theory of relativity by Lorentz and Poincare, extended to the general theory of relativity and quantum mechanics, predicts the disintegration of matter by passing through the event horizon. The zero point vacuum energy is there cut-off at the Planck energy, but Lorentz-invariant all the way up to this energy. The cut-off creates a distinguished reference system in which this energy is at rest. For non-relativistic velocities relative to this reference system, the special and general relativity remain a good approximations, with matter held together in a stable equilibrium by electrostatic forces (or forces acting like them) as a solution of an elliptic partial differential equation derived from Maxwell's equation. But in approaching and crossing the velocity of light in the distinguished reference system, which is equivalent in approaching and crossing of the event horizon, the elliptic differential equation goes over into a hyperbolic differential equation (as in fluid dynamics from subsonic to supersonic flow), and there is no such equilibrium. According to Schwarzschild's interior solution, the event horizon of a collapsing mass appears first as a point in its center, thereafter moving radially outwards, thereby converting all the mass into energy, explaining the observed gamma ray bursters.

Do differences make the heart grow fonder? Associations between differential peer experiences on adolescent sibling conflict and relationship quality.

PubMed

Greer, Kelly Bassett; Campione-Barr, Nicole; Debrown, Brina; Maupin, Cynthia

2014-01-01

Though it is known that different familial relationships influence one another (e.g., Yu & Gamble, 2008) the influence of outside relationships (i.e., peers) on family dynamics (i.e., sibling relationships) is less clear. Thus, the authors examined the association differential peer experiences had on the conflict frequency, conflict intensity, and relationship quality of the sibling relationship. A 1-year longitudinal design measured first-born siblings in Grades 8, 10, and 12 along with their second-born siblings. In the first year, participants were brought to the university to complete questionnaires and in the following year, siblings again participated by completing online questionnaires at home. Results partially confirmed the study hypotheses that adolescents would show greater sibling conflict and poorer relationship quality with greater peer group differences, revealing that when peer group differences between siblings were greater, the youngest siblings reported more intense sibling conflicts (pe = -.10 p < .05), the oldest siblings reported greater relationship positivity (pe = .13 p < .05), and the oldest second-borns reported greater relationship negativity (pe = -.12 p < .10). These findings underscore the importance of investigating siblings' differential experiences beyond familial influence to focus on outside sources to better understand developmental fluctuations in siblings' relationships.

A novel principle for partial agonism of liver X receptor ligands. Competitive recruitment of activators and repressors.

PubMed

Albers, Michael; Blume, Beatrix; Schlueter, Thomas; Wright, Matthew B; Kober, Ingo; Kremoser, Claus; Deuschle, Ulrich; Koegl, Manfred

2006-02-24

Partial, selective activation of nuclear receptors is a central issue in molecular endocrinology but only partly understood. Using LXRs as an example, we show here that purely agonistic ligands can be clearly and quantitatively differentiated from partial agonists by the cofactor interactions they induce. Although a pure agonist induces a conformation that is incompatible with the binding of repressors, partial agonists such as GW3965 induce a state where the interaction not only with coactivators, but also corepressors is clearly enhanced over the unliganded state. The activities of the natural ligand 22(R)-hydroxycholesterol and of a novel quinazolinone ligand, LN6500 can be further differentiated from GW3965 and T0901317 by their weaker induction of coactivator binding. Using biochemical and cell-based assays, we show that the natural ligand of LXR is a comparably weak partial agonist. As predicted, we find that a change in the coactivator to corepressor ratio in the cell will affect NCoR recruiting compounds more dramatically than NCoR-dissociating compounds. Our data show how competitive binding of coactivators and corepressors can explain the tissue-specific behavior of partial agonists and open up new routes to a rational design of partial agonists for LXRs.

Efficient Nonlinear Low-Order Models for Atmospheric and Climate Dynamics

NASA Astrophysics Data System (ADS)

Grady, Kevin A.

The governing equations of atmospheric and climate dynamics present enormous mathematical challenges when studied analytically. Following the pioneering work of Kolmogorov, Lorenz, and Obukhov, a popular approach to handle these difficult partial differential equations (PDEs) is to approximate them with finite systems of ordinary differential equations (ODEs), called low-order models (LOMs). One such LOM is the celebrated Lorenz (1963) model of just three ODEs, but attempts to extend it to larger, more realistic models of atmospheric dynamics have sometimes led to LOMs exhibiting unphysical behavior, such as a lack of energy conservation in the dissipationless limit. These behaviors can be avoided by constructing LOMs using 3-mode nonlinear dynamical systems known in mechanics as Volterra gyrostats, the simplest one being equivalent to the Lorenz model. Gyrostatic LOMs guarantee energy conservation, suggesting they may offer a general framework for deriving efficient LOMs for atmospheric and climate dynamics. This study explores the use of gyrostatic LOMs in three important related problems of atmospheric dynamics. The first is 2D Rayleigh-Benard convection (RBC), where an algorithm for studying gyrostatic LOMs was developed. Before now this had to be done manually, limiting the LOMs that could be studied as well as their size. This algorithm permits the study of LOMs larger than previously possible as well as their conservation properties. It was used here to demonstrate that all physically sound LOMs for this problem from recent publications have a gyrostatic form. The second problem is the interplay of buoyancy and shear in the formation of rolls versus cells in mesoscale shallow convection (MSC). A gyrostatic LOM for 3D RBC with the ability to parameterize buoyancy and shear was developed using an adopted version of the algorithm for 2D RBC. This model was run for hundreds of different combinations of buoyancy and shear, with the results generally matching those of other observational and modeling studies. The third problem is convection driven by internal heating, where the algorithm developed for 2D RBC was applied to derive several gyrostatic LOMs. In general these LOMs were shown to match reasonably well with the actual physics of this problem.

