Soliton solutions to the fifth-order Korteweg-de Vries equation and their applications to surface and internal water waves

NASA Astrophysics Data System (ADS)

Khusnutdinova, K. R.; Stepanyants, Y. A.; Tranter, M. R.

2018-02-01

We study solitary wave solutions of the fifth-order Korteweg-de Vries equation which contains, besides the traditional quadratic nonlinearity and third-order dispersion, additional terms including cubic nonlinearity and fifth order linear dispersion, as well as two nonlinear dispersive terms. An exact solitary wave solution to this equation is derived, and the dependence of its amplitude, width, and speed on the parameters of the governing equation is studied. It is shown that the derived solution can represent either an embedded or regular soliton depending on the equation parameters. The nonlinear dispersive terms can drastically influence the existence of solitary waves, their nature (regular or embedded), profile, polarity, and stability with respect to small perturbations. We show, in particular, that in some cases embedded solitons can be stable even with respect to interactions with regular solitons. The results obtained are applicable to surface and internal waves in fluids, as well as to waves in other media (plasma, solid waveguides, elastic media with microstructure, etc.).

Studies of wheel-running reinforcement: parameters of Herrnstein's (1970) response-strength equation vary with schedule order.

PubMed

Belke, T W

2000-05-01

Six male Wistar rats were exposed to different orders of reinforcement schedules to investigate if estimates from Herrnstein's (1970) single-operant matching law equation would vary systematically with schedule order. Reinforcement schedules were arranged in orders of increasing and decreasing reinforcement rate. Subsequently, all rats were exposed to a single reinforcement schedule within a session to determine within-session changes in responding. For each condition, the operant was lever pressing and the reinforcing consequence was the opportunity to run for 15 s. Estimates of k and R(O) were higher when reinforcement schedules were arranged in order of increasing reinforcement rate. Within a session on a single reinforcement schedule, response rates increased between the beginning and the end of a session. A positive correlation between the difference in parameters between schedule orders and the difference in response rates within a session suggests that the within-session change in response rates may be related to the difference in the asymptotes. These results call into question the validity of parameter estimates from Herrnstein's (1970) equation when reinforcer efficacy changes within a session.

Front and pulse solutions for the complex Ginzburg-Landau equation with higher-order terms.

PubMed

Tian, Huiping; Li, Zhonghao; Tian, Jinping; Zhou, Guosheng

2002-12-01

We investigate one-dimensional complex Ginzburg-Landau equation with higher-order terms and discuss their influences on the multiplicity of solutions. An exact analytic front solution is presented. By stability analysis for the original partial differential equation, we derive its necessary stability condition for amplitude perturbations. This condition together with the exact front solution determine the region of parameter space where the uniformly translating front solution can exist. In addition, stable pulses, chaotic pulses, and attenuation pulses appear generally if the parameters are out of the range. Finally, applying these analysis into the optical transmission system numerically we find that the stable transmission of optical pulses can be achieved if the parameters are appropriately chosen.

Symmetry and singularity properties of second-order ordinary differential equations of Lie's type III

NASA Astrophysics Data System (ADS)

Andriopoulos, K.; Leach, P. G. L.

2007-04-01

We extend the work of Abraham-Shrauner [B. Abraham-Shrauner, Hidden symmetries and linearization of the modified Painleve-Ince equation, J. Math. Phys. 34 (1993) 4809-4816] on the linearization of the modified Painleve-Ince equation to a wider class of nonlinear second-order ordinary differential equations invariant under the symmetries of time translation and self-similarity. In the process we demonstrate a remarkable connection with the parameters obtained in the singularity analysis of this class of equations.

Periodic solutions of second-order nonlinear difference equations containing a small parameter. II - Equivalent linearization

NASA Technical Reports Server (NTRS)

Mickens, R. E.

1985-01-01

The classical method of equivalent linearization is extended to a particular class of nonlinear difference equations. It is shown that the method can be used to obtain an approximation of the periodic solutions of these equations. In particular, the parameters of the limit cycle and the limit points can be determined. Three examples illustrating the method are presented.

On the Singularity Structure of WKB Solution of the Boosted Whittaker Equation: its Relevance to Resurgent Functions with Essential Singularities

NASA Astrophysics Data System (ADS)

Kamimoto, Shingo; Kawai, Takahiro; Koike, Tatsuya

2016-12-01

Inspired by the symbol calculus of linear differential operators of infinite order applied to the Borel transformed WKB solutions of simple-pole type equation [Kamimoto et al. (RIMS Kôkyûroku Bessatsu B 52:127-146, 2014)], which is summarized in Section 1, we introduce in Section 2 the space of simple resurgent functions depending on a parameter with an infra-exponential type growth order, and then we define the assigning operator A which acts on the space and produces resurgent functions with essential singularities. In Section 3, we apply the operator A to the Borel transforms of the Voros coefficient and its exponentiation for the Whittaker equation with a large parameter so that we may find the Borel transforms of the Voros coefficient and its exponentiation for the boosted Whittaker equation with a large parameter. In Section 4, we use these results to find the explicit form of the alien derivatives of the Borel transformed WKB solutions of the boosted Whittaker equation with a large parameter. The results in this paper manifest the importance of resurgent functions with essential singularities in developing the exact WKB analysis, the WKB analysis based on the resurgent function theory. It is also worth emphasizing that the concrete form of essential singularities we encounter is expressed by the linear differential operators of infinite order.

Computer program documentation for the dynamic analysis of a noncontacting mechanical face seal

NASA Technical Reports Server (NTRS)

Auer, B. M.; Etsion, I.

1980-01-01

A computer program is presented which achieves a numerical solution for the equations of motion of a noncontacting mechanical face seal. The flexibly-mounted primary seal ring motion is expressed by a set of second order differential equations for three degrees of freedom. These equations are reduced to a set of first order equations and the GEAR software package is used to solve the set of first order equations. Program input includes seal design parameters and seal operating conditions. Output from the program includes velocities and displacements of the seal ring about the axis of an inertial reference system. One example problem is described.

Exact periodic solutions of the sixth-order generalized Boussinesq equation

NASA Astrophysics Data System (ADS)

Kamenov, O. Y.

2009-09-01

This paper examines a class of nonlinear sixth-order generalized Boussinesq-like equations (SGBE): utt = uxx + 3(u2)xx + uxxxx + αuxxxxxx, α in R, depending on the positive parameter α. Hirota's bilinear transformation method is applied to the above class of non-integrable equations and exact periodic solutions have been obtained. The results confirmed the well-known nonlinear superposition principle.

Explicit least squares system parameter identification for exact differential input/output models

NASA Technical Reports Server (NTRS)

Pearson, A. E.

1993-01-01

The equation error for a class of systems modeled by input/output differential operator equations has the potential to be integrated exactly, given the input/output data on a finite time interval, thereby opening up the possibility of using an explicit least squares estimation technique for system parameter identification. The paper delineates the class of models for which this is possible and shows how the explicit least squares cost function can be obtained in a way that obviates dealing with unknown initial and boundary conditions. The approach is illustrated by two examples: a second order chemical kinetics model and a third order system of Lorenz equations.

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

PubMed

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

2017-04-01

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

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

PubMed Central

Xing, W. W.; Triantafyllidis, V.

2017-01-01

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

Stability analysis of a liquid fuel annular combustion chamber. M.S. Thesis

NASA Technical Reports Server (NTRS)

Mcdonald, G. H.

1978-01-01

High frequency combustion instability problems in a liquid fuel annular combustion chamber are examined. A modified Galerkin method was used to produce a set of modal amplitude equations from the general nonlinear partial differential acoustic wave equation in order to analyze the problem of instability. From these modal amplitude equations, the two variable perturbation method was used to develop a set of approximate equations of a given order of magnitude. These equations were modeled to show the effects of velocity sensitive combustion instabilities by evaluating the effects of certain parameters in the given set of equations.

Approximate solution of space and time fractional higher order phase field equation

NASA Astrophysics Data System (ADS)

Shamseldeen, S.

2018-03-01

This paper is concerned with a class of space and time fractional partial differential equation (STFDE) with Riesz derivative in space and Caputo in time. The proposed STFDE is considered as a generalization of a sixth-order partial phase field equation. We describe the application of the optimal homotopy analysis method (OHAM) to obtain an approximate solution for the suggested fractional initial value problem. An averaged-squared residual error function is defined and used to determine the optimal convergence control parameter. Two numerical examples are studied, considering periodic and non-periodic initial conditions, to justify the efficiency and the accuracy of the adopted iterative approach. The dependence of the solution on the order of the fractional derivative in space and time and model parameters is investigated.

Time-ordered product expansions for computational stochastic system biology.

PubMed

Mjolsness, Eric

2013-06-01

The time-ordered product framework of quantum field theory can also be used to understand salient phenomena in stochastic biochemical networks. It is used here to derive Gillespie's stochastic simulation algorithm (SSA) for chemical reaction networks; consequently, the SSA can be interpreted in terms of Feynman diagrams. It is also used here to derive other, more general simulation and parameter-learning algorithms including simulation algorithms for networks of stochastic reaction-like processes operating on parameterized objects, and also hybrid stochastic reaction/differential equation models in which systems of ordinary differential equations evolve the parameters of objects that can also undergo stochastic reactions. Thus, the time-ordered product expansion can be used systematically to derive simulation and parameter-fitting algorithms for stochastic systems.

Point model equations for neutron correlation counting: Extension of Böhnel's equations to any order

DOE PAGES

Favalli, Andrea; Croft, Stephen; Santi, Peter

2015-06-15

Various methods of autocorrelation neutron analysis may be used to extract information about a measurement item containing spontaneously fissioning material. The two predominant approaches being the time correlation analysis (that make use of a coincidence gate) methods of multiplicity shift register logic and Feynman sampling. The common feature is that the correlated nature of the pulse train can be described by a vector of reduced factorial multiplet rates. We call these singlets, doublets, triplets etc. Within the point reactor model the multiplet rates may be related to the properties of the item, the parameters of the detector, and basic nuclearmore » data constants by a series of coupled algebraic equations – the so called point model equations. Solving, or inverting, the point model equations using experimental calibration model parameters is how assays of unknown items is performed. Currently only the first three multiplets are routinely used. In this work we develop the point model equations to higher order multiplets using the probability generating functions approach combined with the general derivative chain rule, the so called Faà di Bruno Formula. Explicit expression up to 5th order are provided, as well the general iterative formula to calculate any order. This study represents the first necessary step towards determining if higher order multiplets can add value to nondestructive measurement practice for nuclear materials control and accountancy.« less

Holonomicity analysis of electromechanical systems

NASA Astrophysics Data System (ADS)

Wcislik, Miroslaw; Suchenia, Karol

2017-12-01

Electromechanical systems are described using state variables that contain electrical and mechanical components. The equations of motion, both electrical and mechanical, describe the relationships between these components. These equations are obtained using Lagrange functions. On the basis of the function and Lagrange - d'Alembert equation the methodology of obtaining equations for electromechanical systems was presented, together with a discussion of the nonholonomicity of these systems. The electromechanical system in the form of a single-phase reluctance motor was used to verify the presented method. Mechanical system was built as a system, which can oscillate as the element of physical pendulum. On the base of the pendulum oscillation, parameters of the electromechanical system were defined. The identification of the motor electric parameters as a function of the rotation angle was carried out. In this paper the characteristics and motion equations parameters of the motor are presented. The parameters of the motion equations obtained from the experiment and from the second order Lagrange equations are compared.

The Lichnerowicz-Weitzenboeck formula and superconductivity

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

Vargas-Paredes, Alfredo A.; Doria, Mauro M.; Neto, Jose Abdala Helayeel

2013-01-15

We derive the Lichnerowicz-Weitzenboeck formula for the two-component order parameter superconductor, which provides a twofold view of the kinetic energy of the superconductor. For the one component order parameter superconductor we review the connection between the Lichnerowicz-Weitzenboeck formula and the Ginzburg-Landau theory. For the two-component case we claim that this formula opens a venue to describe inhomogeneous superconducting states intertwined by spin correlations and charged dislocation. In this case the Lichnerowicz-Weitzenboeck formula displays local rotational and electromagnetic gauge symmetry (SU(2) Circled-Times U(1)) and relies on local commuting momentum and spin operators. The order parameter lives in a space with curvaturemore » and torsion described by Elie Cartan geometrical formalism. The Lichnerowickz-Weitzenboeck formula leads to first order differential equations that are a three-dimensional version of the Seiberg-Witten equations.« less

Second-order kinetic model for the sorption of cadmium onto tree fern: a comparison of linear and non-linear methods.

PubMed

Ho, Yuh-Shan

2006-01-01

A comparison was made of the linear least-squares method and a trial-and-error non-linear method of the widely used pseudo-second-order kinetic model for the sorption of cadmium onto ground-up tree fern. Four pseudo-second-order kinetic linear equations are discussed. Kinetic parameters obtained from the four kinetic linear equations using the linear method differed but they were the same when using the non-linear method. A type 1 pseudo-second-order linear kinetic model has the highest coefficient of determination. Results show that the non-linear method may be a better way to obtain the desired parameters.

The cubic-quintic-septic complex Ginzburg-Landau equation formulation of optical pulse propagation in 3D doped Kerr media with higher-order dispersions

NASA Astrophysics Data System (ADS)

Djoko, Martin; Kofane, T. C.

2018-06-01

We investigate the propagation characteristics and stabilization of generalized-Gaussian pulse in highly nonlinear homogeneous media with higher-order dispersion terms. The optical pulse propagation has been modeled by the higher-order (3+1)-dimensional cubic-quintic-septic complex Ginzburg-Landau [(3+1)D CQS-CGL] equation. We have used the variational method to find a set of differential equations characterizing the variation of the pulse parameters in fiber optic-links. The variational equations we obtained have been integrated numerically by the means of the fourth-order Runge-Kutta (RK4) method, which also allows us to investigate the evolution of the generalized-Gaussian beam and the pulse evolution along an optical doped fiber. Then, we have solved the original nonlinear (3+1)D CQS-CGL equation with the split-step Fourier method (SSFM), and compare the results with those obtained, using the variational approach. A good agreement between analytical and numerical methods is observed. The evolution of the generalized-Gaussian beam has shown oscillatory propagation, and bell-shaped dissipative optical bullets have been obtained under certain parameter values in both anomalous and normal chromatic dispersion regimes. Using the natural control parameter of the solution as it evolves, named the total energy Q, our numerical simulations reveal the existence of 3D stable vortex dissipative light bullets, 3D stable spatiotemporal optical soliton, stationary and pulsating optical bullets, depending on the used initial input condition (symmetric or elliptic).

Polymer density functional theory approach based on scaling second-order direct correlation function.

PubMed

Zhou, Shiqi

2006-06-01

A second-order direct correlation function (DCF) from solving the polymer-RISM integral equation is scaled up or down by an equation of state for bulk polymer, the resultant scaling second-order DCF is in better agreement with corresponding simulation results than the un-scaling second-order DCF. When the scaling second-order DCF is imported into a recently proposed LTDFA-based polymer DFT approach, an originally associated adjustable but mathematically meaningless parameter now becomes mathematically meaningful, i.e., the numerical value lies now between 0 and 1. When the adjustable parameter-free version of the LTDFA is used instead of the LTDFA, i.e., the adjustable parameter is fixed at 0.5, the resultant parameter-free version of the scaling LTDFA-based polymer DFT is also in good agreement with the corresponding simulation data for density profiles. The parameter-free version of the scaling LTDFA-based polymer DFT is employed to investigate the density profiles of a freely jointed tangent hard sphere chain near a variable sized central hard sphere, again the predictions reproduce accurately the simulational results. Importance of the present adjustable parameter-free version lies in its combination with a recently proposed universal theoretical way, in the resultant formalism, the contact theorem is still met by the adjustable parameter associated with the theoretical way.

Exact solutions to the time-fractional differential equations via local fractional derivatives

NASA Astrophysics Data System (ADS)

Guner, Ozkan; Bekir, Ahmet

2018-01-01

This article utilizes the local fractional derivative and the exp-function method to construct the exact solutions of nonlinear time-fractional differential equations (FDEs). For illustrating the validity of the method, it is applied to the time-fractional Camassa-Holm equation and the time-fractional-generalized fifth-order KdV equation. Moreover, the exact solutions are obtained for the equations which are formed by different parameter values related to the time-fractional-generalized fifth-order KdV equation. This method is an reliable and efficient mathematical tool for solving FDEs and it can be applied to other non-linear FDEs.

One-Dimensional Transport with Inflow and Storage (OTIS): A Solute Transport Model for Streams and Rivers

USGS Publications Warehouse

Runkel, Robert L.

1998-01-01

OTIS is a mathematical simulation model used to characterize the fate and transport of water-borne solutes in streams and rivers. The governing equation underlying the model is the advection-dispersion equation with additional terms to account for transient storage, lateral inflow, first-order decay, and sorption. This equation and the associated equations describing transient storage and sorption are solved using a Crank-Nicolson finite-difference solution. OTIS may be used in conjunction with data from field-scale tracer experiments to quantify the hydrologic parameters affecting solute transport. This application typically involves a trial-and-error approach wherein parameter estimates are adjusted to obtain an acceptable match between simulated and observed tracer concentrations. Additional applications include analyses of nonconservative solutes that are subject to sorption processes or first-order decay. OTIS-P, a modified version of OTIS, couples the solution of the governing equation with a nonlinear regression package. OTIS-P determines an optimal set of parameter estimates that minimize the squared differences between the simulated and observed concentrations, thereby automating the parameter estimation process. This report details the development and application of OTIS and OTIS-P. Sections of the report describe model theory, input/output specifications, sample applications, and installation instructions.

Estimation of Ordinary Differential Equation Parameters Using Constrained Local Polynomial Regression.

PubMed

Ding, A Adam; Wu, Hulin

2014-10-01

We propose a new method to use a constrained local polynomial regression to estimate the unknown parameters in ordinary differential equation models with a goal of improving the smoothing-based two-stage pseudo-least squares estimate. The equation constraints are derived from the differential equation model and are incorporated into the local polynomial regression in order to estimate the unknown parameters in the differential equation model. We also derive the asymptotic bias and variance of the proposed estimator. Our simulation studies show that our new estimator is clearly better than the pseudo-least squares estimator in estimation accuracy with a small price of computational cost. An application example on immune cell kinetics and trafficking for influenza infection further illustrates the benefits of the proposed new method.

Estimation of Ordinary Differential Equation Parameters Using Constrained Local Polynomial Regression

PubMed Central

Ding, A. Adam; Wu, Hulin

2015-01-01

We propose a new method to use a constrained local polynomial regression to estimate the unknown parameters in ordinary differential equation models with a goal of improving the smoothing-based two-stage pseudo-least squares estimate. The equation constraints are derived from the differential equation model and are incorporated into the local polynomial regression in order to estimate the unknown parameters in the differential equation model. We also derive the asymptotic bias and variance of the proposed estimator. Our simulation studies show that our new estimator is clearly better than the pseudo-least squares estimator in estimation accuracy with a small price of computational cost. An application example on immune cell kinetics and trafficking for influenza infection further illustrates the benefits of the proposed new method. PMID:26401093

Periodic and rational solutions of the reduced Maxwell-Bloch equations

NASA Astrophysics Data System (ADS)

Wei, Jiao; Wang, Xin; Geng, Xianguo

2018-06-01

We investigate the reduced Maxwell-Bloch (RMB) equations which describe the propagation of short optical pulses in dielectric materials with resonant non-degenerate transitions. The general Nth-order periodic solutions are provided by means of the Darboux transformation. The Nth-order degenerate periodic and Nth-order rational solutions containing several free parameters with compact determinant representations are derived from two different limiting cases of the obtained general periodic solutions, respectively. Explicit expressions of these solutions from first to second order are presented. Typical nonlinear wave patterns for the four components of the RMB equations such as single-peak, double-peak-double-dip, double-peak and single-dip structures in the second-order rational solutions are shown. This kind of the rational solutions correspond to rogue waves in the reduced Maxwell-Bloch equations.

Numerical scheme approximating solution and parameters in a beam equation

NASA Astrophysics Data System (ADS)

Ferdinand, Robert R.

2003-12-01

We present a mathematical model which describes vibration in a metallic beam about its equilibrium position. This model takes the form of a nonlinear second-order (in time) and fourth-order (in space) partial differential equation with boundary and initial conditions. A finite-element Galerkin approximation scheme is used to estimate model solution. Infinite-dimensional model parameters are then estimated numerically using an inverse method procedure which involves the minimization of a least-squares cost functional. Numerical results are presented and future work to be done is discussed.

CMB spectral distortions as solutions to the Boltzmann equations

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

Ota, Atsuhisa, E-mail: a.ota@th.phys.titech.ac.jp

2017-01-01

We propose to re-interpret the cosmic microwave background spectral distortions as solutions to the Boltzmann equation. This approach makes it possible to solve the second order Boltzmann equation explicitly, with the spectral y distortion and the momentum independent second order temperature perturbation, while generation of μ distortion cannot be explained even at second order in this framework. We also extend our method to higher order Boltzmann equations systematically and find new type spectral distortions, assuming that the collision term is linear in the photon distribution functions, namely, in the Thomson scattering limit. As an example, we concretely construct solutions tomore » the cubic order Boltzmann equation and show that the equations are closed with additional three parameters composed of a cubic order temperature perturbation and two cubic order spectral distortions. The linear Sunyaev-Zel'dovich effect whose momentum dependence is different from the usual y distortion is also discussed in the presence of the next leading order Kompaneets terms, and we show that higher order spectral distortions are also generated as a result of the diffusion process in a framework of higher order Boltzmann equations. The method may be applicable to a wider class of problems and has potential to give a general prescription to non-equilibrium physics.« less

Periodic solutions of second-order nonlinear difference equations containing a small parameter. III - Perturbation theory

NASA Technical Reports Server (NTRS)

Mickens, R. E.

1986-01-01

A technique to construct a uniformly valid perturbation series solution to a particular class of nonlinear difference equations is shown. The method allows the determination of approximations to the periodic solutions to these equations. An example illustrating the technique is presented.

A pictorial study of an invariant torus in phase space of four dimensions.

NASA Technical Reports Server (NTRS)

Baxter, R.; Eiserike, H.; Stokes, A.

1972-01-01

An investigation was conducted with the aid of a computer graphics device at Goddard Space Flight Center to study the behavior of the invariant manifolds of a particular fourth-order equation, as a parameter in the equation is varied over the interval from 0 to 1. The equation consists of two coupled Van der Pol equations. For a small parameter value, the manifold is an asymptotically stable torus, where the flow on the torus is simply a rotation. As the value of the parameter is increased, the only thing that changes is the nature of the flow on the torus, which itself persists throughout the parameter variation. It is shown that ultimately the four periodic cycles which appear play a more significant part in the phase profile of the system than does the torus itself.

Higher-order rational solitons and rogue-like wave solutions of the (2 + 1)-dimensional nonlinear fluid mechanics equations

NASA Astrophysics Data System (ADS)

Wen, Xiao-Yong; Yan, Zhenya

2017-02-01

The novel generalized perturbation (n, M)-fold Darboux transformations (DTs) are reported for the (2 + 1)-dimensional Kadomtsev-Petviashvili (KP) equation and its extension by using the Taylor expansion of the Darboux matrix. The generalized perturbation (1 , N - 1) -fold DTs are used to find their higher-order rational solitons and rogue wave solutions in terms of determinants. The dynamics behaviors of these rogue waves are discussed in detail for different parameters and time, which display the interesting RW and soliton structures including the triangle, pentagon, heptagon profiles, etc. Moreover, we find that a new phenomenon that the parameter (a) can control the wave structures of the KP equation from the higher-order rogue waves (a ≠ 0) into higher-order rational solitons (a = 0) in (x, t)-space with y = const . These results may predict the corresponding dynamical phenomena in the models of fluid mechanics and other physically relevant systems.

Computational Study of Chaotic and Ordered Solutions of the Kuramoto-Sivashinsky Equation

NASA Technical Reports Server (NTRS)

Smyrlis, Yiorgos S.; Papageorgiou, Demetrios T.

1996-01-01

We report the results of extensive numerical experiments on the Kuramoto-Sivashinsky equation in the strongly chaotic regime as the viscosity parameter is decreased and increasingly more linearly unstable modes enter the dynamics. General initial conditions are used and evolving states do not assume odd-parity. A large number of numerical experiments are employed in order to obtain quantitative characteristics of the dynamics. We report on different routes to chaos and provide numerical evidence and construction of strange attractors with self-similar characteristics. As the 'viscosity' parameter decreases the dynamics becomes increasingly more complicated and chaotic. In particular it is found that regular behavior in the form of steady state or steady state traveling waves is supported amidst the time-dependent and irregular motions. We show that multimodal steady states emerge and are supported on decreasing windows in parameter space. In addition we invoke a self-similarity property of the equation, to show that these profiles are obtainable from global fixed point attractors of the Kuramoto-Sivashinsky equation at much larger values of the viscosity.

Modulational instability and dynamics of implicit higher-order rogue wave solutions for the Kundu equation

NASA Astrophysics Data System (ADS)

Wen, Xiao-Yong; Zhang, Guoqiang

2018-01-01

Under investigation in this paper is the Kundu equation, which may be used to describe the propagation process of ultrashort optical pulses in nonlinear optics. The modulational instability of the plane-wave for the possible reason of the formation of the rogue wave (RW) is studied for the system. Based on our proposed generalized perturbation (n,N - n)-fold Darboux transformation (DT), some new higher-order implicit RW solutions in terms of determinants are obtained by means of the generalized perturbation (1,N - 1)-fold DT, when choosing different special parameters, these results will reduce to the RW solutions of the Kaup-Newell (KN) equation, Chen-Lee-Liu (CLL) equation and Gerjikov-Ivanov (GI) equation, respectively. The relevant wave structures are shown graphically, which display abundant interesting wave structures. The dynamical behaviors and propagation stability of the first-order and second-order RW solutions are discussed by using numerical simulations, the higher-order nonlinear terms for the Kundu equation have an impact on the propagation instability of the RW. The method can also be extended to find the higher-order RW or rational solutions of other integrable nonlinear equations.

On solvability of boundary value problems for hyperbolic fourth-order equations with nonlocal boundary conditions of integral type

NASA Astrophysics Data System (ADS)

Popov, Nikolay S.

2017-11-01

Solvability of some initial-boundary value problems for linear hyperbolic equations of the fourth order is studied. A condition on the lateral boundary in these problems relates the values of a solution or the conormal derivative of a solution to the values of some integral operator applied to a solution. Nonlocal boundary-value problems for one-dimensional hyperbolic second-order equations with integral conditions on the lateral boundary were considered in the articles by A.I. Kozhanov. Higher-dimensional hyperbolic equations of higher order with integral conditions on the lateral boundary were not studied earlier. The existence and uniqueness theorems of regular solutions are proven. The method of regularization and the method of continuation in a parameter are employed to establish solvability.

Application of Two-Parameter Stabilizing Functions in Solving a Convolution-Type Integral Equation by Regularization Method

NASA Astrophysics Data System (ADS)

Maslakov, M. L.

2018-04-01

This paper examines the solution of convolution-type integral equations of the first kind by applying the Tikhonov regularization method with two-parameter stabilizing functions. The class of stabilizing functions is expanded in order to improve the accuracy of the resulting solution. The features of the problem formulation for identification and adaptive signal correction are described. A method for choosing regularization parameters in problems of identification and adaptive signal correction is suggested.

Derivation of a hydrodynamic theory for mesoscale dynamics in microswimmer suspensions

NASA Astrophysics Data System (ADS)

Reinken, Henning; Klapp, Sabine H. L.; Bär, Markus; Heidenreich, Sebastian

2018-02-01

In this paper, we systematically derive a fourth-order continuum theory capable of reproducing mesoscale turbulence in a three-dimensional suspension of microswimmers. We start from overdamped Langevin equations for a generic microscopic model (pushers or pullers), which include hydrodynamic interactions on both small length scales (polar alignment of neighboring swimmers) and large length scales, where the solvent flow interacts with the order parameter field. The flow field is determined via the Stokes equation supplemented by an ansatz for the stress tensor. In addition to hydrodynamic interactions, we allow for nematic pair interactions stemming from excluded-volume effects. The results here substantially extend and generalize earlier findings [S. Heidenreich et al., Phys. Rev. E 94, 020601 (2016), 10.1103/PhysRevE.94.020601], in which we derived a two-dimensional hydrodynamic theory. From the corresponding mean-field Fokker-Planck equation combined with a self-consistent closure scheme, we derive nonlinear field equations for the polar and the nematic order parameter, involving gradient terms of up to fourth order. We find that the effective microswimmer dynamics depends on the coupling between solvent flow and orientational order. For very weak coupling corresponding to a high viscosity of the suspension, the dynamics of mesoscale turbulence can be described by a simplified model containing only an effective microswimmer velocity.

Numerical Treatment of the Boltzmann Equation for Self-Propelled Particle Systems

NASA Astrophysics Data System (ADS)

Thüroff, Florian; Weber, Christoph A.; Frey, Erwin

2014-10-01

Kinetic theories constitute one of the most promising tools to decipher the characteristic spatiotemporal dynamics in systems of actively propelled particles. In this context, the Boltzmann equation plays a pivotal role, since it provides a natural translation between a particle-level description of the system's dynamics and the corresponding hydrodynamic fields. Yet, the intricate mathematical structure of the Boltzmann equation substantially limits the progress toward a full understanding of this equation by solely analytical means. Here, we propose a general framework to numerically solve the Boltzmann equation for self-propelled particle systems in two spatial dimensions and with arbitrary boundary conditions. We discuss potential applications of this numerical framework to active matter systems and use the algorithm to give a detailed analysis to a model system of self-propelled particles with polar interactions. In accordance with previous studies, we find that spatially homogeneous isotropic and broken-symmetry states populate two distinct regions in parameter space, which are separated by a narrow region of spatially inhomogeneous, density-segregated moving patterns. We find clear evidence that these three regions in parameter space are connected by first-order phase transitions and that the transition between the spatially homogeneous isotropic and polar ordered phases bears striking similarities to liquid-gas phase transitions in equilibrium systems. Within the density-segregated parameter regime, we find a novel stable limit-cycle solution of the Boltzmann equation, which consists of parallel lanes of polar clusters moving in opposite directions, so as to render the overall symmetry of the system's ordered state nematic, despite purely polar interactions on the level of single particles.

A fully Sinc-Galerkin method for Euler-Bernoulli beam models

NASA Technical Reports Server (NTRS)

Smith, R. C.; Bowers, K. L.; Lund, J.

1990-01-01

A fully Sinc-Galerkin method in both space and time is presented for fourth-order time-dependent partial differential equations with fixed and cantilever boundary conditions. The Sinc discretizations for the second-order temporal problem and the fourth-order spatial problems are presented. Alternate formulations for variable parameter fourth-order problems are given which prove to be especially useful when applying the forward techniques to parameter recovery problems. The discrete system which corresponds to the time-dependent partial differential equations of interest are then formulated. Computational issues are discussed and a robust and efficient algorithm for solving the resulting matrix system is outlined. Numerical results which highlight the method are given for problems with both analytic and singular solutions as well as fixed and cantilever boundary conditions.

Localized states in the conserved Swift-Hohenberg equation with cubic nonlinearity

NASA Astrophysics Data System (ADS)

Thiele, Uwe; Archer, Andrew J.; Robbins, Mark J.; Gomez, Hector; Knobloch, Edgar

2013-04-01

The conserved Swift-Hohenberg equation with cubic nonlinearity provides the simplest microscopic description of the thermodynamic transition from a fluid state to a crystalline state. The resulting phase field crystal model describes a variety of spatially localized structures, in addition to different spatially extended periodic structures. The location of these structures in the temperature versus mean order parameter plane is determined using a combination of numerical continuation in one dimension and direct numerical simulation in two and three dimensions. Localized states are found in the region of thermodynamic coexistence between the homogeneous and structured phases, and may lie outside of the binodal for these states. The results are related to the phenomenon of slanted snaking but take the form of standard homoclinic snaking when the mean order parameter is plotted as a function of the chemical potential, and are expected to carry over to related models with a conserved order parameter.

Bayesian parameter estimation for nonlinear modelling of biological pathways.

PubMed

Ghasemi, Omid; Lindsey, Merry L; Yang, Tianyi; Nguyen, Nguyen; Huang, Yufei; Jin, Yu-Fang

2011-01-01

The availability of temporal measurements on biological experiments has significantly promoted research areas in systems biology. To gain insight into the interaction and regulation of biological systems, mathematical frameworks such as ordinary differential equations have been widely applied to model biological pathways and interpret the temporal data. Hill equations are the preferred formats to represent the reaction rate in differential equation frameworks, due to their simple structures and their capabilities for easy fitting to saturated experimental measurements. However, Hill equations are highly nonlinearly parameterized functions, and parameters in these functions cannot be measured easily. Additionally, because of its high nonlinearity, adaptive parameter estimation algorithms developed for linear parameterized differential equations cannot be applied. Therefore, parameter estimation in nonlinearly parameterized differential equation models for biological pathways is both challenging and rewarding. In this study, we propose a Bayesian parameter estimation algorithm to estimate parameters in nonlinear mathematical models for biological pathways using time series data. We used the Runge-Kutta method to transform differential equations to difference equations assuming a known structure of the differential equations. This transformation allowed us to generate predictions dependent on previous states and to apply a Bayesian approach, namely, the Markov chain Monte Carlo (MCMC) method. We applied this approach to the biological pathways involved in the left ventricle (LV) response to myocardial infarction (MI) and verified our algorithm by estimating two parameters in a Hill equation embedded in the nonlinear model. We further evaluated our estimation performance with different parameter settings and signal to noise ratios. Our results demonstrated the effectiveness of the algorithm for both linearly and nonlinearly parameterized dynamic systems. Our proposed Bayesian algorithm successfully estimated parameters in nonlinear mathematical models for biological pathways. This method can be further extended to high order systems and thus provides a useful tool to analyze biological dynamics and extract information using temporal data.

Higher-Order Corrections to Earthʼs Ionosphere Shocks

NASA Astrophysics Data System (ADS)

Abdelwahed, H. G.; El-Shewy, E. K.

2017-01-01

Nonlinear shock wave structures in unmagnetized collisionless viscous plasmas composed fluid of positive (negative) ions and nonthermally electron distribution are examined. For ion shock formation, a reductive perturbation technique applied to derive Burgers equation for lowest-order potential. As the shock amplitude decreasing or enlarging, its steepness and velocity deviate from Burger equation. Burgers type equation with higher order dissipation must be obtained to avoid this deviation. Solution for the compined two equations has been derived using renormalization analysis. Effects of higher-order, positive- negative mass ratio Q, electron nonthermal parameter δ and kinematic viscosities coefficient of positive (negative) ions {η }1 and {η }2 on the electrostatic shocks in Earth’s ionosphere are also argued. Supported by the Deanship of Scientific Research at Prince Sattam Bin Abdulaziz University under the Research Project No. 2015/01/4787

Reconstructing f(R) modified gravity with dark energy parametrization

NASA Astrophysics Data System (ADS)

Morita, Masaaki; Takahashi, Hirotaka

2014-03-01

We demonstrate the reconstruction of f(R) modified gravity theory with late-time accelerated cosmic expansion. A second-order differential equation for Lagrangian density is obtained from the field equation, and is solved as a function of the cosmic scale factor in two cases. First we begin with the case of a wCDM cosmological model, in which a dark-energy equation-of-state parameter w is constant, for simplicity. Next we extend the method to a case in which the parameter w is epoch-dependent and is expressed as the Chevallier-Polarski-Linder parametrization. Thus we can represent Lagrangian density of f(R) modified gravity theory in terms of dark energy parameters.

Approximate optimal guidance for the advanced launch system

NASA Technical Reports Server (NTRS)

Feeley, T. S.; Speyer, J. L.

1993-01-01

A real-time guidance scheme for the problem of maximizing the payload into orbit subject to the equations of motion for a rocket over a spherical, non-rotating earth is presented. An approximate optimal launch guidance law is developed based upon an asymptotic expansion of the Hamilton - Jacobi - Bellman or dynamic programming equation. The expansion is performed in terms of a small parameter, which is used to separate the dynamics of the problem into primary and perturbation dynamics. For the zeroth-order problem the small parameter is set to zero and a closed-form solution to the zeroth-order expansion term of Hamilton - Jacobi - Bellman equation is obtained. Higher-order terms of the expansion include the effects of the neglected perturbation dynamics. These higher-order terms are determined from the solution of first-order linear partial differential equations requiring only the evaluation of quadratures. This technique is preferred as a real-time, on-line guidance scheme to alternative numerical iterative optimization schemes because of the unreliable convergence properties of these iterative guidance schemes and because the quadratures needed for the approximate optimal guidance law can be performed rapidly and by parallel processing. Even if the approximate solution is not nearly optimal, when using this technique the zeroth-order solution always provides a path which satisfies the terminal constraints. Results for two-degree-of-freedom simulations are presented for the simplified problem of flight in the equatorial plane and compared to the guidance scheme generated by the shooting method which is an iterative second-order technique.

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

NASA Astrophysics Data System (ADS)

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

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

Lie group classification of first-order delay ordinary differential equations

NASA Astrophysics Data System (ADS)

Dorodnitsyn, Vladimir A.; Kozlov, Roman; Meleshko, Sergey V.; Winternitz, Pavel

2018-05-01

A group classification of first-order delay ordinary differential equations (DODEs) accompanied by an equation for the delay parameter (delay relation) is presented. A subset of such systems (delay ordinary differential systems or DODSs), which consists of linear DODEs and solution-independent delay relations, have infinite-dimensional symmetry algebras—as do nonlinear ones that are linearizable by an invertible transformation of variables. Genuinely nonlinear DODSs have symmetry algebras of dimension n, . It is shown how exact analytical solutions of invariant DODSs can be obtained using symmetry reduction.

A family of wave equations with some remarkable properties.

PubMed

da Silva, Priscila Leal; Freire, Igor Leite; Sampaio, Júlio Cesar Santos

2018-02-01

We consider a family of homogeneous nonlinear dispersive equations with two arbitrary parameters. Conservation laws are established from the point symmetries and imply that the whole family admits square integrable solutions. Recursion operators are found for two members of the family investigated. For one of them, a Lax pair is also obtained, proving its complete integrability. From the Lax pair, we construct a Miura-type transformation relating the original equation to the Korteweg-de Vries (KdV) equation. This transformation, on the other hand, enables us to obtain solutions of the equation from the kernel of a Schrödinger operator with potential parametrized by the solutions of the KdV equation. In particular, this allows us to exhibit a kink solution to the completely integrable equation from the 1-soliton solution of the KdV equation. Finally, peakon-type solutions are also found for a certain choice of the parameters, although for this particular case the equation is reduced to a homogeneous second-order nonlinear evolution equation.

Investigation of Bose-Einstein Condensates in q-Deformed Potentials with First Order Perturbation Theory

NASA Astrophysics Data System (ADS)

Nutku, Ferhat; Aydıner, Ekrem

2018-02-01

The Gross-Pitaevskii equation, which is the governor equation of Bose-Einstein condensates, is solved by first order perturbation expansion under various q-deformed potentials. Stationary probability distributions reveal one and two soliton behavior depending on the type of the q-deformed potential. Additionally a spatial shift of the probability distribution is found for the dark soliton solution, when the q parameter is changed.

Chirped femtosecond pulses in the higher-order nonlinear Schrödinger equation with non-Kerr nonlinear terms and cubic-quintic-septic nonlinearities

NASA Astrophysics Data System (ADS)

Triki, Houria; Biswas, Anjan; Milović, Daniela; Belić, Milivoj

2016-05-01

We consider a high-order nonlinear Schrödinger equation with competing cubic-quintic-septic nonlinearities, non-Kerr quintic nonlinearity, self-steepening, and self-frequency shift. The model describes the propagation of ultrashort (femtosecond) optical pulses in highly nonlinear optical fibers. A new ansatz is adopted to obtain nonlinear chirp associated with the propagating femtosecond soliton pulses. It is shown that the resultant elliptic equation of the problem is of high order, contains several new terms and is more general than the earlier reported results, thus providing a systematic way to find exact chirped soliton solutions of the septic model. Novel soliton solutions, including chirped bright, dark, kink and fractional-transform soliton solutions are obtained for special choices of parameters. Furthermore, we present the parameter domains in which these optical solitons exist. The nonlinear chirp associated with each of the solitonic solutions is also determined. It is shown that the chirping is proportional to the intensity of the wave and depends on higher-order nonlinearities. Of special interest is the soliton solution of the bright and dark type, determined for the general case when all coefficients in the equation have nonzero values. These results can be useful for possible chirped-soliton-based applications of highly nonlinear optical fiber systems.

A second-order closure analysis of turbulent diffusion flames. [combustion physics

NASA Technical Reports Server (NTRS)

Varma, A. K.; Fishburne, E. S.; Beddini, R. A.

1977-01-01

A complete second-order closure computer program for the investigation of compressible, turbulent, reacting shear layers was developed. The equations for the means and the second order correlations were derived from the time-averaged Navier-Stokes equations and contain third order and higher order correlations, which have to be modeled in terms of the lower-order correlations to close the system of equations. In addition to fluid mechanical turbulence models and parameters used in previous studies of a variety of incompressible and compressible shear flows, a number of additional scalar correlations were modeled for chemically reacting flows, and a typical eddy model developed for the joint probability density function for all the scalars. The program which is capable of handling multi-species, multistep chemical reactions, was used to calculate nonreacting and reacting flows in a hydrogen-air diffusion flame.

Equation of state for dense nucleonic matter from metamodeling. I. Foundational aspects

NASA Astrophysics Data System (ADS)

Margueron, Jérôme; Hoffmann Casali, Rudiney; Gulminelli, Francesca

2018-02-01

Metamodeling for the nucleonic equation of state (EOS), inspired from a Taylor expansion around the saturation density of symmetric nuclear matter, is proposed and parameterized in terms of the empirical parameters. The present knowledge of nuclear empirical parameters is first reviewed in order to estimate their average values and associated uncertainties, and thus defining the parameter space of the metamodeling. They are divided into isoscalar and isovector types, and ordered according to their power in the density expansion. The goodness of the metamodeling is analyzed against the predictions of the original models. In addition, since no correlation among the empirical parameters is assumed a priori, all arbitrary density dependences can be explored, which might not be accessible in existing functionals. Spurious correlations due to the assumed functional form are also removed. This meta-EOS allows direct relations between the uncertainties on the empirical parameters and the density dependence of the nuclear equation of state and its derivatives, and the mapping between the two can be done with standard Bayesian techniques. A sensitivity analysis shows that the more influential empirical parameters are the isovector parameters Lsym and Ksym, and that laboratory constraints at supersaturation densities are essential to reduce the present uncertainties. The present metamodeling for the EOS for nuclear matter is proposed for further applications in neutron stars and supernova matter.

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.

Velocity and thermal slip effects on MHD third order blood flow in an irregular channel though a porous medium with homogeneous/ heterogeneous reactions

NASA Astrophysics Data System (ADS)

Gnaneswara Reddy, M.

2017-09-01

This communication presents the transportation of third order hydromagnetic fluid with thermal radiation by peristalsis through an irregular channel configuration filled a porous medium under the low Reynolds number and large wavelength approximations. Joule heating, Hall current and homogeneous-heterogeneous reactions effects are considered in the energy and species equations. The Second-order velocity and energy slip restrictions are invoked. Final dimensionless governing transport equations along the boundary restrictions are resolved numerically with the help of NDsolve in Mathematica package. Impact of involved sundry parameters on the non-dimensional axial velocity, fluid temperature and concentration characteristics have been analyzed via plots and tables. It is manifest that an increasing porosity parameter leads to maximum velocity in the core part of the channel. Fluid velocity boosts near the walls of the channel where as the reverse effect in the central part of the channel for higher values of first order slip. Larger values of thermal radiation parameter R reduce the fluid temperature field. Also, an increase in heterogeneous reaction parameter Ks magnifies the concentration profile. The present study has the crucial application of thermal therapy in biomedical engineering.

Discretization analysis of bifurcation based nonlinear amplifiers

NASA Astrophysics Data System (ADS)

Feldkord, Sven; Reit, Marco; Mathis, Wolfgang

2017-09-01

Recently, for modeling biological amplification processes, nonlinear amplifiers based on the supercritical Andronov-Hopf bifurcation have been widely analyzed analytically. For technical realizations, digital systems have become the most relevant systems in signal processing applications. The underlying continuous-time systems are transferred to the discrete-time domain using numerical integration methods. Within this contribution, effects on the qualitative behavior of the Andronov-Hopf bifurcation based systems concerning numerical integration methods are analyzed. It is shown exemplarily that explicit Runge-Kutta methods transform the truncated normalform equation of the Andronov-Hopf bifurcation into the normalform equation of the Neimark-Sacker bifurcation. Dependent on the order of the integration method, higher order terms are added during this transformation.A rescaled normalform equation of the Neimark-Sacker bifurcation is introduced that allows a parametric design of a discrete-time system which corresponds to the rescaled Andronov-Hopf system. This system approximates the characteristics of the rescaled Hopf-type amplifier for a large range of parameters. The natural frequency and the peak amplitude are preserved for every set of parameters. The Neimark-Sacker bifurcation based systems avoid large computational effort that would be caused by applying higher order integration methods to the continuous-time normalform equations.

Dynamics of nonautonomous discrete rogue wave solutions for an Ablowitz-Musslimani equation with PT-symmetric potential.

PubMed

Yu, Fajun

2017-02-01

Starting from a discrete spectral problem, we derive a hierarchy of nonlinear discrete equations which include the Ablowitz-Ladik (AL) equation. We analytically study the discrete rogue-wave (DRW) solutions of AL equation with three free parameters. The trajectories of peaks and depressions of profiles for the first- and second-order DRWs are produced by means of analytical and numerical methods. In particular, we study the solutions with dispersion in parity-time ( PT) symmetric potential for Ablowitz-Musslimani equation. And we consider the non-autonomous DRW solutions, parameters controlling and their interactions with variable coefficients, and predict the long-living rogue wave solutions. Our results might provide useful information for potential applications of synthetic PT symmetric systems in nonlinear optics and condensed matter physics.

Period and amplitude of non-volcanic tremors and repeaters: a dimensional analysis

NASA Astrophysics Data System (ADS)

Nielsen, Stefan

2017-04-01

Since its relatively recent discovery, the origin of non-volcanic tremor has been source of great curiosity and debate. Two main interpretations have been proposed, one based on fluid migration, the other relating to slow slip events on a plate boundary (the latter hypothesis has recently gained considerable ground). Here I define the conditions of slip of one or more small asperities embedded within a larger creeping fault patch. The radiation-damping equation coupled with rate-and-state friction evolution equations results in a system of ordinary differential equations. For a finite size asperity, the system equates to a peculiar non-linear damped oscillator, converging to a limit cycle. Dimensional analysis shows that period and amplitude of the oscillations depend on dimensional parameter combinations formed from a limited set of parameters: asperity dimension Γ, rate and state friction parameters (a, b, L), shear stiffness of the medium G, mass density ρ, background creep rate ˙V and normal stress σ. Under realistic parameter ranges, the asperity may show (1) tremor-like short period oscillations, accelerating to radiate sufficient energy to be barely detectable and a periodicity of the order of one to ten Hertz, as observed for non-volcanic tremor activity at the base of large inter-plate faults; (2) isolated stick-slip events with intervals in the order of days to months, as observed in repeater events of modest magnitude within creeping fault sections.

Calculation of Optical Parameters of Liquid Crystals

NASA Astrophysics Data System (ADS)

Kumar, A.

2007-12-01

Validation of a modified four-parameter model describing temperature effect on liquid crystal refractive indices is being reported in the present article. This model is based upon the Vuks equation. Experimental data of ordinary and extraordinary refractive indices for two liquid crystal samples MLC-9200-000 and MLC-6608 are used to validate the above-mentioned theoretical model. Using these experimental data, birefringence, order parameter, normalized polarizabilities, and the temperature gradient of refractive indices are determined. Two methods: directly using birefringence measurements and using Haller's extrapolation procedure are adopted for the determination of order parameter. Both approches of order parameter calculation are compared. The temperature dependences of all these parameters are discussed. A close agreement between theory and experiment is obtained.

Development of a second order closure model for computation of turbulent diffusion flames

NASA Technical Reports Server (NTRS)

Varma, A. K.; Donaldson, C. D.

1974-01-01

A typical eddy box model for the second-order closure of turbulent, multispecies, reacting flows developed. The model structure was quite general and was valid for an arbitrary number of species. For the case of a reaction involving three species, the nine model parameters were determined from equations for nine independent first- and second-order correlations. The model enabled calculation of any higher-order correlation involving mass fractions, temperatures, and reaction rates in terms of first- and second-order correlations. Model predictions for the reaction rate were in very good agreement with exact solutions of the reaction rate equations for a number of assumed flow distributions.

Uncertainty in Damage Detection, Dynamic Propagation and Just-in-Time Networks

DTIC Science & Technology

2015-08-03

estimated parameter uncertainty in dynamic data sets; high order compact finite difference schemes for Helmholtz equations with discontinuous wave numbers...delay differential equations with a Gamma distributed delay. We found that with the same population size the histogram plots for the solution to the...schemes for Helmholtz equations with discontinuous wave numbers across interfaces. • We carried out numerical sensitivity analysis with respect to

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

NASA Astrophysics Data System (ADS)

Alias Suba, Subbu; Muthucumaraswamy, R.

2018-04-01

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

Performance Parameters Analysis of an XD3P Peugeot Engine Using Artificial Neural Networks (ANN) Concept in MATLAB

NASA Astrophysics Data System (ADS)

Rangaswamy, T.; Vidhyashankar, S.; Madhusudan, M.; Bharath Shekar, H. R.

2015-04-01

The current trends of engineering follow the basic rule of innovation in mechanical engineering aspects. For the engineers to be efficient, problem solving aspects need to be viewed in a multidimensional perspective. One such methodology implemented is the fusion of technologies from other disciplines in order to solve the problems. This paper mainly deals with the application of Neural Networks in order to analyze the performance parameters of an XD3P Peugeot engine (used in Ministry of Defence). The basic propaganda of the work is divided into two main working stages. In the former stage, experimentation of an IC engine is carried out in order to obtain the primary data. In the latter stage the primary database formed is used to design and implement a predictive neural network in order to analyze the output parameters variation with respect to each other. A mathematical governing equation for the neural network is obtained. The obtained polynomial equation describes the characteristic behavior of the built neural network system. Finally, a comparative study of the results is carried out.