Parametric instability analysis of truncated conical shells using the Haar wavelet method

NASA Astrophysics Data System (ADS)

Dai, Qiyi; Cao, Qingjie

2018-05-01

In this paper, the Haar wavelet method is employed to analyze the parametric instability of truncated conical shells under static and time dependent periodic axial loads. The present work is based on the Love first-approximation theory for classical thin shells. The displacement field is expressed as the Haar wavelet series in the axial direction and trigonometric functions in the circumferential direction. Then the partial differential equations are reduced into a system of coupled Mathieu-type ordinary differential equations describing dynamic instability behavior of the shell. Using Bolotin's method, the first-order and second-order approximations of principal instability regions are determined. The correctness of present method is examined by comparing the results with those in the literature and very good agreement is observed. The difference between the first-order and second-order approximations of principal instability regions for tensile and compressive loads is also investigated. Finally, numerical results are presented to bring out the influences of various parameters like static load factors, boundary conditions and shell geometrical characteristics on the domains of parametric instability of conical shells.

A similarity solution of time dependent MHD liquid film flow over stretching sheet with variable physical properties

NASA Astrophysics Data System (ADS)

Idrees, M.; Rehman, Sajid; Shah, Rehan Ali; Ullah, M.; Abbas, Tariq

2018-03-01

An analysis is performed for the fluid dynamics incorporating the variation of viscosity and thermal conductivity on an unsteady two-dimensional free surface flow of a viscous incompressible conducting fluid taking into account the effect of a magnetic field. Surface tension quadratically vary with temperature while fluid viscosity and thermal conductivity are assumed to vary as a linear function of temperature. The boundary layer partial differential equations in cartesian coordinates are transformed into a system of nonlinear ordinary differential equations (ODEs) by similarity transformation. The developed nonlinear equations are solved analytically by Homotopy Analysis Method (HAM) while numerically by using the shooting method. The Effects of natural parameters such as the variable viscosity parameter A, variable thermal conductivity parameter N, Hartmann number Ma, film Thickness, unsteadiness parameter S, Thermocapillary number M and Prandtl number Pr on the velocity and temperature profiles are investigated. The results for the surface skin friction coefficient f″ (0) , Nusselt number (heat flux) -θ‧ (0) and free surface temperature θ (1) are presented graphically and in tabular form.

Dax1 and Nanog act in parallel to stabilize mouse embryonic stem cells and induced pluripotency

PubMed Central

Zhang, Junlei; Liu, Gaoke; Ruan, Yan; Wang, Jiali; Zhao, Ke; Wan, Ying; Liu, Bing; Zheng, Hongting; Peng, Tao; Wu, Wei; He, Ping; Hu, Fu-Quan; Jian, Rui

2014-01-01

Nanog expression is heterogeneous and dynamic in embryonic stem cells (ESCs). However, the mechanism for stabilizing pluripotency during the transitions between Nanoghigh and Nanoglow states is not well understood. Here we report that Dax1 acts in parallel with Nanog to regulate mouse ESC (mESCs) identity. Dax1 stable knockdown mESCs are predisposed towards differentiation but do not lose pluripotency, whereas Dax1 overexpression supports LIF-independent self-renewal. Although partially complementary, Dax1 and Nanog function independently and cannot replace one another. They are both required for full reprogramming to induce pluripotency. Importantly, Dax1 is indispensable for self-renewal of Nanoglow mESCs. Moreover, we report that Dax1 prevents extra-embryonic endoderm (ExEn) commitment by directly repressing Gata6 transcription. Dax1 may also mediate inhibition of trophectoderm differentiation independent or as a downstream effector of Oct4. These findings establish a basal role of Dax1 in maintaining pluripotency during the state transition of mESCs and somatic cell reprogramming. PMID:25284313

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.

A Dynamic Differentiation Framework for Talent Enhancement: Findings from Syntheses and Teachers' Perspectives

ERIC Educational Resources Information Center

Smith, Susen

2015-01-01

Differentiating curriculum and pedagogy is a dynamic process that is dependent on the interrelationship between intrapersonal and environmental factors that can support the unique educational needs of gifted students. A Model of Dynamic Differentiation (MoDD) was developed from a larger study based on the ecological systems theory, an in-depth…

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.