Customized Steady-State Constraints for Parameter Estimation in Non-Linear Ordinary Differential Equation Models

PubMed Central

Rosenblatt, Marcus; Timmer, Jens; Kaschek, Daniel

2016-01-01

Ordinary differential equation models have become a wide-spread approach to analyze dynamical systems and understand underlying mechanisms. Model parameters are often unknown and have to be estimated from experimental data, e.g., by maximum-likelihood estimation. In particular, models of biological systems contain a large number of parameters. To reduce the dimensionality of the parameter space, steady-state information is incorporated in the parameter estimation process. For non-linear models, analytical steady-state calculation typically leads to higher-order polynomial equations for which no closed-form solutions can be obtained. This can be circumvented by solving the steady-state equations for kinetic parameters, which results in a linear equation system with comparatively simple solutions. At the same time multiplicity of steady-state solutions is avoided, which otherwise is problematic for optimization. When solved for kinetic parameters, however, steady-state constraints tend to become negative for particular model specifications, thus, generating new types of optimization problems. Here, we present an algorithm based on graph theory that derives non-negative, analytical steady-state expressions by stepwise removal of cyclic dependencies between dynamical variables. The algorithm avoids multiple steady-state solutions by construction. We show that our method is applicable to most common classes of biochemical reaction networks containing inhibition terms, mass-action and Hill-type kinetic equations. Comparing the performance of parameter estimation for different analytical and numerical methods of incorporating steady-state information, we show that our approach is especially well-tailored to guarantee a high success rate of optimization. PMID:27243005

Customized Steady-State Constraints for Parameter Estimation in Non-Linear Ordinary Differential Equation Models.

PubMed

Rosenblatt, Marcus; Timmer, Jens; Kaschek, Daniel

2016-01-01

Ordinary differential equation models have become a wide-spread approach to analyze dynamical systems and understand underlying mechanisms. Model parameters are often unknown and have to be estimated from experimental data, e.g., by maximum-likelihood estimation. In particular, models of biological systems contain a large number of parameters. To reduce the dimensionality of the parameter space, steady-state information is incorporated in the parameter estimation process. For non-linear models, analytical steady-state calculation typically leads to higher-order polynomial equations for which no closed-form solutions can be obtained. This can be circumvented by solving the steady-state equations for kinetic parameters, which results in a linear equation system with comparatively simple solutions. At the same time multiplicity of steady-state solutions is avoided, which otherwise is problematic for optimization. When solved for kinetic parameters, however, steady-state constraints tend to become negative for particular model specifications, thus, generating new types of optimization problems. Here, we present an algorithm based on graph theory that derives non-negative, analytical steady-state expressions by stepwise removal of cyclic dependencies between dynamical variables. The algorithm avoids multiple steady-state solutions by construction. We show that our method is applicable to most common classes of biochemical reaction networks containing inhibition terms, mass-action and Hill-type kinetic equations. Comparing the performance of parameter estimation for different analytical and numerical methods of incorporating steady-state information, we show that our approach is especially well-tailored to guarantee a high success rate of optimization.

Neoclassical transport including collisional nonlinearity.

PubMed

Candy, J; Belli, E A

2011-06-10

In the standard δf theory of neoclassical transport, the zeroth-order (Maxwellian) solution is obtained analytically via the solution of a nonlinear equation. The first-order correction δf is subsequently computed as the solution of a linear, inhomogeneous equation that includes the linearized Fokker-Planck collision operator. This equation admits analytic solutions only in extreme asymptotic limits (banana, plateau, Pfirsch-Schlüter), and so must be solved numerically for realistic plasma parameters. Recently, numerical codes have appeared which attempt to compute the total distribution f more accurately than in the standard ordering by retaining some nonlinear terms related to finite-orbit width, while simultaneously reusing some form of the linearized collision operator. In this work we show that higher-order corrections to the distribution function may be unphysical if collisional nonlinearities are ignored.

An approximation theory for the identification of linear thermoelastic systems

NASA Technical Reports Server (NTRS)

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

1990-01-01

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

Efficient Determination of Free Energy Landscapes in Multiple Dimensions from Biased Umbrella Sampling Simulations Using Linear Regression.

PubMed

Meng, Yilin; Roux, Benoît

2015-08-11

The weighted histogram analysis method (WHAM) is a standard protocol for postprocessing the information from biased umbrella sampling simulations to construct the potential of mean force with respect to a set of order parameters. By virtue of the WHAM equations, the unbiased density of state is determined by satisfying a self-consistent condition through an iterative procedure. While the method works very effectively when the number of order parameters is small, its computational cost grows rapidly in higher dimension. Here, we present a simple and efficient alternative strategy, which avoids solving the self-consistent WHAM equations iteratively. An efficient multivariate linear regression framework is utilized to link the biased probability densities of individual umbrella windows and yield an unbiased global free energy landscape in the space of order parameters. It is demonstrated with practical examples that free energy landscapes that are comparable in accuracy to WHAM can be generated at a small fraction of the cost.

Efficient Determination of Free Energy Landscapes in Multiple Dimensions from Biased Umbrella Sampling Simulations Using Linear Regression

PubMed Central

2015-01-01

The weighted histogram analysis method (WHAM) is a standard protocol for postprocessing the information from biased umbrella sampling simulations to construct the potential of mean force with respect to a set of order parameters. By virtue of the WHAM equations, the unbiased density of state is determined by satisfying a self-consistent condition through an iterative procedure. While the method works very effectively when the number of order parameters is small, its computational cost grows rapidly in higher dimension. Here, we present a simple and efficient alternative strategy, which avoids solving the self-consistent WHAM equations iteratively. An efficient multivariate linear regression framework is utilized to link the biased probability densities of individual umbrella windows and yield an unbiased global free energy landscape in the space of order parameters. It is demonstrated with practical examples that free energy landscapes that are comparable in accuracy to WHAM can be generated at a small fraction of the cost. PMID:26574437

Stability analysis of a liquid fuel annular combustion chamber. M.S. Thesis

NASA Technical Reports Server (NTRS)

Mcdonald, G. H.

1979-01-01

The problems of combustion instability in an annular combustion chamber are investigated. A modified Galerkin method was used to produce a set of modal amplitude equations from the general nonlinear partial differential acoustic wave equation. From these modal amplitude equations, the two variable perturbation method was used to develop a set of approximate equations of a given order of magnitude. These equations were modeled to show the effects of velocity sensitive combustion instabilities by evaluating the effects of certain parameters in the given set of equations. By evaluating these effects, parameters which cause instabilities to occur in the combustion chamber can be ascertained. It is assumed that in the annular combustion chamber, the liquid propellants are injected uniformly across the injector face, the combustion processes are distributed throughout the combustion chamber, and that no time delay occurs in the combustion processes.

Numerical solution of system of boundary value problems using B-spline with free parameter

NASA Astrophysics Data System (ADS)

Gupta, Yogesh

2017-01-01

This paper deals with method of B-spline solution for a system of boundary value problems. The differential equations are useful in various fields of science and engineering. Some interesting real life problems involve more than one unknown function. These result in system of simultaneous differential equations. Such systems have been applied to many problems in mathematics, physics, engineering etc. In present paper, B-spline and B-spline with free parameter methods for the solution of a linear system of second-order boundary value problems are presented. The methods utilize the values of cubic B-spline and its derivatives at nodal points together with the equations of the given system and boundary conditions, ensuing into the linear matrix equation.

Magnetohydrodynamic Flow by a Stretching Cylinder with Newtonian Heating and Homogeneous-Heterogeneous Reactions

PubMed Central

Hayat, T.; Hussain, Zakir; Alsaedi, A.; Farooq, M.

2016-01-01

This article examines the effects of homogeneous-heterogeneous reactions and Newtonian heating in magnetohydrodynamic (MHD) flow of Powell-Eyring fluid by a stretching cylinder. The nonlinear partial differential equations of momentum, energy and concentration are reduced to the nonlinear ordinary differential equations. Convergent solutions of momentum, energy and reaction equations are developed by using homotopy analysis method (HAM). This method is very efficient for development of series solutions of highly nonlinear differential equations. It does not depend on any small or large parameter like the other methods i. e., perturbation method, δ—perturbation expansion method etc. We get more accurate result as we increase the order of approximations. Effects of different parameters on the velocity, temperature and concentration distributions are sketched and discussed. Comparison of present study with the previous published work is also made in the limiting sense. Numerical values of skin friction coefficient and Nusselt number are also computed and analyzed. It is noticed that the flow accelerates for large values of Powell-Eyring fluid parameter. Further temperature profile decreases and concentration profile increases when Powell-Eyring fluid parameter enhances. Concentration distribution is decreasing function of homogeneous reaction parameter while opposite influence of heterogeneous reaction parameter appears. PMID:27280883

Magnetohydrodynamic Flow by a Stretching Cylinder with Newtonian Heating and Homogeneous-Heterogeneous Reactions.

PubMed

Hayat, T; Hussain, Zakir; Alsaedi, A; Farooq, M

2016-01-01

This article examines the effects of homogeneous-heterogeneous reactions and Newtonian heating in magnetohydrodynamic (MHD) flow of Powell-Eyring fluid by a stretching cylinder. The nonlinear partial differential equations of momentum, energy and concentration are reduced to the nonlinear ordinary differential equations. Convergent solutions of momentum, energy and reaction equations are developed by using homotopy analysis method (HAM). This method is very efficient for development of series solutions of highly nonlinear differential equations. It does not depend on any small or large parameter like the other methods i. e., perturbation method, δ-perturbation expansion method etc. We get more accurate result as we increase the order of approximations. Effects of different parameters on the velocity, temperature and concentration distributions are sketched and discussed. Comparison of present study with the previous published work is also made in the limiting sense. Numerical values of skin friction coefficient and Nusselt number are also computed and analyzed. It is noticed that the flow accelerates for large values of Powell-Eyring fluid parameter. Further temperature profile decreases and concentration profile increases when Powell-Eyring fluid parameter enhances. Concentration distribution is decreasing function of homogeneous reaction parameter while opposite influence of heterogeneous reaction parameter appears.

An extended harmonic balance method based on incremental nonlinear control parameters

NASA Astrophysics Data System (ADS)

Khodaparast, Hamed Haddad; Madinei, Hadi; Friswell, Michael I.; Adhikari, Sondipon; Coggon, Simon; Cooper, Jonathan E.

2017-02-01

A new formulation for calculating the steady-state responses of multiple-degree-of-freedom (MDOF) non-linear dynamic systems due to harmonic excitation is developed. This is aimed at solving multi-dimensional nonlinear systems using linear equations. Nonlinearity is parameterised by a set of 'non-linear control parameters' such that the dynamic system is effectively linear for zero values of these parameters and nonlinearity increases with increasing values of these parameters. Two sets of linear equations which are formed from a first-order truncated Taylor series expansion are developed. The first set of linear equations provides the summation of sensitivities of linear system responses with respect to non-linear control parameters and the second set are recursive equations that use the previous responses to update the sensitivities. The obtained sensitivities of steady-state responses are then used to calculate the steady state responses of non-linear dynamic systems in an iterative process. The application and verification of the method are illustrated using a non-linear Micro-Electro-Mechanical System (MEMS) subject to a base harmonic excitation. The non-linear control parameters in these examples are the DC voltages that are applied to the electrodes of the MEMS devices.

Expanding wave solutions of the Einstein equations that induce an anomalous acceleration into the Standard Model of Cosmology.

PubMed

Temple, Blake; Smoller, Joel

2009-08-25

We derive a system of three coupled equations that implicitly defines a continuous one-parameter family of expanding wave solutions of the Einstein equations, such that the Friedmann universe associated with the pure radiation phase of the Standard Model of Cosmology is embedded as a single point in this family. By approximating solutions near the center to leading order in the Hubble length, the family reduces to an explicit one-parameter family of expanding spacetimes, given in closed form, that represents a perturbation of the Standard Model. By introducing a comoving coordinate system, we calculate the correction to the Hubble constant as well as the exact leading order quadratic correction to the redshift vs. luminosity relation for an observer at the center. The correction to redshift vs. luminosity entails an adjustable free parameter that introduces an anomalous acceleration. We conclude (by continuity) that corrections to the redshift vs. luminosity relation observed after the radiation phase of the Big Bang can be accounted for, at the leading order quadratic level, by adjustment of this free parameter. The next order correction is then a prediction. Since nonlinearities alone could actuate dissipation and decay in the conservation laws associated with the highly nonlinear radiation phase and since noninteracting expanding waves represent possible time-asymptotic wave patterns that could result, we propose to further investigate the possibility that these corrections to the Standard Model might be the source of the anomalous acceleration of the galaxies, an explanation not requiring the cosmological constant or dark energy.

Numerical discretization-based estimation methods for ordinary differential equation models via penalized spline smoothing with applications in biomedical research.

PubMed

Wu, Hulin; Xue, Hongqi; Kumar, Arun

2012-06-01

Differential equations are extensively used for modeling dynamics of physical processes in many scientific fields such as engineering, physics, and biomedical sciences. Parameter estimation of differential equation models is a challenging problem because of high computational cost and high-dimensional parameter space. In this article, we propose a novel class of methods for estimating parameters in ordinary differential equation (ODE) models, which is motivated by HIV dynamics modeling. The new methods exploit the form of numerical discretization algorithms for an ODE solver to formulate estimating equations. First, a penalized-spline approach is employed to estimate the state variables and the estimated state variables are then plugged in a discretization formula of an ODE solver to obtain the ODE parameter estimates via a regression approach. We consider three different order of discretization methods, Euler's method, trapezoidal rule, and Runge-Kutta method. A higher-order numerical algorithm reduces numerical error in the approximation of the derivative, which produces a more accurate estimate, but its computational cost is higher. To balance the computational cost and estimation accuracy, we demonstrate, via simulation studies, that the trapezoidal discretization-based estimate is the best and is recommended for practical use. The asymptotic properties for the proposed numerical discretization-based estimators are established. Comparisons between the proposed methods and existing methods show a clear benefit of the proposed methods in regards to the trade-off between computational cost and estimation accuracy. We apply the proposed methods t an HIV study to further illustrate the usefulness of the proposed approaches. © 2012, The International Biometric Society.

Computational methods and traveling wave solutions for the fourth-order nonlinear Ablowitz-Kaup-Newell-Segur water wave dynamical equation via two methods and its applications

NASA Astrophysics Data System (ADS)

Ali, Asghar; Seadawy, Aly R.; Lu, Dianchen

2018-05-01

The aim of this article is to construct some new traveling wave solutions and investigate localized structures for fourth-order nonlinear Ablowitz-Kaup-Newell-Segur (AKNS) water wave dynamical equation. The simple equation method (SEM) and the modified simple equation method (MSEM) are applied in this paper to construct the analytical traveling wave solutions of AKNS equation. The different waves solutions are derived by assigning special values to the parameters. The obtained results have their importance in the field of physics and other areas of applied sciences. All the solutions are also graphically represented. The constructed results are often helpful for studying several new localized structures and the waves interaction in the high-dimensional models.

Theory of phase diagrams described by thermodynamic potentials with T d symmetry

NASA Astrophysics Data System (ADS)

Mukovnin, A. A.; Talanov, V. M.

2014-09-01

Phase diagrams of crystals induced by irreducible representations with symmetry group ( T d ) are constructed within the phenomenological theory of second-order phase transitions. A model of the Landau thermodynamic potential is studied, state equations of all symmetry-conditioned phases are obtained, and general conditions for their thermodynamic stability are formulated. Equations for the boundaries of phase areas and lines of phase transitions are obtained for the fourth order of expansion of the potential via components of the order parameter. Some types of the collapse of the multicritical point of the phase diagram for the eighth order of potential expansion are studied using computer calculations. The possible existence of phase diagrams that contain one or more triple points and areas of existence of three and four phases is shown for the first time for the potentials with the above symmetry. Examples are given of crystals that undergo phase transitions in the considered symmetry of the order parameter.

Double absorbing boundaries for finite-difference time-domain electromagnetics

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

LaGrone, John, E-mail: jlagrone@smu.edu; Hagstrom, Thomas, E-mail: thagstrom@smu.edu

We describe the implementation of optimal local radiation boundary condition sequences for second order finite difference approximations to Maxwell's equations and the scalar wave equation using the double absorbing boundary formulation. Numerical experiments are presented which demonstrate that the design accuracy of the boundary conditions is achieved and, for comparable effort, exceeds that of a convolution perfectly matched layer with reasonably chosen parameters. An advantage of the proposed approach is that parameters can be chosen using an accurate a priori error bound.

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Uncertainty Quantification in Simulations of Epidemics Using Polynomial Chaos

PubMed Central

Santonja, F.; Chen-Charpentier, B.

2012-01-01

Mathematical models based on ordinary differential equations are a useful tool to study the processes involved in epidemiology. Many models consider that the parameters are deterministic variables. But in practice, the transmission parameters present large variability and it is not possible to determine them exactly, and it is necessary to introduce randomness. In this paper, we present an application of the polynomial chaos approach to epidemiological mathematical models based on ordinary differential equations with random coefficients. Taking into account the variability of the transmission parameters of the model, this approach allows us to obtain an auxiliary system of differential equations, which is then integrated numerically to obtain the first-and the second-order moments of the output stochastic processes. A sensitivity analysis based on the polynomial chaos approach is also performed to determine which parameters have the greatest influence on the results. As an example, we will apply the approach to an obesity epidemic model. PMID:22927889

Magnetohydrodynamics effect on convective boundary layer flow and heat transfer of viscoelastic micropolar fluid past a sphere

NASA Astrophysics Data System (ADS)

Amera Aziz, Laila; Kasim, Abdul Rahman Mohd; Zuki Salleh, Mohd; Syahidah Yusoff, Nur; Shafie, Sharidan

2017-09-01

The main interest of this study is to investigate the effect of MHD on the boundary layer flow and heat transfer of viscoelastic micropolar fluid. Governing equations are transformed into dimensionless form in order to reduce their complexity. Then, the stream function is applied to the dimensionless equations to produce partial differential equations which are then solved numerically using the Keller-box method in Fortran programming. The numerical results are compared to published study to ensure the reliability of present results. The effects of selected physical parameters such as the viscoelastic parameter, K, micropolar parameter, K1 and magnetic parameter, M on the flow and heat transfer are discussed and presented in tabular and graphical form. The findings from this study will be of critical importance in the fields of medicine, chemical as well as industrial processes where magnetic field is involved.

Bayesian methods for characterizing unknown parameters of material models

DOE PAGES

Emery, J. M.; Grigoriu, M. D.; Field Jr., R. V.

2016-02-04

A Bayesian framework is developed for characterizing the unknown parameters of probabilistic models for material properties. In this framework, the unknown parameters are viewed as random and described by their posterior distributions obtained from prior information and measurements of quantities of interest that are observable and depend on the unknown parameters. The proposed Bayesian method is applied to characterize an unknown spatial correlation of the conductivity field in the definition of a stochastic transport equation and to solve this equation by Monte Carlo simulation and stochastic reduced order models (SROMs). As a result, the Bayesian method is also employed tomore » characterize unknown parameters of material properties for laser welds from measurements of peak forces sustained by these welds.« less

Bayesian methods for characterizing unknown parameters of material models

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

Emery, J. M.; Grigoriu, M. D.; Field Jr., R. V.

A Bayesian framework is developed for characterizing the unknown parameters of probabilistic models for material properties. In this framework, the unknown parameters are viewed as random and described by their posterior distributions obtained from prior information and measurements of quantities of interest that are observable and depend on the unknown parameters. The proposed Bayesian method is applied to characterize an unknown spatial correlation of the conductivity field in the definition of a stochastic transport equation and to solve this equation by Monte Carlo simulation and stochastic reduced order models (SROMs). As a result, the Bayesian method is also employed tomore » characterize unknown parameters of material properties for laser welds from measurements of peak forces sustained by these welds.« less

A Dynamic Model for Modern Military Conflict.

DTIC Science & Technology

1982-10-01

within the generalized form of the Lotka - Volterra equations, that can account for the important interactions of modern military conflicts described in...Mx + These equations are seen to be of the generalized Lotka - Volterra form; however, only 20 of the 32 parameters that might possibly be included...determine one equilibrium as the solution of a system of linear equations. The method is derived for the general nth order Lotka - Volterra model in

Numerical Solution of Systems of Loaded Ordinary Differential Equations with Multipoint Conditions

NASA Astrophysics Data System (ADS)

Assanova, A. T.; Imanchiyev, A. E.; Kadirbayeva, Zh. M.

2018-04-01

A system of loaded ordinary differential equations with multipoint conditions is considered. The problem under study is reduced to an equivalent boundary value problem for a system of ordinary differential equations with parameters. A system of linear algebraic equations for the parameters is constructed using the matrices of the loaded terms and the multipoint condition. The conditions for the unique solvability and well-posedness of the original problem are established in terms of the matrix made up of the coefficients of the system of linear algebraic equations. The coefficients and the righthand side of the constructed system are determined by solving Cauchy problems for linear ordinary differential equations. The solutions of the system are found in terms of the values of the desired function at the initial points of subintervals. The parametrization method is numerically implemented using the fourth-order accurate Runge-Kutta method as applied to the Cauchy problems for ordinary differential equations. The performance of the constructed numerical algorithms is illustrated by examples.

A Few New 2+1-Dimensional Nonlinear Dynamics and the Representation of Riemann Curvature Tensors

NASA Astrophysics Data System (ADS)

Wang, Yan; Zhang, Yufeng; Zhang, Xiangzhi

2016-09-01

We first introduced a linear stationary equation with a quadratic operator in ∂x and ∂y, then a linear evolution equation is given by N-order polynomials of eigenfunctions. As applications, by taking N=2, we derived a (2+1)-dimensional generalized linear heat equation with two constant parameters associative with a symmetric space. When taking N=3, a pair of generalized Kadomtsev-Petviashvili equations with the same eigenvalues with the case of N=2 are generated. Similarly, a second-order flow associative with a homogeneous space is derived from the integrability condition of the two linear equations, which is a (2+1)-dimensional hyperbolic equation. When N=3, the third second flow associative with the homogeneous space is generated, which is a pair of new generalized Kadomtsev-Petviashvili equations. Finally, as an application of a Hermitian symmetric space, we established a pair of spectral problems to obtain a new (2+1)-dimensional generalized Schrödinger equation, which is expressed by the Riemann curvature tensors.

Maximum Entropy/Optimal Projection (MEOP) control design synthesis: Optimal quantification of the major design tradeoffs

NASA Technical Reports Server (NTRS)

Hyland, D. C.; Bernstein, D. S.

1987-01-01

The underlying philosophy and motivation of the optimal projection/maximum entropy (OP/ME) stochastic modeling and reduced control design methodology for high order systems with parameter uncertainties are discussed. The OP/ME design equations for reduced-order dynamic compensation including the effect of parameter uncertainties are reviewed. The application of the methodology to several Large Space Structures (LSS) problems of representative complexity is illustrated.

Dispersive optical soliton solutions for higher order nonlinear Sasa-Satsuma equation in mono mode fibers via new auxiliary equation method

NASA Astrophysics Data System (ADS)

Khater, Mostafa M. A.; Seadawy, Aly R.; Lu, Dianchen

2018-01-01

In this research, we apply new technique for higher order nonlinear Schrödinger equation which is representing the propagation of short light pulses in the monomode optical fibers and the evolution of slowly varying packets of quasi-monochromatic waves in weakly nonlinear media that have dispersion. Nonlinear Schrödinger equation is one of the basic model in fiber optics. We apply new auxiliary equation method for nonlinear Sasa-Satsuma equation to obtain a new optical forms of solitary traveling wave solutions. Exact and solitary traveling wave solutions are obtained in different kinds like trigonometric, hyperbolic, exponential, rational functions, …, etc. These forms of solutions that we represent in this research prove the superiority of our new technique on almost thirteen powerful methods. The main merits of this method over the other methods are that it gives more general solutions with some free parameters.

Optimal control problem for linear fractional-order systems, described by equations with Hadamard-type derivative

NASA Astrophysics Data System (ADS)

Postnov, Sergey

2017-11-01

Two kinds of optimal control problem are investigated for linear time-invariant fractional-order systems with lumped parameters which dynamics described by equations with Hadamard-type derivative: the problem of control with minimal norm and the problem of control with minimal time at given restriction on control norm. The problem setting with nonlocal initial conditions studied. Admissible controls allowed to be the p-integrable functions (p > 1) at half-interval. The optimal control problem studied by moment method. The correctness and solvability conditions for the corresponding moment problem are derived. For several special cases the optimal control problems stated are solved analytically. Some analogies pointed for results obtained with the results which are known for integer-order systems and fractional-order systems describing by equations with Caputo- and Riemann-Liouville-type derivatives.

Darboux Transformation and N-soliton Solution for Extended Form of Modified Kadomtsev—Petviashvili Equation with Variable-Coefficient

NASA Astrophysics Data System (ADS)

Luo, Xing-Yu; Chen, Yong

2016-08-01

The extended form of modified Kadomtsev—Petviashvili equation with variable-coefficient is investigated in the framework of Painlevé analysis. The Lax pairs are obtained by analysing two Painlevé branches of this equation. Starting with the Lax pair, the N-times Darboux transformation is constructed and the N-soliton solution formula is given, which contains 2n free parameters and two arbitrary functions. Furthermore, with different combinations of the parameters, several types of soliton solutions are calculated from the first order to the third order. The regularity conditions are discussed in order to avoid the singularity of the solutions. Moreover, we construct the generalized Darboux transformation matrix by considering a special limiting process and find a rational-type solution for this equation. Supported by the Global Change Research Program of China under Grant No. 2015CB953904, National Natural Science Foundation of China under Grant Nos. 11275072 and 11435005, Doctoral Program of Higher Education of China under Grant No. 20120076110024, The Network Information Physics Calculation of basic research innovation research group of China under Grant No. 61321064, Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things under Grant No. ZF1213, Shanghai Minhang District talents of high level scientific research project

Kinetics of adsorption of dyes from aqueous solution using activated carbon prepared from waste apricot.

PubMed

Onal, Yunus

2006-10-11

Adsorbent (WA11Zn5) has been prepared from waste apricot by chemical activation with ZnCl(2). Pore properties of the activated carbon such as BET surface area, pore volume, pore size distribution, and pore diameter were characterized by N(2) adsorption and DFT plus software. Adsorption of three dyes, namely, Methylene Blue (MB), Malachite Green (MG), Crystal Violet (CV), onto activated carbon in aqueous solution was studied in a batch system with respect to contact time, temperature. The kinetics of adsorption of MB, MG and CV have been discussed using six kinetic models, i.e., the pseudo-first-order model, the pseudo-second-order model, the Elovich equation, the intraparticle diffusion model, the Bangham equation, the modified Freundlich equation. Kinetic parameters and correlation coefficients were determined. It was shown that the second-order kinetic equation could describe the adsorption kinetics for three dyes. The dyes uptake process was found to be controlled by external mass transfer at earlier stages (before 5 min) and by intraparticle diffusion at later stages (after 5 min). Thermodynamic parameters, such as DeltaG, DeltaH and DeltaS, have been calculated by using the thermodynamic equilibrium coefficient obtained at different temperatures and concentrations. The thermodynamics of dyes-WA11Zn5 system indicates endothermic process.

Model reference adaptive control (MRAC)-based parameter identification applied to surface-mounted permanent magnet synchronous motor

NASA Astrophysics Data System (ADS)

Zhong, Chongquan; Lin, Yaoyao

2017-11-01

In this work, a model reference adaptive control-based estimated algorithm is proposed for online multi-parameter identification of surface-mounted permanent magnet synchronous machines. By taking the dq-axis equations of a practical motor as the reference model and the dq-axis estimation equations as the adjustable model, a standard model-reference-adaptive-system-based estimator was established. Additionally, the Popov hyperstability principle was used in the design of the adaptive law to guarantee accurate convergence. In order to reduce the oscillation of identification result, this work introduces a first-order low-pass digital filter to improve precision regarding the parameter estimation. The proposed scheme was then applied to an SPM synchronous motor control system without any additional circuits and implemented using a DSP TMS320LF2812. For analysis, the experimental results reveal the effectiveness of the proposed method.

The equilibrium-diffusion limit for radiation hydrodynamics

DOE PAGES

Ferguson, J. M.; Morel, J. E.; Lowrie, R.

2017-07-27

The equilibrium-diffusion approximation (EDA) is used to describe certain radiation-hydrodynamic (RH) environments. When this is done the RH equations reduce to a simplified set of equations. The EDA can be derived by asymptotically analyzing the full set of RH equations in the equilibrium-diffusion limit. Here, we derive the EDA this way and show that it and the associated set of simplified equations are both first-order accurate with transport corrections occurring at second order. Having established the EDA’s first-order accuracy we then analyze the grey nonequilibrium-diffusion approximation and the grey Eddington approximation and show that they both preserve this first-order accuracy.more » Further, these approximations preserve the EDA’s first-order accuracy when made in either the comoving-frame (CMF) or the lab-frame (LF). And while analyzing the Eddington approximation, we found that the CMF and LF radiation-source equations are equivalent when neglecting O(β 2) terms and compared in the LF. Of course, the radiation pressures are not equivalent. It is expected that simplified physical models and numerical discretizations of the RH equations that do not preserve this first-order accuracy will not retain the correct equilibrium-diffusion solutions. As a practical example, we show that nonequilibrium-diffusion radiative-shock solutions devolve to equilibrium-diffusion solutions when the asymptotic parameter is small.« less

Modulational stability of periodic solutions of the Kuramoto-Sivaskinsky equation

NASA Technical Reports Server (NTRS)

Papageorgiou, Demetrios T.; Papanicolaou, George C.; Smyrlis, Yiorgos S.

1993-01-01

We study the long-wave, modulational, stability of steady periodic solutions of the Kuramoto-Sivashinsky equation. The analysis is fully nonlinear at first, and can in principle be carried out to all orders in the small parameter, which is the ratio of the spatial period to a characteristic length of the envelope perturbations. In the linearized regime, we recover a high-order version of the results of Frisch, She, and Thual, which shows that the periodic waves are much more stable than previously expected.

Localized states in an unbounded neural field equation with smooth firing rate function: a multi-parameter analysis.

PubMed

Faye, Grégory; Rankin, James; Chossat, Pascal

2013-05-01

The existence of spatially localized solutions in neural networks is an important topic in neuroscience as these solutions are considered to characterize working (short-term) memory. We work with an unbounded neural network represented by the neural field equation with smooth firing rate function and a wizard hat spatial connectivity. Noting that stationary solutions of our neural field equation are equivalent to homoclinic orbits in a related fourth order ordinary differential equation, we apply normal form theory for a reversible Hopf bifurcation to prove the existence of localized solutions; further, we present results concerning their stability. Numerical continuation is used to compute branches of localized solution that exhibit snaking-type behaviour. We describe in terms of three parameters the exact regions for which localized solutions persist.

Einstein gravity with torsion induced by the scalar field

NASA Astrophysics Data System (ADS)

Özçelik, H. T.; Kaya, R.; Hortaçsu, M.

2018-06-01

We couple a conformal scalar field in (2+1) dimensions to Einstein gravity with torsion. The field equations are obtained by a variational principle. We could not solve the Einstein and Cartan equations analytically. These equations are solved numerically with 4th order Runge-Kutta method. From the numerical solution, we make an ansatz for the rotation parameter in the proposed metric, which gives an analytical solution for the scalar field for asymptotic regions.

A new lumped-parameter approach to simulating flow processes in unsaturated dual-porosity media

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

Zimmerman, R.W.; Hadgu, T.; Bodvarsson, G.S.

We have developed a new lumped-parameter dual-porosity approach to simulating unsaturated flow processes in fractured rocks. Fluid flow between the fracture network and the matrix blocks is described by a nonlinear equation that relates the imbibition rate to the local difference in liquid-phase pressure between the fractures and the matrix blocks. This equation is a generalization of the Warren-Root equation, but unlike the Warren-Root equation, is accurate in both the early and late time regimes. The fracture/matrix interflow equation has been incorporated into a computational module, compatible with the TOUGH simulator, to serve as a source/sink term for fracture elements.more » The new approach achieves accuracy comparable to simulations in which the matrix blocks are discretized, but typically requires an order of magnitude less computational time.« less

Matter rogue waves in an F=1 spinor Bose-Einstein condensate.

PubMed

Qin, Zhenyun; Mu, Gui

2012-09-01

We report new types of matter rogue waves of a spinor (three-component) model of the Bose-Einstein condensate governed by a system of three nonlinearly coupled Gross-Pitaevskii equations. The exact first-order rational solutions containing one free parameter are obtained by means of a Darboux transformation for the integrable system where the mean-field interaction is attractive and the spin-exchange interaction is ferromagnetic. For different choices of the parameter, there exists a variety of different shaped solutions including two peaks in bright rogue waves and four dips in dark rogue waves. Furthermore, by utilizing the relation between the three-component and the one-component versions of the nonlinear Schrödinger equation, we can devise higher-order rational solutions, in which three components have different shapes. In addition, it is noteworthy that dark rogue wave features disappear in the third-order rational solution.

A remark on fractional differential equation involving I-function

NASA Astrophysics Data System (ADS)

Mishra, Jyoti

2018-02-01

The present paper deals with the solution of the fractional differential equation using the Laplace transform operator and its corresponding properties in the fractional calculus; we derive an exact solution of a complex fractional differential equation involving a special function known as I-function. The analysis of the some fractional integral with two parameters is presented using the suggested Theorem 1. In addition, some very useful corollaries are established and their proofs presented in detail. Some obtained exact solutions are depicted to see the effect of each fractional order. Owing to the wider applicability of the I-function, we can conclude that, the obtained results in our work generalize numerous well-known results obtained by specializing the parameters.

Lump solutions with interaction phenomena in the (2+1)-dimensional Ito equation

NASA Astrophysics Data System (ADS)

Zou, Li; Yu, Zong-Bing; Tian, Shou-Fu; Feng, Lian-Li; Li, Jin

2018-03-01

In this paper, we consider the (2+1)-dimensional Ito equation, which was introduced by Ito. By considering the Hirota’s bilinear method, and using the positive quadratic function, we obtain some lump solutions of the Ito equation. In order to ensure rational localization and analyticity of these lump solutions, some sufficient and necessary conditions are provided on the parameters that appeared in the solutions. Furthermore, the interaction solutions between lump solutions and the stripe solitons are discussed by combining positive quadratic function with exponential function. Finally, the dynamic properties of these solutions are shown via the way of graphical analysis by selecting appropriate values of the parameters.

The roles of non-extensivity and dust concentration as bifurcation parameters in dust-ion acoustic traveling waves in magnetized dusty plasma

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

Narayan Ghosh, Uday; Kumar Mandal, Pankaj, E-mail: pankajwbmsd@gmail.com; Chatterjee, Prasanta

Dust ion-acoustic traveling waves are studied in a magnetized dusty plasma in presence of static dust and non-extensive distributed electrons in the framework of Zakharov-Kuznesstov-Burgers (ZKB) equation. System of coupled nonlinear ordinary differential equations is derived from ZKB equation, and equilibrium points are obtained. Nonlinear wave phenomena are studied numerically using fourth order Runge-Kutta method. The change from unstable to stable solution and consequently to asymptotic stable of dust ion acoustic traveling waves is studied through dynamical system approach. It is found that some dramatical features emerge when the non-extensive parameter and the dust concentration parameters are varied. Behavior ofmore » the solution of the system changes from unstable to stable and stable to asymptotic stable depending on the value of the non-extensive parameter. It is also observed that when the dust concentration is increased the solution pattern is changed from oscillatory shocks to periodic solution. Thus, non-extensive and dust concentration parameters play crucial roles in determining the nature of the stability behavior of the system. Thus, the non-extensive parameter and the dust concentration parameters can be treated as bifurcation parameters.« less

Chapman-Enskog expansion for the Vicsek model of self-propelled particles

NASA Astrophysics Data System (ADS)

Ihle, Thomas

2016-08-01

Using the standard Vicsek model, I show how the macroscopic transport equations can be systematically derived from microscopic collision rules. The approach starts with the exact evolution equation for the N-particle probability distribution and, after making the mean-field assumption of molecular chaos, leads to a multi-particle Enskog-type equation. This equation is treated by a non-standard Chapman-Enskog expansion to extract the macroscopic behavior. The expansion includes terms up to third order in a formal expansion parameter ɛ, and involves a fast time scale. A self-consistent closure of the moment equations is presented that leads to a continuity equation for the particle density and a Navier-Stokes-like equation for the momentum density. Expressions for all transport coefficients in these macroscopic equations are given explicitly in terms of microscopic parameters of the model. The transport coefficients depend on specific angular integrals which are evaluated asymptotically in the limit of infinitely many collision partners, using an analogy to a random walk. The consistency of the Chapman-Enskog approach is checked by an independent calculation of the shear viscosity using a Green-Kubo relation.

MHD Flow and Heat Transfer of a Generalized Burgers’ Fluid due to a Periodic Oscillating and Periodic Heating Plate

NASA Astrophysics Data System (ADS)

Bai, Yu; Jiang, Yue-Hua; Zhang, Yan; Zhao, Hao-Jie

2017-10-01

This paper investigates the MHD flow and heat transfer of the incompressible generalized Burgers’ fluid due to a periodic oscillating plate with the effects of the second order slip and periodic heating plate. The momentum equation is formulated with multi-term fractional derivatives, and by means of viscous dissipation, the fractional derivative is considered in the energy equation. A finite difference scheme is established based on the G1-algorithm, whose convergence is confirmed by the comparison with the analytical solution in an example. Meanwhile the numerical solutions of velocity, temperature and shear stress are obtained. The effects of involved parameters on velocity and temperature fields are presented graphically and analyzed in detail. Increasing the fractional derivative parameter α, the velocity and temperature have a decreasing trend, while the influences of fractional derivative parameter β on the velocity and temperature behave conversely. Increasing the absolute value of the first order slip parameter and the second order slip parameter both cause a decrease of velocity. Furthermore, with the decreasing of the magnetic parameter, the shear stress decreases. Supported by the National Natural Science Foundations of China under Grant Nos. 21576023, 51406008, the National Key Research Program of China under Grant Nos. 2016YFC0700601, 2016YFC0700603 and the BUCEA Post Graduate Innovation Project (PG2017032)

Modelling the Spread of an Oil-Slick with Irregular Information

ERIC Educational Resources Information Center

Winkel, Brian

2010-01-01

We describe a modelling activity for students in a course in which modelling with differential equations is appropriate. We have used this model in our coursework for years and have found that it enlightens students as to the model building process and parameter estimation for a linear, first-order, ordinary differential equation. The activity…

Solving the Rational Polynomial Coefficients Based on L Curve

NASA Astrophysics Data System (ADS)

Zhou, G.; Li, X.; Yue, T.; Huang, W.; He, C.; Huang, Y.

2018-05-01

The rational polynomial coefficients (RPC) model is a generalized sensor model, which can achieve high approximation accuracy. And it is widely used in the field of photogrammetry and remote sensing. Least square method is usually used to determine the optimal parameter solution of the rational function model. However the distribution of control points is not uniform or the model is over-parameterized, which leads to the singularity of the coefficient matrix of the normal equation. So the normal equation becomes ill conditioned equation. The obtained solutions are extremely unstable and even wrong. The Tikhonov regularization can effectively improve and solve the ill conditioned equation. In this paper, we calculate pathological equations by regularization method, and determine the regularization parameters by L curve. The results of the experiments on aerial format photos show that the accuracy of the first-order RPC with the equal denominators has the highest accuracy. The high order RPC model is not necessary in the processing of dealing with frame images, as the RPC model and the projective model are almost the same. The result shows that the first-order RPC model is basically consistent with the strict sensor model of photogrammetry. Orthorectification results both the firstorder RPC model and Camera Model (ERDAS9.2 platform) are similar to each other, and the maximum residuals of X and Y are 0.8174 feet and 0.9272 feet respectively. This result shows that RPC model can be used in the aerial photographic compensation replacement sensor model.

Unsteady MHD blood flow through porous medium in a parallel plate channel

NASA Astrophysics Data System (ADS)

Latha, R.; Rushi Kumar, B.

2017-11-01

In this study, we have analyzed heat and mass transfer effects on unsteady blood flow through parallel plate channel in a saturated porous medium in the presence of a transverse magnetic field with thermal radiation. The governing higher order nonlinear PDE’S are converted to dimensionless equations using dimensionless variables. The dimensionless equations are then solved analytically using boundary conditions by choosing the axial flow transport and the fields of concentration and temperature apart from the normal velocity as a function of y and t. The effects of different pertinent parameters appeared in this model viz thermal radiation, Prandtl number, Heat source parameter, Hartmann number, Permeability parameter, Decay parameter on axial flow transport and the normal velocity are analyzed in detail.

Two healing lengths in a two-band GL-model with quadratic terms: Numerical results

NASA Astrophysics Data System (ADS)

Macias-Medri, A. E.; Rodríguez-Núñez, J. J.

2018-05-01

A two-band and quartic interaction order Ginzburg-Landau model in the presence of a single vortex is studied in this work. Interactions of second (quadratic, with coupling parameter γ) and fourth (quartic, with coupling parameter γ˜) order between the two superconducting order parameters (fi with i = 1,2) are incorporated in a functional. Terms beyond quadratic gradient contributions are neglected in the corresponding minimized free energy. The solution of the system of coupled equations is solved by numerical methods to obtain the fi-profiles, where our starting point was the calculation of the superconducting critical temperature Tc. With this at hand, we evaluate fi and the magnetic field along the z-axis, B0, as function of γ, γ˜, the radial distance r/λ1(0) and the temperature T, for T ≈ Tc. The self-consistent equations allow us to compute λ (penetration depth) and the healing lengths of fi (Lhi with i = 1,2) as functions of T, γ and γ˜. At the end, relevant discussions about type-1.5 superconductivity in the compounds we have studied are presented.

Computation of solar perturbations with Poisson series

NASA Technical Reports Server (NTRS)

Broucke, R.

1974-01-01

Description of a project for computing first-order perturbations of natural or artificial satellites by integrating the equations of motion on a computer with automatic Poisson series expansions. A basic feature of the method of solution is that the classical variation-of-parameters formulation is used rather than rectangular coordinates. However, the variation-of-parameters formulation uses the three rectangular components of the disturbing force rather than the classical disturbing function, so that there is no problem in expanding the disturbing function in series. Another characteristic of the variation-of-parameters formulation employed is that six rather unusual variables are used in order to avoid singularities at the zero eccentricity and zero (or 90 deg) inclination. The integration process starts by assuming that all the orbit elements present on the right-hand sides of the equations of motion are constants. These right-hand sides are then simple Poisson series which can be obtained with the use of the Bessel expansions of the two-body problem in conjunction with certain interation methods. These Poisson series can then be integrated term by term, and a first-order solution is obtained.

Stoichiometric network analysis and associated dimensionless kinetic equations. Application to a model of the Bray-Liebhafsky reaction.

PubMed

Schmitz, Guy; Kolar-Anić, Ljiljana Z; Anić, Slobodan R; Cupić, Zeljko D

2008-12-25

The stoichiometric network analysis (SNA) introduced by B. L. Clarke is applied to a simplified model of the complex oscillating Bray-Liebhafsky reaction under batch conditions, which was not examined by this method earlier. This powerful method for the analysis of steady-states stability is also used to transform the classical differential equations into dimensionless equations. This transformation is easy and leads to a form of the equations combining the advantages of classical dimensionless equations with the advantages of the SNA. The used dimensionless parameters have orders of magnitude given by the experimental information about concentrations and currents. This simplifies greatly the study of the slow manifold and shows which parameters are essential for controlling its shape and consequently have an important influence on the trajectories. The effectiveness of these equations is illustrated on two examples: the study of the bifurcations points and a simple sensitivity analysis, different from the classical one, more based on the chemistry of the studied system.

Seismic modeling with radial basis function-generated finite differences (RBF-FD) – a simplified treatment of interfaces

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

Martin, Bradley, E-mail: brma7253@colorado.edu; Fornberg, Bengt, E-mail: Fornberg@colorado.edu

In a previous study of seismic modeling with radial basis function-generated finite differences (RBF-FD), we outlined a numerical method for solving 2-D wave equations in domains with material interfaces between different regions. The method was applicable on a mesh-free set of data nodes. It included all information about interfaces within the weights of the stencils (allowing the use of traditional time integrators), and was shown to solve problems of the 2-D elastic wave equation to 3rd-order accuracy. In the present paper, we discuss a refinement of that method that makes it simpler to implement. It can also improve accuracy formore » the case of smoothly-variable model parameter values near interfaces. We give several test cases that demonstrate the method solving 2-D elastic wave equation problems to 4th-order accuracy, even in the presence of smoothly-curved interfaces with jump discontinuities in the model parameters.« less

Seismic modeling with radial basis function-generated finite differences (RBF-FD) - a simplified treatment of interfaces

NASA Astrophysics Data System (ADS)

Martin, Bradley; Fornberg, Bengt

2017-04-01

In a previous study of seismic modeling with radial basis function-generated finite differences (RBF-FD), we outlined a numerical method for solving 2-D wave equations in domains with material interfaces between different regions. The method was applicable on a mesh-free set of data nodes. It included all information about interfaces within the weights of the stencils (allowing the use of traditional time integrators), and was shown to solve problems of the 2-D elastic wave equation to 3rd-order accuracy. In the present paper, we discuss a refinement of that method that makes it simpler to implement. It can also improve accuracy for the case of smoothly-variable model parameter values near interfaces. We give several test cases that demonstrate the method solving 2-D elastic wave equation problems to 4th-order accuracy, even in the presence of smoothly-curved interfaces with jump discontinuities in the model parameters.

Hypergeometric Series Solution to a Class of Second-Order Boundary Value Problems via Laplace Transform with Applications to Nanofluids

NASA Astrophysics Data System (ADS)

Ebaid, Abdelhalim; Wazwaz, Abdul-Majid; Alali, Elham; Masaedeh, Basem S.

2017-03-01

Very recently, it was observed that the temperature of nanofluids is finally governed by second-order ordinary differential equations with variable coefficients of exponential orders. Such coefficients were then transformed to polynomials type by using new independent variables. In this paper, a class of second-order ordinary differential equations with variable coefficients of polynomials type has been solved analytically. The analytical solution is expressed in terms of a hypergeometric function with generalized parameters. Moreover, applications of the present results have been applied on some selected nanofluids problems in the literature. The exact solutions in the literature were derived as special cases of our generalized analytical solution.

Parameter Estimation of Fractional-Order Chaotic Systems by Using Quantum Parallel Particle Swarm Optimization Algorithm

PubMed Central

Huang, Yu; Guo, Feng; Li, Yongling; Liu, Yufeng

2015-01-01

Parameter estimation for fractional-order chaotic systems is an important issue in fractional-order chaotic control and synchronization and could be essentially formulated as a multidimensional optimization problem. A novel algorithm called quantum parallel particle swarm optimization (QPPSO) is proposed to solve the parameter estimation for fractional-order chaotic systems. The parallel characteristic of quantum computing is used in QPPSO. This characteristic increases the calculation of each generation exponentially. The behavior of particles in quantum space is restrained by the quantum evolution equation, which consists of the current rotation angle, individual optimal quantum rotation angle, and global optimal quantum rotation angle. Numerical simulation based on several typical fractional-order systems and comparisons with some typical existing algorithms show the effectiveness and efficiency of the proposed algorithm. PMID:25603158

An improved algorithm for the determination of the system paramters of a visual binary by least squares

NASA Astrophysics Data System (ADS)

Xu, Yu-Lin

The problem of computing the orbit of a visual binary from a set of observed positions is reconsidered. It is a least squares adjustment problem, if the observational errors follow a bias-free multivariate Gaussian distribution and the covariance matrix of the observations is assumed to be known. The condition equations are constructed to satisfy both the conic section equation and the area theorem, which are nonlinear in both the observations and the adjustment parameters. The traditional least squares algorithm, which employs condition equations that are solved with respect to the uncorrelated observations and either linear in the adjustment parameters or linearized by developing them in Taylor series by first-order approximation, is inadequate in our orbit problem. D.C. Brown proposed an algorithm solving a more general least squares adjustment problem in which the scalar residual function, however, is still constructed by first-order approximation. Not long ago, a completely general solution was published by W.H Jefferys, who proposed a rigorous adjustment algorithm for models in which the observations appear nonlinearly in the condition equations and may be correlated, and in which construction of the normal equations and the residual function involves no approximation. This method was successfully applied in our problem. The normal equations were first solved by Newton's scheme. Practical examples show that this converges fast if the observational errors are sufficiently small and the initial approximate solution is sufficiently accurate, and that it fails otherwise. Newton's method was modified to yield a definitive solution in the case the normal approach fails, by combination with the method of steepest descent and other sophisticated algorithms. Practical examples show that the modified Newton scheme can always lead to a final solution. The weighting of observations, the orthogonal parameters and the efficiency of a set of adjustment parameters are also considered. The definition of efficiency is revised.

f(R)-gravity from Killing tensors

NASA Astrophysics Data System (ADS)

Paliathanasis, Andronikos

2016-04-01

We consider f(R)-gravity in a Friedmann-Lemaître-Robertson-Walker spacetime with zero spatial curvature. We apply the Killing tensors of the minisuperspace in order to specify the functional form of f(R) and for the field equations to be invariant under Lie-Bäcklund transformations, which are linear in momentum (contact symmetries). Consequently, the field equations to admit quadratic conservation laws given by Noether’s theorem. We find three new integrable f(R)-models, for which, with the application of the conservation laws, we reduce the field equations to a system of two first-order ordinary differential equations. For each model we study the evolution of the cosmological fluid. We find that for each integrable model the cosmological fluid has an equation of state parameter, in which there is linear behavior in terms of the scale factor which describes the Chevallier, Polarski and Linder parametric dark energy model.

Matching Pion-Nucleon Roy-Steiner Equations to Chiral Perturbation Theory.

PubMed

Hoferichter, Martin; Ruiz de Elvira, Jacobo; Kubis, Bastian; Meissner, Ulf-G

2015-11-06

We match the results for the subthreshold parameters of pion-nucleon scattering obtained from a solution of Roy-Steiner equations to chiral perturbation theory up to next-to-next-to-next-to-leading order, to extract the pertinent low-energy constants including a comprehensive analysis of systematic uncertainties and correlations. We study the convergence of the chiral series by investigating the chiral expansion of threshold parameters up to the same order and discuss the role of the Δ(1232) resonance in this context. Results for the low-energy constants are also presented in the counting scheme usually applied in chiral nuclear effective field theory, where they serve as crucial input to determine the long-range part of the nucleon-nucleon potential as well as three-nucleon forces.

Matching Pion-Nucleon Roy-Steiner Equations to Chiral Perturbation Theory

NASA Astrophysics Data System (ADS)

Hoferichter, Martin; Ruiz de Elvira, Jacobo; Kubis, Bastian; Meißner, Ulf-G.

2015-11-01

We match the results for the subthreshold parameters of pion-nucleon scattering obtained from a solution of Roy-Steiner equations to chiral perturbation theory up to next-to-next-to-next-to-leading order, to extract the pertinent low-energy constants including a comprehensive analysis of systematic uncertainties and correlations. We study the convergence of the chiral series by investigating the chiral expansion of threshold parameters up to the same order and discuss the role of the Δ (1232 ) resonance in this context. Results for the low-energy constants are also presented in the counting scheme usually applied in chiral nuclear effective field theory, where they serve as crucial input to determine the long-range part of the nucleon-nucleon potential as well as three-nucleon forces.

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.

Solitonic dynamics and excitations of the nonlinear Schrödinger equation with third-order dispersion in non-Hermitian PT-symmetric potentials.

PubMed

Chen, Yong; Yan, Zhenya

2016-03-22

Solitons are of the important significant in many fields of nonlinear science such as nonlinear optics, Bose-Einstein condensates, plamas physics, biology, fluid mechanics, and etc. The stable solitons have been captured not only theoretically and experimentally in both linear and nonlinear Schrödinger (NLS) equations in the presence of non-Hermitian potentials since the concept of the parity-time -symmetry was introduced in 1998. In this paper, we present novel bright solitons of the NLS equation with third-order dispersion in some complex -symmetric potentials (e.g., physically relevant -symmetric Scarff-II-like and harmonic-Gaussian potentials). We find stable nonlinear modes even if the respective linear -symmetric phases are broken. Moreover, we also use the adiabatic changes of the control parameters to excite the initial modes related to exact solitons to reach stable nonlinear modes. The elastic interactions of two solitons are exhibited in the third-order NLS equation with -symmetric potentials. Our results predict the dynamical phenomena of soliton equations in the presence of third-order dispersion and -symmetric potentials arising in nonlinear fiber optics and other physically relevant fields.

Solitonic dynamics and excitations of the nonlinear Schrödinger equation with third-order dispersion in non-Hermitian PT-symmetric potentials

PubMed Central

Chen, Yong; Yan, Zhenya

2016-01-01

Solitons are of the important significant in many fields of nonlinear science such as nonlinear optics, Bose-Einstein condensates, plamas physics, biology, fluid mechanics, and etc. The stable solitons have been captured not only theoretically and experimentally in both linear and nonlinear Schrödinger (NLS) equations in the presence of non-Hermitian potentials since the concept of the parity-time -symmetry was introduced in 1998. In this paper, we present novel bright solitons of the NLS equation with third-order dispersion in some complex -symmetric potentials (e.g., physically relevant -symmetric Scarff-II-like and harmonic-Gaussian potentials). We find stable nonlinear modes even if the respective linear -symmetric phases are broken. Moreover, we also use the adiabatic changes of the control parameters to excite the initial modes related to exact solitons to reach stable nonlinear modes. The elastic interactions of two solitons are exhibited in the third-order NLS equation with -symmetric potentials. Our results predict the dynamical phenomena of soliton equations in the presence of third-order dispersion and -symmetric potentials arising in nonlinear fiber optics and other physically relevant fields. PMID:27002543

Asymptotic orderings and approximations of the Master kinetic equation for large hard spheres systems

NASA Astrophysics Data System (ADS)

Tessarotto, Massimo; Asci, Claudio

2017-05-01

In this paper the problem is posed of determining the physically-meaningful asymptotic orderings holding for the statistical description of a large N-body system of hard spheres, i.e., formed by N ≡1/ε ≫ 1 particles, which are allowed to undergo instantaneous and purely elastic unary, binary or multiple collisions. Starting point is the axiomatic treatment recently developed [Tessarotto et al., 2013-2016] and the related discovery of an exact kinetic equation realized by Master equation which advances in time the 1-body probability density function (PDF) for such a system. As shown in the paper the task involves introducing appropriate asymptotic orderings in terms of ε for all the physically-relevant parameters. The goal is that of identifying the relevant physically-meaningful asymptotic approximations applicable for the Master kinetic equation, together with their possible relationships with the Boltzmann and Enskog kinetic equations, and holding in appropriate asymptotic regimes. These correspond either to dilute or dense systems and are formed either by small-size or finite-size identical hard spheres, the distinction between the various cases depending on suitable asymptotic orderings in terms of ε.

The Bargmann-Wigner equations in spherical space

NASA Astrophysics Data System (ADS)

McKeon, D. G. C.; Sherry, T. N.

2006-01-01

The Bargmann-Wigner formalism is adapted to spherical surfaces embedded in three to eleven dimensions. This is demonstrated to generate wave equations in spherical space for a variety of antisymmetric tensor fields. Some of these equations are gauge invariant for particular values of the parameters characterizing them. For spheres embedded in three, four, and five dimensions, this gauge invariance can be generalized so as to become non-Abelian. This non-Abelian gauge invariance is shown to be a property of second-order models for two index antisymmetric tensor fields in any number of dimensions. The O(3) model is quantized and the two-point function is shown to vanish at the one-loop order.

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

NASA Astrophysics Data System (ADS)

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

2016-01-01

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

Optimal fixed-finite-dimensional compensator for Burgers' equation with unbounded input/output operators

NASA Technical Reports Server (NTRS)

Burns, John A.; Marrekchi, Hamadi

1993-01-01

The problem of using reduced order dynamic compensators to control a class of nonlinear parabolic distributed parameter systems was considered. Concentration was on a system with unbounded input and output operators governed by Burgers' equation. A linearized model was used to compute low-order-finite-dimensional control laws by minimizing certain energy functionals. Then these laws were applied to the nonlinear model. Standard approaches to this problem employ model/controller reduction techniques in conjunction with linear quadratic Gaussian (LQG) theory. The approach used is based on the finite dimensional Bernstein/Hyland optimal projection theory which yields a fixed-finite-order controller.

A general mixture theory. I. Mixtures of spherical molecules

NASA Astrophysics Data System (ADS)

Hamad, Esam Z.

1996-08-01

We present a new general theory for obtaining mixture properties from the pure species equations of state. The theory addresses the composition and the unlike interactions dependence of mixture equation of state. The density expansion of the mixture equation gives the exact composition dependence of all virial coefficients. The theory introduces multiple-index parameters that can be calculated from binary unlike interaction parameters. In this first part of the work, details are presented for the first and second levels of approximations for spherical molecules. The second order model is simple and very accurate. It predicts the compressibility factor of additive hard spheres within simulation uncertainty (equimolar with size ratio of three). For nonadditive hard spheres, comparison with compressibility factor simulation data over a wide range of density, composition, and nonadditivity parameter, gave an average error of 2%. For mixtures of Lennard-Jones molecules, the model predictions are better than the Weeks-Chandler-Anderson perturbation theory.

Group analysis for natural convection from a vertical plate

NASA Astrophysics Data System (ADS)

Rashed, A. S.; Kassem, M. M.

2008-12-01

The steady laminar natural convection of a fluid having chemical reaction of order n past a semi-infinite vertical plate is considered. The solution of the problem by means of one-parameter group method reduces the number of independent variables by one leading to a system of nonlinear ordinary differential equations. Two different similarity transformations are found. In each case the set of differential equations are solved numerically using Runge-Kutta and the shooting method. For each transformation different Schmidt numbers and chemical reaction orders are tested.

Motion of a pendulum with damping and vibrating axis of suspension at unconventional values of parameters

NASA Astrophysics Data System (ADS)

Demidov, Ivan; Sorokin, Vladislav

2018-05-01

Motion of a pendulum with damping and vibrating axis of suspension is considered at unconventional values of parameters. Case when the frequency of external loading and the natural frequency of the pendulum in the absence of this loading are of the same order is studied. Vibration intensity is assumed to be relatively low. In this case, the corresponding equation of the pendulum's motions doesn't involve an explicit small parameter. To solve the equation a new modification of the method of direct separation of motions is used. As the result, stability conditions of the pendulum inverted position are determined. Effects of damping on these conditions are discussed.

General high-order breathers and rogue waves in the (3 + 1) -dimensional KP-Boussinesq equation

NASA Astrophysics Data System (ADS)

Sun, Baonan; Wazwaz, Abdul-Majid

2018-11-01

In this work, we investigate the (3 + 1) -dimensional KP-Boussinesq equation, which can be used to describe the nonlinear dynamic behavior in scientific and engineering applications. We derive general high-order soliton solutions by using the Hirota's bilinear method combined with the perturbation expansion technique. We also obtain periodic solutions comprising of high-order breathers, periodic line waves, and mixed solutions consisting of breathers and periodic line waves upon selecting particular parameter constraints of the obtained soliton solutions. Furthermore, smooth rational solutions are generated by taking a long wave limit of the soliton solutions. These smooth rational solutions include high-order rogue waves, high-order lumps, and hybrid solutions consisting of lumps and line rogue waves. To better understand the dynamical behaviors of these solutions, we discuss some illustrative graphical analyses. It is expected that our results can enrich the dynamical behavior of the (3 + 1) -dimensional nonlinear evolution equations of other forms.

Falkner-Skan Boundary Layer Flow of a Sisko Fluid

NASA Astrophysics Data System (ADS)

Khan, Masood; Shahzad, Azeem

2012-09-01

In this paper, we investigate the steady boundary layer flow of a non-Newtonian fluid, represented by a Sisko fluid, over a wedge in a moving fluid. The equations of motion are derived for boundary layer flow of an incompressible Sisko fluid using appropriate similarity variables. The governing equations are reduced to a single third-order highly nonlinear ordinary differential equation in the dimensionless stream function, which is then solved analytically using the homotopy analysis method. Some important parameters have been discussed by this study, which include the power law index n, the material parameter A, the wedge shape factor b, and the skin friction coefficient Cf. A comprehensive study is made between the results of the Sisko and the power-law fluids.

On Gravitational Effects in the Schrödinger Equation

NASA Astrophysics Data System (ADS)

Pollock, M. D.

2014-04-01

The Schrödinger equation for a particle of rest mass and electrical charge interacting with a four-vector potential can be derived as the non-relativistic limit of the Klein-Gordon equation for the wave function , where and , or equivalently from the one-dimensional action for the corresponding point particle in the semi-classical approximation , both methods yielding the equation in Minkowski space-time , where and . We show that these two methods generally yield equations that differ in a curved background space-time , although they coincide when if is replaced by the effective mass in both the Klein-Gordon action and , allowing for non-minimal coupling to the gravitational field, where is the Ricci scalar and is a constant. In this case , where and , the correctness of the gravitational contribution to the potential having been verified to linear order in the thermal-neutron beam interferometry experiment due to Colella et al. Setting and regarding as the quasi-particle wave function, or order parameter, we obtain the generalization of the fundamental macroscopic Ginzburg-Landau equation of superconductivity to curved space-time. Conservation of probability and electrical current requires both electromagnetic gauge and space-time coordinate conditions to be imposed, which exemplifies the gravito-electromagnetic analogy, particularly in the stationary case, when div, where and . The quantum-cosmological Schrödinger (Wheeler-DeWitt) equation is also discussed in the -dimensional mini-superspace idealization, with particular regard to the vacuum potential and the characteristics of the ground state, assuming a gravitational Lagrangian which contains higher-derivative terms up to order . For the heterotic superstring theory , consists of an infinite series in , where is the Regge slope parameter, and in the perturbative approximation , is positive semi-definite for . The maximally symmetric ground state satisfying the field equations is Minkowski space for and anti-de Sitter space for.

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.

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

Sergyeyev, Artur; Krtous, Pavel; Institute of Theoretical Physics, Faculty of Mathematics and Physics, Charles University in Prague, V Holesovickach 2, Prague

We consider the Klein-Gordon equation in generalized higher-dimensional Kerr-NUT-(A)dS spacetime without imposing any restrictions on the functional parameters characterizing the metric. We establish commutativity of the second-order operators constructed from the Killing tensors found in [J. High Energy Phys. 02 (2007) 004] and show that these operators, along with the first-order operators originating from the Killing vectors, form a complete set of commuting symmetry operators (i.e., integrals of motion) for the Klein-Gordon equation. Moreover, we demonstrate that the separated solutions of the Klein-Gordon equation obtained in [J. High Energy Phys. 02 (2007) 005] are joint eigenfunctions for all of thesemore » operators. We also present an explicit form of the zero mode for the Klein-Gordon equation with zero mass. In the semiclassical approximation we find that the separated solutions of the Hamilton-Jacobi equation for geodesic motion are also solutions for a set of Hamilton-Jacobi-type equations which correspond to the quadratic conserved quantities arising from the above Killing tensors.« less

Three dimensional rotating flow of Powell-Eyring nanofluid with non-Fourier's heat flux and non-Fick's mass flux theory

NASA Astrophysics Data System (ADS)

Ibrahim, Wubshet

2018-03-01

This article numerically examines three dimensional boundary layer flow of a rotating Powell-Eyring nanofluid. In modeling heat transfer processes, non-Fourier heat flux theory and for mass transfer non-Fick's mass flux theory are employed. This theory is recently re-initiated and it becomes the active research area to resolves some drawback associated with the famous Fourier heat flux and mass flux theory. The mathematical model of the flow problem is a system of non-linear partial differential equations which are obtained using the boundary layer analysis. The non-linear partial differential equations have been transformed into non-linear high order ordinary differential equations using similarity transformation. Employing bvp4c algorithm from matlab software routine, the numerical solution of the transformed ordinary differential equations is obtained. The governing equations are constrained by parameters such as rotation parameter λ , the non-Newtonian parameter N, dimensionless thermal relaxation and concentration relaxation parameters δt and δc . The impacts of these parameters have been discussed thoroughly and illustrated using graphs and tables. The findings show that thermal relaxation time δt reduces the thermal and concentration boundary layer thickness. Further, the results reveal that the rotational parameter λ has the effect of decreasing the velocity boundary layer thickness in both x and y directions. Further examination pinpoints that the skin friction coefficient along x-axis is an increasing and skin friction coefficient along y-axis is a decreasing function of rotation parameter λ . Furthermore, the non-Newtonian fluid parameter N has the characteristic of reducing the amount of local Nusselt numbers -f″ (0) and -g″ (0) both in x and y -directions.

Evolutionary optimization with data collocation for reverse engineering of biological networks.

PubMed

Tsai, Kuan-Yao; Wang, Feng-Sheng

2005-04-01

Modern experimental biology is moving away from analyses of single elements to whole-organism measurements. Such measured time-course data contain a wealth of information about the structure and dynamic of the pathway or network. The dynamic modeling of the whole systems is formulated as a reverse problem that requires a well-suited mathematical model and a very efficient computational method to identify the model structure and parameters. Numerical integration for differential equations and finding global parameter values are still two major challenges in this field of the parameter estimation of nonlinear dynamic biological systems. We compare three techniques of parameter estimation for nonlinear dynamic biological systems. In the proposed scheme, the modified collocation method is applied to convert the differential equations to the system of algebraic equations. The observed time-course data are then substituted into the algebraic system equations to decouple system interactions in order to obtain the approximate model profiles. Hybrid differential evolution (HDE) with population size of five is able to find a global solution. The method is not only suited for parameter estimation but also can be applied for structure identification. The solution obtained by HDE is then used as the starting point for a local search method to yield the refined estimates.

Using non-linear analogue of Nyquist diagrams for analysis of the equation describing the hemodynamics in blood vessels near pathologies

NASA Astrophysics Data System (ADS)

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

2016-06-01

This article considers method of describing the behaviour of hemodynamic parameters near vascular pathologies. We study the influence of arterial aneurysms and arteriovenous malformations on the vascular system. The proposed method involves using generalized model of Van der Pol-Duffing to find out the characteristic behaviour of blood flow parameters. These parameters are blood velocity and pressure in the vessel. The velocity and pressure are obtained during the neurosurgery measurements. It is noted that substituting velocity on the right side of the equation gives good pressure approximation. Thus, the model reproduces clinical data well enough. In regard to the right side of the equation, it means external impact on the system. The harmonic functions with various frequencies and amplitudes are substituted on the right side of the equation to investigate its properties. Besides, variation of the right side parameters provides additional information about pressure. Non-linear analogue of Nyquist diagrams is used to find out how the properties of solution depend on the parameter values. We have analysed 60 cases with aneurysms and 14 cases with arteriovenous malformations. It is shown that the diagrams are divided into classes. Also, the classes are replaced by another one in the definite order with increasing of the right side amplitude.

Dual-shaped offset reflector antenna designs from solutions of the geometrical optics first-order partial differential equations

NASA Technical Reports Server (NTRS)

Galindo-Israel, V.; Imbriale, W.; Shogen, K.; Mittra, R.

1990-01-01

In obtaining solutions to the first-order nonlinear partial differential equations (PDEs) for synthesizing offset dual-shaped reflectors, it is found that previously observed computational problems can be avoided if the integration of the PDEs is started from an inner projected perimeter and integrated outward rather than starting from an outer projected perimeter and integrating inward. This procedure, however, introduces a new parameter, the main reflector inner perimeter radius p(o), when given a subreflector inner angle 0(o). Furthermore, a desired outer projected perimeter (e.g., a circle) is no longer guaranteed. Stability of the integration is maintained if some of the initial parameters are determined first from an approximate solution to the PDEs. A one-, two-, or three-parameter optimization algorithm can then be used to obtain a best set of parameters yielding a close fit to the desired projected outer rim. Good low cross-polarization mapping functions are also obtained. These methods are illustrated by synthesis of a high-gain offset-shaped Cassegrainian antenna and a low-noise offset-shaped Gregorian antenna.

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.

General solution of a fractional Parker diffusion-convection equation describing the superdiffusive transport of energetic particles

NASA Astrophysics Data System (ADS)

Tawfik, Ashraf M.; Fichtner, Horst; Elhanbaly, A.; Schlickeiser, Reinhard

2018-06-01

Anomalous diffusion models of energetic particles in space plasmas are developed by introducing the fractional Parker diffusion-convection equation. Analytical solution of the space-time fractional equation is obtained by use of the Caputo and Riesz-Feller fractional derivatives with the Laplace-Fourier transforms. The solution is given in terms of the Fox H-function. Profiles of particle densities are illustrated for different values of the space fractional order and the so-called skewness parameter.

Heat transfer in a micropolar fluid over a stretching sheet with Newtonian heating.

PubMed

Qasim, Muhammad; Khan, Ilyas; Shafie, Sharidan

2013-01-01

This article looks at the steady flow of Micropolar fluid over a stretching surface with heat transfer in the presence of Newtonian heating. The relevant partial differential equations have been reduced to ordinary differential equations. The reduced ordinary differential equation system has been numerically solved by Runge-Kutta-Fehlberg fourth-fifth order method. Influence of different involved parameters on dimensionless velocity, microrotation and temperature is examined. An excellent agreement is found between the present and previous limiting results.

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.

An equation of state for the financial markets: connecting order flow to price formation.

NASA Astrophysics Data System (ADS)

Gerig, Austin; Mike, Szabolcs; Doyne Farmer, J.

2006-03-01

Many of the peculiarities of price formation in the financial marketplace can be understood as the result of a few regularities in the placement and removal of trading orders. Based on a large data set from the London Stock Exchange we show that the distribution of prices where people place orders to buy or sell follows a surprisingly simple functional form that depends on the current best prices. In addition, whether or not an order is to buy or sell is described by a long-memory process, and the cancellation of orders can be described by a few simple rules. When these results are combined, simply by following the rules of the continuous double auction, the resulting simulation model produces good predictions for the distribution of price changes and transaction costs without any adjustment of parameters. We use the model to empirically derive equations of state relating order flow and the statistical properties of prices. In contrast to previous conjectures, our results demonstrate that these distributions are not universal, but rather depend on parameters of individual markets. They also show that factors other than supply and demand play an important role in price formation.

Convergence of high order memory kernels in the Nakajima-Zwanzig generalized master equation and rate constants: Case study of the spin-boson model.

PubMed

Xu, Meng; Yan, Yaming; Liu, Yanying; Shi, Qiang

2018-04-28

The Nakajima-Zwanzig generalized master equation provides a formally exact framework to simulate quantum dynamics in condensed phases. Yet, the exact memory kernel is hard to obtain and calculations based on perturbative expansions are often employed. By using the spin-boson model as an example, we assess the convergence of high order memory kernels in the Nakajima-Zwanzig generalized master equation. The exact memory kernels are calculated by combining the hierarchical equation of motion approach and the Dyson expansion of the exact memory kernel. High order expansions of the memory kernels are obtained by extending our previous work to calculate perturbative expansions of open system quantum dynamics [M. Xu et al., J. Chem. Phys. 146, 064102 (2017)]. It is found that the high order expansions do not necessarily converge in certain parameter regimes where the exact kernel show a long memory time, especially in cases of slow bath, weak system-bath coupling, and low temperature. Effectiveness of the Padé and Landau-Zener resummation approaches is tested, and the convergence of higher order rate constants beyond Fermi's golden rule is investigated.

Convergence of high order memory kernels in the Nakajima-Zwanzig generalized master equation and rate constants: Case study of the spin-boson model

NASA Astrophysics Data System (ADS)

Xu, Meng; Yan, Yaming; Liu, Yanying; Shi, Qiang

2018-04-01

The Nakajima-Zwanzig generalized master equation provides a formally exact framework to simulate quantum dynamics in condensed phases. Yet, the exact memory kernel is hard to obtain and calculations based on perturbative expansions are often employed. By using the spin-boson model as an example, we assess the convergence of high order memory kernels in the Nakajima-Zwanzig generalized master equation. The exact memory kernels are calculated by combining the hierarchical equation of motion approach and the Dyson expansion of the exact memory kernel. High order expansions of the memory kernels are obtained by extending our previous work to calculate perturbative expansions of open system quantum dynamics [M. Xu et al., J. Chem. Phys. 146, 064102 (2017)]. It is found that the high order expansions do not necessarily converge in certain parameter regimes where the exact kernel show a long memory time, especially in cases of slow bath, weak system-bath coupling, and low temperature. Effectiveness of the Padé and Landau-Zener resummation approaches is tested, and the convergence of higher order rate constants beyond Fermi's golden rule is investigated.

The equation of state of Song and Mason applied to fluorine

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

Eslami, H.; Boushehri, A.

1999-03-01

An analytical equation of state is applied to calculate the compressed and saturation thermodynamic properties of fluorine. The equation of state is that of Song and Mason. It is based on a statistical mechanical perturbation theory of hard convex bodies and is a fifth-order polynomial in the density. There exist three temperature-dependent parameters: the second virial coefficient, an effective molecular volume, and a scaling factor for the average contact pair distribution function of hard convex bodies. The temperature-dependent parameters can be calculated if the intermolecular pair potential is known. However, the equation is usable with much less input than themore » full intermolecular potential, since the scaling factor and effective volume are nearly universal functions when expressed in suitable reduced units. The equation of state has been applied to calculate thermodynamic parameters including the critical constants, the vapor pressure curve, the compressibility factor, the fugacity coefficient, the enthalpy, the entropy, the heat capacity at constant pressure, the ratio of heat capacities, the Joule-Thomson coefficient, the Joule-Thomson inversion curve, and the speed of sound for fluorine. The agreement with experiment is good.« less

Reconstruction from scalar-tensor theory and the inhomogeneous equation of state in f( T) gravity

NASA Astrophysics Data System (ADS)

Said, Jackson Levi

2017-12-01

General relativity (GR) characterizes gravity as a geometric properly exhibited as curvature on spacetime. Teleparallelism describes gravity through torsional properties, and can reproduce GR at the level of equations. Similar to f( R) gravity, on taking a generalization, f( T) gravity can produce various modifications its gravitational mechanism. The resulting field equations are inherently distinct to f( R) gravity in that they are second order. In the present work, f( T) gravity is examined in the cosmological context with a number of solutions reconstructed by means of an auxiliary scalar field. To do this, various forms of the Hubble parameter are considered with an f( T) Lagrangian emerging for each instance. In addition, the inhomogeneous equation of state (EoS) is investigated with a particular Hubble parameter model used to show how this can be used to reconstruct the f( T) Lagrangian. Observationally, the auxiliary scalar field and the exotic terms in the FRW field equations give the same results, meaning that the variation in the Hubble parameter may be interpreted as the need to reformulate gravity in some way, as in f( T) gravity.

Galilean-invariant preconditioned central-moment lattice Boltzmann method without cubic velocity errors for efficient steady flow simulations

NASA Astrophysics Data System (ADS)

Hajabdollahi, Farzaneh; Premnath, Kannan N.

2018-05-01

Lattice Boltzmann (LB) models used for the computation of fluid flows represented by the Navier-Stokes (NS) equations on standard lattices can lead to non-Galilean-invariant (GI) viscous stress involving cubic velocity errors. This arises from the dependence of their third-order diagonal moments on the first-order moments for standard lattices, and strategies have recently been introduced to restore Galilean invariance without such errors using a modified collision operator involving corrections to either the relaxation times or the moment equilibria. Convergence acceleration in the simulation of steady flows can be achieved by solving the preconditioned NS equations, which contain a preconditioning parameter that can be used to tune the effective sound speed, and thereby alleviating the numerical stiffness. In the present paper, we present a GI formulation of the preconditioned cascaded central-moment LB method used to solve the preconditioned NS equations, which is free of cubic velocity errors on a standard lattice, for steady flows. A Chapman-Enskog analysis reveals the structure of the spurious non-GI defect terms and it is demonstrated that the anisotropy of the resulting viscous stress is dependent on the preconditioning parameter, in addition to the fluid velocity. It is shown that partial correction to eliminate the cubic velocity defects is achieved by scaling the cubic velocity terms in the off-diagonal third-order moment equilibria with the square of the preconditioning parameter. Furthermore, we develop additional corrections based on the extended moment equilibria involving gradient terms with coefficients dependent locally on the fluid velocity and the preconditioning parameter. Such parameter dependent corrections eliminate the remaining truncation errors arising from the degeneracy of the diagonal third-order moments and fully restore Galilean invariance without cubic defects for the preconditioned LB scheme on a standard lattice. Several conclusions are drawn from the analysis of the structure of the non-GI errors and the associated corrections, with particular emphasis on their dependence on the preconditioning parameter. The GI preconditioned central-moment LB method is validated for a number of complex flow benchmark problems and its effectiveness to achieve convergence acceleration and improvement in accuracy is demonstrated.

Single-photon blockade in a hybrid cavity-optomechanical system via third-order nonlinearity

NASA Astrophysics Data System (ADS)

Sarma, Bijita; Sarma, Amarendra K.

2018-04-01

Photon statistics in a weakly driven optomechanical cavity, with Kerr-type nonlinearity, are analyzed both analytically and numerically. The single-photon blockade effect is demonstrated via calculations of the zero-time-delay second-order correlation function g (2)(0). The analytical results obtained by solving the Schrödinger equation are in complete conformity with the results obtained through numerical solution of the quantum master equation. A systematic study on the parameter regime for observing photon blockade in the weak coupling regime is reported. The parameter regime where the photon blockade is not realizable due to the combined effect of nonlinearities owing to the optomechanical coupling and the Kerr-effect is demonstrated. The experimental feasibility with state-of-the-art device parameters is discussed and it is observed that photon blockade could be generated at the telecommunication wavelength. An elaborate analysis of the thermal effects on photon antibunching is presented. The system is found to be robust against pure dephasing-induced decoherences and thermal phonon number fluctuations.

Combining states without scale hierarchies with ordered parton showers

DOE PAGES

Fischer, Nadine; Prestel, Stefan

2017-09-12

Here, we present a parameter-free scheme to combine fixed-order multi-jet results with parton-shower evolution. The scheme produces jet cross sections with leading-order accuracy in the complete phase space of multiple emissions, resumming large logarithms when appropriate, while not arbitrarily enforcing ordering on momentum configurations beyond the reach of the parton-shower evolution equation. This then requires the development of a matrix-element correction scheme for complex phase-spaces including ordering conditions as well as a systematic scale-setting procedure for unordered phase-space points. Our algorithm does not require a merging-scale parameter. We implement the new method in the Vincia framework and compare to LHCmore » data.« less

Cavity equations for a positive- or negative-refraction-index material with electric and magnetic nonlinearities.

PubMed

Mártin, Daniel A; Hoyuelos, Miguel

2009-11-01

We study evolution equations for electric and magnetic field amplitudes in a ring cavity with plane mirrors. The cavity is filled with a positive or negative-refraction-index material with third-order effective electric and magnetic nonlinearities. Two coupled nonlinear equations for the electric and magnetic amplitudes are obtained. We prove that the description can be reduced to one Lugiato-Lefever equation with generalized coefficients. A stability analysis of the homogeneous solution, complemented with numerical integration, shows that any combination of the parameters should correspond to one of three characteristic behaviors.

Vortex breakdown simulation - A circumspect study of the steady, laminar, axisymmetric model

NASA Technical Reports Server (NTRS)

Salas, M. D.; Kuruvila, G.

1989-01-01

The incompressible axisymmetric steady Navier-Stokes equations are written using the streamfunction-vorticity formulation. The resulting equations are discretized using a second-order central-difference scheme. The discretized equations are linearized and then solved using an exact LU decomposition, Gaussian elimination, and Newton iteration. Solutions are presented for Reynolds numbers (based on vortex core radius) 100-1800 and swirl parameter 0.9-1.1. The effects of inflow boundary conditions, the location of farfield and outflow boundaries, and mesh refinement are examined. Finally, the stability of the steady solutions is investigated by solving the time-dependent equations.

Gyro-Landau fluid models for toroidal geometry

NASA Astrophysics Data System (ADS)

Waltz, R. E.; Dominguez, R. R.; Hammett, G. W.

1992-10-01

Gyro-Landau fluid model equations provide first-order time advancement for a limited number of moments of the gyrokinetic equation, while approximately preserving the effects of the gyroradius averaging and Landau damping. This paper extends the work of Hammett and Perkins [Phys. Rev. Lett. 64, 3019 (1990)] for electrostatic motion parallel to the magnetic field and E×B motion to include the gyroaveraging linearly and the curvature drift motion. The equations are tested by comparing the ion-temperature-gradient mode linear growth rates for the model equations with those of the exact gyrokinetic theory over a full range of parameters.

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.

Hydrodynamics of isotropic and liquid crystalline active polymer solutions.

PubMed

Ahmadi, Aphrodite; Marchetti, M C; Liverpool, T B

2006-12-01

We describe the large-scale collective behavior of solutions of polar biofilaments and stationary and mobile crosslinkers. Both mobile and stationary crosslinkers induce filament alignment promoting either polar or nematic order. In addition, mobile crosslinkers, such as clusters of motor proteins, exchange forces and torques among the filaments and render the homogeneous states unstable via filament bundling. We start from a Smoluchowski equation for rigid filaments in solutions, where pairwise crosslink-mediated interactions among the filaments yield translational and rotational currents. The large-scale properties of the system are described in terms of continuum equations for filament and motor densities, polarization, and alignment tensor obtained by coarse-graining the Smoluchovski equation. The possible homogeneous and inhomogeneous states of the systems are obtained as stable solutions of the dynamical equations and are characterized in terms of experimentally accessible parameters. We make contact with work by other authors and show that our model allows for an estimate of the various parameters in the hydrodynamic equations in terms of physical properties of the crosslinkers.

Lumped Model Generation and Evaluation: Sensitivity and Lie Algebraic Techniques with Applications to Combustion

DTIC Science & Technology

1989-03-03

address global parameter space mapping issues for first order differential equations. The rigorous criteria for the existence of exact lumping by linear projective transformations was also established.

Second-order (2 +1 ) -dimensional anisotropic hydrodynamics

NASA Astrophysics Data System (ADS)

Bazow, Dennis; Heinz, Ulrich; Strickland, Michael

2014-11-01

We present a complete formulation of second-order (2 +1 ) -dimensional anisotropic hydrodynamics. The resulting framework generalizes leading-order anisotropic hydrodynamics by allowing for deviations of the one-particle distribution function from the spheroidal form assumed at leading order. We derive complete second-order equations of motion for the additional terms in the macroscopic currents generated by these deviations from their kinetic definition using a Grad-Israel-Stewart 14-moment ansatz. The result is a set of coupled partial differential equations for the momentum-space anisotropy parameter, effective temperature, the transverse components of the fluid four-velocity, and the viscous tensor components generated by deviations of the distribution from spheroidal form. We then perform a quantitative test of our approach by applying it to the case of one-dimensional boost-invariant expansion in the relaxation time approximation (RTA) in which case it is possible to numerically solve the Boltzmann equation exactly. We demonstrate that the second-order anisotropic hydrodynamics approach provides an excellent approximation to the exact (0+1)-dimensional RTA solution for both small and large values of the shear viscosity.

Statistical Mechanics of Node-perturbation Learning with Noisy Baseline

NASA Astrophysics Data System (ADS)

Hara, Kazuyuki; Katahira, Kentaro; Okada, Masato

2017-02-01

Node-perturbation learning is a type of statistical gradient descent algorithm that can be applied to problems where the objective function is not explicitly formulated, including reinforcement learning. It estimates the gradient of an objective function by using the change in the object function in response to the perturbation. The value of the objective function for an unperturbed output is called a baseline. Cho et al. proposed node-perturbation learning with a noisy baseline. In this paper, we report on building the statistical mechanics of Cho's model and on deriving coupled differential equations of order parameters that depict learning dynamics. We also show how to derive the generalization error by solving the differential equations of order parameters. On the basis of the results, we show that Cho's results are also apply in general cases and show some general performances of Cho's model.

Elucidation of the naproxen sodium adsorption onto activated carbon prepared from waste apricot: kinetic, equilibrium and thermodynamic characterization.

PubMed

Onal, Y; Akmil-Başar, C; Sarici-Ozdemir, C

2007-09-30

In this study, activated carbon (WA11Zn5) was prepared from waste apricot, which is waste in apricot plants in Malatya, by chemical activation with ZnCl(2). BET surface area of activated carbon is determined as 1060 m(2)/g. The ability of WA11Zn5, to remove naproxen sodium from effluent solutions by adsorption has been studied. Equilibrium isotherms for the adsorption of naproxen sodium on activated carbon were measured experimentally. Results were analyzed by the Langmiur, Freundlich equation using linearized correlation coefficient at 298 K. The characteristic parameters for each isotherm have been determined. Langmiur equation is found to best represent the equilibrium data for naproxen sodium-WA11Zn5 systems. The monolayer adsorption capacity of WA11Zn5 for naproxen sodium was found to be 106.38 mg/g at 298 K. The process was favorable and spontaneous. The kinetics of adsorption of naproxen sodium have been discussed using three kinetic models, i.e., the pseudo first-order model, the pseudo second-order model, the intraparticle diffusion model. Kinetic parameters and correlation coefficients were determined. It was shown that the pseudo second-order kinetic equation could describe the adsorption kinetics for naproxen sodium onto WA11Zn5. The thermodynamic parameters, such as DeltaG degrees , DeltaS degrees and DeltaH degrees, were calculated. The thermodynamics of naproxen sodium-WA11Zn5 system indicates endothermic process.

Bright, dark and W-shaped solitons with extended nonlinear Schrödinger's equation for odd and even higher-order terms

NASA Astrophysics Data System (ADS)

Bendahmane, Issam; Triki, Houria; Biswas, Anjan; Saleh Alshomrani, Ali; Zhou, Qin; Moshokoa, Seithuti P.; Belic, Milivoj

2018-02-01

We present solitary wave solutions of an extended nonlinear Schrödinger equation with higher-order odd (third-order) and even (fourth-order) terms by using an ansatz method. The including high-order dispersion terms have significant physical applications in fiber optics, the Heisenberg spin chain, and ocean waves. Exact envelope solutions comprise bright, dark and W-shaped solitary waves, illustrating the potentially rich set of solitary wave solutions of the extended model. Furthermore, we investigate the properties of these solitary waves in nonlinear and dispersive media. Moreover, specific constraints on the system parameters for the existence of these structures are discussed exactly. The results show that the higher-order dispersion and nonlinear effects play a crucial role for the formation and properties of propagating waves.

A new lumped-parameter model for flow in unsaturated dual-porosity media

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

Zimmerman, Robert W.; Hadgu, Teklu; Bodvarsson, Gudmundur S.

A new lumped-parameter approach to simulating unsaturated flow processes in dual-porosity media such as fractured rocks or aggregated soils is presented. Fluid flow between the fracture network and the matrix blocks is described by a non-linear equation that relates the imbibition rate to the local difference in liquid-phase pressure between the fractures and the matrix blocks. Unlike a Warren-Root-type equation, this equation is accurate in both the early and late time regimes. The fracture/matrix interflow equation has been incorporated into an existing unsaturated flow simulator, to serve as a source/sink term for fracture gridblocks. Flow processes are then simulated usingmore » only fracture gridblocks in the computational grid. This new lumped-parameter approach has been tested on two problems involving transient flow in fractured/porous media, and compared with simulations performed using explicit discretization of the matrix blocks. The new procedure seems to accurately simulate flow processes in unsaturated fractured rocks, and typically requires an order of magnitude less computational time than do simulations using fully-discretized matrix blocks. [References: 37]« less

A new approach to exact optical soliton solutions for the nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Morales-Delgado, V. F.; Gómez-Aguilar, J. F.; Baleanu, Dumitru

2018-05-01

By using the modified homotopy analysis transform method, we construct the analytical solutions of the space-time generalized nonlinear Schrödinger equation involving a new fractional conformable derivative in the Liouville-Caputo sense and the fractional-order derivative with the Mittag-Leffler law. Employing theoretical parameters, we present some numerical simulations and compare the solutions obtained.

Estimation in SEM: A Concrete Example

ERIC Educational Resources Information Center

Ferron, John M.; Hess, Melinda R.

2007-01-01

A concrete example is used to illustrate maximum likelihood estimation of a structural equation model with two unknown parameters. The fitting function is found for the example, as are the vector of first-order partial derivatives, the matrix of second-order partial derivatives, and the estimates obtained from each iteration of the Newton-Raphson…

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

PubMed Central

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

2009-01-01

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

Optical quasi-soliton solutions for higher-order nonlinear Schrödinger equation with variable coefficients

NASA Astrophysics Data System (ADS)

Zhang, Jiefang; Yang, Qin; Dai, Chaoqing

2005-04-01

Optical quasi-soliton solutions for higher-order nonlinear Schrödinger equation (HNLS) with variable coefficients are considered. Based on the extended tanh-function method, we successfully obtained bright and dark quasi-soliton solutions under certain parametric conditions. We conclude that the parameter k(z) is unnecessary to be zero compared with [R. Yang et al., Opt. Commun. 242 (2004) 285]. Furthermore, we choose appropriate optical fiber parameters D2(z) and D3(z) to control the velocity of quasi-soliton and time shift, and discuss the evolution behavior of the special quasi-soliton. For D3(z) = α(z) = f(z) = 0, that is to say, under the absence of the higher order terms, we give same results as early reported in [R.Y. Hao, L. Li, Z.H. Li, W.R. Xue, G.S. Zhou, Opt. Commun. 236 (2004) 79]. As discussed examples, we also analyze three optical systems with real physical significance and obtain results which can be recovered in earlier papers.

Constitutive behavior of as-cast AA1050, AA3104, and AA5182

NASA Astrophysics Data System (ADS)

van Haaften, W. M.; Magnin, B.; Kool, W. H.; Katgerman, L.

2002-07-01

Recent thermomechanical modeling to calculate the stress field in industrially direct-chill (DC) cast-aluminum slabs has been successful, but lack of material data limits the accuracy of these calculations. Therefore, the constitutive behavior of three aluminum alloys (AA1050, AA3104, and AA5182) was determined in the as-cast condition using tensile tests at low strain rates and from room temperature to solidus temperature. The parameters of two constitutive equations, the extended Ludwik equation and a combination of the Sellars-Tegart equation with a hardening law, were determined. In order to study the effect of recovery, the constitutive behavior after prestraining at higher temperatures was also investigated. To evaluate the quantified constitutive equations, tensile tests were performed simulating the deformation and cooling history experienced by the material during casting. It is concluded that both constitutive equations perform well, but the combined hardening-Sellars-Tegart (HST) equation has temperature-independent parameters, which makes it easier to implement in a DC casting model. Further, the deformation history of the ingot should be taken into account for accurate stress calculations.

Linear and nonlinear spectroscopy from quantum master equations.

PubMed

Fetherolf, Jonathan H; Berkelbach, Timothy C

2017-12-28

We investigate the accuracy of the second-order time-convolutionless (TCL2) quantum master equation for the calculation of linear and nonlinear spectroscopies of multichromophore systems. We show that even for systems with non-adiabatic coupling, the TCL2 master equation predicts linear absorption spectra that are accurate over an extremely broad range of parameters and well beyond what would be expected based on the perturbative nature of the approach; non-equilibrium population dynamics calculated with TCL2 for identical parameters are significantly less accurate. For third-order (two-dimensional) spectroscopy, the importance of population dynamics and the violation of the so-called quantum regression theorem degrade the accuracy of TCL2 dynamics. To correct these failures, we combine the TCL2 approach with a classical ensemble sampling of slow microscopic bath degrees of freedom, leading to an efficient hybrid quantum-classical scheme that displays excellent accuracy over a wide range of parameters. In the spectroscopic setting, the success of such a hybrid scheme can be understood through its separate treatment of homogeneous and inhomogeneous broadening. Importantly, the presented approach has the computational scaling of TCL2, with the modest addition of an embarrassingly parallel prefactor associated with ensemble sampling. The presented approach can be understood as a generalized inhomogeneous cumulant expansion technique, capable of treating multilevel systems with non-adiabatic dynamics.

Linear and nonlinear spectroscopy from quantum master equations

NASA Astrophysics Data System (ADS)

Fetherolf, Jonathan H.; Berkelbach, Timothy C.

2017-12-01

We investigate the accuracy of the second-order time-convolutionless (TCL2) quantum master equation for the calculation of linear and nonlinear spectroscopies of multichromophore systems. We show that even for systems with non-adiabatic coupling, the TCL2 master equation predicts linear absorption spectra that are accurate over an extremely broad range of parameters and well beyond what would be expected based on the perturbative nature of the approach; non-equilibrium population dynamics calculated with TCL2 for identical parameters are significantly less accurate. For third-order (two-dimensional) spectroscopy, the importance of population dynamics and the violation of the so-called quantum regression theorem degrade the accuracy of TCL2 dynamics. To correct these failures, we combine the TCL2 approach with a classical ensemble sampling of slow microscopic bath degrees of freedom, leading to an efficient hybrid quantum-classical scheme that displays excellent accuracy over a wide range of parameters. In the spectroscopic setting, the success of such a hybrid scheme can be understood through its separate treatment of homogeneous and inhomogeneous broadening. Importantly, the presented approach has the computational scaling of TCL2, with the modest addition of an embarrassingly parallel prefactor associated with ensemble sampling. The presented approach can be understood as a generalized inhomogeneous cumulant expansion technique, capable of treating multilevel systems with non-adiabatic dynamics.

Parameter identification for nonlinear aerodynamic systems

NASA Technical Reports Server (NTRS)

Pearson, Allan E.

1990-01-01

Parameter identification for nonlinear aerodynamic systems is examined. It is presumed that the underlying model can be arranged into an input/output (I/O) differential operator equation of a generic form. The algorithm estimation is especially efficient since the equation error can be integrated exactly given any I/O pair to obtain an algebraic function of the parameters. The algorithm for parameter identification was extended to the order determination problem for linear differential system. The degeneracy in a least squares estimate caused by feedback was addressed. A method of frequency analysis for determining the transfer function G(j omega) from transient I/O data was formulated using complex valued Fourier based modulating functions in contrast with the trigonometric modulating functions for the parameter estimation problem. A simulation result of applying the algorithm is given under noise-free conditions for a system with a low pass transfer function.

Bending analysis of agglomerated carbon nanotube-reinforced beam resting on two parameters modified Vlasov model foundation

NASA Astrophysics Data System (ADS)

Ghorbanpour Arani, A.; Zamani, M. H.

2018-06-01

The present work deals with bending behavior of nanocomposite beam resting on two parameters modified Vlasov model foundation (MVMF), with consideration of agglomeration and distribution of carbon nanotubes (CNTs) in beam matrix. Equivalent fiber based on Eshelby-Mori-Tanaka approach is employed to determine influence of CNTs aggregation on elastic properties of CNT-reinforced beam. The governing equations are deduced using the principle of minimum potential energy under assumption of the Euler-Bernoulli beam theory. The MVMF required the estimation of γ parameter; to this purpose, unique iterative technique based on variational principles is utilized to compute value of the γ and subsequently fourth-order differential equation is solved analytically. Eventually, the transverse displacements and bending stresses are obtained and compared for different agglomeration parameters, various boundary conditions simultaneously and variant elastic foundation without requirement to instate values for foundation parameters.

Ambiguity-free completion of the equations of motion of compact binary systems at the fourth post-Newtonian order

NASA Astrophysics Data System (ADS)

Marchand, Tanguy; Bernard, Laura; Blanchet, Luc; Faye, Guillaume

2018-02-01

We present the first complete (i.e., ambiguity-free) derivation of the equations of motion of two nonspinning compact objects up to the 4PN (post-Newtonian) order, based on the Fokker action of point particles in harmonic coordinates. The last ambiguity parameter is determined from first principle, by resorting to a matching between the near-zone and far-zone fields, and a consistent computation of the 4PN tail effect in d dimensions. Dimensional regularization is used throughout for treating IR divergences appearing at 4PN order, as well as UV divergences due to the modeling of the compact objects as point particles.

Non-local Second Order Closure Scheme for Boundary Layer Turbulence and Convection

NASA Astrophysics Data System (ADS)

Meyer, Bettina; Schneider, Tapio

2017-04-01

There has been scientific consensus that the uncertainty in the cloud feedback remains the largest source of uncertainty in the prediction of climate parameters like climate sensitivity. To narrow down this uncertainty, not only a better physical understanding of cloud and boundary layer processes is required, but specifically the representation of boundary layer processes in models has to be improved. General climate models use separate parameterisation schemes to model the different boundary layer processes like small-scale turbulence, shallow and deep convection. Small scale turbulence is usually modelled by local diffusive parameterisation schemes, which truncate the hierarchy of moment equations at first order and use second-order equations only to estimate closure parameters. In contrast, the representation of convection requires higher order statistical moments to capture their more complex structure, such as narrow updrafts in a quasi-steady environment. Truncations of moment equations at second order may lead to more accurate parameterizations. At the same time, they offer an opportunity to take spatially correlated structures (e.g., plumes) into account, which are known to be important for convective dynamics. In this project, we study the potential and limits of local and non-local second order closure schemes. A truncation of the momentum equations at second order represents the same dynamics as a quasi-linear version of the equations of motion. We study the three-dimensional quasi-linear dynamics in dry and moist convection by implementing it in a LES model (PyCLES) and compare it to a fully non-linear LES. In the quasi-linear LES, interactions among turbulent eddies are suppressed but nonlinear eddy—mean flow interactions are retained, as they are in the second order closure. In physical terms, suppressing eddy—eddy interactions amounts to suppressing, e.g., interactions among convective plumes, while retaining interactions between plumes and the environment (e.g., entrainment and detrainment). In a second part, we employ the possibility to include non-local statistical correlations in a second-order closure scheme. Such non-local correlations allow to directly incorporate the spatially coherent structures that occur in the form of convective updrafts penetrating the boundary layer. This allows us to extend the work that has been done using assumed-PDF schemes for parameterising boundary layer turbulence and shallow convection in a non-local sense.

DEAN: A program for dynamic engine analysis

NASA Technical Reports Server (NTRS)

Sadler, G. G.; Melcher, K. J.

1985-01-01

The Dynamic Engine Analysis program, DEAN, is a FORTRAN code implemented on the IBM/370 mainframe at NASA Lewis Research Center for digital simulation of turbofan engine dynamics. DEAN is an interactive program which allows the user to simulate engine subsystems as well as a full engine systems with relative ease. The nonlinear first order ordinary differential equations which define the engine model may be solved by one of four integration schemes, a second order Runge-Kutta, a fourth order Runge-Kutta, an Adams Predictor-Corrector, or Gear's method for still systems. The numerical data generated by the model equations are displayed at specified intervals between which the user may choose to modify various parameters affecting the model equations and transient execution. Following the transient run, versatile graphics capabilities allow close examination of the data. DEAN's modeling procedure and capabilities are demonstrated by generating a model of simple compressor rig.

Jacobi-Gauss-Lobatto collocation method for the numerical solution of 1+1 nonlinear Schrödinger equations

NASA Astrophysics Data System (ADS)

Doha, E. H.; Bhrawy, A. H.; Abdelkawy, M. A.; Van Gorder, Robert A.

2014-03-01

A Jacobi-Gauss-Lobatto collocation (J-GL-C) method, used in combination with the implicit Runge-Kutta method of fourth order, is proposed as a numerical algorithm for the approximation of solutions to nonlinear Schrödinger equations (NLSE) with initial-boundary data in 1+1 dimensions. Our procedure is implemented in two successive steps. In the first one, the J-GL-C is employed for approximating the functional dependence on the spatial variable, using (N-1) nodes of the Jacobi-Gauss-Lobatto interpolation which depends upon two general Jacobi parameters. The resulting equations together with the two-point boundary conditions induce a system of 2(N-1) first-order ordinary differential equations (ODEs) in time. In the second step, the implicit Runge-Kutta method of fourth order is applied to solve this temporal system. The proposed J-GL-C method, used in combination with the implicit Runge-Kutta method of fourth order, is employed to obtain highly accurate numerical approximations to four types of NLSE, including the attractive and repulsive NLSE and a Gross-Pitaevskii equation with space-periodic potential. The numerical results obtained by this algorithm have been compared with various exact solutions in order to demonstrate the accuracy and efficiency of the proposed method. Indeed, for relatively few nodes used, the absolute error in our numerical solutions is sufficiently small.