Ultrasound speckle reduction based on fractional order differentiation.

PubMed

Shao, Dangguo; Zhou, Ting; Liu, Fan; Yi, Sanli; Xiang, Yan; Ma, Lei; Xiong, Xin; He, Jianfeng

2017-07-01

Ultrasound images show a granular pattern of noise known as speckle that diminishes their quality and results in difficulties in diagnosis. To preserve edges and features, this paper proposes a fractional differentiation-based image operator to reduce speckle in ultrasound. An image de-noising model based on fractional partial differential equations with balance relation between k (gradient modulus threshold that controls the conduction) and v (the order of fractional differentiation) was constructed by the effective combination of fractional calculus theory and a partial differential equation, and the numerical algorithm of it was achieved using a fractional differential mask operator. The proposed algorithm has better speckle reduction and structure preservation than the three existing methods [P-M model, the speckle reducing anisotropic diffusion (SRAD) technique, and the detail preserving anisotropic diffusion (DPAD) technique]. And it is significantly faster than bilateral filtering (BF) in producing virtually the same experimental results. Ultrasound phantom testing and in vivo imaging show that the proposed method can improve the quality of an ultrasound image in terms of tissue SNR, CNR, and FOM values.

Examining sex differentials in the uptake and process of HIV testing in three high prevalence districts of India.

PubMed

Joseph, Saju; Kielmann, Karina; Kudale, Abhay; Sheikh, Kabir; Shinde, Swati; Porter, John; Rangan, Sheela

2010-03-01

Sex differentials in the uptake of HIV testing have been reported in a range of settings, however, men's and women's testing patterns are not consistent across these settings, suggesting the need to set sex differentials against gender norms in patient testing behaviour and provider practices. A community-based, cross-sectional survey among 347 people living with HIV in three HIV high prevalence districts of India examined reasons for undergoing an HIV test, location of testing and conditions under which individuals were tested. HIV testing was almost always provider-initiated for men. Men were more likely to be advised to test by a private practitioner and to test in the private sector. Women were more likely to be advised to test by a family member, and to test in the public sector. Men were more likely to receive pre-test information than women, when tested in the private sector. Men were also more likely to receive direct disclosure of their HIV positive status by a health provider, regardless of the sector in which they tested. More women than men were repeatedly tested for HIV, regardless of sector. These sex differentials in the uptake and process of HIV testing are partially explained through differences in public and private sector testing practices. However, they also reflect women's lack of awareness and agency in HIV care seeking and differential treatment by providers. Examining gender dynamics that underpin sex differentials in HIV testing patterns and practices is essential for a realistic assessment of the challenges and implications of scaling-up HIV testing and mainstreaming gender in HIV/AIDS programmes.

In silico ordinary differential equation/partial differential equation hemodialysis model estimates methadone removal during dialysis

PubMed Central

Linares, Oscar A; Schiesser, William E; Fudin, Jeffrey; Pham, Thien C; Bettinger, Jeffrey J; Mathew, Roy O; Daly, Annemarie L

2015-01-01

Background There is a need to have a model to study methadone’s losses during hemodialysis to provide informed methadone dose recommendations for the practitioner. Aim To build a one-dimensional (1-D), hollow-fiber geometry, ordinary differential equation (ODE) and partial differential equation (PDE) countercurrent hemodialyzer model (ODE/PDE model). Methodology We conducted a cross-sectional study in silico that evaluated eleven hemodialysis patients. Patients received a ceiling dose of methadone hydrochloride 30 mg/day. Outcome measures included: the total amount of methadone removed during dialysis; methadone’s overall intradialytic mass transfer rate coefficient, km; and, methadone’s removal rate, jME. Each metric was measured at dialysate flow rates of 250 mL/min and 800 mL/min. Results The ODE/PDE model revealed a significant increase in the change of methadone’s mass transfer with increased dialysate flow rate, %Δkm=18.56, P=0.02, N=11. The total amount of methadone mass transferred across the dialyzer membrane with high dialysate flow rate significantly increased (0.042±0.016 versus 0.052±0.019 mg/kg, P=0.02, N=11). This was accompanied by a small significant increase in methadone’s mass transfer rate (0.113±0.002 versus 0.014±0.002 mg/kg/h, P=0.02, N=11). The ODE/PDE model accurately predicted methadone’s removal during dialysis. The absolute value of the prediction errors for methadone’s extraction and throughput were less than 2%. Conclusion ODE/PDE modeling of methadone’s hemodialysis is a new approach to study methadone’s removal, in particular, and opioid removal, in general, in patients with end-stage renal disease on hemodialysis. ODE/PDE modeling accurately quantified the fundamental phenomena of methadone’s mass transfer during hemodialysis. This methodology may lead to development of optimally designed intradialytic opioid treatment protocols, and allow dynamic monitoring of outflow plasma opioid concentrations for model predictive control during dialysis in humans. PMID:26229501

Understanding the transmission dynamics of respiratory syncytial virus using multiple time series and nested models.