Cross diffusion effect on MHD mixed convection flow of nonlinear radiative heat and mass transfer of Casson fluid over a vertical plate

NASA Astrophysics Data System (ADS)

Ganesh Kumar, K.; Archana, M.; Gireesha, B. J.; Krishanamurthy, M. R.; Rudraswamy, N. G.

2018-03-01

A study on magnetohydrodynamic mixed convection flow of Casson fluid over a vertical plate has been modelled in the presence of Cross diffusion effect and nonlinear thermal radiation. The governing partial differential equations are remodelled into ordinary differential equations by using similarity transformation. The accompanied differential equations are resolved numerically by using Runge-Kutta-Fehlberg forth-fifth order along with shooting method (RKF45 Method). The results of various physical parameters on velocity and temperature profiles are given diagrammatically. The numerical values of the local skin friction coefficient, local Nusselt number and local Sherwood number also are shown in a tabular form. It is found that, effect of Dufour and Soret parameter increases the temperature and concentration component correspondingly.

Integral-equation based methods for parameter estimation in output pulses of radiation detectors: Application in nuclear medicine and spectroscopy

NASA Astrophysics Data System (ADS)

Mohammadian-Behbahani, Mohammad-Reza; Saramad, Shahyar

2018-04-01

Model based analysis methods are relatively new approaches for processing the output data of radiation detectors in nuclear medicine imaging and spectroscopy. A class of such methods requires fast algorithms for fitting pulse models to experimental data. In order to apply integral-equation based methods for processing the preamplifier output pulses, this article proposes a fast and simple method for estimating the parameters of the well-known bi-exponential pulse model by solving an integral equation. The proposed method needs samples from only three points of the recorded pulse as well as its first and second order integrals. After optimizing the sampling points, the estimation results were calculated and compared with two traditional integration-based methods. Different noise levels (signal-to-noise ratios from 10 to 3000) were simulated for testing the functionality of the proposed method, then it was applied to a set of experimental pulses. Finally, the effect of quantization noise was assessed by studying different sampling rates. Promising results by the proposed method endorse it for future real-time applications.

Features in simulation of crystal growth using the hyperbolic PFC equation and the dependence of the numerical solution on the parameters of the computational grid

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

Starodumov, Ilya; Kropotin, Nikolai

2016-08-10

We investigate the three-dimensional mathematical model of crystal growth called PFC (Phase Field Crystal) in a hyperbolic modification. This model is also called the modified model PFC (originally PFC model is formulated in parabolic form) and allows to describe both slow and rapid crystallization processes on atomic length scales and on diffusive time scales. Modified PFC model is described by the differential equation in partial derivatives of the sixth order in space and second order in time. The solution of this equation is possible only by numerical methods. Previously, authors created the software package for the solution of the Phasemore » Field Crystal problem, based on the method of isogeometric analysis (IGA) and PetIGA program library. During further investigation it was found that the quality of the solution can strongly depends on the discretization parameters of a numerical method. In this report, we show the features that should be taken into account during constructing the computational grid for the numerical simulation.« less

Vibration of initially stressed carbon nanotubes under magneto-thermal environment for nanoparticle delivery via higher-order nonlocal strain gradient theory

NASA Astrophysics Data System (ADS)

Farajpour, M. R.; Shahidi, A. R.; Tabataba'i-Nasab, F.; Farajpour, A.

2018-06-01

In this paper, the forced vibration of a single-walled carbon nanotube (SWCNT) under a moving nanoparticle is investigated based on the higher-order nonlocal strain gradient theory. The SWCNT is subjected to thermo-mechanical stresses and an external longitudinal magnetic field. The influences of higher-order stress gradients in conjunction with the strain gradient nonlocality are taken into account. Using Hamilton's principle and Maxwell's equations, the higher-order differential equations of motion are derived. An analytical solution is obtained for the dynamic deflection of SWCNTs using the Galerkin method. Furthermore, the governing differential equation is solved numerically using the precise integration method. The results of the two solution procedures are compared and an excellent agreement is found between them. Finally, the influences of various scale parameters, the velocity of the moving nanoparticle, the initial axial stress, the temperature change and longitudinal magnetic field on the dynamic response of SWCNTs are investigated.

Simple and complex chimera states in a nonlinearly coupled oscillatory medium

NASA Astrophysics Data System (ADS)

Bolotov, Maxim; Smirnov, Lev; Osipov, Grigory; Pikovsky, Arkady

2018-04-01

We consider chimera states in a one-dimensional medium of nonlinear nonlocally coupled phase oscillators. In terms of a local coarse-grained complex order parameter, the problem of finding stationary rotating nonhomogeneous solutions reduces to a third-order ordinary differential equation. This allows finding chimera-type and other inhomogeneous states as periodic orbits of this equation. Stability calculations reveal that only some of these states are stable. We demonstrate that an oscillatory instability leads to a breathing chimera, for which the synchronous domain splits into subdomains with different mean frequencies. Further development of instability leads to turbulent chimeras.

High-order regularization in lattice-Boltzmann equations

NASA Astrophysics Data System (ADS)

Mattila, Keijo K.; Philippi, Paulo C.; Hegele, Luiz A.

2017-04-01

A lattice-Boltzmann equation (LBE) is the discrete counterpart of a continuous kinetic model. It can be derived using a Hermite polynomial expansion for the velocity distribution function. Since LBEs are characterized by discrete, finite representations of the microscopic velocity space, the expansion must be truncated and the appropriate order of truncation depends on the hydrodynamic problem under investigation. Here we consider a particular truncation where the non-equilibrium distribution is expanded on a par with the equilibrium distribution, except that the diffusive parts of high-order non-equilibrium moments are filtered, i.e., only the corresponding advective parts are retained after a given rank. The decomposition of moments into diffusive and advective parts is based directly on analytical relations between Hermite polynomial tensors. The resulting, refined regularization procedure leads to recurrence relations where high-order non-equilibrium moments are expressed in terms of low-order ones. The procedure is appealing in the sense that stability can be enhanced without local variation of transport parameters, like viscosity, or without tuning the simulation parameters based on embedded optimization steps. The improved stability properties are here demonstrated using the perturbed double periodic shear layer flow and the Sod shock tube problem as benchmark cases.

Finite Difference Modeling of Wave Progpagation in Acoustic TiltedTI Media

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

Zhang, Linbin; Rector III, James W.; Hoversten, G. Michael

2005-03-21

Based on an acoustic assumption (shear wave velocity is zero) and a dispersion relation, we derive an acoustic wave equation for P-waves in tilted transversely isotropic (TTI) media (transversely isotropic media with a tilted symmetry axis). This equation has fewer parameters than an elastic wave equation in TTI media and yields an accurate description of P-wave traveltimes and spreading-related attenuation. Our TTI acoustic wave equation is a fourth-order equation in time and space. We demonstrate that the acoustic approximation allows the presence of shear waves in the solution. The substantial differences in traveltime and amplitude between data created using VTImore » and TTI assumptions is illustrated in examples.« less

Inference of S-wave velocities from well logs using a Neuro-Fuzzy Logic (NFL) approach

NASA Astrophysics Data System (ADS)

Aldana, Milagrosa; Coronado, Ronal; Hurtado, Nuri

2010-05-01

The knowledge of S-wave velocity values is important for a complete characterization and understanding of reservoir rock properties. It could help in determining fracture propagation and also to improve porosity prediction (Cuddy and Glover, 2002). Nevertheless the acquisition of S-wave velocity data is rather expensive; hence, for most reservoirs usually this information is not available. In the present work we applied a hybrid system, that combines Neural Networks and Fuzzy Logic, in order to infer S-wave velocities from porosity (φ), water saturation (Sw) and shale content (Vsh) logs. The Neuro-Fuzzy Logic (NFL) technique was tested in two wells from the Guafita oil field, Apure Basin, Venezuela. We have trained the system using 50% of the data randomly taken from one of the wells, in order to obtain the inference equations (Takani-Sugeno-Kang (TSK) fuzzy model). Equations using just one of the parameters as input (i.e. φ, Sw or Vsh), combined by pairs and all together were obtained. These equations were tested in the whole well. The results indicate that the best inference (correlation between inferred and experimental data close to 80%) is obtained when all the parameters are considered as input data. An increase of the equation number of the TSK model, when one or just two parameters are used, does not improve the performance of the NFL. The best set of equations was tested in a nearby well. The results suggest that the large difference in the petrophysical and lithological characteristics between these two wells, avoid a good inference of S-wave velocities in the tested well and allowed us to analyze the limitations of the method.

The Boundary Layer Flows of a Rivlin-Ericksen Fluid

NASA Astrophysics Data System (ADS)

Sadeghy, K.; Khabazi, N.; Taghavi, S. M.

The present work deals with the two-dimensional incompressible, laminar, steady-state boundary layer equations. First, we determine a family of velocity distributions outside the boundary layer such that these problems may have similarity solutions. We study the Falkner-Skan flow of a viscoelastic fluid governed by second order model, as the Reynolds number Re→ ∞. We obtain an ordinary forth order differential equation to obtain the stream function, velocity profile and the stress. The stream function is then governed by a generalized Falkner-Skan equation. In comparison with Newtonian Falkner-Skan equation that has two coefficients this new one has four coefficients that two of them represent elastic properties of the fluid. The effects of the elastic parameter on the velocity filed have been discussed. As it is shown in the figure there is a good agreement between numerical results and previous special cases confirm the validity of the presented algorithm.

New solitary wave and multiple soliton solutions for fifth order nonlinear evolution equation with time variable coefficients

NASA Astrophysics Data System (ADS)

Jaradat, H. M.; Syam, Muhammed; Jaradat, M. M. M.; Mustafa, Zead; Moman, S.

2018-03-01

In this paper, we investigate the multiple soliton solutions and multiple singular soliton solutions of a class of the fifth order nonlinear evolution equation with variable coefficients of t using the simplified bilinear method based on a transformation method combined with the Hirota's bilinear sense. In addition, we present analysis for some parameters such as the soliton amplitude and the characteristic line. Several equation in the literature are special cases of the class which we discuss such as Caudrey-Dodd-Gibbon equation and Sawada-Kotera. Comparison with several methods in the literature, such as Helmholtz solution of the inverse variational problem, rational exponential function method, tanh method, homotopy perturbation method, exp-function method, and coth method, are made. From these comparisons, we conclude that the proposed method is efficient and our solutions are correct. It is worth mention that the proposed solution can solve many physical problems.

Far-from-equilibrium magnetic granular layers: dynamic patterns, magnetic order and self-assembled swimmers

NASA Astrophysics Data System (ADS)

Snezhko, Alexey

2010-03-01

Ensembles of interacting particles subject to an external periodic forcing often develop nontrivial collective behavior and self-assembled dynamic patterns. We study emergent phenomena in magnetic granular ensembles suspended at a liquid-air and liquid-liquid interfaces and subjected to a transversal alternating magnetic field. Experiments reveal a new type of nontrivially ordered dynamic self-assembled structures (in particular, ``magnetic snakes'', ``asters'', ``clams'') emerging in such systems in a certain range of excitation parameters. These non-equilibrium dynamic structures emerge as a result of the competition between magnetic and hydrodynamic forces and have complex magnetic ordering. Transition between different self-assembled phases with parameters of external driving magnetic field is observed. I will show that above some frequency threshold magnetic snakes spontaneously break the symmetry of the self-induced surface flows (symmetry breaking instability) and turn into swimmers. Self-induced surface flows symmetry can be also broken in a controlled fashion by introduction of a large bead to a magnetic snake (bead-snake hybrid), that transforms it into a robust self-locomoting entity. Some features of the self-localized structures can be understood in the framework of an amplitude equation for parametric waves coupled to the conservation law equation describing the evolution of the magnetic particle density and the Navier-Stokes equation for hydrodynamic flows.

Hydromagnetic flow of a Cu-water nanofluid past a moving wedge with viscous dissipation

NASA Astrophysics Data System (ADS)

M. Salem, A.; Galal, Ismail; Rania, Fathy

2014-04-01

A numerical study is performed to investigate the flow and heat transfer at the surface of a permeable wedge immersed in a copper (Cu)-water-based nanofluid in the presence of magnetic field and viscous dissipation using a nanofluid model proposed by Tiwari and Das (Tiwari I K and Das M K 2007 Int. J. Heat Mass Transfer 50 2002). A similarity solution for the transformed governing equation is obtained, and those equations are solved by employing a numerical shooting technique with a fourth-order Runge-Kutta integration scheme. A comparison with previously published work is carried out and shows that they are in good agreement with each other. The effects of velocity ratio parameter λ, solid volume fraction φ, magnetic field M, viscous dissipation Ec, and suction parameter Fw on the fluid flow and heat transfer characteristics are discussed. The unique and dual solutions for self-similar equations of the flow and heat transfer are analyzed numerically. Moreover, the range of the velocity ratio parameter for which the solution exists increases in the presence of magnetic field and suction parameter.

Eigenvalue and eigenvector sensitivity and approximate analysis for repeated eigenvalue problems

NASA Technical Reports Server (NTRS)

Hou, Gene J. W.; Kenny, Sean P.

1991-01-01

A set of computationally efficient equations for eigenvalue and eigenvector sensitivity analysis are derived, and a method for eigenvalue and eigenvector approximate analysis in the presence of repeated eigenvalues is presented. The method developed for approximate analysis involves a reparamaterization of the multivariable structural eigenvalue problem in terms of a single positive-valued parameter. The resulting equations yield first-order approximations of changes in both the eigenvalues and eigenvectors associated with the repeated eigenvalue problem. Examples are given to demonstrate the application of such equations for sensitivity and approximate analysis.

Chiral symmetry restoration at finite temperature and chemical potential in the improved ladder approximation

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

Taniguchi, Y.; Yoshida, Y.

1997-02-01

The chiral symmetry of QCD is studied at finite temperature and chemical potential using the Schwinger-Dyson equation in the improved ladder approximation. We calculate three order parameters: the vacuum expectation value of the quark bilinear operator, the pion decay constant, and the quark mass gap. We have a second order phase transition at the temperature T{sub c}=169 MeV along the zero chemical potential line, and a first order phase transition at the chemical potential {mu}{sub c}=598 MeV along the zero temperature line. We also calculate the critical exponents of the three order parameters. {copyright} {ital 1997} {ital The American Physicalmore » Society}« less

Theory of repetitively pulsed operation of diode lasers subject to delayed feedback

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

Napartovich, A P; Sukharev, A G

2015-03-31

Repetitively pulsed operation of a diode laser with delayed feedback has been studied theoretically at varying feedback parameters and pump power levels. A new approach has been proposed that allows one to reduce the system of Lang–Kobayashi equations for a steady-state repetitively pulsed operation mode to a first-order nonlinear differential equation. We present partial solutions that allow the pulse shape to be predicted. (lasers)

A Spectral Multi-Domain Penalty Method for Elliptic Problems Arising From a Time-Splitting Algorithm For the Incompressible Navier-Stokes Equations

NASA Astrophysics Data System (ADS)

Diamantopoulos, Theodore; Rowe, Kristopher; Diamessis, Peter

2017-11-01

The Collocation Penalty Method (CPM) solves a PDE on the interior of a domain, while weakly enforcing boundary conditions at domain edges via penalty terms, and naturally lends itself to high-order and multi-domain discretization. Such spectral multi-domain penalty methods (SMPM) have been used to solve the Navier-Stokes equations. Bounds for penalty coefficients are typically derived using the energy method to guarantee stability for time-dependent problems. The choice of collocation points and penalty parameter can greatly affect the conditioning and accuracy of a solution. Effort has been made in recent years to relate various high-order methods on multiple elements or domains under the umbrella of the Correction Procedure via Reconstruction (CPR). Most applications of CPR have focused on solving the compressible Navier-Stokes equations using explicit time-stepping procedures. A particularly important aspect which is still missing in the context of the SMPM is a study of the Helmholtz equation arising in many popular time-splitting schemes for the incompressible Navier-Stokes equations. Stability and convergence results for the SMPM for the Helmholtz equation will be presented. Emphasis will be placed on the efficiency and accuracy of high-order methods.

Real-time approximate optimal guidance laws for the advanced launch system

NASA Technical Reports Server (NTRS)

Speyer, Jason L.; Feeley, Timothy; Hull, David G.

1989-01-01

An approach to optimal ascent guidance for a launch vehicle is developed using an expansion technique. The problem is to maximize the payload put into orbit subject to the equations of motion of a rocket over a rotating spherical earth. It is assumed that the thrust and gravitational forces dominate over the aerodynamic forces. It is shown that these forces can be separated by a small parameter epsilon, where epsilon is the ratio of the atmospheric scale height to the radius of the earth. The Hamilton-Jacobi-Bellman or dynamic programming equation is expanded in a series where the zeroth-order term (epsilon = 0) can be obtained in closed form. The zeroth-order problem is that of putting maximum payload into orbit subject to the equations of motion of a rocket in a vacuum over a flat earth. The neglected inertial and aerodynamic terms are included in higher order terms of the expansion, which are determined from the solution of first-order linear partial differential equations requiring only quadrature integrations. These quadrature integrations can be performed rapidly, so that real-time approximate optimization can be used to construct the launch guidance law.

Numerical Study of Aeroacoustic Sound on Performance of Bladeless Fan

NASA Astrophysics Data System (ADS)

Jafari, Mohammad; Sojoudi, Atta; Hafezisefat, Parinaz

2017-03-01

Aeroacoustic performance of fans is essential due to their widespread application. Therefore, the original aim of this paper is to evaluate the generated noise owing to different geometric parameters. In current study, effect of five geometric parameters was investigated on well performance of a Bladeless fan. Airflow through this fan was analyzed simulating a Bladeless fan within a 2 m×2 m×4 m room. Analysis of the flow field inside the fan and evaluating its performance were obtained by solving conservations of mass and momentum equations for aerodynamic investigations and FW-H noise equations for aeroacoustic analysis. In order to design Bladeless fan Eppler 473 airfoil profile was used as the cross section of this fan. Five distinct parameters, namely height of cross section of the fan, outlet angle of the flow relative to the fan axis, thickness of airflow outlet slit, hydraulic diameter and aspect ratio for circular and quadratic cross sections were considered. Validating acoustic code results, we compared numerical solution of FW-H noise equations for NACA0012 with experimental results. FW-H model was selected to predict the noise generated by the Bladeless fan as the numerical results indicated a good agreement with experimental ones for NACA0012. To validate 3-D numerical results, the experimental results of a round jet showed good agreement with those simulation data. In order to indicate the effect of each mentioned parameter on the fan performance, SPL and OASPL diagrams were illustrated.

Complex Langevin simulation of chiral symmetry restoration at finite baryonic density

NASA Astrophysics Data System (ADS)

Ilgenfritz, Ernst-Michael

1986-12-01

A recently proposed effective SU(3) spin model with chiral order parameter is studied by means of the complex Langevin equation. A first-order chiral symmetry restoring and deconfining transition is observed at sufficiently low temperature at finite baryonic density. Permanent address: Sektion Physik, Karl-Marx Universität, DDR-7010 Leipzig, German Democratic Republic.

A fresh look at linear ordinary differential equations with constant coefficients. Revisiting the impulsive response method using factorization

NASA Astrophysics Data System (ADS)

Camporesi, Roberto

2016-01-01

We present an approach to the impulsive response method for solving linear constant-coefficient ordinary differential equations of any order based on the factorization of the differential operator. The approach is elementary, we only assume a basic knowledge of calculus and linear algebra. In particular, we avoid the use of distribution theory, as well as of the other more advanced approaches: Laplace transform, linear systems, the general theory of linear equations with variable coefficients and variation of parameters. The approach presented here can be used in a first course on differential equations for science and engineering majors.

Constructing analytic solutions on the Tricomi equation

NASA Astrophysics Data System (ADS)

Ghiasi, Emran Khoshrouye; Saleh, Reza

2018-04-01

In this paper, homotopy analysis method (HAM) and variational iteration method (VIM) are utilized to derive the approximate solutions of the Tricomi equation. Afterwards, the HAM is optimized to accelerate the convergence of the series solution by minimizing its square residual error at any order of the approximation. It is found that effect of the optimal values of auxiliary parameter on the convergence of the series solution is not negligible. Furthermore, the present results are found to agree well with those obtained through a closed-form equation available in the literature. To conclude, it is seen that the two are effective to achieve the solution of the partial differential equations.

Ground state of the time-independent Gross Pitaevskii equation

NASA Astrophysics Data System (ADS)

Dion, Claude M.; Cancès, Eric

2007-11-01

We present a suite of programs to determine the ground state of the time-independent Gross-Pitaevskii equation, used in the simulation of Bose-Einstein condensates. The calculation is based on the Optimal Damping Algorithm, ensuring a fast convergence to the true ground state. Versions are given for the one-, two-, and three-dimensional equation, using either a spectral method, well suited for harmonic trapping potentials, or a spatial grid. Program summaryProgram title: GPODA Catalogue identifier: ADZN_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADZN_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 5339 No. of bytes in distributed program, including test data, etc.: 19 426 Distribution format: tar.gz Programming language: Fortran 90 Computer: ANY (Compilers under which the program has been tested: Absoft Pro Fortran, The Portland Group Fortran 90/95 compiler, Intel Fortran Compiler) RAM: From <1 MB in 1D to ˜10 MB for a large 3D grid Classification: 2.7, 4.9 External routines: LAPACK, BLAS, DFFTPACK Nature of problem: The order parameter (or wave function) of a Bose-Einstein condensate (BEC) is obtained, in a mean field approximation, by the Gross-Pitaevskii equation (GPE) [F. Dalfovo, S. Giorgini, L.P. Pitaevskii, S. Stringari, Rev. Mod. Phys. 71 (1999) 463]. The GPE is a nonlinear Schrödinger-like equation, including here a confining potential. The stationary state of a BEC is obtained by finding the ground state of the time-independent GPE, i.e., the order parameter that minimizes the energy. In addition to the standard three-dimensional GPE, tight traps can lead to effective two- or even one-dimensional BECs, so the 2D and 1D GPEs are also considered. Solution method: The ground state of the time-independent of the GPE is calculated using the Optimal Damping Algorithm [E. Cancès, C. Le Bris, Int. J. Quantum Chem. 79 (2000) 82]. Two sets of programs are given, using either a spectral representation of the order parameter [C.M. Dion, E. Cancès, Phys. Rev. E 67 (2003) 046706], suitable for a (quasi) harmonic trapping potential, or by discretizing the order parameter on a spatial grid. Running time: From seconds in 1D to a few hours for large 3D grids

Nonparaxial Dark-Hollow Gaussian Beams

NASA Astrophysics Data System (ADS)

Gao, Zeng-Hui; Lü, Bai-Da

2006-01-01

The concept of nonparaxial dark-hollow Gaussian beams (DHGBs) is introduced. By using the Rayleigh-Sommerfeld diffraction integral, the analytical propagation equation of DHGBs in free space is derived. The on-axis intensity, far-field equation and, in particular, paraxial expressions are given and treated as special cases of our result. It is shown that the parameter f = 1/kw0 with k being the wave number and w0 being the waist width determines the nonparaxiality of DHGBs. However, the parameter range, within which the paraxial approach is valid, depends on the propagation distance. The beam order affects the beam profile and position of maximum on-axis intensity.

Model predictive control of attitude maneuver of a geostationary flexible satellite based on genetic algorithm

NASA Astrophysics Data System (ADS)

TayyebTaher, M.; Esmaeilzadeh, S. Majid

2017-07-01

This article presents an application of Model Predictive Controller (MPC) to the attitude control of a geostationary flexible satellite. SIMO model has been used for the geostationary satellite, using the Lagrange equations. Flexibility is also included in the modelling equations. The state space equations are expressed in order to simplify the controller. Naturally there is no specific tuning rule to find the best parameters of an MPC controller which fits the desired controller. Being an intelligence method for optimizing problem, Genetic Algorithm has been used for optimizing the performance of MPC controller by tuning the controller parameter due to minimum rise time, settling time, overshoot of the target point of the flexible structure and its mode shape amplitudes to make large attitude maneuvers possible. The model included geosynchronous orbit environment and geostationary satellite parameters. The simulation results of the flexible satellite with attitude maneuver shows the efficiency of proposed optimization method in comparison with LQR optimal controller.

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

Nonautonomous solitons for an extended forced Korteweg-de Vries equation with variable coefficients in the fluid or plasma

NASA Astrophysics Data System (ADS)

Wang, Yong-Yan; Su, Chuan-Qi; Liu, Xue-Qing; Li, Jian-Guang

2018-07-01

Under investigation in this paper is an extended forced Korteweg-de Vries equation with variable coefficients in the fluid or plasma. Lax pair, bilinear forms, and bilinear Bäcklund transformations are derived. Based on the bilinear forms, the first-, second-, and third-order nonautonomous soliton solutions are derived. Propagation and interaction of the nonautonomous solitons are investigated and influence of the variable coefficients is also discussed: Amplitude of the first-order nonautonomous soliton is determined by the spectral parameter and perturbed factor; there exist two kinds of the solitons, namely the elevation and depression solitons, depending on the sign of the spectral parameter; the background where the nonautonomous soliton exists is influenced by the perturbed factor and external force coefficient; breather solutions can be constructed under the conjugate condition, and period of the breather is related to the dispersive and nonuniform coefficients.

Boundary condition at a two-phase interface in the lattice Boltzmann method for the convection-diffusion equation.

PubMed

Yoshida, Hiroaki; Kobayashi, Takayuki; Hayashi, Hidemitsu; Kinjo, Tomoyuki; Washizu, Hitoshi; Fukuzawa, Kenji

2014-07-01

A boundary scheme in the lattice Boltzmann method (LBM) for the convection-diffusion equation, which correctly realizes the internal boundary condition at the interface between two phases with different transport properties, is presented. The difficulty in satisfying the continuity of flux at the interface in a transient analysis, which is inherent in the conventional LBM, is overcome by modifying the collision operator and the streaming process of the LBM. An asymptotic analysis of the scheme is carried out in order to clarify the role played by the adjustable parameters involved in the scheme. As a result, the internal boundary condition is shown to be satisfied with second-order accuracy with respect to the lattice interval, if we assign appropriate values to the adjustable parameters. In addition, two specific problems are numerically analyzed, and comparison with the analytical solutions of the problems numerically validates the proposed scheme.

Robust fast controller design via nonlinear fractional differential equations.

PubMed

Zhou, Xi; Wei, Yiheng; Liang, Shu; Wang, Yong

2017-07-01

A new method for linear system controller design is proposed whereby the closed-loop system achieves both robustness and fast response. The robustness performance considered here means the damping ratio of closed-loop system can keep its desired value under system parameter perturbation, while the fast response, represented by rise time of system output, can be improved by tuning the controller parameter. We exploit techniques from both the nonlinear systems control and the fractional order systems control to derive a novel nonlinear fractional order controller. For theoretical analysis of the closed-loop system performance, two comparison theorems are developed for a class of fractional differential equations. Moreover, the rise time of the closed-loop system can be estimated, which facilitates our controller design to satisfy the fast response performance and maintain the robustness. Finally, numerical examples are given to illustrate the effectiveness of our methods. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Complex modal analysis of transverse free vibrations for axially moving nanobeams based on the nonlocal strain gradient theory

NASA Astrophysics Data System (ADS)

Wang, Jing; Shen, Huoming; Zhang, Bo; Liu, Juan; Zhang, Yingrong

2018-07-01

We investigate the transverse free vibration behaviour of axially moving nanobeams based on the nonlocal strain gradient theory. Considering the geometrical nonlinearity, which takes the form of von Kármán strains, the coupled plane motion equations and related boundary conditions of a new size-dependent beam model of Euler-Bernoulli type are developed using the generalized Hamilton principle. Using the simply supported axially moving nanobeams as an example, the complex modal analysis method is adopted to solve the governing equation; then, the effect of the order of modal truncation on the natural frequencies is discussed. Subsequently, the roles of the nonlocal parameter, material characteristic parameter, axial speed, stiffness and axial support rigidity parameter on the free vibration are comprehensively addressed. The material characteristic parameter induces the stiffness hardening of nanobeams, while the nonlocal parameter induces stiffness softening. In addition, the roles of small-scale parameters on the flutter critical velocity and stability are explained.

Moment of inertia, quadrupole moment, Love number of neutron star and their relations with strange-matter equations of state

NASA Astrophysics Data System (ADS)

Bandyopadhyay, Debades; Bhat, Sajad A.; Char, Prasanta; Chatterjee, Debarati

2018-02-01

We investigate the impact of strange-matter equations of state involving Λ hyperons, Bose-Einstein condensate of K- mesons and first-order hadron-quark phase transition on moment of inertia, quadrupole moment and tidal deformability parameter of slowly rotating neutron stars. All these equations of state are compatible with the 2 M_{solar} constraint. The main findings of this investigation are the universality of the I- Q and I -Love number relations, which are preserved by the EoSs including Λ hyperons and antikaon condensates, but broken in the presence of a first-order hadron-quark phase transition. Furthermore, it is also noted that the quadrupole moment approaches the Kerr value of a black hole for maximum-mass neutron stars.

Stability analysis of gyroscopic systems with delay via decomposition

NASA Astrophysics Data System (ADS)

Aleksandrov, A. Yu.; Zhabko, A. P.; Chen, Y.

2018-05-01

A mechanical system describing by the second order linear differential equations with a positive parameter at the velocity forces and with time delay in the positional forces is studied. Using the decomposition method and Lyapunov-Krasovskii functionals, conditions are obtained under which from the asymptotic stability of two auxiliary first order subsystems it follows that, for sufficiently large values of the parameter, the original system is also asymptotically stable. Moreover, it is shown that the proposed approach can be applied to the stability investigation of linear gyroscopic systems with switched positional forces.

Transoptr — A second order beam transport design code with optimization and constraints

NASA Astrophysics Data System (ADS)

Heighway, E. A.; Hutcheon, R. M.

1981-08-01

This code was written initially to design an achromatic and isochronous reflecting magnet and has been extended to compete in capability (for constrained problems) with TRANSPORT. Its advantage is its flexibility in that the user writes a routine to describe his transport system. The routine allows the definition of general variables from which the system parameters can be derived. Further, the user can write any constraints he requires as algebraic equations relating the parameters. All variables may be used in either a first or second order optimization.

Convergence of fractional adaptive systems using gradient approach.

PubMed

Gallegos, Javier A; Duarte-Mermoud, Manuel A

2017-07-01

Conditions for boundedness and convergence of the output error and the parameter error for various Caputo's fractional order adaptive schemes based on the steepest descent method are derived in this paper. To this aim, the concept of sufficiently exciting signals is introduced, characterized and related to the concept of persistently exciting signals used in the integer order case. An application is designed in adaptive indirect control of integer order systems using fractional equations to adjust parameters. This application is illustrated for a pole placement adaptive problem. Advantages of using fractional adjustment in control adaptive schemes are experimentally obtained. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Finite Difference Formulation for Prediction of Water Pollution

NASA Astrophysics Data System (ADS)

Johari, Hanani; Rusli, Nursalasawati; Yahya, Zainab

2018-03-01

Water is an important component of the earth. Human being and living organisms are demand for the quality of water. Human activity is one of the causes of the water pollution. The pollution happened give bad effect to the physical and characteristic of water contents. It is not practical to monitor all aspects of water flow and transport distribution. So, in order to help people to access to the polluted area, a prediction of water pollution concentration must be modelled. This study proposed a one-dimensional advection diffusion equation for predicting the water pollution concentration transport. The numerical modelling will be produced in order to predict the transportation of water pollution concentration. In order to approximate the advection diffusion equation, the implicit Crank Nicolson is used. For the purpose of the simulation, the boundary condition and initial condition, the spatial steps and time steps as well as the approximations of the advection diffusion equation have been encoded. The results of one dimensional advection diffusion equation have successfully been used to predict the transportation of water pollution concentration by manipulating the velocity and diffusion parameters.

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

PubMed

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

2001-08-01

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

Ghost Dark Energy with Sign-changeable Interaction Term

NASA Astrophysics Data System (ADS)

Zadeh, M. Abdollahi; Sheykhi, A.; Moradpour, H.

2017-11-01

Regarding the Veneziano ghost of QCD and its generalized form, we consider a Friedmann-Robertson-Walker (FRW) universe filled by a pressureless matter and a dark energy component interacting with each other through a mutual sign-changeable interaction of positive coupling constant. Our study shows that, at the late time, for the deceleration parameter we have q → -1, while the equation of state parameter of the interacting ghost dark energy (GDE) does not cross the phantom line, namely ω D ≥ -1. We also extend our study to the generalized ghost dark energy (GGDE) model and show that, at late time, the equation of state parameter of the interacting GGDE also respects the phantom line in both flat and non-flat universes. Moreover, we find out that, unlike the non-flat universe, we have q → -1 at late time for flat FRW universe. In order to make the behavior of the underlying models more clear, the deceleration parameter q as well as the equation of state parameter w D for flat and closed universes have been plotted against the redshift parameter, z. All of the studied cases admit a transition in the expansion history of universe from a deceleration phase to an accelerated one around z ≈ 0.6.

Impact of fitting algorithms on errors of parameter estimates in dynamic contrast-enhanced MRI

NASA Astrophysics Data System (ADS)

Debus, C.; Floca, R.; Nörenberg, D.; Abdollahi, A.; Ingrisch, M.

2017-12-01

Parameter estimation in dynamic contrast-enhanced MRI (DCE MRI) is usually performed by non-linear least square (NLLS) fitting of a pharmacokinetic model to a measured concentration-time curve. The two-compartment exchange model (2CXM) describes the compartments ‘plasma’ and ‘interstitial volume’ and their exchange in terms of plasma flow and capillary permeability. The model function can be defined by either a system of two coupled differential equations or a closed-form analytical solution. The aim of this study was to compare these two representations in terms of accuracy, robustness and computation speed, depending on parameter combination and temporal sampling. The impact on parameter estimation errors was investigated by fitting the 2CXM to simulated concentration-time curves. Parameter combinations representing five tissue types were used, together with two arterial input functions, a measured and a theoretical population based one, to generate 4D concentration images at three different temporal resolutions. Images were fitted by NLLS techniques, where the sum of squared residuals was calculated by either numeric integration with the Runge-Kutta method or convolution. Furthermore two example cases, a prostate carcinoma and a glioblastoma multiforme patient, were analyzed in order to investigate the validity of our findings in real patient data. The convolution approach yields improved results in precision and robustness of determined parameters. Precision and stability are limited in curves with low blood flow. The model parameter ve shows great instability and little reliability in all cases. Decreased temporal resolution results in significant errors for the differential equation approach in several curve types. The convolution excelled in computational speed by three orders of magnitude. Uncertainties in parameter estimation at low temporal resolution cannot be compensated by usage of the differential equations. Fitting with the convolution approach is superior in computational time, with better stability and accuracy at the same time.

Inverse problem of HIV cell dynamics using Genetic Algorithms

NASA Astrophysics Data System (ADS)

González, J. A.; Guzmán, F. S.

2017-01-01

In order to describe the cell dynamics of T-cells in a patient infected with HIV, we use a flavour of Perelson's model. This is a non-linear system of Ordinary Differential Equations that describes the evolution of healthy, latently infected, infected T-cell concentrations and the free viral cells. Different parameters in the equations give different dynamics. Considering the concentration of these types of cells is known for a particular patient, the inverse problem consists in estimating the parameters in the model. We solve this inverse problem using a Genetic Algorithm (GA) that minimizes the error between the solutions of the model and the data from the patient. These errors depend on the parameters of the GA, like mutation rate and population, although a detailed analysis of this dependence will be described elsewhere.

A parameters optimization method for planar joint clearance model and its application for dynamics simulation of reciprocating compressor

NASA Astrophysics Data System (ADS)

Hai-yang, Zhao; Min-qiang, Xu; Jin-dong, Wang; Yong-bo, Li

2015-05-01

In order to improve the accuracy of dynamics response simulation for mechanism with joint clearance, a parameter optimization method for planar joint clearance contact force model was presented in this paper, and the optimized parameters were applied to the dynamics response simulation for mechanism with oversized joint clearance fault. By studying the effect of increased clearance on the parameters of joint clearance contact force model, the relation of model parameters between different clearances was concluded. Then the dynamic equation of a two-stage reciprocating compressor with four joint clearances was developed using Lagrange method, and a multi-body dynamic model built in ADAMS software was used to solve this equation. To obtain a simulated dynamic response much closer to that of experimental tests, the parameters of joint clearance model, instead of using the designed values, were optimized by genetic algorithms approach. Finally, the optimized parameters were applied to simulate the dynamics response of model with oversized joint clearance fault according to the concluded parameter relation. The dynamics response of experimental test verified the effectiveness of this application.

Cause and cure of sloppiness in ordinary differential equation models.

PubMed

Tönsing, Christian; Timmer, Jens; Kreutz, Clemens

2014-08-01

Data-based mathematical modeling of biochemical reaction networks, e.g., by nonlinear ordinary differential equation (ODE) models, has been successfully applied. In this context, parameter estimation and uncertainty analysis is a major task in order to assess the quality of the description of the system by the model. Recently, a broadened eigenvalue spectrum of the Hessian matrix of the objective function covering orders of magnitudes was observed and has been termed as sloppiness. In this work, we investigate the origin of sloppiness from structures in the sensitivity matrix arising from the properties of the model topology and the experimental design. Furthermore, we present strategies using optimal experimental design methods in order to circumvent the sloppiness issue and present nonsloppy designs for a benchmark model.

Cause and cure of sloppiness in ordinary differential equation models

NASA Astrophysics Data System (ADS)

Tönsing, Christian; Timmer, Jens; Kreutz, Clemens

2014-08-01

Data-based mathematical modeling of biochemical reaction networks, e.g., by nonlinear ordinary differential equation (ODE) models, has been successfully applied. In this context, parameter estimation and uncertainty analysis is a major task in order to assess the quality of the description of the system by the model. Recently, a broadened eigenvalue spectrum of the Hessian matrix of the objective function covering orders of magnitudes was observed and has been termed as sloppiness. In this work, we investigate the origin of sloppiness from structures in the sensitivity matrix arising from the properties of the model topology and the experimental design. Furthermore, we present strategies using optimal experimental design methods in order to circumvent the sloppiness issue and present nonsloppy designs for a benchmark model.

Mixed Effects Modeling Using Stochastic Differential Equations: Illustrated by Pharmacokinetic Data of Nicotinic Acid in Obese Zucker Rats.

PubMed

Leander, Jacob; Almquist, Joachim; Ahlström, Christine; Gabrielsson, Johan; Jirstrand, Mats

2015-05-01

Inclusion of stochastic differential equations in mixed effects models provides means to quantify and distinguish three sources of variability in data. In addition to the two commonly encountered sources, measurement error and interindividual variability, we also consider uncertainty in the dynamical model itself. To this end, we extend the ordinary differential equation setting used in nonlinear mixed effects models to include stochastic differential equations. The approximate population likelihood is derived using the first-order conditional estimation with interaction method and extended Kalman filtering. To illustrate the application of the stochastic differential mixed effects model, two pharmacokinetic models are considered. First, we use a stochastic one-compartmental model with first-order input and nonlinear elimination to generate synthetic data in a simulated study. We show that by using the proposed method, the three sources of variability can be successfully separated. If the stochastic part is neglected, the parameter estimates become biased, and the measurement error variance is significantly overestimated. Second, we consider an extension to a stochastic pharmacokinetic model in a preclinical study of nicotinic acid kinetics in obese Zucker rats. The parameter estimates are compared between a deterministic and a stochastic NiAc disposition model, respectively. Discrepancies between model predictions and observations, previously described as measurement noise only, are now separated into a comparatively lower level of measurement noise and a significant uncertainty in model dynamics. These examples demonstrate that stochastic differential mixed effects models are useful tools for identifying incomplete or inaccurate model dynamics and for reducing potential bias in parameter estimates due to such model deficiencies.

Effects of the non-extensive parameter on the propagation of ion acoustic waves in five-component cometary plasma system

NASA Astrophysics Data System (ADS)

Mahmoud, Abeer A.

2018-01-01

Some important evolution nonlinear partial differential equations are derived using the reductive perturbation method for unmagnetized collisionless system of five component plasma. This plasma system is a multi-ion contains negatively and positively charged Oxygen ions (heavy ions), positive Hydrogen ions (lighter ions), hot electrons from solar origin and colder electrons from cometary origin. The positive Hydrogen ion and the two types of electrons obey q-non-extensive distributions. The derived equations have three types of ion acoustic waves, which are soliton waves, shock waves and kink waves. The effects of the non-extensive parameters for the hot electrons, the colder electrons and the Hydrogen ions on the propagation of the envelope waves are studied. The compressive and rarefactive shapes of the three envelope waves appear in this system for the first order of the power of the nonlinearity strength with different values of non-extensive parameters. For the second order, the strength of nonlinearity will increase and the compressive type of the envelope wave only appears.

Double stratification effects in chemically reactive squeezed Sutterby fluid flow with thermal radiation and mixed convection

NASA Astrophysics Data System (ADS)

Ahmad, S.; Farooq, M.; Javed, M.; Anjum, Aisha

2018-03-01

A current analysis is carried out to study theoretically the mixed convection characteristics in squeezing flow of Sutterby fluid in squeezed channel. The constitutive equation of Sutterby model is utilized to characterize the rheology of squeezing phenomenon. Flow characteristics are explored with dual stratification. In flowing fluid which contains heat and mass transport, the first order chemical reaction and radiative heat flux affect the transport phenomenon. The systems of non-linear governing equations have been modulating which then solved by mean of convergent approach (Homotopy Analysis Method). The graphs are reported and illustrated for emerging parameters. Through graphical explanations, drag force, rate of heat and mass transport are conversed for different pertinent parameters. It is found that heat and mass transport rate decays with dominant double stratified parameters and chemical reaction parameter. The present two-dimensional examination is applicable in some of the engineering processes and industrial fluid mechanics.

Mass eigenstates in bimetric theory with matter coupling

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

Schmidt-May, Angnis, E-mail: angnis.schmidt-may@fysik.su.se

2015-01-01

In this paper we study the ghost-free bimetric action extended by a recently proposed coupling to matter through a composite metric. The equations of motion for this theory are derived using a method which avoids varying the square-root matrix that appears in the matter coupling. We make an ansatz for which the metrics are proportional to each other and find that it can solve the equations provided that one parameter in the action is fixed. In this case, the proportional metrics as well as the effective metric that couples to matter solve Einstein's equations of general relativity including a mattermore » source. Around these backgrounds we derive the quadratic action for perturbations and diagonalize it into generalized mass eigenstates. It turns out that matter only interacts with the massless spin-2 mode whose equation of motion has exactly the form of the linearized Einstein equations, while the field with Fierz-Pauli mass term is completely decoupled. Hence, bimetric theory, with one parameter fixed such that proportional solutions exist, is degenerate with general relativity up to linear order around these backgrounds.« less

Bifurcation and Stability Analysis of the Equilibrium States in Thermodynamic Systems in a Small Vicinity of the Equilibrium Values of Parameters

NASA Astrophysics Data System (ADS)

Barsuk, Alexandr A.; Paladi, Florentin

2018-04-01

The dynamic behavior of thermodynamic system, described by one order parameter and one control parameter, in a small neighborhood of ordinary and bifurcation equilibrium values of the system parameters is studied. Using the general methods of investigating the branching (bifurcations) of solutions for nonlinear equations, we performed an exhaustive analysis of the order parameter dependences on the control parameter in a small vicinity of the equilibrium values of parameters, including the stability analysis of the equilibrium states, and the asymptotic behavior of the order parameter dependences on the control parameter (bifurcation diagrams). The peculiarities of the transition to an unstable state of the system are discussed, and the estimates of the transition time to the unstable state in the neighborhood of ordinary and bifurcation equilibrium values of parameters are given. The influence of an external field on the dynamic behavior of thermodynamic system is analyzed, and the peculiarities of the system dynamic behavior are discussed near the ordinary and bifurcation equilibrium values of parameters in the presence of external field. The dynamic process of magnetization of a ferromagnet is discussed by using the general methods of bifurcation and stability analysis presented in the paper.

Towards adjoint-based inversion for rheological parameters in nonlinear viscous mantle flow

NASA Astrophysics Data System (ADS)

Worthen, Jennifer; Stadler, Georg; Petra, Noemi; Gurnis, Michael; Ghattas, Omar

2014-09-01

We address the problem of inferring mantle rheological parameter fields from surface velocity observations and instantaneous nonlinear mantle flow models. We formulate this inverse problem as an infinite-dimensional nonlinear least squares optimization problem governed by nonlinear Stokes equations. We provide expressions for the gradient of the cost functional of this optimization problem with respect to two spatially-varying rheological parameter fields: the viscosity prefactor and the exponent of the second invariant of the strain rate tensor. Adjoint (linearized) Stokes equations, which are characterized by a 4th order anisotropic viscosity tensor, facilitates efficient computation of the gradient. A quasi-Newton method for the solution of this optimization problem is presented, which requires the repeated solution of both nonlinear forward Stokes and linearized adjoint Stokes equations. For the solution of the nonlinear Stokes equations, we find that Newton’s method is significantly more efficient than a Picard fixed point method. Spectral analysis of the inverse operator given by the Hessian of the optimization problem reveals that the numerical eigenvalues collapse rapidly to zero, suggesting a high degree of ill-posedness of the inverse problem. To overcome this ill-posedness, we employ Tikhonov regularization (favoring smooth parameter fields) or total variation (TV) regularization (favoring piecewise-smooth parameter fields). Solution of two- and three-dimensional finite element-based model inverse problems show that a constant parameter in the constitutive law can be recovered well from surface velocity observations. Inverting for a spatially-varying parameter field leads to its reasonable recovery, in particular close to the surface. When inferring two spatially varying parameter fields, only an effective viscosity field and the total viscous dissipation are recoverable. Finally, a model of a subducting plate shows that a localized weak zone at the plate boundary can be partially recovered, especially with TV regularization.

Learning partial differential equations via data discovery and sparse optimization

NASA Astrophysics Data System (ADS)

Schaeffer, Hayden

2017-01-01

We investigate the problem of learning an evolution equation directly from some given data. This work develops a learning algorithm to identify the terms in the underlying partial differential equations and to approximate the coefficients of the terms only using data. The algorithm uses sparse optimization in order to perform feature selection and parameter estimation. The features are data driven in the sense that they are constructed using nonlinear algebraic equations on the spatial derivatives of the data. Several numerical experiments show the proposed method's robustness to data noise and size, its ability to capture the true features of the data, and its capability of performing additional analytics. Examples include shock equations, pattern formation, fluid flow and turbulence, and oscillatory convection.

Improved Bond Equations for Fiber-Reinforced Polymer Bars in Concrete.

PubMed

Pour, Sadaf Moallemi; Alam, M Shahria; Milani, Abbas S

2016-08-30

This paper explores a set of new equations to predict the bond strength between fiber reinforced polymer (FRP) rebar and concrete. The proposed equations are based on a comprehensive statistical analysis and existing experimental results in the literature. Namely, the most effective parameters on bond behavior of FRP concrete were first identified by applying a factorial analysis on a part of the available database. Then the database that contains 250 pullout tests were divided into four groups based on the concrete compressive strength and the rebar surface. Afterward, nonlinear regression analysis was performed for each study group in order to determine the bond equations. The results show that the proposed equations can predict bond strengths more accurately compared to the other previously reported models.

Learning partial differential equations via data discovery and sparse optimization.

PubMed

Schaeffer, Hayden

2017-01-01

We investigate the problem of learning an evolution equation directly from some given data. This work develops a learning algorithm to identify the terms in the underlying partial differential equations and to approximate the coefficients of the terms only using data. The algorithm uses sparse optimization in order to perform feature selection and parameter estimation. The features are data driven in the sense that they are constructed using nonlinear algebraic equations on the spatial derivatives of the data. Several numerical experiments show the proposed method's robustness to data noise and size, its ability to capture the true features of the data, and its capability of performing additional analytics. Examples include shock equations, pattern formation, fluid flow and turbulence, and oscillatory convection.

Learning partial differential equations via data discovery and sparse optimization

PubMed Central

2017-01-01

We investigate the problem of learning an evolution equation directly from some given data. This work develops a learning algorithm to identify the terms in the underlying partial differential equations and to approximate the coefficients of the terms only using data. The algorithm uses sparse optimization in order to perform feature selection and parameter estimation. The features are data driven in the sense that they are constructed using nonlinear algebraic equations on the spatial derivatives of the data. Several numerical experiments show the proposed method's robustness to data noise and size, its ability to capture the true features of the data, and its capability of performing additional analytics. Examples include shock equations, pattern formation, fluid flow and turbulence, and oscillatory convection. PMID:28265183

Solving the interval type-2 fuzzy polynomial equation using the ranking method

NASA Astrophysics Data System (ADS)

Rahman, Nurhakimah Ab.; Abdullah, Lazim

2014-07-01

Polynomial equations with trapezoidal and triangular fuzzy numbers have attracted some interest among researchers in mathematics, engineering and social sciences. There are some methods that have been developed in order to solve these equations. In this study we are interested in introducing the interval type-2 fuzzy polynomial equation and solving it using the ranking method of fuzzy numbers. The ranking method concept was firstly proposed to find real roots of fuzzy polynomial equation. Therefore, the ranking method is applied to find real roots of the interval type-2 fuzzy polynomial equation. We transform the interval type-2 fuzzy polynomial equation to a system of crisp interval type-2 fuzzy polynomial equation. This transformation is performed using the ranking method of fuzzy numbers based on three parameters, namely value, ambiguity and fuzziness. Finally, we illustrate our approach by numerical example.

SIVA/DIVA- INITIAL VALUE ORDINARY DIFFERENTIAL EQUATION SOLUTION VIA A VARIABLE ORDER ADAMS METHOD

NASA Technical Reports Server (NTRS)

Krogh, F. T.

1994-01-01

The SIVA/DIVA package is a collection of subroutines for the solution of ordinary differential equations. There are versions for single precision and double precision arithmetic. These solutions are applicable to stiff or nonstiff differential equations of first or second order. SIVA/DIVA requires fewer evaluations of derivatives than other variable order Adams predictor-corrector methods. There is an option for the direct integration of second order equations which can make integration of trajectory problems significantly more efficient. Other capabilities of SIVA/DIVA include: monitoring a user supplied function which can be separate from the derivative; dynamically controlling the step size; displaying or not displaying output at initial, final, and step size change points; saving the estimated local error; and reverse communication where subroutines return to the user for output or computation of derivatives instead of automatically performing calculations. The user must supply SIVA/DIVA with: 1) the number of equations; 2) initial values for the dependent and independent variables, integration stepsize, error tolerance, etc.; and 3) the driver program and operational parameters necessary for subroutine execution. SIVA/DIVA contains an extensive diagnostic message library should errors occur during execution. SIVA/DIVA is written in FORTRAN 77 for batch execution and is machine independent. It has a central memory requirement of approximately 120K of 8 bit bytes. This program was developed in 1983 and last updated in 1987.

Numerical computations on one-dimensional inverse scattering problems

NASA Technical Reports Server (NTRS)

Dunn, M. H.; Hariharan, S. I.

1983-01-01

An approximate method to determine the index of refraction of a dielectric obstacle is presented. For simplicity one dimensional models of electromagnetic scattering are treated. The governing equations yield a second order boundary value problem, in which the index of refraction appears as a functional parameter. The availability of reflection coefficients yield two additional boundary conditions. The index of refraction by a k-th order spline which can be written as a linear combination of B-splines is approximated. For N distinct reflection coefficients, the resulting N boundary value problems yield a system of N nonlinear equations in N unknowns which are the coefficients of the B-splines.

Higher-order rogue wave-like solutions for a nonautonomous nonlinear Schrödinger equation with external potentials

NASA Astrophysics Data System (ADS)

Liu, Lei; Tian, Bo; Wu, Xiao-Yu; Sun, Yan

2018-02-01

Under investigation in this paper is the higher-order rogue wave-like solutions for a nonautonomous nonlinear Schrödinger equation with external potentials which can be applied in the nonlinear optics, hydrodynamics, plasma physics and Bose-Einstein condensation. Based on the Kadomtsev-Petviashvili hierarchy reduction, we construct the Nth order rogue wave-like solutions in terms of the Gramian under the integrable constraint. With the help of the analytic and graphic analysis, we exhibit the first-, second- and third-order rogue wave-like solutions through the different dispersion, nonlinearity and linear potential coefficients. We find that only if the dispersion and nonlinearity coefficients are proportional to each other, heights of the background of those rogue waves maintain unchanged with time increasing. Due to the existence of complex parameters, such nonautonomous rogue waves in the higher-order cases have more complex features than those in the lower.

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

NASA Astrophysics Data System (ADS)

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

2017-07-01

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

Theory of the Effects of Small Gravitational Levels on Droplet Gasification

NASA Technical Reports Server (NTRS)

Beitelmal, A.; Shaw, B. D.

1995-01-01

A mathematical model taking into account small (and constant) gravitational levels is developed for vaporization of an isolated liquid droplet suspended in a stagnant atmosphere. A goal of the present analysis is to see how small gravitational levels affect droplet gasification characteristics. Attention is focused upon determining the effects on gas-phase phenomena. The conservation equations arc normalized and nondimensionalized, and a small parameter that accounts for the effects of gravity is identified. This parameter is the square of the inverse of a Froude number based on the gravitational acceleration, the droplet radius, and a characteristic gas-phase velocity at the droplet surface. Asymptotic analyses are developed in terms of this parameter. In the analyses, different spatial regions are identified. Near a droplet, gravitational effects are negligible in the first approximation, and the flowfield is spherically symmetric to the leading order. Analysis shows, however, that outer zones exist where gravitational effects cannot be neglected; it is expected that a stagnation point will be present in an outer zone that is not present when gravity is totally absent. The leading order and higher-order differential equations for each zone are derived and solved. The solutions allow the effects of gravity on vaporization rates and temperature, velocity and species fields to be determined.

Bright solitons for a generalized nonautonomous nonlinear equation in a nonlinear inhomogeneous fiber

NASA Astrophysics Data System (ADS)

Xie, Xi-Yang; Tian, Bo; Liu, Lei; Guan, Yue-Yang; Jiang, Yan

2017-06-01

In this paper, we investigate a generalized nonautonomous nonlinear equation, which describes the ultrashort optical pulse propagating in a nonlinear inhomogeneous fiber. Under certain integrable constraints, bilinear forms, bright one- and two-soliton solutions are obtained. Via certain transformation, we investigate the properties of the solitons with the first-order dispersion parameter σ1(x, t), second-order dispersion parameter σ2(x, t), third-order dispersion parameter σ3(x, t), phase modulation and gain (loss) v(x, t). Soliton propagation and collision are graphically presented and analyzed: One soliton is shown to maintain its amplitude and width during the propagation. When we choose σ1(x, t), σ2(x, t) and σ3(x, t) differently, travelling direction of the soliton is found to alter. v(x, t) is observed to affect the amplitude of the soliton. Head-on collision between the two solitons is presented with σ1(x, t), σ2(x, t), σ3(x, t) and v(x, t) as the constants, and solitons' amplitudes are the same before and after the collision. When σ1(x, t), σ2(x, t) and σ3(x, t) are chosen as certain functions, the solitons' traveling directions change during the collision. v(x, t) can influence the amplitudes of the two solitons.

Hierarchical Order Parameters for Macromolecular Assembly Simulations I: Construction and Dynamical Properties of Order Parameters

PubMed Central

Singharoy, Abhishek; Sereda, Yuriy

2012-01-01

Macromolecular assemblies often display a hierarchical organization of macromolecules or their sub-assemblies. To model this, we have formulated a space warping method that enables capturing overall macromolecular structure and dynamics via a set of coarse-grained order parameters (OPs). This article is the first of two describing the construction and computational implementation of an additional class of OPs that has built into them the hierarchical architecture of macromolecular assemblies. To accomplish this, first, the system is divided into subsystems, each of which is described via a representative set of OPs. Then, a global set of variables is constructed from these subsystem-centered OPs to capture overall system organization. Dynamical properties of the resulting OPs are compared to those of our previous nonhierarchical ones, and implied conceptual and computational advantages are discussed for a 100ns, 2 million atom solvated Human Papillomavirus-like particle simulation. In the second article, the hierarchical OPs are shown to enable a multiscale analysis that starts with the N-atom Liouville equation and yields rigorous Langevin equations of stochastic OP dynamics. The latter is demonstrated via a force-field based simulation algorithm that probes key structural transition pathways, simultaneously accounting for all-atom details and overall structure. PMID:22661911

Second-order rogue wave breathers in the nonlinear Schrödinger equation with quadratic potential modulated by a spatially-varying diffraction coefficient.

PubMed

Zhong, Wei-Ping; Belić, Milivoj; Zhang, Yiqi

2015-02-09

Nonlinear Schrödinger equation with simple quadratic potential modulated by a spatially-varying diffraction coefficient is investigated theoretically. Second-order rogue wave breather solutions of the model are constructed by using the similarity transformation. A modal quantum number is introduced, useful for classifying and controlling the solutions. From the solutions obtained, the behavior of second order Kuznetsov-Ma breathers (KMBs), Akhmediev breathers (ABs), and Peregrine solitons is analyzed in particular, by selecting different modulation frequencies and quantum modal parameter. We show how to generate interesting second order breathers and related hybrid rogue waves. The emergence of true rogue waves - single giant waves that are generated in the interaction of KMBs, ABs, and Peregrine solitons - is explicitly displayed in our analytical solutions.

Finite element formulation of viscoelastic sandwich beams using fractional derivative operators

NASA Astrophysics Data System (ADS)

Galucio, A. C.; Deü, J.-F.; Ohayon, R.

This paper presents a finite element formulation for transient dynamic analysis of sandwich beams with embedded viscoelastic material using fractional derivative constitutive equations. The sandwich configuration is composed of a viscoelastic core (based on Timoshenko theory) sandwiched between elastic faces (based on Euler-Bernoulli assumptions). The viscoelastic model used to describe the behavior of the core is a four-parameter fractional derivative model. Concerning the parameter identification, a strategy to estimate the fractional order of the time derivative and the relaxation time is outlined. Curve-fitting aspects are focused, showing a good agreement with experimental data. In order to implement the viscoelastic model into the finite element formulation, the Grünwald definition of the fractional operator is employed. To solve the equation of motion, a direct time integration method based on the implicit Newmark scheme is used. One of the particularities of the proposed algorithm lies in the storage of displacement history only, reducing considerably the numerical efforts related to the non-locality of fractional operators. After validations, numerical applications are presented in order to analyze truncation effects (fading memory phenomena) and solution convergence aspects.

A phase-transition model for the rise and collapse of ancient civilizations: A pre-ceramic Andean case study

NASA Astrophysics Data System (ADS)

Flores, J. C.

2015-12-01

For ancient civilizations, the shift from disorder to organized urban settlements is viewed as a phase-transition simile. The number of monumental constructions, assumed to be a signature of civilization processes, corresponds to the order parameter, and effective connectivity becomes related to the control parameter. Based on parameter estimations from archaeological and paleo-climatological data, this study analyzes the rise and fall of the ancient Caral civilization on the South Pacific coast during a period of small ENSO fluctuations (approximately 4500 BP). Other examples considered include civilizations on Easter Island and the Maya Lowlands. This work considers a typical nonlinear third order evolution equation and numerical simulations.

Hypersonic three-dimensional nonequilibrium boundary-layer equations in generalized curvilinear coordinates

NASA Technical Reports Server (NTRS)

Lee, Jong-Hun

1993-01-01

The basic governing equations for the second-order three-dimensional hypersonic thermal and chemical nonequilibrium boundary layer are derived by means of an order-of-magnitude analysis. A two-temperature concept is implemented into the system of boundary-layer equations by simplifying the rather complicated general three-temperature thermal gas model. The equations are written in a surface-oriented non-orthogonal curvilinear coordinate system, where two curvilinear coordinates are non-orthogonial and a third coordinate is normal to the surface. The equations are described with minimum use of tensor expressions arising from the coordinate transformation, to avoid unnecessary confusion for readers. The set of equations obtained will be suitable for the development of a three-dimensional nonequilibrium boundary-layer code. Such a code could be used to determine economically the aerodynamic/aerothermodynamic loads to the surfaces of hypersonic vehicles with general configurations. In addition, the basic equations for three-dimensional stagnation flow, of which solution is required as an initial value for space-marching integration of the boundary-layer equations, are given along with the boundary conditions, the boundary-layer parameters, and the inner-outer layer matching procedure. Expressions for the chemical reaction rates and the thermodynamic and transport properties in the thermal nonequilibrium environment are explicitly given.

Global Dynamics of Certain Homogeneous Second-Order Quadratic Fractional Difference Equation

PubMed Central

Garić-Demirović, M.; Kulenović, M. R. S.; Nurkanović, M.

2013-01-01

We investigate the basins of attraction of equilibrium points and minimal period-two solutions of the difference equation of the form x n+1 = x n−1 2/(ax n 2 + bx n x n−1 + cx n−1 2), n = 0,1, 2,…, where the parameters a,  b, and  c are positive numbers and the initial conditions x −1 and x 0 are arbitrary nonnegative numbers. The unique feature of this equation is the coexistence of an equilibrium solution and the minimal period-two solution both of which are locally asymptotically stable. PMID:24369451

Regularization of the Perturbed Spatial Restricted Three-Body Problem by L-Transformations

NASA Astrophysics Data System (ADS)

Poleshchikov, S. M.

2018-03-01

Equations of motion for the perturbed circular restricted three-body problem have been regularized in canonical variables in a moving coordinate system. Two different L-matrices of the fourth order are used in the regularization. Conditions for generalized symplecticity of the constructed transform have been checked. In the unperturbed case, the regular equations have a polynomial structure. The regular equations have been numerically integrated using the Runge-Kutta-Fehlberg method. The results of numerical experiments are given for the Earth-Moon system parameters taking into account the perturbation of the Sun for different L-matrices.

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

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

Modelling of the internal dynamics and density in a tens of joules plasma focus device

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

Marquez, Ariel; Gonzalez, Jose; Tarifeno-Saldivia, Ariel

2012-01-15

Using MHD theory, coupled differential equations were generated using a lumped parameter model to describe the internal behaviour of the pinch compression phase in plasma focus discharges. In order to provide these equations with appropriate initial conditions, the modelling of previous phases was included by describing the plasma sheath as planar shockwaves. The equations were solved numerically, and the results were contrasted against experimental measurements performed on the device PF-50J. The model is able to predict satisfactorily the timing and the radial electron density profile at the maximum compression.

Global dynamics for switching systems and their extensions by linear differential equations

NASA Astrophysics Data System (ADS)

Huttinga, Zane; Cummins, Bree; Gedeon, Tomáš; Mischaikow, Konstantin

2018-03-01

Switching systems use piecewise constant nonlinearities to model gene regulatory networks. This choice provides advantages in the analysis of behavior and allows the global description of dynamics in terms of Morse graphs associated to nodes of a parameter graph. The parameter graph captures spatial characteristics of a decomposition of parameter space into domains with identical Morse graphs. However, there are many cellular processes that do not exhibit threshold-like behavior and thus are not well described by a switching system. We consider a class of extensions of switching systems formed by a mixture of switching interactions and chains of variables governed by linear differential equations. We show that the parameter graphs associated to the switching system and any of its extensions are identical. For each parameter graph node, there is an order-preserving map from the Morse graph of the switching system to the Morse graph of any of its extensions. We provide counterexamples that show why possible stronger relationships between the Morse graphs are not valid.

Fractional blood flow in oscillatory arteries with thermal radiation and magnetic field effects

NASA Astrophysics Data System (ADS)

Bansi, C. D. K.; Tabi, C. B.; Motsumi, T. G.; Mohamadou, A.

2018-06-01

A fractional model is proposed to study the effect of heat transfer and magnetic field on the blood flowing inside oscillatory arteries. The flow is due to periodic pressure gradient and the fractional model equations include body acceleration. The proposed velocity and temperature distribution equations are solved using the Laplace and Hankel transforms. The effect of the fluid parameters such as the Reynolds number (Re), the magnetic parameter (M) and the radiation parameter (N) is studied graphically with changing the fractional-order parameter. It is found that the fractional derivative is a valuable tool to control both the temperature and velocity of blood when flow parameters change under treatment, for example. Besides, this work highlights the fact that in the presence of strong magnetic field, blood velocity and temperature reduce. A reversed effect is observed where the applied thermal radiation increase; the velocity and temperature of blood increase. However, the temperature remains high around the artery centerline, which is appropriate during treatment to avoid tissues damage.

Global dynamics for switching systems and their extensions by linear differential equations.

PubMed

Huttinga, Zane; Cummins, Bree; Gedeon, Tomáš; Mischaikow, Konstantin

2018-03-15

Switching systems use piecewise constant nonlinearities to model gene regulatory networks. This choice provides advantages in the analysis of behavior and allows the global description of dynamics in terms of Morse graphs associated to nodes of a parameter graph. The parameter graph captures spatial characteristics of a decomposition of parameter space into domains with identical Morse graphs. However, there are many cellular processes that do not exhibit threshold-like behavior and thus are not well described by a switching system. We consider a class of extensions of switching systems formed by a mixture of switching interactions and chains of variables governed by linear differential equations. We show that the parameter graphs associated to the switching system and any of its extensions are identical. For each parameter graph node, there is an order-preserving map from the Morse graph of the switching system to the Morse graph of any of its extensions. We provide counterexamples that show why possible stronger relationships between the Morse graphs are not valid.

Resummed memory kernels in generalized system-bath master equations

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

Mavros, Michael G.; Van Voorhis, Troy, E-mail: tvan@mit.edu

2014-08-07

Generalized master equations provide a concise formalism for studying reduced population dynamics. Usually, these master equations require a perturbative expansion of the memory kernels governing the dynamics; in order to prevent divergences, these expansions must be resummed. Resummation techniques of perturbation series are ubiquitous in physics, but they have not been readily studied for the time-dependent memory kernels used in generalized master equations. In this paper, we present a comparison of different resummation techniques for such memory kernels up to fourth order. We study specifically the spin-boson Hamiltonian as a model system bath Hamiltonian, treating the diabatic coupling between themore » two states as a perturbation. A novel derivation of the fourth-order memory kernel for the spin-boson problem is presented; then, the second- and fourth-order kernels are evaluated numerically for a variety of spin-boson parameter regimes. We find that resumming the kernels through fourth order using a Padé approximant results in divergent populations in the strong electronic coupling regime due to a singularity introduced by the nature of the resummation, and thus recommend a non-divergent exponential resummation (the “Landau-Zener resummation” of previous work). The inclusion of fourth-order effects in a Landau-Zener-resummed kernel is shown to improve both the dephasing rate and the obedience of detailed balance over simpler prescriptions like the non-interacting blip approximation, showing a relatively quick convergence on the exact answer. The results suggest that including higher-order contributions to the memory kernel of a generalized master equation and performing an appropriate resummation can provide a numerically-exact solution to system-bath dynamics for a general spectral density, opening the way to a new class of methods for treating system-bath dynamics.« less

A class of traveling wave solutions for space-time fractional biological population model in mathematical physics

NASA Astrophysics Data System (ADS)

Akram, Ghazala; Batool, Fiza

2017-10-01

The (G'/G)-expansion method is utilized for a reliable treatment of space-time fractional biological population model. The method has been applied in the sense of the Jumarie's modified Riemann-Liouville derivative. Three classes of exact traveling wave solutions, hyperbolic, trigonometric and rational solutions of the associated equation are characterized with some free parameters. A generalized fractional complex transform is applied to convert the fractional equations to ordinary differential equations which subsequently resulted in number of exact solutions. It should be mentioned that the (G'/G)-expansion method is very effective and convenient for solving nonlinear partial differential equations of fractional order whose balancing number is a negative integer.

Darboux transformation of the coupled nonisospectral Gross-Pitaevskii system and its multi-component generalization

NASA Astrophysics Data System (ADS)

Xu, Tao; Chen, Yong

2018-04-01

In this paper, we extend the one-component Gross-Pitaevskii (GP) equation to the two-component coupled GP system including damping term, linear and parabolic density profiles. The Lax pair with nonisospectral parameter and infinitely-many conservation laws of this coupled GP system are presented. Actually, the Darboux transformation (DT) for this kind of nonautonomous system is essentially different from the autonomous case. Consequently, we construct the DT of the coupled GP equations, besides, nonautonomous multi-solitons, one-breather and the first-order rogue wave are also obtained. Various kinds of one-soliton solution are constructed, which include stationary one-soliton and nonautonomous one-soliton propagating along the negative (positive) direction of x-axis. The interaction of two solitons and two-soliton bound state are demonstrated respectively. We get the nonautonomous one-breather on a curved background and this background is completely controlled by the parameter β. Using a limiting process, the nonautonomous first-order rogue wave can be obtained. Furthermore, some dynamic structures of these analytical solutions are discussed in detail. In addition, the multi-component generalization of GP equations are given, then the corresponding Lax pair and DT are also constructed.

On an application of Tikhonov's fixed point theorem to a nonlocal Cahn-Hilliard type system modeling phase separation

NASA Astrophysics Data System (ADS)

Colli, Pierluigi; Gilardi, Gianni; Sprekels, Jürgen

2016-06-01

This paper investigates a nonlocal version of a model for phase separation on an atomic lattice that was introduced by P. Podio-Guidugli (2006) [36]. The model consists of an initial-boundary value problem for a nonlinearly coupled system of two partial differential equations governing the evolution of an order parameter ρ and the chemical potential μ. Singular contributions to the local free energy in the form of logarithmic or double-obstacle potentials are admitted. In contrast to the local model, which was studied by P. Podio-Guidugli and the present authors in a series of recent publications, in the nonlocal case the equation governing the evolution of the order parameter contains in place of the Laplacian a nonlocal expression that originates from nonlocal contributions to the free energy and accounts for possible long-range interactions between the atoms. It is shown that just as in the local case the model equations are well posed, where the technique of proving existence is entirely different: it is based on an application of Tikhonov's fixed point theorem in a rather unusual separable and reflexive Banach space.

Generalized nonlinear Schrödinger equation and ultraslow optical solitons in a cold four-state atomic system.

PubMed

Hang, Chao; Huang, Guoxiang; Deng, L

2006-03-01

We investigate the influence of high-order dispersion and nonlinearity on the propagation of ultraslow optical solitons in a lifetime broadened four-state atomic system under a Raman excitation. Using a standard method of multiple-scales we derive a generalized nonlinear Schrödinger equation and show that for realistic physical parameters and at the pulse duration of 10(-6)s, the effects of third-order linear dispersion, nonlinear dispersion, and delay in nonlinear refractive index can be significant and may not be considered as perturbations. We provide exact soliton solutions for the generalized nonlinear Schrödinger equation and demonstrate that optical solitons obtained may still have ultraslow propagating velocity. Numerical simulations on the stability and interaction of these ultraslow optical solitons in the presence of linear and differential absorptions are also presented.

Fermi field and Dirac oscillator in a Som-Raychaudhuri space-time

NASA Astrophysics Data System (ADS)

de Montigny, Marc; Zare, Soroush; Hassanabadi, Hassan

2018-05-01

We investigate the relativistic dynamics of a Dirac field in the Som-Raychaudhuri space-time, which is described by a Gödel-type metric and a stationary cylindrical symmetric solution of Einstein field equations for a charged dust distribution in rigid rotation. In order to analyze the effect of various physical parameters of this space-time, we solve the Dirac equation in the Som-Raychaudhuri space-time and obtain the energy levels and eigenfunctions of the Dirac operator by using the Nikiforov-Uvarov method. We also examine the behaviour of the Dirac oscillator in the Som-Raychaudhuri space-time, in particular, the effect of its frequency and the vorticity parameter.

Latent transition models with latent class predictors: attention deficit hyperactivity disorder subtypes and high school marijuana use

PubMed Central

Reboussin, Beth A.; Ialongo, Nicholas S.

2011-01-01

Summary Attention deficit hyperactivity disorder (ADHD) is a neurodevelopmental disorder which is most often diagnosed in childhood with symptoms often persisting into adulthood. Elevated rates of substance use disorders have been evidenced among those with ADHD, but recent research focusing on the relationship between subtypes of ADHD and specific drugs is inconsistent. We propose a latent transition model (LTM) to guide our understanding of how drug use progresses, in particular marijuana use, while accounting for the measurement error that is often found in self-reported substance use data. We extend the LTM to include a latent class predictor to represent empirically derived ADHD subtypes that do not rely on meeting specific diagnostic criteria. We begin by fitting two separate latent class analysis (LCA) models by using second-order estimating equations: a longitudinal LCA model to define stages of marijuana use, and a cross-sectional LCA model to define ADHD subtypes. The LTM model parameters describing the probability of transitioning between the LCA-defined stages of marijuana use and the influence of the LCA-defined ADHD subtypes on these transition rates are then estimated by using a set of first-order estimating equations given the LCA parameter estimates. A robust estimate of the LTM parameter variance that accounts for the variation due to the estimation of the two sets of LCA parameters is proposed. Solving three sets of estimating equations enables us to determine the underlying latent class structures independently of the model for the transition rates and simplifying assumptions about the correlation structure at each stage reduces the computational complexity. PMID:21461139

Estimability of geodetic parameters from space VLBI observables

NASA Technical Reports Server (NTRS)

Adam, Jozsef

1990-01-01

The feasibility of space very long base interferometry (VLBI) observables for geodesy and geodynamics is investigated. A brief review of space VLBI systems from the point of view of potential geodetic application is given. A selected notational convention is used to jointly treat the VLBI observables of different types of baselines within a combined ground/space VLBI network. The basic equations of the space VLBI observables appropriate for convariance analysis are derived and included. The corresponding equations for the ground-to-ground baseline VLBI observables are also given for a comparison. The simplified expression of the mathematical models for both space VLBI observables (time delay and delay rate) include the ground station coordinates, the satellite orbital elements, the earth rotation parameters, the radio source coordinates, and clock parameters. The observation equations with these parameters were examined in order to determine which of them are separable or nonseparable. Singularity problems arising from coordinate system definition and critical configuration are studied. Linear dependencies between partials are analytically derived. The mathematical models for ground-space baseline VLBI observables were tested with simulation data in the frame of some numerical experiments. Singularity due to datum defect is confirmed.

Buoyancy effects on the radiative magneto Micropolar nanofluid flow with double stratification, activation energy and binary chemical reaction.

PubMed

Ramzan, M; Ullah, Naeem; Chung, Jae Dong; Lu, Dianchen; Farooq, Umer

2017-10-10

A mathematical model has been developed to examine the magneto hydrodynamic micropolar nanofluid flow with buoyancy effects. Flow analysis is carried out in the presence of nonlinear thermal radiation and dual stratification. The impact of binary chemical reaction with Arrhenius activation energy is also considered. Apposite transformations are engaged to transform nonlinear partial differential equations to differential equations with high nonlinearity. Resulting nonlinear system of differential equations is solved by differential solver method in Maple software which uses Runge-Kutta fourth and fifth order technique (RK45). To authenticate the obtained results, a comparison with the preceding article is also made. The evaluations are executed graphically for numerous prominent parameters versus velocity, micro rotation component, temperature, and concentration distributions. Tabulated numerical calculations of Nusselt and Sherwood numbers with respective well-argued discussions are also presented. Our findings illustrate that the angular velocity component declines for opposing buoyancy forces and enhances for aiding buoyancy forces by changing the micropolar parameter. It is also found that concentration profile increases for higher values of chemical reaction parameter, whereas it diminishes for growing values of solutal stratification parameter.

Influence of optical activity on rogue waves propagating in chiral optical fibers.

PubMed

Temgoua, D D Estelle; Kofane, T C

2016-06-01

We derive the nonlinear Schrödinger (NLS) equation in chiral optical fiber with right- and left-hand nonlinear polarization. We use the similarity transformation to reduce the generalized chiral NLS equation to the higher-order integrable Hirota equation. We present the first- and second-order rational solutions of the chiral NLS equation with variable and constant coefficients, based on the modified Darboux transformation method. For some specific set of parameters, the features of chiral optical rogue waves are analyzed from analytical results, showing the influence of optical activity on waves. We also generate the exact solutions of the two-component coupled nonlinear Schrödinger equations, which describe optical activity effects on the propagation of rogue waves, and their properties in linear and nonlinear coupling cases are investigated. The condition of modulation instability of the background reveals the existence of vector rogue waves and the number of stable and unstable branches. Controllability of chiral optical rogue waves is examined by numerical simulations and may bring potential applications in optical fibers and in many other physical systems.

Galerkin Spectral Method for the 2D Solitary Waves of Boussinesq Paradigm Equation

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

Christou, M. A.; Christov, C. I.

2009-10-29

We consider the 2D stationary propagating solitary waves of the so-called Boussinesq Paradigm equation. The fourth- order elliptic boundary value problem on infinite interval is solved by a Galerkin spectral method. An iterative procedure based on artificial time ('false transients') and operator splitting is used. Results are obtained for the shapes of the solitary waves for different values of the dispersion parameters for both subcritical and supercritical phase speeds.

Distributed Blowing and Suction for the Purpose of Streak Control in a Boundary Layer Subjected to a Favorable Pressure Gradient

NASA Technical Reports Server (NTRS)

Forgoston, Eric; Tumin, Anatoli; Ashpis, David E.

2005-01-01

An analysis of the optimal control by blowing and suction in order to generate stream- wise velocity streaks is presented. The problem is examined using an iterative process that employs the Parabolized Stability Equations for an incompressible uid along with its adjoint equations. In particular, distributions of blowing and suction are computed for both the normal and tangential velocity perturbations for various choices of parameters.

Effects of high-frequency damping on iterative convergence of implicit viscous solver

NASA Astrophysics Data System (ADS)

Nishikawa, Hiroaki; Nakashima, Yoshitaka; Watanabe, Norihiko

2017-11-01

This paper discusses effects of high-frequency damping on iterative convergence of an implicit defect-correction solver for viscous problems. The study targets a finite-volume discretization with a one parameter family of damped viscous schemes. The parameter α controls high-frequency damping: zero damping with α = 0, and larger damping for larger α (> 0). Convergence rates are predicted for a model diffusion equation by a Fourier analysis over a practical range of α. It is shown that the convergence rate attains its minimum at α = 1 on regular quadrilateral grids, and deteriorates for larger values of α. A similar behavior is observed for regular triangular grids. In both quadrilateral and triangular grids, the solver is predicted to diverge for α smaller than approximately 0.5. Numerical results are shown for the diffusion equation and the Navier-Stokes equations on regular and irregular grids. The study suggests that α = 1 and 4/3 are suitable values for robust and efficient computations, and α = 4 / 3 is recommended for the diffusion equation, which achieves higher-order accuracy on regular quadrilateral grids. Finally, a Jacobian-Free Newton-Krylov solver with the implicit solver (a low-order Jacobian approximately inverted by a multi-color Gauss-Seidel relaxation scheme) used as a variable preconditioner is recommended for practical computations, which provides robust and efficient convergence for a wide range of α.

Removal of ibuprofen, naproxen and carbamazepine in aqueous solution onto natural clay: equilibrium, kinetics, and thermodynamic study

NASA Astrophysics Data System (ADS)

Khazri, Hassen; Ghorbel-Abid, Ibtissem; Kalfat, Rafik; Trabelsi-Ayadi, Malika

2017-10-01

This study aimed to describe the adsorption of three pharmaceuticals compounds (ibuprofen, naproxen and carbamazepine) onto natural clay on the basis of equilibrium parameters such as a function of time, effect of pH, varying of the concentration and the temperature. Adsorption kinetic data were modeled using the Lagergren's first-order and the pseudo-second-order kinetic equations. The kinetic results of adsorption are described better using the pseudo-second order model. The isotherm results were tested in the Langmuir, Freundlich and Dubinin-Radushkevich models. The thermodynamic parameters obtained indicate that the adsorption of pharmaceuticals on the clay is a spontaneous and endothermic process.

Miura-type transformations for lattice equations and Lie group actions associated with Darboux-Lax representations

NASA Astrophysics Data System (ADS)

Berkeley, George; Igonin, Sergei

2016-07-01

Miura-type transformations (MTs) are an essential tool in the theory of integrable nonlinear partial differential and difference equations. We present a geometric method to construct MTs for differential-difference (lattice) equations from Darboux-Lax representations (DLRs) of such equations. The method is applicable to parameter-dependent DLRs satisfying certain conditions. We construct MTs and modified lattice equations from invariants of some Lie group actions on manifolds associated with such DLRs. Using this construction, from a given suitable DLR one can obtain many MTs of different orders. The main idea behind this method is closely related to the results of Drinfeld and Sokolov on MTs for the partial differential KdV equation. Considered examples include the Volterra, Narita-Itoh-Bogoyavlensky, Toda, and Adler-Postnikov lattices. Some of the constructed MTs and modified lattice equations seem to be new.

Visualization in mechanics: the dynamics of an unbalanced roller

NASA Astrophysics Data System (ADS)

Cumber, Peter S.

2017-04-01

It is well known that mechanical engineering students often find mechanics a difficult area to grasp. This article describes a system of equations describing the motion of a balanced and an unbalanced roller constrained by a pivot arm. A wide range of dynamics can be simulated with the model. The equations of motion are embedded in a graphical user interface for its numerical solution in MATLAB. This allows a student's focus to be on the influence of different parameters on the system dynamics. The simulation tool can be used as a dynamics demonstrator in a lecture or as an educational tool driven by the imagination of the student. By way of demonstration the simulation tool has been applied to a range of roller-pivot arm configurations. In addition, approximations to the equations of motion are explored and a second-order model is shown to be accurate for a limited range of parameters.

Thermodynamic properties and static structure factor for a Yukawa fluid in the mean spherical approximation.

PubMed

Montes-Perez, J; Cruz-Vera, A; Herrera, J N

2011-12-01

This work presents the full analytic expressions for the thermodynamic properties and the static structure factor for a hard sphere plus 1-Yukawa fluid within the mean spherical approximation. To obtain these properties of the fluid type Yukawa analytically it was necessary to solve an equation of fourth order for the scaling parameter on a large scale. The physical root of this equation was determined by imposing physical conditions. The results of this work are obtained from seminal papers of Blum and Høye. We show that is not necessary the use the series expansion to solve the equation for the scaling parameter. We applied our theoretical result to find the thermodynamic and the static structure factor for krypton. Our results are in good agreement with those obtained in an experimental form or by simulation using the Monte Carlo method.

Reconstructions of the dark-energy equation of state and the inflationary potential

NASA Astrophysics Data System (ADS)

Barrow, John D.; Paliathanasis, Andronikos

2018-07-01

We use a mathematical approach based on the constraints systems in order to reconstruct the equation of state and the inflationary potential for the inflaton field from the observed spectral indices for the density perturbations ns and the tensor to scalar ratio r. From the astronomical data, we can observe that the measured values of these two indices lie on a two-dimensional surface. We express these indices in terms of the Hubble slow-roll parameters and we assume that ns-1=h( r) . For the function h( r) , we consider three cases, where h( r) is constant, linear and quadratic, respectively. From this, we derive second-order equations whose solutions provide us with the explicit forms for the expansion scale-factor, the scalar-field potential, and the effective equation of state for the scalar field. Finally, we show that for there exist mappings which transform one cosmological solution to another and allow new solutions to be generated from existing ones.

A new high pressure and temperature equation of state of fcc cobalt

DOE PAGES

Armentrout, Matthew M.; Kavner, Abby

2015-11-20

The high pressure and temperature equation of state of cobalt metal in the face-centered cubic phase was measured up to 57 GPa and 2400 K using the laser heated diamond anvil cell in conjunction with synchrotron X-ray diffraction. The measured region is bisected by a ferromagnetic to paramagnetic transition across the Curie temperature necessitating use of an equation of state that incorporates a 2nd order phase transition within its formalism. A third order Birch-Murnaghan equation of state with a Mie-Grüneisen-Debye thermal correction and a Hillert-Jarl magnetic correction is employed to describe the data above and below the Curie temperature. Furthermore,more » we find best fit parameters of V 0 = 6.753 (fixed) cm 3/mol, K 0 – 196 (3) GPa, K' – 4.7 (2), γ 0 – 2.00 (11), q – 1.3 (5), and θ 0 – 385 K (fixed).« less

Design of a broadband band-pass filter with notch-band using new models of coupled transmission lines.

PubMed

Daryasafar, Navid; Baghbani, Somaye; Moghaddasi, Mohammad Naser; Sadeghzade, Ramezanali

2014-01-01

We intend to design a broadband band-pass filter with notch-band, which uses coupled transmission lines in the structure, using new models of coupled transmission lines. In order to realize and present the new model, first, previous models will be simulated in the ADS program. Then, according to the change of their equations and consequently change of basic parameters of these models, optimization and dependency among these parameters and also their frequency response are attended and results of these changes in order to design a new filter are converged.

Spatiotemporal chaos of fractional order logistic equation in nonlinear coupled lattices

NASA Astrophysics Data System (ADS)

Zhang, Ying-Qian; Wang, Xing-Yuan; Liu, Li-Yan; He, Yi; Liu, Jia

2017-11-01

We investigate a new spatiotemporal dynamics with fractional order differential logistic map and spatial nonlinear coupling. The spatial nonlinear coupling features such as the higher percentage of lattices in chaotic behaviors for most of parameters and none periodic windows in bifurcation diagrams are held, which are more suitable for encryptions than the former adjacent coupled map lattices. Besides, the proposed model has new features such as the wider parameter range and wider range of state amplitude for ergodicity, which contributes a wider range of key space when applied in encryptions. The simulations and theoretical analyses are developed in this paper.

Biosorption of Cu(II) from aqueous solutions by mimosa tannin gel.

PubMed

Sengil, I Ayhan; Ozacar, Mahmut

2008-09-15

The biosorption of Cu(II) from aqueous solutions by mimosa tannin resin (MTR) was investigated as a function of particle size, initial pH, contact time and initial metal ion concentration. The aim of this study was to understand the mechanisms that govern copper removal and find a suitable equilibrium isotherm and kinetic model for the copper removal in a batch reactor. The experimental isotherm data were analysed using the Langmuir, Freundlich and Temkin equations. The equilibrium data fit well in the Langmiur isotherm. The experimental data were analysed using four sorption kinetic models -- the pseudo-first- and second-order equations, and the Elovich and the intraparticle diffusion equation -- to determine the best fit equation for the biosorption of copper ions onto mimosa tannin resin. Results show that the pseudo-second-order equation provides the best correlation for the biosorption process, whereas the Elovich equation also fits the experimental data well. Thermodynamic parameters such as the entropy change, enthalpy change and Gibb's free energy change were found out to be 153.0 J mol(-1)K(-1), 42.09 kJ mol(-1) and -2.47 kJ mol(-1), respectively.

Test particle propagation in magnetostatic turbulence. 2: The local approximation method

NASA Technical Reports Server (NTRS)

Klimas, A. J.; Sandri, G.; Scudder, J. D.; Howell, D. R.

1976-01-01

An approximation method for statistical mechanics is presented and applied to a class of problems which contains a test particle propagation problem. All of the available basic equations used in statistical mechanics are cast in the form of a single equation which is integrodifferential in time and which is then used as the starting point for the construction of the local approximation method. Simplification of the integrodifferential equation is achieved through approximation to the Laplace transform of its kernel. The approximation is valid near the origin in the Laplace space and is based on the assumption of small Laplace variable. No other small parameter is necessary for the construction of this approximation method. The n'th level of approximation is constructed formally, and the first five levels of approximation are calculated explicitly. It is shown that each level of approximation is governed by an inhomogeneous partial differential equation in time with time independent operator coefficients. The order in time of these partial differential equations is found to increase as n does. At n = 0 the most local first order partial differential equation which governs the Markovian limit is regained.

Exact analytic solutions for a global equation of plant cell growth.

PubMed

Pietruszka, Mariusz

2010-05-21

A generalization of the Lockhart equation for plant cell expansion in isotropic case is presented. The goal is to account for the temporal variation in the wall mechanical properties--in this case by making the wall extensibility a time dependent parameter. We introduce a time-differential equation describing the plant growth process with some key biophysical aspects considered. The aim of this work was to improve prior modeling efforts by taking into account the dynamic character of the plant cell wall with characteristics reminiscent of damped (aperiodic) motion. The equations selected to encapsulate the time evolution of the wall extensibility offer a new insight into the control of cell wall expansion. We find that the solutions to the time dependent second order differential equation reproduce much of the known experimental data for long- and short-time scales. Additionally, in order to support the biomechanical approach, a new growth equation based on the action of expansin proteins is proposed. Remarkably, both methods independently converge to the same kind, sigmoid-shaped, growth description functional V(t) proportional, exp(-exp(-t)), properly describing the volumetric growth and, consequently, growth rate as its time derivative. Copyright (c) 2010 Elsevier Ltd. All rights reserved.

Engineering applications and analysis of vibratory motion fourth order fluid film over the time dependent heated flat plate

NASA Astrophysics Data System (ADS)

Mohmand, Muhammad Ismail; Mamat, Mustafa Bin; Shah, Qayyum

2017-07-01

This article deals with the time dependent analysis of thermally conducting and Magneto-hydrodynamic (MHD) liquid film flow of a fourth order fluid past a vertical and vibratory plate. In this article have been developed for higher order complex nature fluids. The governing-equations have been modeled in the terms of nonlinear partial differential equations with the help of physical boundary circumstances. Two different analytical approaches i.e. Adomian decomposition method (ADM) and the optimal homotopy asymptotic method (OHAM), have been used for discoveryof the series clarification of the problems. Solutions obtained via two diversemethods have been compared using the graphs, tables and found an excellent contract. Variants of the embedded flow parameters in the solution have been analysed through the graphical diagrams.

Third order maximum-principle-satisfying direct discontinuous Galerkin methods for time dependent convection diffusion equations on unstructured triangular meshes

DOE PAGES

Chen, Zheng; Huang, Hongying; Yan, Jue

2015-12-21

We develop 3rd order maximum-principle-satisfying direct discontinuous Galerkin methods [8], [9], [19] and [21] for convection diffusion equations on unstructured triangular mesh. We carefully calculate the normal derivative numerical flux across element edges and prove that, with proper choice of parameter pair (β 0,β 1) in the numerical flux formula, the quadratic polynomial solution satisfies strict maximum principle. The polynomial solution is bounded within the given range and third order accuracy is maintained. There is no geometric restriction on the meshes and obtuse triangles are allowed in the partition. As a result, a sequence of numerical examples are carried outmore » to demonstrate the accuracy and capability of the maximum-principle-satisfying limiter.« less

Gas-kinetic theory and Boltzmann equation of share price within an equilibrium market hypothesis and ad hoc strategy

NASA Astrophysics Data System (ADS)

Ausloos, M.

2000-09-01

Recent observations have indicated that the traditional equilibrium market hypothesis (EMH; also known as Efficient Market Hypothesis) is unrealistic. It is shown here that it is the analog of a Boltzmann equation in physics, thus having some bad properties of mean-field approximations like a Gaussian distribution of price fluctuations. A kinetic theory for prices can be simply derived, considering in a first approach that market actors have all identical relaxation times, and solved within a Chapman-Enskog like formalism. In closing the set of equations, (i) an equation of state with a pressure and (ii) the equilibrium (isothermal) equation for the price (taken as the order parameter) of a stock as a function of the volume of money available are obtained.

Improved Bond Equations for Fiber-Reinforced Polymer Bars in Concrete

PubMed Central

Pour, Sadaf Moallemi; Alam, M. Shahria; Milani, Abbas S.

2016-01-01

This paper explores a set of new equations to predict the bond strength between fiber reinforced polymer (FRP) rebar and concrete. The proposed equations are based on a comprehensive statistical analysis and existing experimental results in the literature. Namely, the most effective parameters on bond behavior of FRP concrete were first identified by applying a factorial analysis on a part of the available database. Then the database that contains 250 pullout tests were divided into four groups based on the concrete compressive strength and the rebar surface. Afterward, nonlinear regression analysis was performed for each study group in order to determine the bond equations. The results show that the proposed equations can predict bond strengths more accurately compared to the other previously reported models. PMID:28773859

[Correlation between physical characteristics of sticks and quality of traditional Chinese medicine pills prepared by plastic molded method].

PubMed

Wang, Ling; Xian, Jiechen; Hong, Yanlong; Lin, Xiao; Feng, Yi

2012-05-01

To quantify the physical characteristics of sticks of traditional Chinese medicine (TCM) honeyed pills prepared by the plastic molded method and the correlation of adhesiveness and plasticity-related parameters of sticks and quality of pills, in order to find major parameters and the appropriate range impacting pill quality. Sticks were detected by texture analyzer for their physical characteristic parameters such as hardness and compression action, and pills were observed by visual evaluation for their quality. The correlation of both data was determined by the stepwise discriminant analysis. Stick physical characteristic parameter l(CD) can exactly depict the adhesiveness, with the discriminant equation of Y0 - Y1 = 6.415 - 41.594l(CD). When Y0 < Y1, pills were scattered well; when Y0 > Y1, pills were adhesive with each other. Pills' physical characteristic parameters l(CD) and l(AC), Ar, Tr can exactly depict smoothness of pills, with the discriminant equation of Z0 - Z1 = -195.318 + 78.79l(AC) - 3 258. 982Ar + 3437.935Tr. When Z0 < Z1, pills were smooth on surface. When Z0 > Z1, pills were rough on surface. The stepwise discriminant analysis is made to show the obvious correlation between key physical characteristic parameters l(CD) and l(AC), Ar, Tr of sticks and appearance quality of pills, defining the molding process for preparing pills by the plastic molded and qualifying ranges of key physical characteristic parameters characterizing intermediate sticks, in order to provide theoretical basis for prescription screening and technical parameter adjustment for pills.

Numerical Calculation and Exergy Equations of Spray Heat Exchanger Attached to a Main Fan Diffuser

NASA Astrophysics Data System (ADS)

Cui, H.; Wang, H.; Chen, S.

2015-04-01

In the present study, the energy depreciation rule of spray heat exchanger, which is attached to a main fan diffuser, is analyzed based on the second law of thermodynamics. Firstly, the exergy equations of the exchanger are deduced. The equations are numerically calculated by the fourth-order Runge-Kutta method, and the exergy destruction is quantitatively effected by the exchanger structure parameters, working fluid (polluted air, i.e., PA; sprayed water, i.e., SW) initial state parameters and the ambient reference parameters. The results are showed: (1) heat transfer is given priority to latent transfer at the bottom of the exchanger, and heat transfer of convection and is equivalent to that of condensation in the upper. (2) With the decrease of initial temperature of SW droplet, the decrease of PA velocity or the ambient reference temperature, and with the increase of a SW droplet size or initial PA temperature, exergy destruction both increase. (3) The exergy efficiency of the exchanger is 72.1 %. An approach to analyze the energy potential of the exchanger may be provided for engineering designs.

Modelling uncertainties in the diffusion-advection equation for radon transport in soil using interval arithmetic.

PubMed

Chakraverty, S; Sahoo, B K; Rao, T D; Karunakar, P; Sapra, B K

2018-02-01

Modelling radon transport in the earth crust is a useful tool to investigate the changes in the geo-physical processes prior to earthquake event. Radon transport is modeled generally through the deterministic advection-diffusion equation. However, in order to determine the magnitudes of parameters governing these processes from experimental measurements, it is necessary to investigate the role of uncertainties in these parameters. Present paper investigates this aspect by combining the concept of interval uncertainties in transport parameters such as soil diffusivity, advection velocity etc, occurring in the radon transport equation as applied to soil matrix. The predictions made with interval arithmetic have been compared and discussed with the results of classical deterministic model. The practical applicability of the model is demonstrated through a case study involving radon flux measurements at the soil surface with an accumulator deployed in steady-state mode. It is possible to detect the presence of very low levels of advection processes by applying uncertainty bounds on the variations in the observed concentration data in the accumulator. The results are further discussed. Copyright © 2017 Elsevier Ltd. All rights reserved.

Electrostatic potential jump across fast-mode collisionless shocks

NASA Technical Reports Server (NTRS)

Mandt, M. E.; Kan, J. R.

1991-01-01

The electrostatic potential jump across fast-mode collisionless shocks is examined by comparing published observations, hybrid simulations, and a simple model, in order to better characterize its dependence on the various shock parameters. In all three, it is assumed that the electrons can be described by an isotropic power-law equation of state. The observations show that the cross-shock potential jump correlates well with the shock strength but shows very little correlation with other shock parameters. Assuming that the electrons obey an isotropic power law equation of state, the correlation of the potential jump with the shock strength follows naturally from the increased shock compression and an apparent dependence of the power law exponent on the Mach number which the observations indicate. It is found that including a Mach number dependence for the power law exponent in the electron equation of state in the simple model produces a potential jump which better fits the observations. On the basis of the simulation results and theoretical estimates of the cross-shock potential, it is discussed how the cross-shock potential might be expected to depend on the other shock parameters.

Effect of multiple slip on a chemically reactive MHD non-Newtonian nanofluid power law fluid flow over a stretching sheet with microorganism

NASA Astrophysics Data System (ADS)

Basir, Mohammad Faisal Mohd; Ismail, Fazreen Amira; Amirsom, Nur Ardiana; Latiff, Nur Amalina Abdul; Ismail, Ahmad Izani Md.

2017-04-01

The effect of multiple slip on a chemically reactive magnetohydrodynamic (MHD) non-Newtonian power law fluid flow over a stretching sheet with microorganism was numerically investigated. The governing partial differential equations were transformed into nonlinear ordinary differential equations using the similarity transformations developed by Lie group analysis. The reduced governing nonlinear ordinary differential equations were then numerically solved using the Runge-Kutta-Fehlberg fourth-fifth order method. Good agreement was found between the present numerical solutions with the existing published results to support the validity and the accuracy of the numerical computations. The influences of the velocity, thermal, mass and microorganism slips, the magnetic field parameter and the chemical reaction parameter on the dimensionless velocity, temperature, nanoparticle volume fraction, microorganism concentration, the distribution of the density of motile microorganisms have been illustrated graphically. The effects of the governing parameters on the physical quantities, namely, the local heat transfer rate, the local mass transfer rate and the local microorganism transfer rate were analyzed and discussed.

Chemical association in simple models of molecular and ionic fluids. III. The cavity function

NASA Astrophysics Data System (ADS)

Zhou, Yaoqi; Stell, George

1992-01-01

Exact equations which relate the cavity function to excess solvation free energies and equilibrium association constants are rederived by using a thermodynamic cycle. A zeroth-order approximation, derived previously by us as a simple interpolation scheme, is found to be very accurate if the associative bonding occurs on or near the surface of the repulsive core of the interaction potential. If the bonding radius is substantially less than the core radius, the approximation overestimates the association degree and the association constant. For binary association, the zeroth-order approximation is equivalent to the first-order thermodynamic perturbation theory (TPT) of Wertheim. For n-particle association, the combination of the zeroth-order approximation with a ``linear'' approximation (for n-particle distribution functions in terms of the two-particle function) yields the first-order TPT result. Using our exact equations to go beyond TPT, near-exact analytic results for binary hard-sphere association are obtained. Solvent effects on binary hard-sphere association and ionic association are also investigated. A new rule which generalizes Le Chatelier's principle is used to describe the three distinct forms of behaviors involving solvent effects that we find. The replacement of the dielectric-continuum solvent model by a dipolar hard-sphere model leads to improved agreement with an experimental observation. Finally, equation of state for an n-particle flexible linear-chain fluid is derived on the basis of a one-parameter approximation that interpolates between the generalized Kirkwood superposition approximation and the linear approximation. A value of the parameter that appears to be near optimal in the context of this application is obtained from comparison with computer-simulation data.

Masses from an inhomogeneous partial difference equation with higher-order isospin contributions

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

Masson, P.J.; Jaenecke, J.