PubMed

White, L J; Mandl, J N; Gomes, M G M; Bodley-Tickell, A T; Cane, P A; Perez-Brena, P; Aguilar, J C; Siqueira, M M; Portes, S A; Straliotto, S M; Waris, M; Nokes, D J; Medley, G F

2007-09-01

The nature and role of re-infection and partial immunity are likely to be important determinants of the transmission dynamics of human respiratory syncytial virus (hRSV). We propose a single model structure that captures four possible host responses to infection and subsequent reinfection: partial susceptibility, altered infection duration, reduced infectiousness and temporary immunity (which might be partial). The magnitude of these responses is determined by four homotopy parameters, and by setting some of these parameters to extreme values we generate a set of eight nested, deterministic transmission models. In order to investigate hRSV transmission dynamics, we applied these models to incidence data from eight international locations. Seasonality is included as cyclic variation in transmission. Parameters associated with the natural history of the infection were assumed to be independent of geographic location, while others, such as those associated with seasonality, were assumed location specific. Models incorporating either of the two extreme assumptions for immunity (none or solid and lifelong) were unable to reproduce the observed dynamics. Model fits with either waning or partial immunity to disease or both were visually comparable. The best fitting structure was a lifelong partial immunity to both disease and infection. Observed patterns were reproduced by stochastic simulations using the parameter values estimated from the deterministic models.

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.

Numerical method based on the lattice Boltzmann model for the Fisher equation.

PubMed

Yan, Guangwu; Zhang, Jianying; Dong, Yinfeng

2008-06-01

In this paper, a lattice Boltzmann model for the Fisher equation is proposed. First, the Chapman-Enskog expansion and the multiscale time expansion are used to describe higher-order moment of equilibrium distribution functions and a series of partial differential equations in different time scales. Second, the modified partial differential equation of the Fisher equation with the higher-order truncation error is obtained. Third, comparison between numerical results of the lattice Boltzmann models and exact solution is given. The numerical results agree well with the classical ones.

Generation of three-dimensional body-fitted grids by solving hyperbolic partial differential equations

NASA Technical Reports Server (NTRS)

Steger, Joseph L.

1989-01-01

Hyperbolic grid generation procedures are described which have been used in external flow simulations about complex configurations. For many practical applications a single well-ordered (i.e., structured) grid can be used to mesh an entire configuration, in other problems, composite or unstructured grid procedures are needed. Although the hyperbolic partial differential equation grid generation procedure has mainly been utilized to generate structured grids, an extension of the procedure to semiunstructured grids is briefly described. Extensions of the methodology are also described using two-dimensional equations.

Generation of three-dimensional body-fitted grids by solving hyperbolic and parabolic partial differential equations

NASA Technical Reports Server (NTRS)

Steger, Joseph L.

1989-01-01

Hyperbolic grid generation procedures are described which have been used in external flow simulations about complex configurations. For many practical applications a single well-ordered (i.e., structured) grid can be used to mesh an entire configuration, in other problems, composite or unstructured grid procedures are needed. Although the hyperbolic partial differential equation grid generation procedure has mainly been utilized to generate structured grids, extension of the procedure to semiunstructured grids is briefly described. Extensions of the methodology are also described using two-dimensional equations.

Computer transformation of partial differential equations into any coordinate system

NASA Technical Reports Server (NTRS)

Sullivan, R. D.

1977-01-01

The use of tensors to provide a compact way of writing partial differential equations in a form valid in all coordinate systems is discussed. In order to find solutions to the equations with their boundary conditions they must be expressed in terms of the coordinate system under consideration. The process of arriving at these expressions from the tensor formulation was automated by a software system, TENSR. An allied system that analyzes the resulting expressions term by term and drops those that are negligible is also described.

Partial differential equation models in macroeconomics.

PubMed

Achdou, Yves; Buera, Francisco J; Lasry, Jean-Michel; Lions, Pierre-Louis; Moll, Benjamin

2014-11-13

The purpose of this article is to get mathematicians interested in studying a number of partial differential equations (PDEs) that naturally arise in macroeconomics. These PDEs come from models designed to study some of the most important questions in economics. At the same time, they are highly interesting for mathematicians because their structure is often quite difficult. We present a number of examples of such PDEs, discuss what is known about their properties, and list some open questions for future research. © 2014 The Author(s) Published by the Royal Society. All rights reserved.

Dynamic least-squares kernel density modeling of Fokker-Planck equations with application to neural population.