In the present work, a mass equation obtained as the solution of an inhomogeneous partial difference equation is used to predict masses of unknown neutron-rich and proton-rich nuclei. The inhomogeneous source terms contain shell-dependent symmetry energy expressions (quadratic in isospin), and include, as well, an independently derived shell-model Coulomb energy equation which describes all known Coulomb displacement energies with a standarad deviation of sigma/sub c/ = 41 keV. Perturbations of higher order in isospin, previously recognized as a cause of systematic effects in long-range mass extrapolations, are also incorporated. The most general solutions of the inhomogeneous difference equation have beenmore » deduced from a chi/sup 2/-minimization procedure based on the recent atomic mass adjustment of Wapstra, Audi, and Hoekstra. Subjecting the solutions further to the condition of charge symmetry preserves the accuracy of Coulomb energies and allows mass predictions for nuclei with both Ngreater than or equal toZ and Z>N. The solutions correspond to a mass equation with 470 parameters. Using this equation, 4385 mass values have been calculated for nuclei with Agreater than or equal to16 (except N = Z = odd for A<40), with a standard deviation of sigma/sub m/ = 194 keV from the experimental masses. copyright 1988 Academic Press, Inc.« less

Modeling the [NTf2] pyridinium ionic liquids family and their mixtures with the soft statistical associating fluid theory equation of state.

PubMed

Oliveira, M B; Llovell, F; Coutinho, J A P; Vega, L F

2012-08-02

In this work, the soft statistical associating fluid theory (soft-SAFT) equation of state (EoS) has been used to provide an accurate thermodynamic characterization of the pyridinium-based family of ionic liquids (ILs) with the bis(trifluoromethylsulfonyl)imide anion [NTf(2)](-). On the basis of recent molecular simulation studies for this family, a simple molecular model was proposed within the soft-SAFT EoS framework. The chain length value was transferred from the equivalent imidazolium-based ILs family, while the dispersive energy and the molecular parameters describing the cation-anion interactions were set to constant values for all of the compounds. With these assumptions, an appropriate set of molecular parameters was found for each compound fitting to experimental temperature-density data at atmospheric pressure. Correlations for the nonconstant parameters (describing the volume of the IL) with the molecular weight were established, allowing the prediction of the parameters for other pyridiniums not included in the fitting. Then, the suitability of the proposed model and its optimized parameters were tested by predicting high-pressure densities and second-order thermodynamic derivative properties such as isothermal compressibilities of selected [NTf(2)] pyridinium ILs, in a large range of thermodynamic conditions. The surface tension was also provided using the density gradient theory coupled to the soft-SAFT equation. Finally, the soft-SAFT EoS was applied to describe the phase behavior of several binary mixtures of [NTf(2)] pyridinium ILs with carbon dioxide, sulfur dioxide, and water. In all cases, a temperature-independent binary parameter was enough to reach quantitative agreement with the experimental data. The description of the solubility of CO(2) in these ILs also allowed identification of a relation between the binary parameter and the molecular weight of the ionic liquid, allowing the prediction of the CO(2) + C(12)py[NTf(2)] mixture. The good agreement with the experimental data shows the excellent ability of the soft-SAFT EoS to describe the thermophysical properties of ILs as well as their phase behavior. Results prove that this equation of state can be a valuable tool to assist the design of ILs (in what concerns cation and anion selection) in order to obtain ILs with the desired properties and, consequently, enhancing their potential industrial applications.

High-order rogue wave solutions of the classical massive Thirring model equations

NASA Astrophysics Data System (ADS)

Guo, Lijuan; Wang, Lihong; Cheng, Yi; He, Jingsong

2017-11-01

The nth-order solutions of the classical massive Thirring model (MTM) equations are derived by using the n-fold Darboux transformation. These solutions are expressed by the ratios of the two determinants consisted of 2n eigenfunctions under the reduction conditions. Using this method, rogue waves are constructed explicitly up to the third-order. Three patterns, i.e., fundamental, triangular and circular patterns, of the rogue waves are discussed. The parameter μ in the MTM model plays the role of the mass in the relativistic field theory while in optics it is related to the medium periodic constant, which also results in a significant rotation and a remarkable lengthening of the first-order rogue wave. These results provide new opportunities to observe rouge waves by using a combination of electromagnetically induced transparency and the Bragg scattering four-wave mixing because of large amplitudes.

A new solution procedure for a nonlinear infinite beam equation of motion

NASA Astrophysics Data System (ADS)

Jang, T. S.

2016-10-01

Our goal of this paper is of a purely theoretical question, however which would be fundamental in computational partial differential equations: Can a linear solution-structure for the equation of motion for an infinite nonlinear beam be directly manipulated for constructing its nonlinear solution? Here, the equation of motion is modeled as mathematically a fourth-order nonlinear partial differential equation. To answer the question, a pseudo-parameter is firstly introduced to modify the equation of motion. And then, an integral formalism for the modified equation is found here, being taken as a linear solution-structure. It enables us to formulate a nonlinear integral equation of second kind, equivalent to the original equation of motion. The fixed point approach, applied to the integral equation, results in proposing a new iterative solution procedure for constructing the nonlinear solution of the original beam equation of motion, which consists luckily of just the simple regular numerical integration for its iterative process; i.e., it appears to be fairly simple as well as straightforward to apply. A mathematical analysis is carried out on both natures of convergence and uniqueness of the iterative procedure by proving a contractive character of a nonlinear operator. It follows conclusively,therefore, that it would be one of the useful nonlinear strategies for integrating the equation of motion for a nonlinear infinite beam, whereby the preceding question may be answered. In addition, it may be worth noticing that the pseudo-parameter introduced here has double roles; firstly, it connects the original beam equation of motion with the integral equation, second, it is related with the convergence of the iterative method proposed here.

Light bullets in coupled nonlinear Schrödinger equations with variable coefficients and a trapping potential.

PubMed

Xu, Si-Liu; Zhao, Guo-Peng; Belić, Milivoj R; He, Jun-Rong; Xue, Li

2017-04-17

We analyze three-dimensional (3D) vector solitary waves in a system of coupled nonlinear Schrödinger equations with spatially modulated diffraction and nonlinearity, under action of a composite self-consistent trapping potential. Exact vector solitary waves, or light bullets (LBs), are found using the self-similarity method. The stability of vortex 3D LB pairs is examined by direct numerical simulations; the results show that only low-order vortex soliton pairs with the mode parameter values n ≤ 1, l ≤ 1 and m = 0 can be supported by the spatially modulated interaction in the composite trap. Higher-order LBs are found unstable over prolonged distances.

Abundant closed form solutions of the conformable time fractional Sawada-Kotera-Ito equation using (G‧ / G) -expansion method

NASA Astrophysics Data System (ADS)

Al-Shawba, Altaf Abdulkarem; Gepreel, K. A.; Abdullah, F. A.; Azmi, A.

2018-06-01

In current study, we use the (G‧ / G) -expansion method to construct the closed form solutions of the seventh order time fractional Sawada-Kotera-Ito (TFSKI) equation based on conformable fractional derivative. As a result, trigonometric, hyperbolic and rational functions solutions with arbitrary constants are obtained. When the arbitrary constants are taken some special values, the periodic and soliton solutions are obtained from the travelling wave solutions. The obtained solutions are new and not found elsewhere. The effect of the fractional order on some of these solutions are represented graphically to illustrate the behavior of the exact solutions when the parameter take some special choose.

Pair density waves in superconducting vortex halos

NASA Astrophysics Data System (ADS)

Wang, Yuxuan; Edkins, Stephen D.; Hamidian, Mohammad H.; Davis, J. C. Séamus; Fradkin, Eduardo; Kivelson, Steven A.

2018-05-01

We analyze the interplay between a d -wave uniform superconducting and a pair-density-wave (PDW) order parameter in the neighborhood of a vortex. We develop a phenomenological nonlinear sigma model, solve the saddle-point equation for the order-parameter configuration, and compute the resulting local density of states in the vortex halo. The intertwining of the two superconducting orders leads to a charge density modulation with the same periodicity as the PDW, which is twice the period of the charge density wave that arises as a second harmonic of the PDW itself. We discuss key features of the charge density modulation that can be directly compared with recent results from scanning tunneling microscopy and speculate on the role PDW order may play in the global phase diagram of the hole-doped cuprates.

Effect of shear stress on cell cultures and other reactor problems

NASA Technical Reports Server (NTRS)

Schleier, H.

1981-01-01

Anchorage dependent cell cultures in fluidized beds are tested. Feasibility calculations indicate the allowed parameters and estimate the shear stresses therein. In addition, the diffusion equation with first order reaction is solved for the spherical shell (double bubble) reactor with various constraints.

Large gyres as a shallow-water asymptotic solution of Euler's equation in spherical coordinates

NASA Astrophysics Data System (ADS)

Constantin, A.; Johnson, R. S.

2017-04-01

Starting from the Euler equation expressed in a rotating frame in spherical coordinates, coupled with the equation of mass conservation and the appropriate boundary conditions, a thin-layer (i.e. shallow water) asymptotic approximation is developed. The analysis is driven by a single, overarching assumption based on the smallness of one parameter: the ratio of the average depth of the oceans to the radius of the Earth. Consistent with this, the magnitude of the vertical velocity component through the layer is necessarily much smaller than the horizontal components along the layer. A choice of the size of this speed ratio is made, which corresponds, roughly, to the observational data for gyres; thus the problem is characterized by, and reduced to an analysis based on, a single small parameter. The nonlinear leading-order problem retains all the rotational contributions of the moving frame, describing motion in a thin spherical shell. There are many solutions of this system, corresponding to different vorticities, all described by a novel vorticity equation: this couples the vorticity generated by the spin of the Earth with the underlying vorticity due to the movement of the oceans. Some explicit solutions are obtained, which exhibit gyre-like flows of any size; indeed, the technique developed here allows for many different choices of the flow field and of any suitable free-surface profile. We comment briefly on the next order problem, which provides the structure through the layer. Some observations about the new vorticity equation are given, and a brief indication of how these results can be extended is offered.

Moving overlapping grids with adaptive mesh refinement for high-speed reactive and non-reactive flow

NASA Astrophysics Data System (ADS)

Henshaw, William D.; Schwendeman, Donald W.

2006-08-01

We consider the solution of the reactive and non-reactive Euler equations on two-dimensional domains that evolve in time. The domains are discretized using moving overlapping grids. In a typical grid construction, boundary-fitted grids are used to represent moving boundaries, and these grids overlap with stationary background Cartesian grids. Block-structured adaptive mesh refinement (AMR) is used to resolve fine-scale features in the flow such as shocks and detonations. Refinement grids are added to base-level grids according to an estimate of the error, and these refinement grids move with their corresponding base-level grids. The numerical approximation of the governing equations takes place in the parameter space of each component grid which is defined by a mapping from (fixed) parameter space to (moving) physical space. The mapped equations are solved numerically using a second-order extension of Godunov's method. The stiff source term in the reactive case is handled using a Runge-Kutta error-control scheme. We consider cases when the boundaries move according to a prescribed function of time and when the boundaries of embedded bodies move according to the surface stress exerted by the fluid. In the latter case, the Newton-Euler equations describe the motion of the center of mass of the each body and the rotation about it, and these equations are integrated numerically using a second-order predictor-corrector scheme. Numerical boundary conditions at slip walls are described, and numerical results are presented for both reactive and non-reactive flows that demonstrate the use and accuracy of the numerical approach.

Quantum Gravitational Corrections to the Real Klein-Gordon Field in the Presence of a Minimal Length

NASA Astrophysics Data System (ADS)

Moayedi, S. K.; Setare, M. R.; Moayeri, H.

2010-09-01

The ( D+1)-dimensional ( β, β')-two-parameter Lorentz-covariant deformed algebra introduced by Quesne and Tkachuk (J. Phys., A Math. Gen. 39, 10909, 2006), leads to a nonzero minimal uncertainty in position (minimal length). The Klein-Gordon equation in a (3+1)-dimensional space-time described by Quesne-Tkachuk Lorentz-covariant deformed algebra is studied in the case where β'=2 β up to first order over deformation parameter β. It is shown that the modified Klein-Gordon equation which contains fourth-order derivative of the wave function describes two massive particles with different masses. We have shown that physically acceptable mass states can only exist for β<1/8m^{2c2} which leads to an isotropic minimal length in the interval 10-17 m<(Δ X i )0<10-15 m. Finally, we have shown that the above estimation of minimal length is in good agreement with the results obtained in previous investigations.

Classical r matrix of the su(2 vertical bar 2) super Yang-Mills spin chain

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

Torrielli, Alessandro

2007-05-15

In this note we straightforwardly derive and make use of the quantum R matrix for the su(2 vertical bar 2) super Yang-Mills spin chain in the manifest su(1 vertical bar 2)-invariant formulation, which solves the standard quantum Yang-Baxter equation, in order to obtain the correspondent (undressed) classical r matrix from the first order expansion in the 'deformation' parameter 2{pi}/{radical}({lambda}) and check that this last solves the standard classical Yang-Baxter equation. We analyze its bialgebra structure, its dependence on the spectral parameters, and its pole structure. We notice that it still preserves an su(1 vertical bar 2) subalgebra, thereby admitting anmore » expression in terms of a combination of projectors, which spans only a subspace of su(1 vertical bar 2)xsu(1 vertical bar 2). We study the residue at its simple pole at the origin and comment on the applicability of the classical Belavin-Drinfeld type of analysis.« less

Unsteady translational motion of a slip sphere in a viscous fluid using the fractional Navier-Stokes equation

NASA Astrophysics Data System (ADS)

Ashmawy, E. A.

2017-03-01

In this paper, we investigate the translational motion of a slip sphere with time-dependent velocity in an incompressible viscous fluid. The modified Navier-Stokes equation with fractional order time derivative is used. The linear slip boundary condition is applied on the spherical boundary. The integral Laplace transform technique is employed to solve the problem. The solution in the physical domain is obtained analytically by inverting the Laplace transform using the complex inversion formula together with contour integration. An exact formula for the drag force exerted by the fluid on the spherical object is deduced. This formula is applied to some flows, namely damping oscillation, sine oscillation and sudden motion. The numerical results showed that the order of the fractional derivative contributes considerably to the drag force. The increase in this parameter resulted in an increase in the drag force. In addition, the values of the drag force increased with the increase in the slip parameter.

Self-consistent generalized Langevin-equation theory for liquids of nonspherically interacting particles.

PubMed

Elizondo-Aguilera, L F; Zubieta Rico, P F; Ruiz-Estrada, H; Alarcón-Waess, O

2014-11-01

A self-consistent generalized Langevin-equation theory is proposed to describe the self- and collective dynamics of a liquid of linear Brownian particles. The equations of motion for the spherical harmonics projections of the collective and self-intermediate-scattering functions, F_{lm,lm}(k,t) and F_{lm,lm}^{S}(k,t), are derived as a contraction of the description involving the stochastic equations of the corresponding tensorial one-particle density n_{lm}(k,t) and the translational (α=T) and rotational (α=R) current densities j_{lm}^{α}(k,t). Similar to the spherical case, these dynamic equations require as an external input the equilibrium structural properties of the system contained in the projections of the static structure factor, denoted by S_{lm,lm}(k). Complementing these exact equations with simple (Vineyard-like) approximate relations for the collective and the self-memory functions we propose a closed self-consistent set of equations for the dynamic properties involved. In the long-time asymptotic limit, these equations become the so-called bifurcation equations, whose solutions (the nonergodicity parameters) can be written, extending the spherical case, in terms of one translational and one orientational scalar dynamic order parameter, γ_{T} and γ_{R}, which characterize the possible dynamical arrest transitions of the system. As a concrete illustrative application of this theory we determine the dynamic arrest diagram of the dipolar hard-sphere fluid. In qualitative agreement with mode coupling theory, the present self-consistent equations also predict three different regions in the state space spanned by the macroscopic control parameters η (volume fraction) and T* (scaled temperature): a region of fully ergodic states, a region of mixed states, in which the translational degrees of freedom become arrested while the orientational degrees of freedom remain ergodic, and a region of fully nonergodic states.

Alternating direction implicit methods for parabolic equations with a mixed derivative

NASA Technical Reports Server (NTRS)

Beam, R. M.; Warming, R. F.

1980-01-01

Alternating direction implicit (ADI) schemes for two-dimensional parabolic equations with a mixed derivative are constructed by using the class of all A(0)-stable linear two-step methods in conjunction with the method of approximate factorization. The mixed derivative is treated with an explicit two-step method which is compatible with an implicit A(0)-stable method. The parameter space for which the resulting ADI schemes are second-order accurate and unconditionally stable is determined. Some numerical examples are given.

Alternating direction implicit methods for parabolic equations with a mixed derivative

NASA Technical Reports Server (NTRS)

Beam, R. M.; Warming, R. F.

1979-01-01

Alternating direction implicit (ADI) schemes for two-dimensional parabolic equations with a mixed derivative are constructed by using the class of all A sub 0-stable linear two-step methods in conjunction with the method of approximation factorization. The mixed derivative is treated with an explicit two-step method which is compatible with an implicit A sub 0-stable method. The parameter space for which the resulting ADI schemes are second order accurate and unconditionally stable is determined. Some numerical examples are given.

Order parameter description of walk-off effect on pattern selection in degenerate optical parametric oscillators

NASA Astrophysics Data System (ADS)

Taki, Majid; San Miguel, Maxi; Santagiustina, Marco

2000-02-01

Degenerate optical parametric oscillators can exhibit both uniformly translating fronts and nonuniformly translating envelope fronts under the walk-off effect. The nonlinear dynamics near threshold is shown to be described by a real convective Swift-Hohenberg equation, which provides the main characteristics of the walk-off effect on pattern selection. The predictions of the selected wave vector and the absolute instability threshold are in very good quantitative agreement with numerical solutions found from the equations describing the optical parametric oscillator.

Steady boundary layer slip flow along with heat and mass transfer over a flat porous plate embedded in a porous medium.

PubMed

Aziz, Asim; Siddique, J I; Aziz, Taha

2014-01-01

In this paper, a simplified model of an incompressible fluid flow along with heat and mass transfer past a porous flat plate embedded in a Darcy type porous medium is investigated. The velocity, thermal and mass slip conditions are utilized that has not been discussed in the literature before. The similarity transformations are used to transform the governing partial differential equations (PDEs) into a nonlinear ordinary differential equations (ODEs). The resulting system of ODEs is then reduced to a system of first order differential equations which was solved numerically by using Matlab bvp4c code. The effects of permeability, suction/injection parameter, velocity parameter and slip parameter on the structure of velocity, temperature and mass transfer rates are examined with the aid of several graphs. Moreover, observations based on Schmidt number and Soret number are also presented. The result shows, the increase in permeability of the porous medium increase the velocity and decrease the temperature profile. This happens due to a decrease in drag of the fluid flow. In the case of heat transfer, the increase in permeability and slip parameter causes an increase in heat transfer. However for the case of increase in thermal slip parameter there is a decrease in heat transfer. An increase in the mass slip parameter causes a decrease in the concentration field. The suction and injection parameter has similar effect on concentration profile as for the case of velocity profile.

Steady Boundary Layer Slip Flow along with Heat and Mass Transfer over a Flat Porous Plate Embedded in a Porous Medium

PubMed Central

Aziz, Asim; Siddique, J. I.; Aziz, Taha

2014-01-01

In this paper, a simplified model of an incompressible fluid flow along with heat and mass transfer past a porous flat plate embedded in a Darcy type porous medium is investigated. The velocity, thermal and mass slip conditions are utilized that has not been discussed in the literature before. The similarity transformations are used to transform the governing partial differential equations (PDEs) into a nonlinear ordinary differential equations (ODEs). The resulting system of ODEs is then reduced to a system of first order differential equations which was solved numerically by using Matlab bvp4c code. The effects of permeability, suction/injection parameter, velocity parameter and slip parameter on the structure of velocity, temperature and mass transfer rates are examined with the aid of several graphs. Moreover, observations based on Schmidt number and Soret number are also presented. The result shows, the increase in permeability of the porous medium increase the velocity and decrease the temperature profile. This happens due to a decrease in drag of the fluid flow. In the case of heat transfer, the increase in permeability and slip parameter causes an increase in heat transfer. However for the case of increase in thermal slip parameter there is a decrease in heat transfer. An increase in the mass slip parameter causes a decrease in the concentration field. The suction and injection parameter has similar effect on concentration profile as for the case of velocity profile. PMID:25531301

Asymptotic solutions for the case of nearly symmetric gravitational lens systems

NASA Astrophysics Data System (ADS)

Wertz, O.; Pelgrims, V.; Surdej, J.

2012-08-01

Gravitational lensing provides a powerful tool to determine the Hubble parameter H0 from the measurement of the time delay Δt between two lensed images of a background variable source. Nevertheless, knowledge of the deflector mass distribution constitutes a hurdle. We propose in the present work interesting solutions for the case of nearly symmetric gravitational lens systems. For the case of a small misalignment between the source, the deflector and the observer, we first consider power-law (ɛ) axially symmetric models for which we derive an analytical relation between the amplification ratio and source position which is independent of the power-law slope ɛ. According to this relation, we deduce an expression for H0 also irrespective of the value ɛ. Secondly, we consider the power-law axially symmetric lens models with an external large-scale gravitational field, the shear γ, resulting in the so-called ɛ-γ models, for which we deduce simple first-order equations linking the model parameters and the lensed image positions, the latter being observable quantities. We also deduce simple relations between H0 and observables quantities only. From these equations, we may estimate the value of the Hubble parameter in a robust way. Nevertheless, comparison between the ɛ-γ and singular isothermal ellipsoid (SIE) models leads to the conclusion that these models remain most often distinct. Therefore, even for the case of a small misalignment, use of the first-order equations and precise astrometric measurements of the positions of the lensed images with respect to the centre of the deflector enables one to discriminate between these two families of models. Finally, we confront the models with numerical simulations to evaluate the intrinsic error of the first-order expressions used when deriving the model parameters under the assumption of a quasi-alignment between the source, the deflector and the observer. From these same simulations, we estimate for the case of the ɛ-γ family of models that the standard deviation affecting H0 is ? which merely reflects the adopted astrometric uncertainties on the relative image positions, typically ? arcsec. In conclusions, we stress the importance of getting very accurate measurements of the relative positions of the multiple lensed images and of the time delays for the case of nearly symmetric gravitational lens systems, in order to derive robust and precise values of the Hubble parameter.

Lax pair, conservation laws and solitons for a (2 + 1)-dimensional fourth-order nonlinear Schrödinger equation governing an α-helical protein

NASA Astrophysics Data System (ADS)

Chai, Jun; Tian, Bo; Zhen, Hui-Ling; Sun, Wen-Rong

2015-11-01

Energy transfer through a (2+1)-dimensional α-helical protein can be described by a (2+1)-dimensional fourth-order nonlinear Schrödinger equation. For such an equation, a Lax pair and the infinitely-many conservation laws are derived. Using an auxiliary function and a bilinear formulation, we get the one-, two-, three- and N-soliton solutions via the Hirota method. The soliton velocity is linearly related to the lattice parameter γ, while the soliton' direction and amplitude do not depend on γ. Interactions between the two solitons are elastic, while those among the three solitons are pairwise elastic. Oblique, head-on and overtaking interactions between the two solitons are displayed. Oblique interaction among the three solitons and interactions among the two parallel solitons and a single one are presented as well.

Solving transient conduction and radiation heat transfer problems using the lattice Boltzmann method and the finite volume method

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

Mishra, Subhash C.; Roy, Hillol K.

2007-04-10

The lattice Boltzmann method (LBM) was used to solve the energy equation of a transient conduction-radiation heat transfer problem. The finite volume method (FVM) was used to compute the radiative information. To study the compatibility of the LBM for the energy equation and the FVM for the radiative transfer equation, transient conduction and radiation heat transfer problems in 1-D planar and 2-D rectangular geometries were considered. In order to establish the suitability of the LBM, the energy equations of the two problems were also solved using the FVM of the computational fluid dynamics. The FVM used in the radiative heatmore » transfer was employed to compute the radiative information required for the solution of the energy equation using the LBM or the FVM (of the CFD). To study the compatibility and suitability of the LBM for the solution of energy equation and the FVM for the radiative information, results were analyzed for the effects of various parameters such as the scattering albedo, the conduction-radiation parameter and the boundary emissivity. The results of the LBM-FVM combination were found to be in excellent agreement with the FVM-FVM combination. The number of iterations and CPU times in both the combinations were found comparable.« less

The optimal modified variational iteration method for the Lane-Emden equations with Neumann and Robin boundary conditions

NASA Astrophysics Data System (ADS)

Singh, Randhir; Das, Nilima; Kumar, Jitendra

2017-06-01

An effective analytical technique is proposed for the solution of the Lane-Emden equations. The proposed technique is based on the variational iteration method (VIM) and the convergence control parameter h . In order to avoid solving a sequence of nonlinear algebraic or complicated integrals for the derivation of unknown constant, the boundary conditions are used before designing the recursive scheme for solution. The series solutions are found which converges rapidly to the exact solution. Convergence analysis and error bounds are discussed. Accuracy, applicability of the method is examined by solving three singular problems: i) nonlinear Poisson-Boltzmann equation, ii) distribution of heat sources in the human head, iii) second-kind Lane-Emden equation.

Equations of motion for a flexible spacecraft-lumped parameter idealization

NASA Technical Reports Server (NTRS)

Storch, Joel; Gates, Stephen

1982-01-01

The equations of motion for a flexible vehicle capable of arbitrary translational and rotational motions in inertial space accompanied by small elastic deformations are derived in an unabridged form. The vehicle is idealized as consisting of a single rigid body with an ensemble of mass particles interconnected by massless elastic structure. The internal elastic restoring forces are quantified in terms of a stiffness matrix. A transformation and truncation of elastic degrees of freedom is made in the interest of numerical integration efficiency. Deformation dependent terms are partitioned into a hierarchy of significance. The final set of motion equations are brought to a fully assembled first order form suitable for direct digital implementation. A FORTRAN program implementing the equations is given and its salient features described.

I -Love- Q relations for white dwarf stars

NASA Astrophysics Data System (ADS)

Boshkayev, K.; Quevedo, H.; Zhami, B.

2017-02-01

We investigate the equilibrium configurations of uniformly rotating white dwarfs, using Chandrasekhar and Salpeter equations of state in the framework of Newtonian physics. The Hartle formalism is applied to integrate the field equation together with the hydrostatic equilibrium condition. We consider the equations of structure up to the second order in the angular velocity, and compute all basic parameters of rotating white dwarfs to test the so-called moment of inertia, rotational Love number, and quadrupole moment (I-Love-Q) relations. We found that the I-Love-Q relations are also valid for white dwarfs regardless of the equation of state and nuclear composition. In addition, we show that the moment of inertia, quadrupole moment, and eccentricity (I-Q-e) relations are valid as well.

Higher-Order Nonlinear Effects on Wave Structures in a Multispecies Plasma with Nonisothermal Electrons

NASA Astrophysics Data System (ADS)

Gill, Tarsem Singh; Bala, Parveen; Kaur, Harvinder

2010-04-01

In the present investigation, we have studied ion-acoustic solitary waves in a plasma consisting of warm positive and negative ions and nonisothermal electron distribution. We have used reductive perturbation theory (RPT) and derived a dispersion relation which supports only two ion-acoustic modes, viz. slow and fast. The expression for phase velocities of these modes is observed to be a function of parameters like nonisothermality, charge and mass ratio, and relative temperature of ions. A modified Korteweg-de Vries (KdV) equation with a (1+1/2) nonlinearity, also known as Schamel-mKdV model, is derived. RPT is further extended to include the contribution of higher-order terms. The results of numerical computation for such contributions are shown in the form of graphs in different parameter regimes for both, slow and fast ion-acoustic solitary waves having several interesting features. For the departure from the isothermally distributed electrons, a generalized KdV equation is derived and solved. It is observed that both rarefactive and compressive solitons exist for the isothermal case. However, nonisothermality supports only the compressive type of solitons in the given parameter regime.

Optimization of methylene blue using Ca(2+) and Zn(2+) bio-polymer hydrogel beads: A comparative study.

PubMed

Kumar, M; Tamilarasan, R; Arthanareeswaran, G; Ismail, A F

2015-11-01

Recently noted that the methylene blue cause severe central nervous system toxicity. It is essential to optimize the methylene blue from aqueous environment. In this study, a comparison of an optimization of methylene blue was investigated by using modified Ca(2+) and Zn(2+) bio-polymer hydrogel beads. A batch mode study was conducted using various parameters like time, dye concentration, bio-polymer dose, pH and process temperature. The isotherms, kinetics, diffusion and thermodynamic studies were performed for feasibility of the optimization process. Freundlich and Langmuir isotherm equations were used for the prediction of isotherm parameters and correlated with dimensionless separation factor (RL). Pseudo-first order and pseudo-second order Lagegren's kinetic equations were used for the correlation of kinetic parameters. Intraparticle diffusion model was employed for diffusion of the optimization process. The Fourier Transform Infrared Spectroscopy (FTIR) shows different absorbent peaks of Ca(2+) and Zn(2+) beads and the morphology of the bio-polymer material analyzed with Scanning Electron Microscope (SEM). The TG & DTA studies show that good thermal stability with less humidity without production of any non-degraded products. Copyright © 2015 Elsevier Inc. All rights reserved.

Comment on "A note on generalized radial mesh generation for plasma electronic structure"

NASA Astrophysics Data System (ADS)

Pain, J.-Ch.

2011-12-01

In a recent note, B.G. Wilson and V. Sonnad [1] proposed a very useful closed form expression for the efficient generation of analytic log-linear radial meshes. The central point of the note is an implicit equation for the parameter h, involving Lambert's function W[x]. The authors mention that they are unaware of any direct proof of this equation (they obtained it by re-summing the Taylor expansion of h[α] using high-order coefficients obtained by analytic differentiation of the implicit definition using symbolic manipulation). In the present comment, we propose a direct proof of that equation.

Evolution of statistical averages: An interdisciplinary proposal using the Chapman-Enskog method

NASA Astrophysics Data System (ADS)

Mariscal-Sanchez, A.; Sandoval-Villalbazo, A.

2017-08-01

This work examines the idea of applying the Chapman-Enskog (CE) method for approximating the solution of the Boltzmann equation beyond the realm of physics, using an information theory approach. Equations describing the evolution of averages and their fluctuations in a generalized phase space are established up to first-order in the Knudsen parameter which is defined as the ratio of the time between interactions (mean free time) and a characteristic macroscopic time. Although the general equations here obtained may be applied in a wide range of disciplines, in this paper, only a particular case related to the evolution of averages in speculative markets is examined.

Selection of site specific vibration equation by using analytic hierarchy process in a quarry

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

Kalayci, Ulku, E-mail: ukalayci@istanbul.edu.tr; Ozer, Umit, E-mail: uozer@istanbul.edu.tr

This paper presents a new approach for the selection of the most accurate SSVA (Site Specific Vibration Attenuation) equation for blasting processes in a quarry located near settlements in Istanbul, Turkey. In this context, the SSVA equations obtained from the same study area in the literature were considered in terms of distance between the shot points and buildings and the amount of explosive charge. In this purpose, 11 different SSVA equations obtained from the study area in the past 12 years, forecasting capabilities according to designated new conditions, using 102 vibration records as test data obtained from the study areamore » was investigated. In this study, AHP (Analytic Hierarchy Process) was selected as an analysis method in order to determine the most accurate equation among 11 SSAV equations, and the parameters such as year, distance, charge, and r{sup 2} of the equations were used as criteria for AHP. Finally, the most appropriate equation was selected among the existing ones, and the process of selecting according to different target criteria was presented. Furthermore, it was noted that the forecasting results of the selected equation is more accurate than that formed using the test results. - Highlights: • The optimum Site Specific Vibration Attenuation equation for blasting in a quarry located near settlements was determined. • It is indicated that SSVA equations changing over the years don’t give always accurate estimates at changing conditions. • Selection of the blast induced SSVA equation was made using AHP. • Equation selection method was highlighted based on parameters such as charge, distance, and quarry geometry changes (year).« less

Alternative stable qP wave equations in TTI media with their applications for reverse time migration

NASA Astrophysics Data System (ADS)

Zhou, Yang; Wang, Huazhong; Liu, Wenqing

2015-10-01

Numerical instabilities may arise if the spatial variation of symmetry axis is handled improperly when implementing P-wave modeling and reverse time migration in heterogeneous tilted transversely isotropic (TTI) media, especially in the cases where fast changes exist in TTI symmetry axis’ directions. Based on the pseudo-acoustic approximation to anisotropic elastic wave equations in Cartesian coordinates, alternative second order qP (quasi-P) wave equations in TTI media are derived in this paper. Compared with conventional stable qP wave equations, the proposed equations written in stress components contain only spatial derivatives of wavefield variables (stress components) and are free from spatial derivatives involving media parameters. These lead to an easy and efficient implementation for stable P-wave modeling and imaging. Numerical experiments demonstrate the stability and computational efficiency of the presented equations in complex TTI media.

A new perturbative approach to nonlinear partial differential equations

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

Bender, C.M.; Boettcher, S.; Milton, K.A.

1991-11-01

This paper shows how to solve some nonlinear wave equations as perturbation expansions in powers of a parameter that expresses the degree of nonlinearity. For the case of the Burgers equation {ital u}{sub {ital t}}+{ital uu}{sub {ital x}}={ital u}{sub {ital xx}}, the general nonlinear equation {ital u}{sub {ital t}}+{ital u}{sup {delta}}{ital u}{sub {ital x}}={ital u}{sub {ital xx}} is considered and expanded in powers of {delta}. The coefficients of the {delta} series to sixth order in powers of {delta} is determined and Pade summation is used to evaluate the perturbation series for large values of {delta}. The numerical results are accuratemore » and the method is very general; it applies to other well-studied partial differential equations such as the Korteweg--de Vries equation, {ital u}{sub {ital t}}+{ital uu}{sub {ital x}} ={ital u}{sub {ital xxx}}.« less

Accelerated pharmacokinetic map determination for dynamic contrast enhanced MRI using frequency-domain based Tofts model.

PubMed

Vajuvalli, Nithin N; Nayak, Krupa N; Geethanath, Sairam

2014-01-01

Dynamic Contrast Enhanced Magnetic Resonance Imaging (DCE-MRI) is widely used in the diagnosis of cancer and is also a promising tool for monitoring tumor response to treatment. The Tofts model has become a standard for the analysis of DCE-MRI. The process of curve fitting employed in the Tofts equation to obtain the pharmacokinetic (PK) parameters is time-consuming for high resolution scans. Current work demonstrates a frequency-domain approach applied to the standard Tofts equation to speed-up the process of curve-fitting in order to obtain the pharmacokinetic parameters. The results obtained show that using the frequency domain approach, the process of curve fitting is computationally more efficient compared to the time-domain approach.

Average activity of excitatory and inhibitory neural populations

NASA Astrophysics Data System (ADS)

Roulet, Javier; Mindlin, Gabriel B.

2016-09-01

We develop an extension of the Ott-Antonsen method [E. Ott and T. M. Antonsen, Chaos 18(3), 037113 (2008)] that allows obtaining the mean activity (spiking rate) of a population of excitable units. By means of the Ott-Antonsen method, equations for the dynamics of the order parameters of coupled excitatory and inhibitory populations of excitable units are obtained, and their mean activities are computed. Two different excitable systems are studied: Adler units and theta neurons. The resulting bifurcation diagrams are compared with those obtained from studying the phenomenological Wilson-Cowan model in some regions of the parameter space. Compatible behaviors, as well as higher dimensional chaotic solutions, are observed. We study numerical simulations to further validate the equations.

Simulation on Natural Convection of a Nanofluid along an Isothermal Inclined Plate

NASA Astrophysics Data System (ADS)

Mitra, Asish

2017-08-01

A numerical algorithm is presented for studying laminar natural convection flow of a nanofluid along an isothermal inclined plate. By means of similarity transformation, the original nonlinear partial differential equations of flow are transformed to a set of nonlinear ordinary differential equations. Subsequently they are reduced to a first order system and integrated using Newton Raphson and adaptive Runge-Kutta methods. The computer codes are developed for this numerical analysis in Matlab environment. Dimensionless velocity, temperature profiles and nanoparticle concentration for various angles of inclination are illustrated graphically. The effects of Prandtl number, Brownian motion parameter and thermophoresis parameter on Nusselt number are also discussed. The results of the present simulation are then compared with previous one available in literature with good agreement.

Average activity of excitatory and inhibitory neural populations

PubMed Central

Mindlin, Gabriel B.

2016-01-01

We develop an extension of the Ott-Antonsen method [E. Ott and T. M. Antonsen, Chaos 18(3), 037113 (2008)] that allows obtaining the mean activity (spiking rate) of a population of excitable units. By means of the Ott-Antonsen method, equations for the dynamics of the order parameters of coupled excitatory and inhibitory populations of excitable units are obtained, and their mean activities are computed. Two different excitable systems are studied: Adler units and theta neurons. The resulting bifurcation diagrams are compared with those obtained from studying the phenomenological Wilson-Cowan model in some regions of the parameter space. Compatible behaviors, as well as higher dimensional chaotic solutions, are observed. We study numerical simulations to further validate the equations. PMID:27781447

Breather solutions of a fourth-order nonlinear Schrödinger equation in the degenerate, soliton, and rogue wave limits

NASA Astrophysics Data System (ADS)

Chowdury, Amdad; Krolikowski, Wieslaw; Akhmediev, N.

2017-10-01

We present one- and two-breather solutions of the fourth-order nonlinear Schrödinger equation. With several parameters to play with, the solution may take a variety of forms. We consider most of these cases including the general form and limiting cases when the modulation frequencies are 0 or coincide. The zero-frequency limit produces a combination of breather-soliton structures on a constant background. The case of equal modulation frequencies produces a degenerate solution that requires a special technique for deriving. A zero-frequency limit of this degenerate solution produces a rational second-order rogue wave solution with a stretching factor involved. Taking, in addition, the zero limit of the stretching factor transforms the second-order rogue waves into a soliton. Adding a differential shift in the degenerate solution results in structural changes in the wave profile. Moreover, the zero-frequency limit of the degenerate solution with differential shift results in a rogue wave triplet. The zero limit of the stretching factor in this solution, in turn, transforms the triplet into a singlet plus a low-amplitude soliton on the background. A large value of the differential shift parameter converts the triplet into a pure singlet.

Breather solutions of a fourth-order nonlinear Schrödinger equation in the degenerate, soliton, and rogue wave limits.

PubMed

Chowdury, Amdad; Krolikowski, Wieslaw; Akhmediev, N

2017-10-01

We present one- and two-breather solutions of the fourth-order nonlinear Schrödinger equation. With several parameters to play with, the solution may take a variety of forms. We consider most of these cases including the general form and limiting cases when the modulation frequencies are 0 or coincide. The zero-frequency limit produces a combination of breather-soliton structures on a constant background. The case of equal modulation frequencies produces a degenerate solution that requires a special technique for deriving. A zero-frequency limit of this degenerate solution produces a rational second-order rogue wave solution with a stretching factor involved. Taking, in addition, the zero limit of the stretching factor transforms the second-order rogue waves into a soliton. Adding a differential shift in the degenerate solution results in structural changes in the wave profile. Moreover, the zero-frequency limit of the degenerate solution with differential shift results in a rogue wave triplet. The zero limit of the stretching factor in this solution, in turn, transforms the triplet into a singlet plus a low-amplitude soliton on the background. A large value of the differential shift parameter converts the triplet into a pure singlet.

Solutions for a local equation of anisotropic plant cell growth: an analytical study of expansin activity

PubMed Central

Pietruszka, Mariusz

2011-01-01

This paper presents a generalization of the Lockhart equation for plant cell/organ expansion in the anisotropic case. The intent is to take into account the temporal and spatial variation in the cell wall mechanical properties by considering the wall ‘extensibility’ (Φ), a time- and space-dependent parameter. A dynamic linear differential equation of a second-order tensor is introduced by describing the anisotropic growth process with some key biochemical aspects included. The distortion and expansion of plant cell walls initiated by expansins, a class of proteins known to enhance cell wall ‘extensibility’, is also described. In this approach, expansin proteins are treated as active agents participating in isotropic/anisotropic growth. Two-parameter models and an equation for describing α- and β-expansin proteins are proposed by delineating the extension of isolated wall samples, allowing turgor-driven polymer creep, where expansins weaken the non-covalent binding between wall polysaccharides. We observe that the calculated halftime (t1/2 = εΦ0 log 2) of stress relaxation due to expansin action can be described in mechanical terms. PMID:21227964

Lens elliptic gamma function solution of the Yang-Baxter equation at roots of unity

NASA Astrophysics Data System (ADS)

Kels, Andrew P.; Yamazaki, Masahito

2018-02-01

We study the root of unity limit of the lens elliptic gamma function solution of the star-triangle relation, for an integrable model with continuous and discrete spin variables. This limit involves taking an elliptic nome to a primitive rNth root of unity, where r is an existing integer parameter of the lens elliptic gamma function, and N is an additional integer parameter. This is a singular limit of the star-triangle relation, and at subleading order of an asymptotic expansion, another star-triangle relation is obtained for a model with discrete spin variables in {Z}rN . Some special choices of solutions of equation of motion are shown to result in well-known discrete spin solutions of the star-triangle relation. The saddle point equations themselves are identified with three-leg forms of ‘3D-consistent’ classical discrete integrable equations, known as Q4 and Q3(δ=0) . We also comment on the implications for supersymmetric gauge theories, and in particular comment on a close parallel with the works of Nekrasov and Shatashvili.

Investigation of Laser Parameters in Silicon Pulsed Laser Conduction Welding

NASA Astrophysics Data System (ADS)

Shayganmanesh, Mahdi; Khoshnoud, Afsaneh

2016-03-01

In this paper, laser welding of silicon in conduction mode is investigated numerically. In this study, the effects of laser beam characteristics on the welding have been studied. In order to model the welding process, heat conduction equation is solved numerically and laser beam energy is considered as a boundary condition. Time depended heat conduction equation is used in our calculations to model pulsed laser welding. Thermo-physical and optical properties of the material are considered to be temperature dependent in our calculations. Effects of spatial and temporal laser beam parameters such as laser beam spot size, laser beam quality, laser beam polarization, laser incident angle, laser pulse energy, laser pulse width, pulse repetition frequency and welding speed on the welding characteristics are assessed. The results show that how the temperature dependent thermo-physical and optical parameters of the material are important in laser welding modeling. Also the results show how the parameters of the laser beam influence the welding characteristics.

Influence of heat conducting substrates on explosive crystallization in thin layers

NASA Astrophysics Data System (ADS)

Schneider, Wilhelm

2017-09-01

Crystallization in a thin, initially amorphous layer is considered. The layer is in thermal contact with a substrate of very large dimensions. The energy equation of the layer contains source and sink terms. The source term is due to liberation of latent heat in the crystallization process, while the sink term is due to conduction of heat into the substrate. To determine the latter, the heat diffusion equation for the substrate is solved by applying Duhamel's integral. Thus, the energy equation of the layer becomes a heat diffusion equation with a time integral as an additional term. The latter term indicates that the heat loss due to the substrate depends on the history of the process. To complete the set of equations, the crystallization process is described by a rate equation for the degree of crystallization. The governing equations are then transformed to a moving co-ordinate system in order to analyze crystallization waves that propagate with invariant properties. Dual solutions are found by an asymptotic expansion for large activation energies of molecular diffusion. By introducing suitable variables, the results can be presented in a universal form that comprises the influence of all non-dimensional parameters that govern the process. Of particular interest for applications is the prediction of a critical heat loss parameter for the existence of crystallization waves with invariant properties.

Magnon modes and magnon-vortex scattering in two-dimensional easy-plane ferromagnets

NASA Astrophysics Data System (ADS)

Ivanov, B. A.; Schnitzer, H. J.; Mertens, F. G.; Wysin, G. M.

1998-10-01

We calculate the magnon modes in the presence of a vortex on a circular system, combining analytical calculations in the continuum limit with a numerical diagonalization of the discrete system. The magnon modes are expressed by the S matrix for magnon-vortex scattering, as a function of the parameters and the size of the system and for different boundary conditions. Certain quasilocal translational modes are identified with the frequencies which appear in the trajectory X-->(t) of the vortex center in recent molecular dynamics simulations of the full many-spin model. Using these quasilocal modes we calculate the two parameters of a third-order equation of motion for X-->(t). This equation was recently derived by a collective variable theory and describes very well the trajectories observed in the simulations. Both parameters, the vortex mass and the factor in front of X-->⃛, depend strongly on the boundary conditions.

Phase space analysis for anisotropic universe with nonlinear bulk viscosity

NASA Astrophysics Data System (ADS)

Sharif, M.; Mumtaz, Saadia

2018-06-01

In this paper, we discuss phase space analysis of locally rotationally symmetric Bianchi type I universe model by taking a noninteracting mixture of dust like and viscous radiation like fluid whose viscous pressure satisfies a nonlinear version of the Israel-Stewart transport equation. An autonomous system of equations is established by defining normalized dimensionless variables. In order to investigate stability of the system, we evaluate corresponding critical points for different values of the parameters. We also compute power-law scale factor whose behavior indicates different phases of the universe model. It is found that our analysis does not provide a complete immune from fine-tuning because the exponentially expanding solution occurs only for a particular range of parameters. We conclude that stable solutions exist in the presence of nonlinear model for bulk viscosity with different choices of the constant parameter m for anisotropic universe.

Identification and feedback control in structures with piezoceramic actuators

NASA Technical Reports Server (NTRS)

Banks, H. T.; Ito, K.; Wang, Y.

1992-01-01

In this lecture we give fundamental well-posedness results for a variational formulation of a class of damped second order partial differential equations with unbounded input or control coefficients. Included as special cases in this class are structures with piezoceramic actuators. We consider approximation techniques leading to computational methods in the context of both parameter estimation and feedback control problems for these systems. Rigorous convergence results for parameter estimates and feedback gains are discussed.

Prestack reverse time migration for tilted transversely isotropic media

NASA Astrophysics Data System (ADS)

Jang, Seonghyung; Hien, Doan Huy

2013-04-01

According to having interest in unconventional resource plays, anisotropy problem is naturally considered as an important step for improving the seismic image quality. Although it is well known prestack depth migration for the seismic reflection data is currently one of the powerful tools for imaging complex geological structures, it may lead to migration error without considering anisotropy. Asymptotic analysis of wave propagation in transversely isotropic (TI) media yields a dispersion relation of couple P- and SV wave modes that can be converted to a fourth order scalar partial differential equation (PDE). By setting the shear wave velocity equal zero, the fourth order PDE, called an acoustic wave equation for TI media, can be reduced to couple of second order PDE systems and we try to solve the second order PDE by the finite difference method (FDM). The result of this P wavefield simulation is kinematically similar to elastic and anisotropic wavefield simulation. We develop prestack depth migration algorithm for tilted transversely isotropic media using reverse time migration method (RTM). RTM is a method for imaging the subsurface using inner product of source wavefield extrapolation in forward and receiver wavefield extrapolation in backward. We show the subsurface image in TTI media using the inner product of partial derivative wavefield with respect to physical parameters and observation data. Since the partial derivative wavefields with respect to the physical parameters require extremely huge computing time, so we implemented the imaging condition by zero lag crosscorrelation of virtual source and back propagating wavefield instead of partial derivative wavefields. The virtual source is calculated directly by solving anisotropic acoustic wave equation, the back propagating wavefield on the other hand is calculated by the shot gather used as the source function in the anisotropic acoustic wave equation. According to the numerical model test for a simple geological model including syncline and anticline, the prestack depth migration using TTI-RTM in weak anisotropic media shows the subsurface image is similar to the true geological model used to generate the shot gathers.

Aeroelastic System Development Using Proper Orthogonal Decomposition and Volterra Theory

NASA Technical Reports Server (NTRS)

Lucia, David J.; Beran, Philip S.; Silva, Walter A.

2003-01-01

This research combines Volterra theory and proper orthogonal decomposition (POD) into a hybrid methodology for reduced-order modeling of aeroelastic systems. The out-come of the method is a set of linear ordinary differential equations (ODEs) describing the modal amplitudes associated with both the structural modes and the POD basis functions for the uid. For this research, the structural modes are sine waves of varying frequency, and the Volterra-POD approach is applied to the fluid dynamics equations. The structural modes are treated as forcing terms which are impulsed as part of the uid model realization. Using this approach, structural and uid operators are coupled into a single aeroelastic operator. This coupling converts a free boundary uid problem into an initial value problem, while preserving the parameter (or parameters) of interest for sensitivity analysis. The approach is applied to an elastic panel in supersonic cross ow. The hybrid Volterra-POD approach provides a low-order uid model in state-space form. The linear uid model is tightly coupled with a nonlinear panel model using an implicit integration scheme. The resulting aeroelastic model provides correct limit-cycle oscillation prediction over a wide range of panel dynamic pressure values. Time integration of the reduced-order aeroelastic model is four orders of magnitude faster than the high-order solution procedure developed for this research using traditional uid and structural solvers.

Transport of bisphenol-A in sandy aquifer sediment: Column experiment.

PubMed

Zakari, Sissou; Liu, Hui; Tong, Lei; Wang, Yan; Liu, Jianfeng

2016-02-01

The present paper aims to study the transport behavior of bisphenol-A (BPA) in sandy aquifer so as to provide important parameters for the prediction and control of contaminant plume in aquifer. Miscible displacement experiments were conducted and the breakthrough curves (BTCs) were simulated using HYDRUS-1D software. The effects of pore-water velocity (10-52 cm h(-1)) and initial concentration (2.5-40 mg L(-1)) on the sorption were also investigated. The BTCs of BPA fit the linear first-order non-equilibrium two-site model. The parameters such as partition coefficient (K(d)), the fraction of instantaneous adsorption on "Type-1" sites (F), the first order sorption rate coefficient for the kinetic non-equilibrium (type-2) sites (α), the retardation coefficient (R), and sorption capacity (q(column)) were computed. Results showed that BPA transported 0.11-0.83 m with various pore water velocity in sandy sediment column when water flowed 1 m. The sorption of BPA was mainly caused by the instantaneous surface adsorption as F varied from 0.596 to 0.908. The transport velocity of BPA was affected by pore water velocity (v) and followed the linear equation 1/R = 0.0600 + 0.0110v (r(2) = 0.9724). The parameter K(d) were also closely related to v and followed the equation LnK(d) = 1.0023-0.0482v (r(2) = 0.9690). The sorption capacity was more related to the initial BPA concentration (C0) and followed the linear equation q(column) = 0.265 + 0.253C0 (r(2) = 0.9727). The parameter α was affected by both v and C0 whereas F was not dramatically affected by both. Copyright © 2015 Elsevier Ltd. All rights reserved.

Coupled magneto-electro-mechanical lumped parameter model for a novel vibration-based magneto-electro-elastic energy harvesting systems

NASA Astrophysics Data System (ADS)

Shirbani, Meisam Moory; Shishesaz, Mohammad; Hajnayeb, Ali; Sedighi, Hamid Mohammad

2017-06-01

The objective of this paper is to present a coupled magneto-electro-mechanical (MEM) lumped parameter model for the response of the proposed magneto-electro-elastic (MEE) energy harvesting systems under base excitation. The proposed model can be used to create self-powering systems, which are not limited to a finite battery energy. As a novel approach, the MEE composites are used instead of the conventional piezoelectric materials in order to enhance the harvested electrical power. The considered structure consists of a MEE layer deposited on a layer of non-MEE material, in the framework of unimorph cantilever bars (longitudinal displacement) and beams (transverse displacement). To use the generated electrical potential, two electrodes are connected to the top and bottom surfaces of the MEE layer. Additionally, a stationary external coil is wrapped around the vibrating structure to induce a voltage in the coil by the magnetic field generated in the MEE layer. In order to simplify the design procedure of the proposed energy harvester and obtain closed form solutions, a lumped parameter model is prepared. As a first step in modeling process, the governing constitutive equations, Gauss's and Faraday's laws, are used to derive the coupled MEM differential equations. The derived equations are then solved analytically to obtain the dynamic behavior and the harvested voltages and powers of the proposed energy harvesting systems. Finally, the influences of the parameters that affect the performance of the MEE energy harvesters such as excitation frequency, external resistive loads and number of coil turns are discussed in detail. The results clearly show the benefit of the coil circuit implementation, whereby significant increases in the total useful harvested power as much as 38% and 36% are obtained for the beam and bar systems, respectively.

Application of Hill's equation for estimating area under the concentration-time curve (AUC) and use of time to AUC 90% for expressing kinetics of drug disposition.

PubMed

Cheng, Hsien C

2009-01-01

Half life and its derived pharmacokinetic parameters are calculated on an assumption that the terminal phase of drug disposition follows a constant rate of disposition. In reality, this assumption may not necessarily be the case. A new method is needed for analyzing PK parameters if the disposition does not follow a first order PK kinetic. Cumulative area under the concentration-time curve (AUC) is plotted against time to yield a hyperbolic (or sigmoidal) AUC-time relationship curve which is then analyzed by Hill's equation to yield AUC(inf), time to achieving AUC50% (T(AUC50%)) or AUC90% (T(AUC90%)), and the Hill's slope. From these parameters, an AUC-time relationship curve can be reconstructed. Projected plasma concentration can be calculated for any time point. Time at which cumulative AUC reaches 90% (T(AUC90%)) can be used as an indicator for expressing how fast a drug is cleared. Clearance is calculated in a traditional manner (i.v. dose/AUC(inf)), and the volume of distribution is proposed to be calculated at T(AUC50%) (0.5 i.v. dose/plasma concentration at T(AUC50%)). This method of estimating AUC is applicable for both i.v. and oral data. It is concluded that the Hill's equation can be used as an alternative method for estimating AUC and analysis of PK parameters if the disposition does not follow a first order kinetic. T(AUC90%) is proposed to be used as an indicator for expressing how fast a drug is cleared from the system.

Three-dimensional seismic depth migration

NASA Astrophysics Data System (ADS)

Zhou, Hongbo

1998-12-01

One-pass 3-D modeling and migration for poststack seismic data may be implemented by replacing the traditional 45sp° one-way wave equation (a third-order partial differential equation) with a pair of second and first order partial differential equations. Except for an extra correction term, the resulting second order equation has a form similar to Claerbout's 15sp° one-way wave equation, which is known to have a nearly circular horizontal impulse response. In this approach, there is no need to compensate for splitting errors. Numerical tests on synthetic data show that this algorithm has the desirable attributes of being second-order in accuracy and economical to solve. A modification of the Crank-Nicholson implementation maintains stability. Absorbing boundary conditions play an important role in one-way wave extrapolations by reducing reflections at grid edges. Clayton and Engquist's 2-D absorbing boundary conditions for one-way wave extrapolation by depth-stepping in the frequency domain are extended to 3-D using paraxial approximations of the scalar wave equation. Internal consistency is retained by incorporating the interior extrapolation equation with the absorbing boundary conditions. Numerical schemes are designed to make the proposed absorbing boundary conditions both mathematically correct and efficient with negligible extra cost. Synthetic examples illustrate the effectiveness of the algorithm for extrapolation with the 3-D 45sp° one-way wave equation. Frequency-space domain Butterworth and Chebyshev dip filters are implemented. By regrouping the product terms in the filter transfer function into summations, a cascaded (serial) Butterworth dip filter can be made parallel. A parallel Chebyshev dip filter can be similarly obtained, and has the same form as the Butterworth filter; but has different coeffcients. One of the advantages of the Chebyshev filter is that it has a sharper transition zone than that of Butterworth filter of the same order. Both filters are incorporated into 3-D one-way frequency-space depth migration for evanescent energy removal and for phase compensation of splitting errors; a single filter achieves both goals. Synthetic examples illustrate the behavior of the parallel filters. For a given order of filter, the cost of the Butterworth and Chebyshev filters is the same. A Chebyshev filter is more effective for phase compensation than the Butterworth filter of the same order, at the expense of some wavenumber-dependent amplitude ripples. An analytical formula for geometrical spreading is derived for a horizontally layered transversely isotropic medium with a vertical symmetry axis. Under this expression, geometrical spreading can be determined only by the anisotropic parameters in the first layer, the traveltime derivatives, and source-receiver offset. An explicit, numerically feasible expression for geometrical spreading can be further obtained by considering some of the special cases of transverse isotropy, such as weak anisotropy or elliptic anisotropy. Therefore, with the techniques of non-hyerbolic moveout for transverse isotropic media, geometrical spreading can be calculated by using picked traveltimes of primary P-wave reflections without having to know the actual parameters in the deeper subsurface; no ray tracing is needed. Synthetic examples verify the algorithm and show that it is numerically feasible for calculation of geometrical spreading.

A homotopy algorithm for digital optimal projection control GASD-HADOC

NASA Technical Reports Server (NTRS)

Collins, Emmanuel G., Jr.; Richter, Stephen; Davis, Lawrence D.

1993-01-01

The linear-quadratic-gaussian (LQG) compensator was developed to facilitate the design of control laws for multi-input, multi-output (MIMO) systems. The compensator is computed by solving two algebraic equations for which standard closed-loop solutions exist. Unfortunately, the minimal dimension of an LQG compensator is almost always equal to the dimension of the plant and can thus often violate practical implementation constraints on controller order. This deficiency is especially highlighted when considering control-design for high-order systems such as flexible space structures. This deficiency motivated the development of techniques that enable the design of optimal controllers whose dimension is less than that of the design plant. A homotopy approach based on the optimal projection equations that characterize the necessary conditions for optimal reduced-order control. Homotopy algorithms have global convergence properties and hence do not require that the initializing reduced-order controller be close to the optimal reduced-order controller to guarantee convergence. However, the homotopy algorithm previously developed for solving the optimal projection equations has sublinear convergence properties and the convergence slows at higher authority levels and may fail. A new homotopy algorithm for synthesizing optimal reduced-order controllers for discrete-time systems is described. Unlike the previous homotopy approach, the new algorithm is a gradient-based, parameter optimization formulation and was implemented in MATLAB. The results reported may offer the foundation for a reliable approach to optimal, reduced-order controller design.

p -wave superconductivity in weakly repulsive 2D Hubbard model with Zeeman splitting and weak Rashba spin-orbit coupling

NASA Astrophysics Data System (ADS)

Hugdal, Henning G.; Sudbø, Asle

2018-01-01

We study the superconducting order in a two-dimensional square lattice Hubbard model with weak repulsive interactions, subject to a Zeeman field and weak Rashba spin-orbit interactions. Diagonalizing the noninteracting Hamiltonian leads to two separate bands, and by deriving an effective low-energy interaction we find the mean field gap equations for the superconducting order parameter on the bands. Solving the gap equations just below the critical temperature, we find that superconductivity is caused by Kohn-Luttinger-type interaction, while the pairing symmetry of the bands is indirectly affected by the spin-orbit coupling. The dominating attractive momentum channel of the Kohn-Luttinger term depends on the filling fraction n of the system, and it is therefore possible to change the momentum dependence of the order parameter by tuning n . Moreover, n also determines which band has the highest critical temperature. Rotating the magnetic field changes the momentum dependence from states that for small momenta reduce to a chiral px±i py type state for out-of-plane fields, to a nodal p -wave-type state for purely in-plane fields.

Traversable wormholes satisfying the weak energy condition in third-order Lovelock gravity

NASA Astrophysics Data System (ADS)

Zangeneh, Mahdi Kord; Lobo, Francisco S. N.; Dehghani, Mohammad Hossein

2015-12-01

In this paper, we consider third-order Lovelock gravity with a cosmological constant term in an n -dimensional spacetime M4×Kn -4, where Kn -4 is a constant curvature space. We decompose the equations of motion to four and higher dimensional ones and find wormhole solutions by considering a vacuum Kn -4 space. Applying the latter constraint, we determine the second- and third-order Lovelock coefficients and the cosmological constant in terms of specific parameters of the model, such as the size of the extra dimensions. Using the obtained Lovelock coefficients and Λ , we obtain the four-dimensional matter distribution threading the wormhole. Furthermore, by considering the zero tidal force case and a specific equation of state, given by ρ =(γ p -τ )/[ω (1 +γ )], we find the exact solution for the shape function which represents both asymptotically flat and nonflat wormhole solutions. We show explicitly that these wormhole solutions in addition to traversibility satisfy the energy conditions for suitable choices of parameters and that the existence of a limited spherically symmetric traversable wormhole with normal matter in a four-dimensional spacetime implies a negative effective cosmological constant.

Thermodynamic Analysis of Chemically Reacting Mixtures-Comparison of First and Second Order Models.

PubMed

Pekař, Miloslav

2018-01-01

Recently, a method based on non-equilibrium continuum thermodynamics which derives thermodynamically consistent reaction rate models together with thermodynamic constraints on their parameters was analyzed using a triangular reaction scheme. The scheme was kinetically of the first order. Here, the analysis is further developed for several first and second order schemes to gain a deeper insight into the thermodynamic consistency of rate equations and relationships between chemical thermodynamic and kinetics. It is shown that the thermodynamic constraints on the so-called proper rate coefficient are usually simple sign restrictions consistent with the supposed reaction directions. Constraints on the so-called coupling rate coefficients are more complex and weaker. This means more freedom in kinetic coupling between reaction steps in a scheme, i.e., in the kinetic effects of other reactions on the rate of some reaction in a reacting system. When compared with traditional mass-action rate equations, the method allows a reduction in the number of traditional rate constants to be evaluated from data, i.e., a reduction in the dimensionality of the parameter estimation problem. This is due to identifying relationships between mass-action rate constants (relationships which also include thermodynamic equilibrium constants) which have so far been unknown.

A numerical study of adaptive space and time discretisations for Gross–Pitaevskii equations

PubMed Central

Thalhammer, Mechthild; Abhau, Jochen

2012-01-01

As a basic principle, benefits of adaptive discretisations are an improved balance between required accuracy and efficiency as well as an enhancement of the reliability of numerical computations. In this work, the capacity of locally adaptive space and time discretisations for the numerical solution of low-dimensional nonlinear Schrödinger equations is investigated. The considered model equation is related to the time-dependent Gross–Pitaevskii equation arising in the description of Bose–Einstein condensates in dilute gases. The performance of the Fourier-pseudo spectral method constrained to uniform meshes versus the locally adaptive finite element method and of higher-order exponential operator splitting methods with variable time stepsizes is studied. Numerical experiments confirm that a local time stepsize control based on a posteriori local error estimators or embedded splitting pairs, respectively, is effective in different situations with an enhancement either in efficiency or reliability. As expected, adaptive time-splitting schemes combined with fast Fourier transform techniques are favourable regarding accuracy and efficiency when applied to Gross–Pitaevskii equations with a defocusing nonlinearity and a mildly varying regular solution. However, the numerical solution of nonlinear Schrödinger equations in the semi-classical regime becomes a demanding task. Due to the highly oscillatory and nonlinear nature of the problem, the spatial mesh size and the time increments need to be of the size of the decisive parameter 0<ε≪1, especially when it is desired to capture correctly the quantitative behaviour of the wave function itself. The required high resolution in space constricts the feasibility of numerical computations for both, the Fourier pseudo-spectral and the finite element method. Nevertheless, for smaller parameter values locally adaptive time discretisations facilitate to determine the time stepsizes sufficiently small in order that the numerical approximation captures correctly the behaviour of the analytical solution. Further illustrations for Gross–Pitaevskii equations with a focusing nonlinearity or a sharp Gaussian as initial condition, respectively, complement the numerical study. PMID:25550676

A numerical study of adaptive space and time discretisations for Gross-Pitaevskii equations.

PubMed

Thalhammer, Mechthild; Abhau, Jochen

2012-08-15

As a basic principle, benefits of adaptive discretisations are an improved balance between required accuracy and efficiency as well as an enhancement of the reliability of numerical computations. In this work, the capacity of locally adaptive space and time discretisations for the numerical solution of low-dimensional nonlinear Schrödinger equations is investigated. The considered model equation is related to the time-dependent Gross-Pitaevskii equation arising in the description of Bose-Einstein condensates in dilute gases. The performance of the Fourier-pseudo spectral method constrained to uniform meshes versus the locally adaptive finite element method and of higher-order exponential operator splitting methods with variable time stepsizes is studied. Numerical experiments confirm that a local time stepsize control based on a posteriori local error estimators or embedded splitting pairs, respectively, is effective in different situations with an enhancement either in efficiency or reliability. As expected, adaptive time-splitting schemes combined with fast Fourier transform techniques are favourable regarding accuracy and efficiency when applied to Gross-Pitaevskii equations with a defocusing nonlinearity and a mildly varying regular solution. However, the numerical solution of nonlinear Schrödinger equations in the semi-classical regime becomes a demanding task. Due to the highly oscillatory and nonlinear nature of the problem, the spatial mesh size and the time increments need to be of the size of the decisive parameter [Formula: see text], especially when it is desired to capture correctly the quantitative behaviour of the wave function itself. The required high resolution in space constricts the feasibility of numerical computations for both, the Fourier pseudo-spectral and the finite element method. Nevertheless, for smaller parameter values locally adaptive time discretisations facilitate to determine the time stepsizes sufficiently small in order that the numerical approximation captures correctly the behaviour of the analytical solution. Further illustrations for Gross-Pitaevskii equations with a focusing nonlinearity or a sharp Gaussian as initial condition, respectively, complement the numerical study.

A unified model for transfer alignment at random misalignment angles based on second-order EKF

NASA Astrophysics Data System (ADS)

Cui, Xiao; Mei, Chunbo; Qin, Yongyuan; Yan, Gongmin; Liu, Zhenbo

2017-04-01

In the transfer alignment process of inertial navigation systems (INSs), the conventional linear error model based on the small misalignment angle assumption cannot be applied to large misalignment situations. Furthermore, the nonlinear model based on the large misalignment angle suffers from redundant computation with nonlinear filters. This paper presents a unified model for transfer alignment suitable for arbitrary misalignment angles. The alignment problem is transformed into an estimation of the relative attitude between the master INS (MINS) and the slave INS (SINS), by decomposing the attitude matrix of the latter. Based on the Rodriguez parameters, a unified alignment model in the inertial frame with the linear state-space equation and a second order nonlinear measurement equation are established, without making any assumptions about the misalignment angles. Furthermore, we employ the Taylor series expansions on the second-order nonlinear measurement equation to implement the second-order extended Kalman filter (EKF2). Monte-Carlo simulations demonstrate that the initial alignment can be fulfilled within 10 s, with higher accuracy and much smaller computational cost compared with the traditional unscented Kalman filter (UKF) at large misalignment angles.

Perturbation expansions of stochastic wavefunctions for open quantum systems

NASA Astrophysics Data System (ADS)

Ke, Yaling; Zhao, Yi

2017-11-01

Based on the stochastic unravelling of the reduced density operator in the Feynman path integral formalism for an open quantum system in touch with harmonic environments, a new non-Markovian stochastic Schrödinger equation (NMSSE) has been established that allows for the systematic perturbation expansion in the system-bath coupling to arbitrary order. This NMSSE can be transformed in a facile manner into the other two NMSSEs, i.e., non-Markovian quantum state diffusion and time-dependent wavepacket diffusion method. Benchmarked by numerically exact results, we have conducted a comparative study of the proposed method in its lowest order approximation, with perturbative quantum master equations in the symmetric spin-boson model and the realistic Fenna-Matthews-Olson complex. It is found that our method outperforms the second-order time-convolutionless quantum master equation in the whole parameter regime and even far better than the fourth-order in the slow bath and high temperature cases. Besides, the method is applicable on an equal footing for any kind of spectral density function and is expected to be a powerful tool to explore the quantum dynamics of large-scale systems, benefiting from the wavefunction framework and the time-local appearance within a single stochastic trajectory.

Perturbation method for the second-order nonlinear effect of focused acoustic field around a scatterer in an ideal fluid.

PubMed

Liu, Gang; Jayathilake, Pahala Gedara; Khoo, Boo Cheong

2014-02-01

Two nonlinear models are proposed to investigate the focused acoustic waves that the nonlinear effects will be important inside the liquid around the scatterer. Firstly, the one dimensional solutions for the widely used Westervelt equation with different coordinates are obtained based on the perturbation method with the second order nonlinear terms. Then, by introducing the small parameter (Mach number), a dimensionless formulation and asymptotic perturbation expansion via the compressible potential flow theory is applied. This model permits the decoupling between the velocity potential and enthalpy to second order, with the first potential solutions satisfying the linear wave equation (Helmholtz equation), whereas the second order solutions are associated with the linear non-homogeneous equation. Based on the model, the local nonlinear effects of focused acoustic waves on certain volume are studied in which the findings may have important implications for bubble cavitation/initiation via focused ultrasound called HIFU (High Intensity Focused Ultrasound). The calculated results show that for the domain encompassing less than ten times the radius away from the center of the scatterer, the non-linear effect exerts a significant influence on the focused high intensity acoustic wave. Moreover, at the comparatively higher frequencies, for the model of spherical wave, a lower Mach number may result in stronger nonlinear effects. Copyright © 2013 Elsevier B.V. All rights reserved.

Nanofluid flow and heat transfer due to a stretching cylinder in the presence of magnetic field

NASA Astrophysics Data System (ADS)

Ashorynejad, H. R.; Sheikholeslami, M.; Pop, I.; Ganji, D. D.

2013-03-01

In this paper, flow and heat transfer of a nanofluid over a stretching cylinder in the presence of magnetic field has been investigated. The governing partial differential equations with the corresponding boundary conditions are reduced to a set of ordinary differential equations with the appropriate boundary conditions using similarity transformation, which is then solved numerically by the fourth order Runge-Kutta integration scheme featuring a shooting technique. Different types of nanoparticles as copper (Cu), silver (Ag), alumina (Al2O3) and titanium oxide (TiO2) with water as their base fluid has been considered. The influence of significant parameters such as nanoparticle volume fraction, nanofluids type, magnetic parameter and Reynolds number on the flow and heat transfer characteristics is discussed. It was found that the Nusselt number increases as each of Reynolds number or nanoparticles volume fraction increase, but it decreases as magnetic parameter increase. Also it can be found that choosing copper (for small of magnetic parameter) and alumina (for large values of magnetic parameter) leads to the highest cooling performance for this problem.

Quadratic Convective Flow of a Micropolar Fluid along an Inclined Plate in a Non-Darcy Porous Medium with Convective Boundary Condition

NASA Astrophysics Data System (ADS)

RamReddy, Ch.; Naveen, P.; Srinivasacharya, D.

2017-06-01

The objective of the present study is to investigate the effect of nonlinear variation of density with temperature and concentration on the mixed convective flow of a micropolar fluid over an inclined flat plate in a non-Darcy porous medium in the presence of the convective boundary condition. In order to analyze all the essential features, the governing non-dimensional partial differential equations are transformed into a system of ordinary differential equations using a local non-similarity procedure and then the resulting boundary value problem is solved using a successive linearisation method (SLM). By insisting the comparison between vertical, horizontal and inclined plates, the physical quantities of the flow and its characteristics are exhibited graphically and quantitatively with various parameters. An increase in the micropolar parameter and non-Darcy parameter tend to increase the skin friction and the reverse change is observed in wall couple stress, mass and heat transfer rates. The influence of the nonlinear concentration parameter is more prominent on all the physical characteristics of the present model, compared with that of nonlinear temperature parameter.

Rhelogical constraints on ridge formation on Icy Satellites

NASA Astrophysics Data System (ADS)

Rudolph, M. L.; Manga, M.

2010-12-01

The processes responsible for forming ridges on Europa remain poorly understood. We use a continuum damage mechanics approach to model ridge formation. The main objectives of this contribution are to constrain (1) choice of rheological parameters and (2) maximum ridge size and rate of formation. The key rheological parameters to constrain appear in the evolution equation for a damage variable (D): ˙ {D} = B <<σ >>r}(1-D){-k-α D (p)/(μ ) and in the equation relating damage accumulation to volumetric changes, Jρ 0 = δ (1-D). Similar damage evolution laws have been applied to terrestrial glaciers and to the analysis of rock mechanics experiments. However, it is reasonable to expect that, like viscosity, the rheological constants B, α , and δ depend strongly on temperature, composition, and ice grain size. In order to determine whether the damage model is appropriate for Europa’s ridges, we must find values of the unknown damage parameters that reproduce ridge topography. We perform a suite of numerical experiments to identify the region of parameter space conducive to ridge production and show the sensitivity to changes in each unknown parameter.

Symmetries and integrability of a fourth-order Euler-Bernoulli beam equation

NASA Astrophysics Data System (ADS)

Bokhari, Ashfaque H.; Mahomed, F. M.; Zaman, F. D.

2010-05-01

The complete symmetry group classification of the fourth-order Euler-Bernoulli ordinary differential equation, where the elastic modulus and the area moment of inertia are constants and the applied load is a function of the normal displacement, is obtained. We perform the Lie and Noether symmetry analysis of this problem. In the Lie analysis, the principal Lie algebra which is one dimensional extends in four cases, viz. the linear, exponential, general power law, and a negative fractional power law. It is further shown that two cases arise in the Noether classification with respect to the standard Lagrangian. That is, the linear case for which the Noether algebra dimension is one less than the Lie algebra dimension as well as the negative fractional power law. In the latter case the Noether algebra is three dimensional and is isomorphic to the Lie algebra which is sl(2,R). This exceptional case, although admitting the nonsolvable algebra sl(2,R), remarkably allows for a two-parameter family of exact solutions via the Noether integrals. The Lie reduction gives a second-order ordinary differential equation which has nonlocal symmetry.

A real-time approximate optimal guidance law for flight in a plane

NASA Technical Reports Server (NTRS)

Feeley, Timothy S.; Speyer, Jason L.

1990-01-01

A real-time guidance scheme is presented for the problem of maximizing the payload into orbit subject to the equations of motion of a rocket over a nonrotating spherical earth. The flight is constrained to a path in the equatorial plane while reaching an orbital altitude at orbital injection speeds. The dynamics of the problem can be separated into primary and perturbation effects by a small parameter, epsilon, which is the ratio of the atmospheric scale height to the radius of the earth. The Hamilton-Jacobi-Bellman or dynamic programming equation is expanded in an asymptotic series where the zeroth-order term (epsilon = 0) can be obtained in closed form. The neglected perturbation terms are included in the higher-order terms of the expansion, which are determined from the solution of first-order linear partial differential equations requiring only integrations which are quadratures. The quadratures can be performed rapidly with emerging computer capability, so that real-time approximate optimization can be used to construct the launch guidance law. The application of this technique to flight in three-dimensions is made apparent from the solution presented.

Quantum action for time-dependent Ginzburg-Landau equations

NASA Astrophysics Data System (ADS)

Thompson, R. S.

1994-02-01

A gauge-invariant formula is derived for the quantum action of a dirty superconductor with strong pair breaking. The major complication is the coupling between the order parameter and the electro-chemical potential, which is most simply expressed as an imaginary time integral. The perturbative modes of excitation are identified.

A stability analysis of the power-law steady state of marine size spectra.

PubMed

Datta, Samik; Delius, Gustav W; Law, Richard; Plank, Michael J

2011-10-01

This paper investigates the stability of the power-law steady state often observed in marine ecosystems. Three dynamical systems are considered, describing the abundance of organisms as a function of body mass and time: a "jump-growth" equation, a first order approximation which is the widely used McKendrick-von Foerster equation, and a second order approximation which is the McKendrick-von Foerster equation with a diffusion term. All of these yield a power-law steady state. We derive, for the first time, the eigenvalue spectrum for the linearised evolution operator, under certain constraints on the parameters. This provides new knowledge of the stability properties of the power-law steady state. It is shown analytically that the steady state of the McKendrick-von Foerster equation without the diffusion term is always unstable. Furthermore, numerical plots show that eigenvalue spectra of the McKendrick-von Foerster equation with diffusion give a good approximation to those of the jump-growth equation. The steady state is more likely to be stable with a low preferred predator:prey mass ratio, a large diet breadth and a high feeding efficiency. The effects of demographic stochasticity are also investigated and it is concluded that these are likely to be small in real systems.

On a simple molecular–statistical model of a liquid-crystal suspension of anisometric particles

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

Zakhlevnykh, A. N., E-mail: anz@psu.ru; Lubnin, M. S.; Petrov, D. A.

2016-11-15

A molecular–statistical mean-field theory is constructed for suspensions of anisometric particles in nematic liquid crystals (NLCs). The spherical approximation, well known in the physics of ferromagnetic materials, is considered that allows one to obtain an analytic expression for the free energy and simple equations for the orientational state of a suspension that describe the temperature dependence of the order parameters of the suspension components. The transition temperature from ordered to isotropic state and the jumps in the order parameters at the phase-transition point are studied as a function of the anchoring energy of dispersed particles to the matrix, the concentrationmore » of the impurity phase, and the size of particles. The proposed approach allows one to generalize the model to the case of biaxial ordering.« less

The surface-induced spatial-temporal structures in confined binary alloys

NASA Astrophysics Data System (ADS)

Krasnyuk, Igor B.; Taranets, Roman M.; Chugunova, Marina

2014-12-01

This paper examines surface-induced ordering in confined binary alloys. The hyperbolic initial boundary value problem (IBVP) is used to describe a scenario of spatiotemporal ordering in a disordered phase for concentration of one component of binary alloy and order parameter with non-linear dynamic boundary conditions. This hyperbolic model consists of two coupled second order differential equations for order parameter and concentration. It also takes into account effects of the “memory” on the ordering of atoms and their densities in the alloy. The boundary conditions characterize surface velocities of order parameter and concentration changing which is due to surface (super)cooling on walls confining the binary alloy. It is shown that for large times there are three classes of dynamic non-linear boundary conditions which lead to three different types of attractor’s elements for the IBVP. Namely, the elements of attractor are the limit periodic simple shock waves with fronts of “discontinuities” Γ. If Γ is finite, then the attractor contains spatiotemporal functions of relaxation type. If Γ is infinite and countable then we observe the functions of pre-turbulent type. If Γ is infinite and uncountable then we obtain the functions of turbulent type.

Nonlinear Stage of Modulation Instability for a Fifth-Order Nonlinear Schrödinger Equation

NASA Astrophysics Data System (ADS)

Jia, Hui-Xian; Shan, Dong-Ming

2017-10-01

In this article, a fifth-order nonlinear Schrödinger equation, which can be used to characterise the solitons in the optical fibre and inhomogeneous Heisenberg ferromagnetic spin system, has been investigated. Akhmediev breather, Kuzentsov soliton, and generalised soliton have all been attained via the Darbox transformation. Propagation and interaction for three-type breathers have been studied: the types of breather are determined by the module and complex angle of parameter ξ; interaction between Akhmediev breather and generalised soliton displays a phase shift, whereas the others do not. Modulation instability of the generalised solitons have been analysed: a small perturbation can develop into a rogue wave, which is consistent with the results of rogue wave solutions.

Structure and orientational ordering in a fluid of elongated quadrupolar molecules

NASA Astrophysics Data System (ADS)

Singh, Ram Chandra

2013-01-01

A second-order density-functional theory is used to study the effect of quadrupolar interactions on the isotropic-nematic transition in a system of fluids of elongated molecules interacting via the Gay-Berne potential. The direct pair-correlation functions of the coexisting isotropic fluid that enter in the theory as input information are obtained by solving the Ornstein-Zernike equation using the Percus-Yevick integral equation theory in the (reduced) temperature range of 1.6≤T∗≤3.0 for different densities, temperatures and quadrupole moments. Using the harmonic coefficients of the direct pair-correlation functions, isotropic-nematic phase coexistence and thermodynamic parameters have been calculated. The theoretical results have been compared with the available computer simulation results.

Some aspects of reconstruction using a scalar field in f( T) gravity

NASA Astrophysics Data System (ADS)

Chakrabarti, Soumya; Said, Jackson Levi; Farrugia, Gabriel

2017-12-01

General relativity characterizes gravity as a geometric property exhibited on spacetime by massive objects, while teleparallel gravity achieves the same results at the level of equations, by taking a torsional perspective of gravity. Similar to the f( R) theory teleparallel gravity can also be generalized to f( T), with the resulting field equations being inherently distinct from f( R) gravity in that they are second order, while in the former case they turn out to be fourth order. In the present case, a minimally coupled scalar field is investigated in the f( T) gravity context for several forms of the scalar field potential. A number of new f( T) solutions are found for these potentials. Their respective state parameters are also being examined.

Prediction of stream volatilization coefficients

USGS Publications Warehouse

Rathbun, Ronald E.

1990-01-01

Equations are developed for predicting the liquid-film and gas-film reference-substance parameters for quantifying volatilization of organic solutes from streams. Molecular weight and molecular-diffusion coefficients of the solute are used as correlating parameters. Equations for predicting molecular-diffusion coefficients of organic solutes in water and air are developed, with molecular weight and molal volume as parameters. Mean absolute errors of prediction for diffusion coefficients in water are 9.97% for the molecular-weight equation, 6.45% for the molal-volume equation. The mean absolute error for the diffusion coefficient in air is 5.79% for the molal-volume equation. Molecular weight is not a satisfactory correlating parameter for diffusion in air because two equations are necessary to describe the values in the data set. The best predictive equation for the liquid-film reference-substance parameter has a mean absolute error of 5.74%, with molal volume as the correlating parameter. The best equation for the gas-film parameter has a mean absolute error of 7.80%, with molecular weight as the correlating parameter.

Analysis and optimization of cyclic methods in orbit computation

NASA Technical Reports Server (NTRS)

Pierce, S.

1973-01-01

The mathematical analysis and computation of the K=3, order 4; K=4, order 6; and K=5, order 7 cyclic methods and the K=5, order 6 Cowell method and some results of optimizing the 3 backpoint cyclic multistep methods for solving ordinary differential equations are presented. Cyclic methods have the advantage over traditional methods of having higher order for a given number of backpoints while at the same time having more free parameters. After considering several error sources the primary source for the cyclic methods has been isolated. The free parameters for three backpoint methods were used to minimize the effects of some of these error sources. They now yield more accuracy with the same computing time as Cowell's method on selected problems. This work is being extended to the five backpoint methods. The analysis and optimization are more difficult here since the matrices are larger and the dimension of the optimizing space is larger. Indications are that the primary error source can be reduced. This will still leave several parameters free to minimize other sources.

[Comparison of three stand-level biomass estimation methods].

PubMed

Dong, Li Hu; Li, Feng Ri

2016-12-01

At present, the forest biomass methods of regional scale attract most of attention of the researchers, and developing the stand-level biomass model is popular. Based on the forestry inventory data of larch plantation (Larix olgensis) in Jilin Province, we used non-linear seemly unrelated regression (NSUR) to estimate the parameters in two additive system of stand-level biomass equations, i.e., stand-level biomass equations including the stand variables and stand biomass equations including the biomass expansion factor (i.e., Model system 1 and Model system 2), listed the constant biomass expansion factor for larch plantation and compared the prediction accuracy of three stand-level biomass estimation methods. The results indicated that for two additive system of biomass equations, the adjusted coefficient of determination (R a 2 ) of the total and stem equations was more than 0.95, the root mean squared error (RMSE), the mean prediction error (MPE) and the mean absolute error (MAE) were smaller. The branch and foliage biomass equations were worse than total and stem biomass equations, and the adjusted coefficient of determination (R a 2 ) was less than 0.95. The prediction accuracy of a constant biomass expansion factor was relatively lower than the prediction accuracy of Model system 1 and Model system 2. Overall, although stand-level biomass equation including the biomass expansion factor belonged to the volume-derived biomass estimation method, and was different from the stand biomass equations including stand variables in essence, but the obtained prediction accuracy of the two methods was similar. The constant biomass expansion factor had the lower prediction accuracy, and was inappropriate. In addition, in order to make the model parameter estimation more effective, the established stand-level biomass equations should consider the additivity in a system of all tree component biomass and total biomass equations.

Identifying mechanical property parameters of planetary soil using in-situ data obtained from exploration rovers

NASA Astrophysics Data System (ADS)

Ding, Liang; Gao, Haibo; Liu, Zhen; Deng, Zongquan; Liu, Guangjun

2015-12-01

Identifying the mechanical property parameters of planetary soil based on terramechanics models using in-situ data obtained from autonomous planetary exploration rovers is both an important scientific goal and essential for control strategy optimization and high-fidelity simulations of rovers. However, identifying all the terrain parameters is a challenging task because of the nonlinear and coupling nature of the involved functions. Three parameter identification methods are presented in this paper to serve different purposes based on an improved terramechanics model that takes into account the effects of slip, wheel lugs, etc. Parameter sensitivity and coupling of the equations are analyzed, and the parameters are grouped according to their sensitivity to the normal force, resistance moment and drawbar pull. An iterative identification method using the original integral model is developed first. In order to realize real-time identification, the model is then simplified by linearizing the normal and shearing stresses to derive decoupled closed-form analytical equations. Each equation contains one or two groups of soil parameters, making step-by-step identification of all the unknowns feasible. Experiments were performed using six different types of single-wheels as well as a four-wheeled rover moving on planetary soil simulant. All the unknown model parameters were identified using the measured data and compared with the values obtained by conventional experiments. It is verified that the proposed iterative identification method provides improved accuracy, making it suitable for scientific studies of soil properties, whereas the step-by-step identification methods based on simplified models require less calculation time, making them more suitable for real-time applications. The models have less than 10% margin of error comparing with the measured results when predicting the interaction forces and moments using the corresponding identified parameters.

Asymptotic matching by the symbolic manipulator MACSYMA

NASA Technical Reports Server (NTRS)

Lo, L. L.

1985-01-01

The delegation of the labor of calculating higher-order terms in singular perturbation (SP) expansions to a computer by the use of MACSYMA is considered. The method of matched asymptotic expansions is studied in detail for two model SP problems: a model resembling the boundary layer equation with a small parameter multiplying the highest derivatives; and a turning-point problem. It is shown that MACSYMA has successfully performed the higher-order matching in both problems.

Progress Toward Improving Jet Noise Predictions in Hot Jets

NASA Technical Reports Server (NTRS)

Khavaran, Abbas; Kenzakowski, Donald C.

2007-01-01

An acoustic analogy methodology for improving noise predictions in hot round jets is presented. Past approaches have often neglected the impact of temperature fluctuations on the predicted sound spectral density, which could be significant for heated jets, and this has yielded noticeable acoustic under-predictions in such cases. The governing acoustic equations adopted here are a set of linearized, inhomogeneous Euler equations. These equations are combined into a single third order linear wave operator when the base flow is considered as a locally parallel mean flow. The remaining second-order fluctuations are regarded as the equivalent sources of sound and are modeled. It is shown that the hot jet effect may be introduced primarily through a fluctuating velocity/enthalpy term. Modeling this additional source requires specialized inputs from a RANS-based flowfield simulation. The information is supplied using an extension to a baseline two equation turbulence model that predicts total enthalpy variance in addition to the standard parameters. Preliminary application of this model to a series of unheated and heated subsonic jets shows significant improvement in the acoustic predictions at the 90 degree observer angle.

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

NASA Astrophysics Data System (ADS)

Waubke, Holger; Kasess, Christian H.

2016-11-01

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

Propagation of mechanical waves through a stochastic medium with spherical symmetry

NASA Astrophysics Data System (ADS)

Avendaño, Carlos G.; Reyes, J. Adrián

2018-01-01

We theoretically analyze the propagation of outgoing mechanical waves through an infinite isotropic elastic medium possessing spherical symmetry whose Lamé coefficients and density are spatial random functions characterized by well-defined statistical parameters. We derive the differential equation that governs the average displacement for a system whose properties depend on the radial coordinate. We show that such an equation is an extended version of the well-known Bessel differential equation whose perturbative additional terms contain coefficients that depend directly on the squared noise intensities and the autocorrelation lengths in an exponential decay fashion. We numerically solve the second order differential equation for several values of noise intensities and autocorrelation lengths and compare the corresponding displacement profiles with that of the exact analytic solution for the case of absent inhomogeneities.

The Effect of Multigrid Parameters in a 3D Heat Diffusion Equation

NASA Astrophysics Data System (ADS)

Oliveira, F. De; Franco, S. R.; Pinto, M. A. Villela

2018-02-01

The aim of this paper is to reduce the necessary CPU time to solve the three-dimensional heat diffusion equation using Dirichlet boundary conditions. The finite difference method (FDM) is used to discretize the differential equations with a second-order accuracy central difference scheme (CDS). The algebraic equations systems are solved using the lexicographical and red-black Gauss-Seidel methods, associated with the geometric multigrid method with a correction scheme (CS) and V-cycle. Comparisons are made between two types of restriction: injection and full weighting. The used prolongation process is the trilinear interpolation. This work is concerned with the study of the influence of the smoothing value (v), number of mesh levels (L) and number of unknowns (N) on the CPU time, as well as the analysis of algorithm complexity.

Partial compensation interferometry for measurement of surface parameter error of high-order aspheric surfaces

NASA Astrophysics Data System (ADS)

Hao, Qun; Li, Tengfei; Hu, Yao

2018-01-01

Surface parameters are the properties to describe the shape characters of aspheric surface, which mainly include vertex radius of curvature (VROC) and conic constant (CC). The VROC affects the basic properties, such as focal length of an aspheric surface, while the CC is the basis of classification for aspheric surface. The deviations of the two parameters are defined as surface parameter error (SPE). Precisely measuring SPE is critical for manufacturing and aligning aspheric surface. Generally, SPE of aspheric surface is measured directly by curvature fitting on the absolute profile measurement data from contact or non-contact testing. And most interferometry-based methods adopt null compensators or null computer-generated holograms to measure SPE. To our knowledge, there is no effective way to measure SPE of highorder aspheric surface with non-null interferometry. In this paper, based on the theory of slope asphericity and the best compensation distance (BCD) established in our previous work, we propose a SPE measurement method for high-order aspheric surface in partial compensation interferometry (PCI) system. In the procedure, firstly, we establish the system of two element equations by utilizing the SPE-caused BCD change and surface shape change. Then, we can simultaneously obtain the VROC error and CC error in PCI system by solving the equations. Simulations are made to verify the method, and the results show a high relative accuracy.

A bioconvection model for a squeezing flow of nanofluid between parallel plates in the presence of gyrotactic microorganisms

NASA Astrophysics Data System (ADS)

Bin-Mohsin, Bandar; Ahmed, Naveed; Adnan; Khan, Umar; Tauseef Mohyud-Din, Syed

2017-04-01

This article deals with the bioconvection flow in a parallel-plate channel. The plates are parallel and the flowing fluid is saturated with nanoparticles, and water is considered as a base fluid because microorganisms can survive only in water. A highly nonlinear and coupled system of partial differential equations presenting the model of bioconvection flow between parallel plates is reduced to a nonlinear and coupled system (nondimensional bioconvection flow model) of ordinary differential equations with the help of feasible nondimensional variables. In order to find the convergent solution of the system, a semi-analytical technique is utilized called variation of parameters method (VPM). Numerical solution is also computed and the Runge-Kutta scheme of fourth order is employed for this purpose. Comparison between these solutions has been made on the domain of interest and found to be in excellent agreement. Also, influence of various parameters has been discussed for the nondimensional velocity, temperature, concentration and density of the motile microorganisms both for suction and injection cases. Almost inconsequential influence of thermophoretic and Brownian motion parameters on the temperature field is observed. An interesting variation are inspected for the density of the motile microorganisms due to the varying bioconvection parameter in suction and injection cases. At the end, we make some concluding remarks in the light of this article.

f(R) gravity on non-linear scales: the post-Friedmann expansion and the vector potential

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

Thomas, D.B.; Bruni, M.; Koyama, K.

2015-07-01

Many modified gravity theories are under consideration in cosmology as the source of the accelerated expansion of the universe and linear perturbation theory, valid on the largest scales, has been examined in many of these models. However, smaller non-linear scales offer a richer phenomenology with which to constrain modified gravity theories. Here, we consider the Hu-Sawicki form of f(R) gravity and apply the post-Friedmann approach to derive the leading order equations for non-linear scales, i.e. the equations valid in the Newtonian-like regime. We reproduce the standard equations for the scalar field, gravitational slip and the modified Poisson equation in amore » coherent framework. In addition, we derive the equation for the leading order correction to the Newtonian regime, the vector potential. We measure this vector potential from f(R) N-body simulations at redshift zero and one, for two values of the f{sub R{sub 0}} parameter. We find that the vector potential at redshift zero in f(R) gravity can be close to 50% larger than in GR on small scales for |f{sub R{sub 0}}|=1.289 × 10{sup −5}, although this is less for larger scales, earlier times and smaller values of the f{sub R{sub 0}} parameter. Similarly to in GR, the small amplitude of this vector potential suggests that the Newtonian approximation is highly accurate for f(R) gravity, and also that the non-linear cosmological behaviour of f(R) gravity can be completely described by just the scalar potentials and the f(R) field.« less

Physical Intrepretation of Mathematically Invariant K(r,P) Type Equations of State for Hydrodynamically Driven Flow

NASA Astrophysics Data System (ADS)

Hrbek, George

2001-06-01

At SCCM Shock 99, Lie Group Theory was applied to the problem of temperature independent, hydrodynamic shock in a Birch-Murnaghan continuum. (1) Ratios of the group parameters were shown to be linked to the physical parameters specified in the second, third, and fourth order BM-EOS approximations. This effort has subsequently been extended to provide a general formalism for a wide class of mathematical forms (i.e., K(r,P)) of the equation of state. Variations in material expansion and resistance (i.e., counter pressure) are shown to be functions of compression and material variation ahead of the expanding front. Specific examples included the Birch-Murnaghan, Vinet, Brennan-Stacey, Shanker, Tait, Poirier, and Jones-Wilkins-Lee (JWL) forms. (2) With these ratios defined, the next step is to predict the behavior of these K(r,P) type solids. To do this, one must introduce the group ratios into a numerical simulation for the flow and generate the density, pressure, and particle velocity profiles as the shock moves through the material. This will allow the various equations of state, and their respective fitting coefficients, to be compared with experiments, and additionally, allow the empirical coefficients for these EOS forms to be adjusted accordingly. (1) Hrbek, G. M., Invariant Functional Forms For The Second, Third, And Fourth Order Birch-Murnaghan Equation of State For Materials Subject to Hydrodynamic Shock, Proceedings of the 11th American Physical Society Topical Group Meeting on Shock Compression of Condensed Matter (SCCM Shock 99), Snowbird, Utah (2) Hrbek, G. M., Invariant Functional Forms For K(r,P) Type Equations Of State For Hydrodynamically Driven Flows, Submitted to the 12th American Physical Society Topical Group Meeting on Shock Compression of Condensed Matter (SCCM Shock 01), Atlanta, Georgia

Using global sensitivity analysis to understand higher order interactions in complex models: an application of GSA on the Revised Universal Soil Loss Equation (RUSLE) to quantify model sensitivity and implications for ecosystem services management in Costa Rica

NASA Astrophysics Data System (ADS)

Fremier, A. K.; Estrada Carmona, N.; Harper, E.; DeClerck, F.

2011-12-01

Appropriate application of complex models to estimate system behavior requires understanding the influence of model structure and parameter estimates on model output. To date, most researchers perform local sensitivity analyses, rather than global, because of computational time and quantity of data produced. Local sensitivity analyses are limited in quantifying the higher order interactions among parameters, which could lead to incomplete analysis of model behavior. To address this concern, we performed a GSA on a commonly applied equation for soil loss - the Revised Universal Soil Loss Equation. USLE is an empirical model built on plot-scale data from the USA and the Revised version (RUSLE) includes improved equations for wider conditions, with 25 parameters grouped into six factors to estimate long-term plot and watershed scale soil loss. Despite RUSLE's widespread application, a complete sensitivity analysis has yet to be performed. In this research, we applied a GSA to plot and watershed scale data from the US and Costa Rica to parameterize the RUSLE in an effort to understand the relative importance of model factors and parameters across wide environmental space. We analyzed the GSA results using Random Forest, a statistical approach to evaluate parameter importance accounting for the higher order interactions, and used Classification and Regression Trees to show the dominant trends in complex interactions. In all GSA calculations the management of cover crops (C factor) ranks the highest among factors (compared to rain-runoff erosivity, topography, support practices, and soil erodibility). This is counter to previous sensitivity analyses where the topographic factor was determined to be the most important. The GSA finding is consistent across multiple model runs, including data from the US, Costa Rica, and a synthetic dataset of the widest theoretical space. The three most important parameters were: Mass density of live and dead roots found in the upper inch of soil (C factor), slope angle (L and S factor), and percentage of land area covered by surface cover (C factor). Our findings give further support to the importance of vegetation as a vital ecosystem service provider - soil loss reduction. Concurrent, progress is already been made in Costa Rica, where dam managers are moving forward on a Payment for Ecosystem Services scheme to help keep private lands forested and to improve crop management through targeted investments. Use of complex watershed models, such as RUSLE can help managers quantify the effect of specific land use changes. Moreover, effective land management of vegetation has other important benefits, such as bundled ecosystem services (e.g. pollination, habitat connectivity, etc) and improvements of communities' livelihoods.

Two-parameter asymptotics in magnetic Weyl calculus

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

Lein, Max

2010-12-15

This paper is concerned with small parameter asymptotics of magnetic quantum systems. In addition to a semiclassical parameter {epsilon}, the case of small coupling {lambda} to the magnetic vector potential naturally occurs in this context. Magnetic Weyl calculus is adapted to incorporate both parameters, at least one of which needs to be small. Of particular interest is the expansion of the Weyl product which can be used to expand the product of operators in a small parameter, a technique which is prominent to obtain perturbation expansions. Three asymptotic expansions for the magnetic Weyl product of two Hoermander class symbols aremore » proven as (i) {epsilon}<< 1 and {lambda}<< 1, (ii) {epsilon}<< 1 and {lambda}= 1, as well as (iii) {epsilon}= 1 and {lambda}<< 1. Expansions (i) and (iii) are impossible to obtain with ordinary Weyl calculus. Furthermore, I relate the results derived by ordinary Weyl calculus with those obtained with magnetic Weyl calculus by one- and two-parameter expansions. To show the power and versatility of magnetic Weyl calculus, I derive the semirelativistic Pauli equation as a scaling limit from the Dirac equation up to errors of fourth order in 1/c.« less

Regionalization of response routine parameters

NASA Astrophysics Data System (ADS)

Tøfte, Lena S.; Sultan, Yisak A.

2013-04-01

When area distributed hydrological models are to be calibrated or updated, fewer calibration parameters is of a considerable advantage. Based on, among others, Kirchner, we have developed a simple non-threshold response model for drainage in natural catchments, to be used in the gridded hydrological model ENKI. The new response model takes only the hydrogram into account, it has one state and two parameters, and is adapted to catchments that are dominated by terrain drainage. The method is based on the assumption that in catchments where precipitation, evaporation and snowmelt is neglect able, the discharge is entirely determined by the amount of stored water. It can then be characterized as a simple first-order nonlinear dynamical system, where the governing equations can be found directly from measured stream flow fluctuations. This means that the response in the catchment can be modelled by using hydrogram data where all data from periods with rain, snowmelt or evaporation is left out, and adjust these series to a two or three parameter equation. A large number of discharge series from catchments in different regions in Norway are analyzed, and parameters found for all the series. By combining the computed parameters and known catchments characteristics, we try to regionalize the parameters. Then the parameters in the response routine can easily be found also for ungauged catchments, from maps or data bases.

Unsteady Convection Flow and Heat Transfer over a Vertical Stretching Surface

PubMed Central

Cai, Wenli; Su, Ning; Liu, Xiangdong

2014-01-01

This paper investigates the effect of thermal radiation on unsteady convection flow and heat transfer over a vertical permeable stretching surface in porous medium, where the effects of temperature dependent viscosity and thermal conductivity are also considered. By using a similarity transformation, the governing time-dependent boundary layer equations for momentum and thermal energy are first transformed into coupled, non-linear ordinary differential equations with variable coefficients. Numerical solutions to these equations subject to appropriate boundary conditions are obtained by the numerical shooting technique with fourth-fifth order Runge-Kutta scheme. Numerical results show that as viscosity variation parameter increases both the absolute value of the surface friction coefficient and the absolute value of the surface temperature gradient increase whereas the temperature decreases slightly. With the increase of viscosity variation parameter, the velocity decreases near the sheet surface but increases far away from the surface of the sheet in the boundary layer. The increase in permeability parameter leads to the decrease in both the temperature and the absolute value of the surface friction coefficient, and the increase in both the velocity and the absolute value of the surface temperature gradient. PMID:25264737

Unsteady convection flow and heat transfer over a vertical stretching surface.