PubMed

Shotorban, Babak

2010-04-01

The dynamic least-squares kernel density (LSQKD) model [C. Pantano and B. Shotorban, Phys. Rev. E 76, 066705 (2007)] is used to solve the Fokker-Planck equations. In this model the probability density function (PDF) is approximated by a linear combination of basis functions with unknown parameters whose governing equations are determined by a global least-squares approximation of the PDF in the phase space. In this work basis functions are set to be Gaussian for which the mean, variance, and covariances are governed by a set of partial differential equations (PDEs) or ordinary differential equations (ODEs) depending on what phase-space variables are approximated by Gaussian functions. Three sample problems of univariate double-well potential, bivariate bistable neurodynamical system [G. Deco and D. Martí, Phys. Rev. E 75, 031913 (2007)], and bivariate Brownian particles in a nonuniform gas are studied. The LSQKD is verified for these problems as its results are compared against the results of the method of characteristics in nondiffusive cases and the stochastic particle method in diffusive cases. For the double-well potential problem it is observed that for low to moderate diffusivity the dynamic LSQKD well predicts the stationary PDF for which there is an exact solution. A similar observation is made for the bistable neurodynamical system. In both these problems least-squares approximation is made on all phase-space variables resulting in a set of ODEs with time as the independent variable for the Gaussian function parameters. In the problem of Brownian particles in a nonuniform gas, this approximation is made only for the particle velocity variable leading to a set of PDEs with time and particle position as independent variables. Solving these PDEs, a very good performance by LSQKD is observed for a wide range of diffusivities.

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.

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.

The impact of new polarization data from Bonn, Mainz and Jefferson Laboratory on γ p → π N multipoles

NASA Astrophysics Data System (ADS)

Anisovich, A. V.; Beck, R.; Döring, M.; Gottschall, M.; Hartmann, J.; Kashevarov, V.; Klempt, E.; Meißner, Ulf-G.; Nikonov, V.; Ostrick, M.; Rönchen, D.; Sarantsev, A.; Strakovsky, I.; Thiel, A.; Tiator, L.; Thoma, U.; Workman, R.; Wunderlich, Y.

2016-09-01

New data on pion-photoproduction off the proton have been included in the partial-wave analyses Bonn-Gatchina and SAID and in the dynamical coupled-channel approach Jülich-Bonn. All reproduce the recent new data well: the double-polarization data for E, G, H, P and T in γ p→ π0p from ELSA, the beam asymmetry Σ for γ p→ π0p and π+n from Jefferson Laboratory, and the precise new differential cross section and beam asymmetry data Σ for γ p→ π0p from MAMI. The new fit results for the multipoles are compared with predictions not taking into account the new data. The mutual agreement is improved considerably but still far from being perfect.

Mathematical analysis of dynamic spread of Pine Wilt disease.

PubMed

Dimitrijevic, D D; Bacic, J

2013-01-01

Since its detection in Portugal in 1999, the pinewood nematode Bursaphelenchus xylophilus (Steiner and Buhrer), a causal agent of Pine Wilt Disease, represents a threat to European forestry. Significant amount of money has been spent on its monitoring and eradication. This paper presents mathematical analysis of spread of pine wilt disease using a set of partial differential equations with space (longitude and latitude) and time as parameters of estimated spread of disease. This methodology can be used to evaluate risk of various assumed entry points of disease and make defense plans in advance. In case of an already existing outbreak, it can be used to draw optimal line of defense and plan removal of trees. Optimization constraints are economic loss of removal of susceptible trees as well as budgetary constraints of workforce cost.

Drekar v.2.0

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

Seefeldt, Ben; Sondak, David; Hensinger, David M.

Drekar is an application code that solves partial differential equations for fluids that can be optionally coupled to electromagnetics. Drekar solves low-mach compressible and incompressible computational fluid dynamics (CFD), compressible and incompressible resistive magnetohydrodynamics (MHD), and multiple species plasmas interacting with electromagnetic fields. Drekar discretization technology includes continuous and discontinuous finite element formulations, stabilized finite element formulations, mixed integration finite element bases (nodal, edge, face, volume) and an initial arbitrary Lagrangian Eulerian (ALE) capability. Drekar contains the implementation of the discretized physics and leverages the open source Trilinos project for both parallel solver capabilities and general finite element discretization tools.more » The code will be released open source under a BSD license. The code is used for fundamental research for simulation of fluids and plasmas on high performance computing environments.« less

Well-posed continuum equations for granular flow with compressibility and μ(I)-rheology

NASA Astrophysics Data System (ADS)

Barker, T.; Schaeffer, D. G.; Shearer, M.; Gray, J. M. N. T.

2017-05-01

Continuum modelling of granular flow has been plagued with the issue of ill-posed dynamic equations for a long time. Equations for incompressible, two-dimensional flow based on the Coulomb friction law are ill-posed regardless of the deformation, whereas the rate-dependent μ(I)-rheology is ill-posed when the non-dimensional inertial number I is too high or too low. Here, incorporating ideas from critical-state soil mechanics, we derive conditions for well-posedness of partial differential equations that combine compressibility with I-dependent rheology. When the I-dependence comes from a specific friction coefficient μ(I), our results show that, with compressibility, the equations are well-posed for all deformation rates provided that μ(I) satisfies certain minimal, physically natural, inequalities.

Hot-spot evolution and the global tectonics of Venus

NASA Astrophysics Data System (ADS)

Phillips, R. J.; Grimm, R. E.; Malin, M. C.

1991-05-01

The global tectonics of Venus may be dominated by plumes rising from the mantle and impinging on the lithosphere, giving rise to hot spots. Global sea-floor spreading does not take place, but direct convective coupling of mantle flow fields to the lithosphere leads to regional-scale deformation and may allow lithospheric transport on a limited scale. A hot-spot evolutionary sequence comprises (1) a broad domal uplift resulting from a rising mantle plume, (2) massive partial melting in the plume head and generation of a thickened crust or crustal plateau, (3) collapse of dynamic topography, and (4) creep spreading of the crustal plateau. Crust on Venus is produced by gradual vertical differentiation with little recycling rather than by the rapid horizontal creation and consumption characteristic of terrestrial sea-floor spreading.

Continuum mechanics and thermodynamics in the Hamilton and the Godunov-type formulations

NASA Astrophysics Data System (ADS)

Peshkov, Ilya; Pavelka, Michal; Romenski, Evgeniy; Grmela, Miroslav

2018-01-01

Continuum mechanics with dislocations, with the Cattaneo-type heat conduction, with mass transfer, and with electromagnetic fields is put into the Hamiltonian form and into the form of the Godunov-type system of the first-order, symmetric hyperbolic partial differential equations (SHTC equations). The compatibility with thermodynamics of the time reversible part of the governing equations is mathematically expressed in the former formulation as degeneracy of the Hamiltonian structure and in the latter formulation as the existence of a companion conservation law. In both formulations the time irreversible part represents gradient dynamics. The Godunov-type formulation brings the mathematical rigor (the local well posedness of the Cauchy initial value problem) and the possibility to discretize while keeping the physical content of the governing equations (the Godunov finite volume discretization).

Workshop on Engineering Turbulence Modeling

NASA Technical Reports Server (NTRS)

Povinelli, Louis A. (Editor); Liou, W. W. (Editor); Shabbir, A. (Editor); Shih, T.-H. (Editor)

1992-01-01

Discussed here is the future direction of various levels of engineering turbulence modeling related to computational fluid dynamics (CFD) computations for propulsion. For each level of computation, there are a few turbulence models which represent the state-of-the-art for that level. However, it is important to know their capabilities as well as their deficiencies in order to help engineers select and implement the appropriate models in their real world engineering calculations. This will also help turbulence modelers perceive the future directions for improving turbulence models. The focus is on one-point closure models (i.e., from algebraic models to higher order moment closure schemes and partial differential equation methods) which can be applied to CFD computations. However, other schemes helpful in developing one-point closure models, are also discussed.

Well-posed continuum equations for granular flow with compressibility and μ(I)-rheology

PubMed Central

Schaeffer, D. G.; Shearer, M.; Gray, J. M. N. T.

2017-01-01

Continuum modelling of granular flow has been plagued with the issue of ill-posed dynamic equations for a long time. Equations for incompressible, two-dimensional flow based on the Coulomb friction law are ill-posed regardless of the deformation, whereas the rate-dependent μ(I)-rheology is ill-posed when the non-dimensional inertial number I is too high or too low. Here, incorporating ideas from critical-state soil mechanics, we derive conditions for well-posedness of partial differential equations that combine compressibility with I-dependent rheology. When the I-dependence comes from a specific friction coefficient μ(I), our results show that, with compressibility, the equations are well-posed for all deformation rates provided that μ(I) satisfies certain minimal, physically natural, inequalities. PMID:28588402

Tuning and performance evaluation of PID controller for superheater steam temperature control of 200 MW boiler using gain phase assignment algorithm

NASA Astrophysics Data System (ADS)

Begum, A. Yasmine; Gireesh, N.

2018-04-01

In superheater, steam temperature is controlled in a cascade control loop. The cascade control loop consists of PI and PID controllers. To improve the superheater steam temperature control the controller's gains in a cascade control loop has to be tuned efficiently. The mathematical model of the superheater is derived by sets of nonlinear partial differential equations. The tuning methods taken for study here are designed for delay plus first order transfer function model. Hence from the dynamical model of the superheater, a FOPTD model is derived using frequency response method. Then by using Chien-Hrones-Reswick Tuning Algorithm and Gain-Phase Assignment Algorithm optimum controller gains has been found out based on the least value of integral time weighted absolute error.

Well-posed continuum equations for granular flow with compressibility and μ(I)-rheology.

PubMed

Barker, T; Schaeffer, D G; Shearer, M; Gray, J M N T

2017-05-01

Continuum modelling of granular flow has been plagued with the issue of ill-posed dynamic equations for a long time. Equations for incompressible, two-dimensional flow based on the Coulomb friction law are ill-posed regardless of the deformation, whereas the rate-dependent μ ( I )-rheology is ill-posed when the non-dimensional inertial number I is too high or too low. Here, incorporating ideas from critical-state soil mechanics, we derive conditions for well-posedness of partial differential equations that combine compressibility with I -dependent rheology. When the I -dependence comes from a specific friction coefficient μ ( I ), our results show that, with compressibility, the equations are well-posed for all deformation rates provided that μ ( I ) satisfies certain minimal, physically natural, inequalities.

Hot-spot evolution and the global tectonics of Venus

NASA Technical Reports Server (NTRS)

Phillips, Roger J.; Grimm, Robert E.; Malin, Michael C.

1991-01-01

The global tectonics of Venus may be dominated by plumes rising from the mantle and impinging on the lithosphere, giving rise to hot spots. Global sea-floor spreading does not take place, but direct convective coupling of mantle flow fields to the lithosphere leads to regional-scale deformation and may allow lithospheric transport on a limited scale. A hot-spot evolutionary sequence comprises (1) a broad domal uplift resulting from a rising mantle plume, (2) massive partial melting in the plume head and generation of a thickened crust or crustal plateau, (3) collapse of dynamic topography, and (4) creep spreading of the crustal plateau. Crust on Venus is produced by gradual vertical differentiation with little recycling rather than by the rapid horizontal creation and consumption characteristic of terrestrial sea-floor spreading.

Hot-spot evolution and the global tectonics of venus.

PubMed

Phillips, R J; Grimm, R E; Malin, M C

1991-05-03

The global tectonics of Venus may be dominated by plumes rising from the mantle and impinging on the lithosphere, giving rise to hot spots. Global sea-floor spreading does not take place, but direct convective coupling of mantle flow fields to the lithosphere leads to regional-scale deformation and may allow lithospheric transport on a limited scale. A hot-spot evolutionary sequence comprises (i) a broad domal uplift resulting from a rising mantle plume, (ii) massive partial melting in the plume head and generation of a thickened crust or crustal plateau, (iii) collapse of dynamic topography, and (iv) creep spreading of the crustal plateau. Crust on Venus is produced by gradual vertical differentiation with little recycling rather than by the rapid horizontal creation and consumption characteristic of terrestrial sea-floor spreading.

Single-bubble sonoluminescence in sulfuric acid and water: bubble dynamics, stability, and continuous spectra.

PubMed

Puente, Gabriela F; García-Martínez, Pablo; Bonetto, Fabián J

2007-01-01

We present theoretical calculations of an argon bubble in a liquid solution of 85%wt sulfuric acid and 15%wt water in single-bubble sonoluminescence. We used a model without free parameters to be adjusted. We predict from first principles the region in parameter space for stable bubble evolution, the temporal evolution of the bubble radius, the maximum temperature, pressures, and the light spectra due to thermal emissions. We also used a partial differential equation based model (hydrocode) to compute the temperature and pressure evolutions at the center of the bubble during maximum compression. We found the behavior of this liquid mixture to be very different from water in several aspects. Most of the models in sonoluminescence were compared with water experimental results.

A hybrid algorithm for coupling partial differential equation and compartment-based dynamics.

PubMed

Harrison, Jonathan U; Yates, Christian A

2016-09-01

Stochastic simulation methods can be applied successfully to model exact spatio-temporally resolved reaction-diffusion systems. However, in many cases, these methods can quickly become extremely computationally intensive with increasing particle numbers. An alternative description of many of these systems can be derived in the diffusive limit as a deterministic, continuum system of partial differential equations (PDEs). Although the numerical solution of such PDEs is, in general, much more efficient than the full stochastic simulation, the deterministic continuum description is generally not valid when copy numbers are low and stochastic effects dominate. Therefore, to take advantage of the benefits of both of these types of models, each of which may be appropriate in different parts of a spatial domain, we have developed an algorithm that can be used to couple these two types of model together. This hybrid coupling algorithm uses an overlap region between the two modelling regimes. By coupling fluxes at one end of the interface and using a concentration-matching condition at the other end, we ensure that mass is appropriately transferred between PDE- and compartment-based regimes. Our methodology gives notable reductions in simulation time in comparison with using a fully stochastic model, while maintaining the important stochastic features of the system and providing detail in appropriate areas of the domain. We test our hybrid methodology robustly by applying it to several biologically motivated problems including diffusion and morphogen gradient formation. Our analysis shows that the resulting error is small, unbiased and does not grow over time. © 2016 The Authors.

A hybrid algorithm for coupling partial differential equation and compartment-based dynamics

PubMed Central

Yates, Christian A.

2016-01-01

Stochastic simulation methods can be applied successfully to model exact spatio-temporally resolved reaction–diffusion systems. However, in many cases, these methods can quickly become extremely computationally intensive with increasing particle numbers. An alternative description of many of these systems can be derived in the diffusive limit as a deterministic, continuum system of partial differential equations (PDEs). Although the numerical solution of such PDEs is, in general, much more efficient than the full stochastic simulation, the deterministic continuum description is generally not valid when copy numbers are low and stochastic effects dominate. Therefore, to take advantage of the benefits of both of these types of models, each of which may be appropriate in different parts of a spatial domain, we have developed an algorithm that can be used to couple these two types of model together. This hybrid coupling algorithm uses an overlap region between the two modelling regimes. By coupling fluxes at one end of the interface and using a concentration-matching condition at the other end, we ensure that mass is appropriately transferred between PDE- and compartment-based regimes. Our methodology gives notable reductions in simulation time in comparison with using a fully stochastic model, while maintaining the important stochastic features of the system and providing detail in appropriate areas of the domain. We test our hybrid methodology robustly by applying it to several biologically motivated problems including diffusion and morphogen gradient formation. Our analysis shows that the resulting error is small, unbiased and does not grow over time. PMID:27628171

In-depth characterization of breast cancer tumor-promoting cell transcriptome by RNA sequencing and microarrays

PubMed Central

Soldà, Giulia; Merlino, Giuseppe; Fina, Emanuela; Brini, Elena; Moles, Anna; Cappelletti, Vera; Daidone, Maria Grazia

2016-01-01

Numerous studies have reported the existence of tumor-promoting cells (TPC) with self-renewal potential and a relevant role in drug resistance. However, pathways and modifications involved in the maintenance of such tumor subpopulations are still only partially understood. Sequencing-based approaches offer the opportunity for a detailed study of TPC including their transcriptome modulation. Using microarrays and RNA sequencing approaches, we compared the transcriptional profiles of parental MCF7 breast cancer cells with MCF7-derived TPC (i.e. MCFS). Data were explored using different bioinformatic approaches, and major findings were experimentally validated. The different analytical pipelines (Lifescope and Cufflinks based) yielded similar although not identical results. RNA sequencing data partially overlapped microarray results and displayed a higher dynamic range, although overall the two approaches concordantly predicted pathway modifications. Several biological functions were altered in TPC, ranging from production of inflammatory cytokines (i.e., IL-8 and MCP-1) to proliferation and response to steroid hormones. More than 300 non-coding RNAs were defined as differentially expressed, and 2,471 potential splicing events were identified. A consensus signature of genes up-regulated in TPC was derived and was found to be significantly associated with insensitivity to fulvestrant in a public breast cancer patient dataset. Overall, we obtained a detailed portrait of the transcriptome of a breast cancer TPC line, highlighted the role of non-coding RNAs and differential splicing, and identified a gene signature with a potential as a context-specific biomarker in patients receiving endocrine treatment. PMID:26556871

Scale-freeness or partial synchronization in neural mass phase oscillator networks: Pick one of two?

PubMed

Daffertshofer, Andreas; Ton, Robert; Pietras, Bastian; Kringelbach, Morten L; Deco, Gustavo

2018-04-04

Modeling and interpreting (partial) synchronous neural activity can be a challenge. We illustrate this by deriving the phase dynamics of two seminal neural mass models: the Wilson-Cowan firing rate model and the voltage-based Freeman model. We established that the phase dynamics of these models differed qualitatively due to an attractive coupling in the first and a repulsive coupling in the latter. Using empirical structural connectivity matrices, we determined that the two dynamics cover the functional connectivity observed in resting state activity. We further searched for two pivotal dynamical features that have been reported in many experimental studies: (1) a partial phase synchrony with a possibility of a transition towards either a desynchronized or a (fully) synchronized state; (2) long-term autocorrelations indicative of a scale-free temporal dynamics of phase synchronization. Only the Freeman phase model exhibited scale-free behavior. Its repulsive coupling, however, let the individual phases disperse and did not allow for a transition into a synchronized state. The Wilson-Cowan phase model, by contrast, could switch into a (partially) synchronized state, but it did not generate long-term correlations although being located close to the onset of synchronization, i.e. in its critical regime. That is, the phase-reduced models can display one of the two dynamical features, but not both. Copyright © 2018 The Authors. Published by Elsevier Inc. All rights reserved.

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.

Reproductive isolation between populations of Iris atropurpurea is associated with ecological differentiation

PubMed Central

Yardeni, Gil; Tessler, Naama; Imbert, Eric; Sapir, Yuval

2016-01-01

Background and Aims Speciation is often described as a continuous dynamic process, expressed by different magnitudes of reproductive isolation (RI) among groups in different levels of divergence. Studying intraspecific partial RI can shed light on mechanisms underlying processes of population divergence. Intraspecific divergence can be driven by spatially stochastic accumulation of genetic differences following reduced gene flow, resulting in increased RI with increased geographical distance, or by local adaptation, resulting in increased RI with environmental difference. Methods We tested for RI as a function of both geographical distance and ecological differentiation in Iris atropurpurea, an endemic Israeli coastal plant. We crossed plants in the Netanya Iris Reserve population with plants from 14 populations across the species’ full distribution, and calculated RI and reproductive success based on fruit set, seed set and fraction of seed viability. Key Results We found that total RI was not significantly associated with geographical distance, but significantly increased with ecological distance. Similarly, reproductive success of the crosses, estimated while controlling for the dependency of each component on the previous stage, significantly reduced with increased ecological distance. Conclusions Our results indicate that the rise of post-pollination reproductive barriers in I. atropurpurea is more affected by ecological differentiation between populations than by geographical distance, supporting the hypothesis that ecological differentiation is predominant over isolation by distance and by reduced gene flow in this species. These findings also affect conservation management, such as genetic rescue, in the highly fragmented and endangered I. atropurpurea. PMID:27436798