PubMed

Cai, Wenli; Su, Ning; Liu, Xiangdong

2014-01-01

This paper investigates the effect of thermal radiation on unsteady convection flow and heat transfer over a vertical permeable stretching surface in porous medium, where the effects of temperature dependent viscosity and thermal conductivity are also considered. By using a similarity transformation, the governing time-dependent boundary layer equations for momentum and thermal energy are first transformed into coupled, non-linear ordinary differential equations with variable coefficients. Numerical solutions to these equations subject to appropriate boundary conditions are obtained by the numerical shooting technique with fourth-fifth order Runge-Kutta scheme. Numerical results show that as viscosity variation parameter increases both the absolute value of the surface friction coefficient and the absolute value of the surface temperature gradient increase whereas the temperature decreases slightly. With the increase of viscosity variation parameter, the velocity decreases near the sheet surface but increases far away from the surface of the sheet in the boundary layer. The increase in permeability parameter leads to the decrease in both the temperature and the absolute value of the surface friction coefficient, and the increase in both the velocity and the absolute value of the surface temperature gradient.

Uncertainty propagation by using spectral methods: A practical application to a two-dimensional turbulence fluid model

NASA Astrophysics Data System (ADS)

Riva, Fabio; Milanese, Lucio; Ricci, Paolo

2017-10-01

To reduce the computational cost of the uncertainty propagation analysis, which is used to study the impact of input parameter variations on the results of a simulation, a general and simple to apply methodology based on decomposing the solution to the model equations in terms of Chebyshev polynomials is discussed. This methodology, based on the work by Scheffel [Am. J. Comput. Math. 2, 173-193 (2012)], approximates the model equation solution with a semi-analytic expression that depends explicitly on time, spatial coordinates, and input parameters. By employing a weighted residual method, a set of nonlinear algebraic equations for the coefficients appearing in the Chebyshev decomposition is then obtained. The methodology is applied to a two-dimensional Braginskii model used to simulate plasma turbulence in basic plasma physics experiments and in the scrape-off layer of tokamaks, in order to study the impact on the simulation results of the input parameter that describes the parallel losses. The uncertainty that characterizes the time-averaged density gradient lengths, time-averaged densities, and fluctuation density level are evaluated. A reasonable estimate of the uncertainty of these distributions can be obtained with a single reduced-cost simulation.

Scalar field as a Bose-Einstein condensate?

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

Castellanos, Elías; Escamilla-Rivera, Celia; Macías, Alfredo

We discuss the analogy between a classical scalar field with a self-interacting potential, in a curved spacetime described by a quasi-bounded state, and a trapped Bose-Einstein condensate. In this context, we compare the Klein-Gordon equation with the Gross-Pitaevskii equation. Moreover, the introduction of a curved background spacetime endows, in a natural way, an equivalence to the Gross-Pitaevskii equation with an explicit confinement potential. The curvature also induces a position dependent self-interaction parameter. We exploit this analogy by means of the Thomas-Fermi approximation, commonly used to describe the Bose-Einstein condensate, in order to analyze the quasi bound scalar field distribution surroundingmore » a black hole.« less

Traveling wave and exact solutions for the perturbed nonlinear Schrödinger equation with Kerr law nonlinearity

NASA Astrophysics Data System (ADS)

Akram, Ghazala; Mahak, Nadia

2018-06-01

The nonlinear Schrödinger equation (NLSE) with the aid of three order dispersion terms is investigated to find the exact solutions via the extended (G'/G2)-expansion method and the first integral method. Many exact traveling wave solutions, such as trigonometric, hyperbolic, rational, soliton and complex function solutions, are characterized with some free parameters of the problem studied. It is corroborated that the proposed techniques are manageable, straightforward and powerful tools to find the exact solutions of nonlinear partial differential equations (PDEs). Some figures are plotted to describe the propagation of traveling wave solutions expressed by the hyperbolic functions, trigonometric functions and rational functions.

Apparatus and method for determining solids circulation rate

DOEpatents

Ludlow, J Christopher [Morgantown, WV; Spenik, James L [Morgantown, WV

2012-02-14

The invention relates to a method of determining bed velocity and solids circulation rate in a standpipe experiencing a moving packed bed flow, such as the in the standpipe section of a circulating bed fluidized reactor The method utilizes in-situ measurement of differential pressure over known axial lengths of the standpipe in conjunction with in-situ gas velocity measurement for a novel application of Ergun equations allowing determination of standpipe void fraction and moving packed bed velocity. The method takes advantage of the moving packed bed property of constant void fraction in order to integrate measured parameters into simultaneous solution of Ergun-based equations and conservation of mass equations across multiple sections of the standpipe.

A mixed finite difference/Galerkin method for three-dimensional Rayleigh-Benard convection

NASA Technical Reports Server (NTRS)

Buell, Jeffrey C.

1988-01-01

A fast and accurate numerical method, for nonlinear conservation equation systems whose solutions are periodic in two of the three spatial dimensions, is presently implemented for the case of Rayleigh-Benard convection between two rigid parallel plates in the parameter region where steady, three-dimensional convection is known to be stable. High-order streamfunctions secure the reduction of the system of five partial differential equations to a system of only three. Numerical experiments are presented which verify both the expected convergence rates and the absolute accuracy of the method.

Freak waves in random oceanic sea states.

PubMed

Onorato, M; Osborne, A R; Serio, M; Bertone, S

2001-06-18

Freak waves are very large, rare events in a random ocean wave train. Here we study their generation in a random sea state characterized by the Joint North Sea Wave Project spectrum. We assume, to cubic order in nonlinearity, that the wave dynamics are governed by the nonlinear Schrödinger (NLS) equation. We show from extensive numerical simulations of the NLS equation how freak waves in a random sea state are more likely to occur for large values of the Phillips parameter alpha and the enhancement coefficient gamma. Comparison with linear simulations is also reported.

Influence of the electromagnetic parameters on the surface wave attenuation in thin absorbing layers

NASA Astrophysics Data System (ADS)

Li, Yinrui; Li, Dongmeng; Wang, Xian; Nie, Yan; Gong, Rongzhou

2018-05-01

This paper describes the relationships between the surface wave attenuation properties and the electromagnetic parameters of radar absorbing materials (RAMs). In order to conveniently obtain the attenuation constant of TM surface waves over a wide frequency range, the simplified dispersion equations in thin absorbing materials were firstly deduced. The validity of the proposed method was proved by comparing with the classical dispersion equations. Subsequently, the attenuation constants were calculated separately for the absorbing layers with hypothetical relative permittivity and permeability. It is found that the surface wave attenuation properties can be strongly tuned by the permeability of RAM. Meanwhile, the permittivity should be appropriate so as to maintain high cutoff frequency. The present work provides specific methods and designs to improve the attenuation performances of radar absorbing materials.

Criteria for the use of regression analysis for remote sensing of sediment and pollutants

NASA Technical Reports Server (NTRS)

Whitlock, C. H.; Kuo, C. Y.; Lecroy, S. R.

1982-01-01

An examination of limitations, requirements, and precision of the linear multiple-regression technique for quantification of marine environmental parameters is conducted. Both environmental and optical physics conditions have been defined for which an exact solution to the signal response equations is of the same form as the multiple regression equation. Various statistical parameters are examined to define a criteria for selection of an unbiased fit when upwelled radiance values contain error and are correlated with each other. Field experimental data are examined to define data smoothing requirements in order to satisfy the criteria of Daniel and Wood (1971). Recommendations are made concerning improved selection of ground-truth locations to maximize variance and to minimize physical errors associated with the remote sensing experiment.

Reference Ellipsoid and Geoid in Chronometric Geodesy

NASA Astrophysics Data System (ADS)

Kopeikin, Sergei M.

2016-02-01

Chronometric geodesy applies general relativity to study the problem of the shape of celestial bodies including the earth, and their gravitational field. The present paper discusses the relativistic problem of construction of a background geometric manifold that is used for describing a reference ellipsoid, geoid, the normal gravity field of the earth and for calculating geoid's undulation (height). We choose the perfect fluid with an ellipsoidal mass distribution uniformly rotating around a fixed axis as a source of matter generating the geometry of the background manifold through the Einstein equations. We formulate the post-Newtonian hydrodynamic equations of the rotating fluid to find out the set of algebraic equations defining the equipotential surface of the gravity field. In order to solve these equations we explicitly perform all integrals characterizing the interior gravitational potentials in terms of elementary functions depending on the parameters defining the shape of the body and the mass distribution. We employ the coordinate freedom of the equations to choose these parameters to make the shape of the rotating fluid configuration to be an ellipsoid of rotation. We derive expressions of the post-Newtonian mass and angular momentum of the rotating fluid as functions of the rotational velocity and the parameters of the ellipsoid including its bare density, eccentricity and semi-major axes. We formulate the post-Newtonian Pizzetti and Clairaut theorems that are used in geodesy to connect the parameters of the reference ellipsoid to the polar and equatorial values of force of gravity. We expand the post-Newtonian geodetic equations characterizing the reference ellipsoid into the Taylor series with respect to the eccentricity of the ellipsoid, and discuss the small-eccentricity approximation. Finally, we introduce the concept of relativistic geoid and its undulation with respect to the reference ellipsoid, and discuss how to calculate it in chronometric geodesy by making use of the anomalous gravity potential.

The Kadomtsev-Petviashvili equation under rapid forcing

NASA Astrophysics Data System (ADS)

Moroz, Irene M.

1997-06-01

We consider the initial value problem for the forced Kadomtsev-Petviashvili equation (KP) when the forcing is assumed to be fast compared to the evolution of the unforced equation. This suggests the introduction of two time scales. Solutions to the forced KP are sought by expanding the dependent variable in powers of a small parameter, which is inversely related to the forcing time scale. The unforced system describes weakly nonlinear, weakly dispersive, weakly two-dimensional wave propagation and is studied in two forms, depending upon whether gravity dominates surface tension or vice versa. We focus on the effect that the forcing has on the one-lump solution to the KPI equation (where surface tension dominates) and on the one- and two-line soliton solutions to the KPII equation (when gravity dominates). Solutions to second order in the expansion are computed analytically for some specific choices of the forcing function, which are related to the choice of initial data.

Roy-Steiner equations for pion-nucleon scattering

NASA Astrophysics Data System (ADS)

Ditsche, C.; Hoferichter, M.; Kubis, B.; Meißner, U.-G.

2012-06-01

Starting from hyperbolic dispersion relations, we derive a closed system of Roy-Steiner equations for pion-nucleon scattering that respects analyticity, unitarity, and crossing symmetry. We work out analytically all kernel functions and unitarity relations required for the lowest partial waves. In order to suppress the dependence on the high energy regime we also consider once- and twice-subtracted versions of the equations, where we identify the subtraction constants with subthreshold parameters. Assuming Mandelstam analyticity we determine the maximal range of validity of these equations. As a first step towards the solution of the full system we cast the equations for the π π to overline N N partial waves into the form of a Muskhelishvili-Omnès problem with finite matching point, which we solve numerically in the single-channel approximation. We investigate in detail the role of individual contributions to our solutions and discuss some consequences for the spectral functions of the nucleon electromagnetic form factors.

Manipulating matter rogue waves and breathers in Bose-Einstein condensates.

PubMed

Manikandan, K; Muruganandam, P; Senthilvelan, M; Lakshmanan, M

2014-12-01

We construct higher-order rogue wave solutions and breather profiles for the quasi-one-dimensional Gross-Pitaevskii equation with a time-dependent interatomic interaction and external trap through the similarity transformation technique. We consider three different forms of traps: (i) the time-independent expulsive trap, (ii) time-dependent monotonous trap, and (iii) time-dependent periodic trap. Our results show that when we change a parameter appearing in the time-independent or time-dependent trap the second- and third-order rogue waves transform into the first-order-like rogue waves. We also analyze the density profiles of breather solutions. Here we also show that the shapes of the breathers change when we tune the strength of the trap parameter. Our results may help to manage rogue waves experimentally in a BEC system.

Numerical studies of identification in nonlinear distributed parameter systems

NASA Technical Reports Server (NTRS)

Banks, H. T.; Lo, C. K.; Reich, Simeon; Rosen, I. G.

1989-01-01

An abstract approximation framework and convergence theory for the identification of first and second order nonlinear distributed parameter systems developed previously by the authors and reported on in detail elsewhere are summarized and discussed. The theory is based upon results for systems whose dynamics can be described by monotone operators in Hilbert space and an abstract approximation theorem for the resulting nonlinear evolution system. The application of the theory together with numerical evidence demonstrating the feasibility of the general approach are discussed in the context of the identification of a first order quasi-linear parabolic model for one dimensional heat conduction/mass transport and the identification of a nonlinear dissipation mechanism (i.e., damping) in a second order one dimensional wave equation. Computational and implementational considerations, in particular, with regard to supercomputing, are addressed.

Cookbook asymptotics for spiral and scroll waves in excitable media.

PubMed

Margerit, Daniel; Barkley, Dwight

2002-09-01

Algebraic formulas predicting the frequencies and shapes of waves in a reaction-diffusion model of excitable media are presented in the form of four recipes. The formulas themselves are based on a detailed asymptotic analysis (published elsewhere) of the model equations at leading order and first order in the asymptotic parameter. The importance of the first order contribution is stressed throughout, beginning with a discussion of the Fife limit, Fife scaling, and Fife regime. Recipes are given for spiral waves and detailed comparisons are presented between the asymptotic predictions and the solutions of the full reaction-diffusion equations. Recipes for twisted scroll waves with straight filaments are given and again comparisons are shown. The connection between the asymptotic results and filament dynamics is discussed, and one of the previously unknown coefficients in the theory of filament dynamics is evaluated in terms of its asymptotic expansion. (c) 2002 American Institute of Physics.

An arbitrary-order staggered time integrator for the linear acoustic wave equation

NASA Astrophysics Data System (ADS)

Lee, Jaejoon; Park, Hyunseo; Park, Yoonseo; Shin, Changsoo

2018-02-01

We suggest a staggered time integrator whose order of accuracy can arbitrarily be extended to solve the linear acoustic wave equation. A strategy to select the appropriate order of accuracy is also proposed based on the error analysis that quantitatively predicts the truncation error of the numerical solution. This strategy not only reduces the computational cost several times, but also allows us to flexibly set the modelling parameters such as the time step length, grid interval and P-wave speed. It is demonstrated that the proposed method can almost eliminate temporal dispersive errors during long term simulations regardless of the heterogeneity of the media and time step lengths. The method can also be successfully applied to the source problem with an absorbing boundary condition, which is frequently encountered in the practical usage for the imaging algorithms or the inverse problems.

Cookbook asymptotics for spiral and scroll waves in excitable media

NASA Astrophysics Data System (ADS)

Margerit, Daniel; Barkley, Dwight

2002-09-01

Algebraic formulas predicting the frequencies and shapes of waves in a reaction-diffusion model of excitable media are presented in the form of four recipes. The formulas themselves are based on a detailed asymptotic analysis (published elsewhere) of the model equations at leading order and first order in the asymptotic parameter. The importance of the first order contribution is stressed throughout, beginning with a discussion of the Fife limit, Fife scaling, and Fife regime. Recipes are given for spiral waves and detailed comparisons are presented between the asymptotic predictions and the solutions of the full reaction-diffusion equations. Recipes for twisted scroll waves with straight filaments are given and again comparisons are shown. The connection between the asymptotic results and filament dynamics is discussed, and one of the previously unknown coefficients in the theory of filament dynamics is evaluated in terms of its asymptotic expansion.

Fractional Order Two-Temperature Dual-Phase-Lag Thermoelasticity with Variable Thermal Conductivity

PubMed Central

Mallik, Sadek Hossain; Kanoria, M.

2014-01-01

A new theory of two-temperature generalized thermoelasticity is constructed in the context of a new consideration of dual-phase-lag heat conduction with fractional orders. The theory is then adopted to study thermoelastic interaction in an isotropic homogenous semi-infinite generalized thermoelastic solids with variable thermal conductivity whose boundary is subjected to thermal and mechanical loading. The basic equations of the problem have been written in the form of a vector-matrix differential equation in the Laplace transform domain, which is then solved by using a state space approach. The inversion of Laplace transforms is computed numerically using the method of Fourier series expansion technique. The numerical estimates of the quantities of physical interest are obtained and depicted graphically. Some comparisons of the thermophysical quantities are shown in figures to study the effects of the variable thermal conductivity, temperature discrepancy, and the fractional order parameter. PMID:27419210

Master equation and two heat reservoirs.

PubMed

Trimper, Steffen

2006-11-01

A simple spin-flip process is analyzed under the presence of two heat reservoirs. While one flip process is triggered by a bath at temperature T, the inverse process is activated by a bath at a different temperature T'. The situation can be described by using a master equation approach in a second quantized Hamiltonian formulation. The stationary solution leads to a generalized Fermi-Dirac distribution with an effective temperature Te. Likewise the relaxation time is given in terms of Te. Introducing a spin representation we perform a Landau expansion for the averaged spin as order parameter and consequently, a free energy functional can be derived. Owing to the two reservoirs the model is invariant with respect to a simultaneous change sigma<-->-sigma and T<-->T'. This symmetry generates a third order term in the free energy which gives rise a dynamically induced first order transition.

An improved numerical method for the kernel density functional estimation of disperse flow

NASA Astrophysics Data System (ADS)

Smith, Timothy; Ranjan, Reetesh; Pantano, Carlos

2014-11-01

We present an improved numerical method to solve the transport equation for the one-point particle density function (pdf), which can be used to model disperse flows. The transport equation, a hyperbolic partial differential equation (PDE) with a source term, is derived from the Lagrangian equations for a dilute particle system by treating position and velocity as state-space variables. The method approximates the pdf by a discrete mixture of kernel density functions (KDFs) with space and time varying parameters and performs a global Rayleigh-Ritz like least-square minimization on the state-space of velocity. Such an approximation leads to a hyperbolic system of PDEs for the KDF parameters that cannot be written completely in conservation form. This system is solved using a numerical method that is path-consistent, according to the theory of non-conservative hyperbolic equations. The resulting formulation is a Roe-like update that utilizes the local eigensystem information of the linearized system of PDEs. We will present the formulation of the base method, its higher-order extension and further regularization to demonstrate that the method can predict statistics of disperse flows in an accurate, consistent and efficient manner. This project was funded by NSF Project NSF-DMS 1318161.

3-D Forward modeling of Induced Polarization Effects of Transient Electromagnetic Method

NASA Astrophysics Data System (ADS)

Wu, Y.; Ji, Y.; Guan, S.; Li, D.; Wang, A.

2017-12-01

In transient electromagnetic (TEM) detection, Induced polarization (IP) effects are so important that they cannot be ignored. The authors simulate the three-dimensional (3-D) induced polarization effects in time-domain directly by applying the finite-difference time-domain method (FDTD) based on Cole-Cole model. Due to the frequency dispersion characteristics of the electrical conductivity, the computations of convolution in the generalized Ohm's law of fractional order system makes the forward modeling particularly complicated. Firstly, we propose a method to approximate the fractional order function of Cole-Cole model using a lower order rational transfer function based on error minimum theory in the frequency domain. In this section, two auxiliary variables are introduced to transform nonlinear least square fitting problem of the fractional order system into a linear programming problem, thus avoiding having to solve a system of equations and nonlinear problems. Secondly, the time-domain expression of Cole-Cole model is obtained by using Inverse Laplace transform. Then, for the calculation of Ohm's law, we propose an e-index auxiliary equation of conductivity to transform the convolution to non-convolution integral; in this section, the trapezoid rule is applied to compute the integral. We then substitute the recursion equation into Maxwell's equations to derive the iterative equations of electromagnetic field using the FDTD method. Finally, we finish the stimulation of 3-D model and evaluate polarization parameters. The results are compared with those obtained from the digital filtering solution of the analytical equation in the homogeneous half space, as well as with the 3-D model results from the auxiliary ordinary differential equation method (ADE). Good agreements are obtained across the three methods. In terms of the 3-D model, the proposed method has higher efficiency and lower memory requirements as execution times and memory usage were reduced by 20% compared with ADE method.

Spatio-temporal dynamics induced by competing instabilities in two asymmetrically coupled nonlinear evolution equations.

PubMed

Schüler, D; Alonso, S; Torcini, A; Bär, M

2014-12-01

Pattern formation often occurs in spatially extended physical, biological, and chemical systems due to an instability of the homogeneous steady state. The type of the instability usually prescribes the resulting spatio-temporal patterns and their characteristic length scales. However, patterns resulting from the simultaneous occurrence of instabilities cannot be expected to be simple superposition of the patterns associated with the considered instabilities. To address this issue, we design two simple models composed by two asymmetrically coupled equations of non-conserved (Swift-Hohenberg equations) or conserved (Cahn-Hilliard equations) order parameters with different characteristic wave lengths. The patterns arising in these systems range from coexisting static patterns of different wavelengths to traveling waves. A linear stability analysis allows to derive a two parameter phase diagram for the studied models, in particular, revealing for the Swift-Hohenberg equations, a co-dimension two bifurcation point of Turing and wave instability and a region of coexistence of stationary and traveling patterns. The nonlinear dynamics of the coupled evolution equations is investigated by performing accurate numerical simulations. These reveal more complex patterns, ranging from traveling waves with embedded Turing patterns domains to spatio-temporal chaos, and a wide hysteretic region, where waves or Turing patterns coexist. For the coupled Cahn-Hilliard equations the presence of a weak coupling is sufficient to arrest the coarsening process and to lead to the emergence of purely periodic patterns. The final states are characterized by domains with a characteristic length, which diverges logarithmically with the coupling amplitude.

Interpreting experimental data on egg production--applications of dynamic differential equations.

PubMed

France, J; Lopez, S; Kebreab, E; Dijkstra, J

2013-09-01

This contribution focuses on applying mathematical models based on systems of ordinary first-order differential equations to synthesize and interpret data from egg production experiments. Models based on linear systems of differential equations are contrasted with those based on nonlinear systems. Regression equations arising from analytical solutions to linear compartmental schemes are considered as candidate functions for describing egg production curves, together with aspects of parameter estimation. Extant candidate functions are reviewed, a role for growth functions such as the Gompertz equation suggested, and a function based on a simple new model outlined. Structurally, the new model comprises a single pool with an inflow and an outflow. Compartmental simulation models based on nonlinear systems of differential equations, and thus requiring numerical solution, are next discussed, and aspects of parameter estimation considered. This type of model is illustrated in relation to development and evaluation of a dynamic model of calcium and phosphorus flows in layers. The model consists of 8 state variables representing calcium and phosphorus pools in the crop, stomachs, plasma, and bone. The flow equations are described by Michaelis-Menten or mass action forms. Experiments that measure Ca and P uptake in layers fed different calcium concentrations during shell-forming days are used to evaluate the model. In addition to providing a useful management tool, such a simulation model also provides a means to evaluate feeding strategies aimed at reducing excretion of potential pollutants in poultry manure to the environment.

Modeling tracer transport in randomly heterogeneous porous media by nonlocal moment equations: Anomalous transport

NASA Astrophysics Data System (ADS)

Morales-Casique, E.; Lezama-Campos, J. L.; Guadagnini, A.; Neuman, S. P.

2013-05-01

Modeling tracer transport in geologic porous media suffers from the corrupt characterization of the spatial distribution of hydrogeologic properties of the system and the incomplete knowledge of processes governing transport at multiple scales. Representations of transport dynamics based on a Fickian model of the kind considered in the advection-dispersion equation (ADE) fail to capture (a) the temporal variation associated with the rate of spreading of a tracer, and (b) the distribution of early and late arrival times which are often observed in field and/or laboratory scenarios and are considered as the signature of anomalous transport. Elsewhere we have presented exact stochastic moment equations to model tracer transport in randomly heterogeneous aquifers. We have also developed a closure scheme which enables one to provide numerical solutions of such moment equations at different orders of approximations. The resulting (ensemble) average and variance of concentration fields were found to display a good agreement against Monte Carlo - based simulation results for mildly heterogeneous (or well-conditioned strongly heterogeneous) media. Here we explore the ability of the moment equations approach to describe the distribution of early arrival times and late time tailing effects which can be observed in Monte-Carlo based breakthrough curves (BTCs) of the (ensemble) mean concentration. We show that BTCs of mean resident concentration calculated at a fixed space location through higher-order approximations of moment equations display long tailing features of the kind which is typically associated with anomalous transport behavior and are not represented by an ADE model with constant dispersive parameter, such as the zero-order approximation.

Modulation stability and dispersive optical soliton solutions of higher order nonlinear Schrödinger equation and its applications in mono-mode optical fibers

NASA Astrophysics Data System (ADS)

Arshad, Muhammad; Seadawy, Aly R.; Lu, Dianchen

2018-01-01

In mono-mode optical fibers, the higher order non-linear Schrödinger equation (NLSE) describes the propagation of enormously short light pulses. We constructed optical solitons and, solitary wave solutions of higher order NLSE mono-mode optical fibers via employing modified extended mapping method which has important applications in Mathematics and physics. Furthermore, the formation conditions are also given on parameters in which optical bright and dark solitons can exist for this media. The moment of the obtained solutions are also given graphically, that helps to realize the physical phenomena's of this model. The modulation instability analysis is utilized to discuss the model stability, which verifies that all obtained solutions are exact and stable. Many other such types of models arising in applied sciences can also be solved by this reliable, powerful and effective method. The method can also be functional to other sorts of higher order nonlinear problems in contemporary areas of research.

Thermal nanostructure: An order parameter multiscale ensemble approach

NASA Astrophysics Data System (ADS)

Cheluvaraja, S.; Ortoleva, P.

2010-02-01

Deductive all-atom multiscale techniques imply that many nanosystems can be understood in terms of the slow dynamics of order parameters that coevolve with the quasiequilibrium probability density for rapidly fluctuating atomic configurations. The result of this multiscale analysis is a set of stochastic equations for the order parameters whose dynamics is driven by thermal-average forces. We present an efficient algorithm for sampling atomistic configurations in viruses and other supramillion atom nanosystems. This algorithm allows for sampling of a wide range of configurations without creating an excess of high-energy, improbable ones. It is implemented and used to calculate thermal-average forces. These forces are then used to search the free-energy landscape of a nanosystem for deep minima. The methodology is applied to thermal structures of Cowpea chlorotic mottle virus capsid. The method has wide applicability to other nanosystems whose properties are described by the CHARMM or other interatomic force field. Our implementation, denoted SIMNANOWORLD™, achieves calibration-free nanosystem modeling. Essential atomic-scale detail is preserved via a quasiequilibrium probability density while overall character is provided via predicted values of order parameters. Applications from virology to the computer-aided design of nanocapsules for delivery of therapeutic agents and of vaccines for nonenveloped viruses are envisioned.

Analysis of nonlocal neural fields for both general and gamma-distributed connectivities

NASA Astrophysics Data System (ADS)

Hutt, Axel; Atay, Fatihcan M.

2005-04-01

This work studies the stability of equilibria in spatially extended neuronal ensembles. We first derive the model equation from statistical properties of the neuron population. The obtained integro-differential equation includes synaptic and space-dependent transmission delay for both general and gamma-distributed synaptic connectivities. The latter connectivity type reveals infinite, finite, and vanishing self-connectivities. The work derives conditions for stationary and nonstationary instabilities for both kernel types. In addition, a nonlinear analysis for general kernels yields the order parameter equation of the Turing instability. To compare the results to findings for partial differential equations (PDEs), two typical PDE-types are derived from the examined model equation, namely the general reaction-diffusion equation and the Swift-Hohenberg equation. Hence, the discussed integro-differential equation generalizes these PDEs. In the case of the gamma-distributed kernels, the stability conditions are formulated in terms of the mean excitatory and inhibitory interaction ranges. As a novel finding, we obtain Turing instabilities in fields with local inhibition-lateral excitation, while wave instabilities occur in fields with local excitation and lateral inhibition. Numerical simulations support the analytical results.

GLASS VISCOSITY AS A FUNCTION OF TEMPERATURE AND COMPOSITION: A MODEL BASED ON ADAM-GIBBS EQUATION

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

Hrma, Pavel R.

2008-07-01

Within the temperature range and composition region of processing and product forming, the viscosity of commercial and waste glasses spans over 12 orders of magnitude. This paper shows that a generalized Adam-Gibbs relationship reasonably approximates the real behavior of glasses with four temperature-independent parameters of which two are linear functions of the composition vector. The equation is subjected to two constraints, one requiring that the viscosity-temperature relationship approaches the Arrhenius function at high temperatures with a composition-independent pre-exponential factor and the other that the viscosity value is independent of composition at the glass-transition temperature. Several sets of constant coefficients weremore » obtained by fitting the generalized Adam-Gibbs equation to data of two glass families: float glass and Hanford waste glass. Other equations (the Vogel-Fulcher-Tammann equation, original and modified, the Avramov equation, and the Douglass-Doremus equation) were fitted to float glass data series and compared with the Adam-Gibbs equation, showing that Adam-Gibbs glass appears an excellent approximation of real glasses even as compared with other candidate constitutive relations.« less

A Smoluchowski model of crystallization dynamics of small colloidal clusters

NASA Astrophysics Data System (ADS)

Beltran-Villegas, Daniel J.; Sehgal, Ray M.; Maroudas, Dimitrios; Ford, David M.; Bevan, Michael A.

2011-10-01

We investigate the dynamics of colloidal crystallization in a 32-particle system at a fixed value of interparticle depletion attraction that produces coexisting fluid and solid phases. Free energy landscapes (FELs) and diffusivity landscapes (DLs) are obtained as coefficients of 1D Smoluchowski equations using as order parameters either the radius of gyration or the average crystallinity. FELs and DLs are estimated by fitting the Smoluchowski equations to Brownian dynamics (BD) simulations using either linear fits to locally initiated trajectories or global fits to unbiased trajectories using Bayesian inference. The resulting FELs are compared to Monte Carlo Umbrella Sampling results. The accuracy of the FELs and DLs for modeling colloidal crystallization dynamics is evaluated by comparing mean first-passage times from BD simulations with analytical predictions using the FEL and DL models. While the 1D models accurately capture dynamics near the free energy minimum fluid and crystal configurations, predictions near the transition region are not quantitatively accurate. A preliminary investigation of ensemble averaged 2D order parameter trajectories suggests that 2D models are required to capture crystallization dynamics in the transition region.

A new method for distortion magnetic field compensation of a geomagnetic vector measurement system

NASA Astrophysics Data System (ADS)

Liu, Zhongyan; Pan, Mengchun; Tang, Ying; Zhang, Qi; Geng, Yunling; Wan, Chengbiao; Chen, Dixiang; Tian, Wugang

2016-12-01

The geomagnetic vector measurement system mainly consists of three-axis magnetometer and an INS (inertial navigation system), which have many ferromagnetic parts on them. The magnetometer is always distorted by ferromagnetic parts and other electric equipments such as INS and power circuit module within the system, which can lead to geomagnetic vector measurement error of thousands of nT. Thus, the geomagnetic vector measurement system has to be compensated in order to guarantee the measurement accuracy. In this paper, a new distortion magnetic field compensation method is proposed, in which a permanent magnet with different relative positions is used to change the ambient magnetic field to construct equations of the error model parameters, and the parameters can be accurately estimated by solving linear equations. In order to verify effectiveness of the proposed method, the experiment is conducted, and the results demonstrate that, after compensation, the components errors of measured geomagnetic field are reduced significantly. It demonstrates that the proposed method can effectively improve the accuracy of the geomagnetic vector measurement system.

Kinetics modelling of color deterioration during thermal processing of tomato paste with the use of response surface methodology

NASA Astrophysics Data System (ADS)

Ganje, Mohammad; Jafari, Seid Mahdi; Farzaneh, Vahid; Malekjani, Narges

2018-06-01

To study the kinetics of color degradation, the tomato paste was designed to be processed at three different temperatures including 60, 70 and 80 °C for 25, 50, 75 and 100 min. a/b ratio, total color difference, saturation index and hue angle were calculated with the use of three main color parameters including L (lightness), a (redness-greenness) and b (yellowness-blueness) values. Kinetics of color degradation was developed by Arrhenius equation and the alterations were modelled with the use of response surface methodology (RSM). It was detected that all of the studied responses followed a first order reaction kinetics with an exception in TCD parameter (zeroth order). TCD and a/b respectively with the highest and lowest activation energy presented the highest sensitivity to the temperature alterations. The maximum and minimum rates of alterations were observed by TCD and b parameters, respectively. It was obviously determined that all of the studied parameters (responses) were affected by the selected independent parameters.

The Magnus problem in Rodrigues-Hamilton parameters

NASA Astrophysics Data System (ADS)

Koshliakov, V. N.

1984-04-01

The formalism of Rodrigues-Hamilton parameters is applied to the Magnus problem related to the systematic drift of a gimbal-mounted astatic gyroscope due to the nutational vibration of the main axis of the rotor. It is shown that the use of the above formalism makes it possible to limit the analysis to a consideration of a linear system of differential equations written in perturbed values of Rodrigues-Hamilton parameters. A refined formula for the drift of the main axis of the gyroscope rotor is obtained, and an estimation is made of the effect of the truncation of higher-order terms.

Hydrolysis rate constants and activation parameters for phosphate- and phosphonate-bridged phthalonitrile monomers under acid, neutral and alkali conditions.

PubMed

Belsky, Kirill S; Sulimov, Artem V; Bulgakov, Boris A; Babkin, Alexandr V; Kepman, Alexey V

2017-08-01

Hydrolysis data for Bis(3-(3,4-dicyanophenoxy)phenyl) phenyl phosphate and Bis(3-(3,4-dicyanophenoxy)phenyl) phenylphosphonate under pH 4, 7 and 10 are presented. Conversion/time plots collected by HPLC analysis, typical chromatograms and NMR spectra of the reactions products are given. Pseudo-first order rate constants are determined for both substrates at 25, 50 and 80 °C. Activation parameters were calculated from Arrhenius equation.

Global dynamics of oscillator populations under common noise

NASA Astrophysics Data System (ADS)

Braun, W.; Pikovsky, A.; Matias, M. A.; Colet, P.

2012-07-01

Common noise acting on a population of identical oscillators can synchronize them. We develop a description of this process which is not limited to the states close to synchrony, but provides a global picture of the evolution of the ensembles. The theory is based on the Watanabe-Strogatz transformation, allowing us to obtain closed stochastic equations for the global variables. We show that at the initial stage, the order parameter grows linearly in time, while at the later stages the convergence to synchrony is exponentially fast. Furthermore, we extend the theory to nonidentical ensembles with the Lorentzian distribution of natural frequencies and determine the stationary values of the order parameter in dependence on driving noise and mismatch.

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

NASA Technical Reports Server (NTRS)

Izmailov, Alexander; Myerson, Allan S.

1993-01-01

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

A frequency domain global parameter estimation method for multiple reference frequency response measurements

NASA Astrophysics Data System (ADS)

Shih, C. Y.; Tsuei, Y. G.; Allemang, R. J.; Brown, D. L.

1988-10-01

A method of using the matrix Auto-Regressive Moving Average (ARMA) model in the Laplace domain for multiple-reference global parameter identification is presented. This method is particularly applicable to the area of modal analysis where high modal density exists. The method is also applicable when multiple reference frequency response functions are used to characterise linear systems. In order to facilitate the mathematical solution, the Forsythe orthogonal polynomial is used to reduce the ill-conditioning of the formulated equations and to decouple the normal matrix into two reduced matrix blocks. A Complex Mode Indicator Function (CMIF) is introduced, which can be used to determine the proper order of the rational polynomials.

Extension of the KLI approximation toward the exact optimized effective potential.

PubMed

Iafrate, G J; Krieger, J B

2013-03-07

The integral equation for the optimized effective potential (OEP) is utilized in a compact form from which an accurate OEP solution for the spin-unrestricted exchange-correlation potential, Vxcσ, is obtained for any assumed orbital-dependent exchange-correlation energy functional. The method extends beyond the Krieger-Li-Iafrate (KLI) approximation toward the exact OEP result. The compact nature of the OEP equation arises by replacing the integrals involving the Green's function terms in the traditional OEP equation by an equivalent first-order perturbation theory wavefunction often referred to as the "orbital shift" function. Significant progress is then obtained by solving the equation for the first order perturbation theory wavefunction by use of Dalgarno functions which are determined from well known methods of partial differential equations. The use of Dalgarno functions circumvents the need to explicitly address the Green's functions and the associated problems with "sum over states" numerics; as well, the Dalgarno functions provide ease in dealing with inherent singularities arising from the origin and the zeros of the occupied orbital wavefunctions. The Dalgarno approach for finding a solution to the OEP equation is described herein, and a detailed illustrative example is presented for the special case of a spherically symmetric exchange-correlation potential. For the case of spherical symmetry, the relevant Dalgarno function is derived by direct integration of the appropriate radial equation while utilizing a user friendly method which explicitly treats the singular behavior at the origin and at the nodal singularities arising from the zeros of the occupied states. The derived Dalgarno function is shown to be an explicit integral functional of the exact OEP Vxcσ, thus allowing for the reduction of the OEP equation to a self-consistent integral equation for the exact exchange-correlation potential; the exact solution to this integral equation can be determined by iteration with the natural zeroth order correction given by the KLI exchange-correlation potential. Explicit analytic results are provided to illustrate the first order iterative correction beyond the KLI approximation. The derived correction term to the KLI potential explicitly involves spatially weighted products of occupied orbital densities in any assumed orbital-dependent exchange-correlation energy functional; as well, the correction term is obtained with no adjustable parameters. Moreover, if the equation for the exact optimized effective potential is further iterated, one can obtain the OEP as accurately as desired.

Extension of the KLI approximation toward the exact optimized effective potential

NASA Astrophysics Data System (ADS)

Iafrate, G. J.; Krieger, J. B.

2013-03-01

The integral equation for the optimized effective potential (OEP) is utilized in a compact form from which an accurate OEP solution for the spin-unrestricted exchange-correlation potential, Vxcσ, is obtained for any assumed orbital-dependent exchange-correlation energy functional. The method extends beyond the Krieger-Li-Iafrate (KLI) approximation toward the exact OEP result. The compact nature of the OEP equation arises by replacing the integrals involving the Green's function terms in the traditional OEP equation by an equivalent first-order perturbation theory wavefunction often referred to as the "orbital shift" function. Significant progress is then obtained by solving the equation for the first order perturbation theory wavefunction by use of Dalgarno functions which are determined from well known methods of partial differential equations. The use of Dalgarno functions circumvents the need to explicitly address the Green's functions and the associated problems with "sum over states" numerics; as well, the Dalgarno functions provide ease in dealing with inherent singularities arising from the origin and the zeros of the occupied orbital wavefunctions. The Dalgarno approach for finding a solution to the OEP equation is described herein, and a detailed illustrative example is presented for the special case of a spherically symmetric exchange-correlation potential. For the case of spherical symmetry, the relevant Dalgarno function is derived by direct integration of the appropriate radial equation while utilizing a user friendly method which explicitly treats the singular behavior at the origin and at the nodal singularities arising from the zeros of the occupied states. The derived Dalgarno function is shown to be an explicit integral functional of the exact OEP Vxcσ, thus allowing for the reduction of the OEP equation to a self-consistent integral equation for the exact exchange-correlation potential; the exact solution to this integral equation can be determined by iteration with the natural zeroth order correction given by the KLI exchange-correlation potential. Explicit analytic results are provided to illustrate the first order iterative correction beyond the KLI approximation. The derived correction term to the KLI potential explicitly involves spatially weighted products of occupied orbital densities in any assumed orbital-dependent exchange-correlation energy functional; as well, the correction term is obtained with no adjustable parameters. Moreover, if the equation for the exact optimized effective potential is further iterated, one can obtain the OEP as accurately as desired.

Stratified wakes, the high Froude number approximation, and potential flow

NASA Astrophysics Data System (ADS)

Vasholz, David P.

2011-12-01

Properties of a steady wake generated by a body moving uniformly at constant depth through a stratified fluid are studied as a function of two parameters inserted into the linearized equations of motion. The first parameter, μ, multiplies the along-track gradient term in the source equation. When formal solutions for an arbitrary buoyancy frequency profile are written as eigenfunction expansions, one finds that the limit μ → 0 corresponds to a high Froude number approximation accompanied by a substantial reduction in the complexity of the calculation. For μ = 1, upstream effects are present and the eigenvalues correspond to critical speeds above which transverse waves disappear for any given mode. For sufficiently high modes, the high Froude number approximation is valid. The second tracer multiplies the square of the buoyancy frequency term in the linearized conservation of mass equation and enables direct comparisons with the limit of potential flow. Detailed results are given for the simplest possible profile, in which the buoyancy frequency is independent of depth; emphasis is placed upon quantities that can, in principle, be experimentally measured in a laboratory experiment. The vertical displacement field is written in terms of a stratified wake form factor {{H}} , which is the sum of a wavelike contribution that is non-zero downstream and an evanescent contribution that appears symmetrically upstream and downstream. First- and second-order cross-track moments of {{H}} are analyzed. First-order results predict enhanced upstream vertical displacements. Second-order results expand upon previous predictions of wavelike resonances and also predict evanescent resonance effects.

Spherically symmetric Einstein-aether perfect fluid models

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

Coley, Alan A.; Latta, Joey; Leon, Genly

We investigate spherically symmetric cosmological models in Einstein-aether theory with a tilted (non-comoving) perfect fluid source. We use a 1+3 frame formalism and adopt the comoving aether gauge to derive the evolution equations, which form a well-posed system of first order partial differential equations in two variables. We then introduce normalized variables. The formalism is particularly well-suited for numerical computations and the study of the qualitative properties of the models, which are also solutions of Horava gravity. We study the local stability of the equilibrium points of the resulting dynamical system corresponding to physically realistic inhomogeneous cosmological models and astrophysicalmore » objects with values for the parameters which are consistent with current constraints. In particular, we consider dust models in (β−) normalized variables and derive a reduced (closed) evolution system and we obtain the general evolution equations for the spatially homogeneous Kantowski-Sachs models using appropriate bounded normalized variables. We then analyse these models, with special emphasis on the future asymptotic behaviour for different values of the parameters. Finally, we investigate static models for a mixture of a (necessarily non-tilted) perfect fluid with a barotropic equations of state and a scalar field.« less

Existence and numerical simulation of periodic traveling wave solutions to the Casimir equation for the Ito system

NASA Astrophysics Data System (ADS)

Abbasbandy, S.; Van Gorder, R. A.; Hajiketabi, M.; Mesrizadeh, M.

2015-10-01

We consider traveling wave solutions to the Casimir equation for the Ito system (a two-field extension of the KdV equation). These traveling waves are governed by a nonlinear initial value problem with an interesting nonlinearity (which actually amplifies in magnitude as the size of the solution becomes small). The nonlinear problem is parameterized by two initial constant values, and we demonstrate that the existence of solutions is strongly tied to these parameter values. For our interests, we are concerned with positive, bounded, periodic wave solutions. We are able to classify parameter regimes which admit such solutions in full generality, thereby obtaining a nice existence result. Using the existence result, we are then able to numerically simulate the positive, bounded, periodic solutions. We elect to employ a group preserving scheme in order to numerically study these solutions, and an outline of this approach is provided. The numerical simulations serve to illustrate the properties of these solutions predicted analytically through the existence result. Physically, these results demonstrate the existence of a type of space-periodic structure in the Casimir equation for the Ito model, which propagates as a traveling wave.

Nonlinear Waves In A Stenosed Elastic Tube Filled With Viscous Fluid: Forced Perturbed Korteweg-De Vries Equation

NASA Astrophysics Data System (ADS)

Gaik*, Tay Kim; Demiray, Hilmi; Tiong, Ong Chee

In the present work, treating the artery as a prestressed thin-walled and long circularly cylindrical elastic tube with a mild symmetrical stenosis and the blood as an incompressible Newtonian fluid, we have studied the pro pagation of weakly nonlinear waves in such a composite medium, in the long wave approximation, by use of the reductive perturbation method. By intro ducing a set of stretched coordinates suitable for the boundary value type of problems and expanding the field variables into asymptotic series of the small-ness parameter of nonlinearity and dispersion, we obtained a set of nonlinear differential equations governing the terms at various order. By solving these nonlinear differential equations, we obtained the forced perturbed Korteweg-de Vries equation with variable coefficient as the nonlinear evolution equation. By use of the coordinate transformation, it is shown that this type of nonlinear evolution equation admits a progressive wave solution with variable wave speed.

Pure quasi-P-wave calculation in transversely isotropic media using a hybrid method

NASA Astrophysics Data System (ADS)

Wu, Zedong; Liu, Hongwei; Alkhalifah, Tariq

2018-07-01

The acoustic approximation for anisotropic media is widely used in current industry imaging and inversion algorithms mainly because Pwaves constitute the majority of the energy recorded in seismic exploration. The resulting acoustic formulae tend to be simpler, resulting in more efficient implementations, and depend on fewer medium parameters. However, conventional solutions of the acoustic wave equation with higher-order derivatives suffer from shear wave artefacts. Thus, we derive a new acoustic wave equation for wave propagation in transversely isotropic (TI) media, which is based on a partially separable approximation of the dispersion relation for TI media and free of shear wave artefacts. Even though our resulting equation is not a partial differential equation, it is still a linear equation. Thus, we propose to implement this equation efficiently by combining the finite difference approximation with spectral evaluation of the space-independent parts. The resulting algorithm provides solutions without the constraint ɛ ≥ δ. Numerical tests demonstrate the effectiveness of the approach.

Gyrokinetic equations and full f solution method based on Dirac's constrained Hamiltonian and inverse Kruskal iteration

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

Heikkinen, J. A.; Nora, M.

2011-02-15

Gyrokinetic equations of motion, Poisson equation, and energy and momentum conservation laws are derived based on the reduced-phase-space Lagrangian and inverse Kruskal iteration introduced by Pfirsch and Correa-Restrepo [J. Plasma Phys. 70, 719 (2004)]. This formalism, together with the choice of the adiabatic invariant J= as one of the averaging coordinates in phase space, provides an alternative to the standard gyrokinetics. Within second order in gyrokinetic parameter, the new equations do not show explicit ponderomotivelike or polarizationlike terms. Pullback of particle information with an iterated gyrophase and field dependent gyroradius function from the gyrocenter position defined by gyroaveraged coordinates allowsmore » direct numerical integration of the gyrokinetic equations in particle simulation of the field and particles with full distribution function. As an example, gyrokinetic systems with polarization drift either present or absent in the equations of motion are considered.« less

Combined effects of nonparaxiality, optical activity, and walk-off on rogue wave propagation in optical fibers filled with chiral materials.

PubMed

Temgoua, D D Estelle; Tchokonte, M B Tchoula; Kofane, T C

2018-04-01

The generalized nonparaxial nonlinear Schrödinger (NLS) equation in optical fibers filled with chiral materials is reduced to the higher-order integrable Hirota equation. Based on the modified Darboux transformation method, the nonparaxial chiral optical rogue waves are constructed from the scalar model with modulated coefficients. We show that the parameters of nonparaxiality, third-order dispersion, and differential gain or loss term are the main keys to control the amplitude, linear, and nonlinear effects in the model. Moreover, the influence of nonparaxiality, optical activity, and walk-off effect are also evidenced under the defocusing and focusing regimes of the vector nonparaxial NLS equations with constant and modulated coefficients. Through an algorithm scheme of wider applicability on nonparaxial beam propagation methods, the most influential effect and the simultaneous controllability of combined effects are underlined, showing their properties and their potential applications in optical fibers and in a variety of complex dynamical systems.

Combined effects of nonparaxiality, optical activity, and walk-off on rogue wave propagation in optical fibers filled with chiral materials

NASA Astrophysics Data System (ADS)

Temgoua, D. D. Estelle; Tchokonte, M. B. Tchoula; Kofane, T. C.

2018-04-01

The generalized nonparaxial nonlinear Schrödinger (NLS) equation in optical fibers filled with chiral materials is reduced to the higher-order integrable Hirota equation. Based on the modified Darboux transformation method, the nonparaxial chiral optical rogue waves are constructed from the scalar model with modulated coefficients. We show that the parameters of nonparaxiality, third-order dispersion, and differential gain or loss term are the main keys to control the amplitude, linear, and nonlinear effects in the model. Moreover, the influence of nonparaxiality, optical activity, and walk-off effect are also evidenced under the defocusing and focusing regimes of the vector nonparaxial NLS equations with constant and modulated coefficients. Through an algorithm scheme of wider applicability on nonparaxial beam propagation methods, the most influential effect and the simultaneous controllability of combined effects are underlined, showing their properties and their potential applications in optical fibers and in a variety of complex dynamical systems.

Effect of thermal radiation and chemical reaction on non-Newtonian fluid through a vertically stretching porous plate with uniform suction

NASA Astrophysics Data System (ADS)

Khan, Zeeshan; Khan, Ilyas; Ullah, Murad; Tlili, I.

2018-06-01

In this work, we discuss the unsteady flow of non-Newtonian fluid with the properties of heat source/sink in the presence of thermal radiation moving through a binary mixture embedded in a porous medium. The basic equations of motion including continuity, momentum, energy and concentration are simplified and solved analytically by using Homotopy Analysis Method (HAM). The energy and concentration fields are coupled with Dankohler and Schmidt numbers. By applying suitable transformation, the coupled nonlinear partial differential equations are converted to couple ordinary differential equations. The effect of physical parameters involved in the solutions of velocity, temperature and concentration profiles are discussed by assign numerical values and results obtained shows that the velocity, temperature and concentration profiles are influenced appreciably by the radiation parameter, Prandtl number, suction/injection parameter, reaction order index, solutal Grashof number and the thermal Grashof. It is observed that the non-Newtonian parameter H leads to an increase in the boundary layer thickness. It was established that the Prandtl number decreases thee thermal boundary layer thickness which helps in maintaining system temperature of the fluid flow. It is observed that the temperature profiles higher for heat source parameter and lower for heat sink parameter throughout the boundary layer. Fromm this simulation it is analyzed that an increase in the Schmidt number decreases the concentration boundary layer thickness. Additionally, for the sake of comparison numerical method (ND-Solve) and Adomian Decomposition Method are also applied and good agreement is found.

Approximate analysis for repeated eigenvalue problems with applications to controls-structure integrated design

NASA Technical Reports Server (NTRS)

Kenny, Sean P.; Hou, Gene J. W.

1994-01-01

A method for eigenvalue and eigenvector approximate analysis for the case of repeated eigenvalues with distinct first derivatives is presented. The approximate analysis method developed involves a reparameterization of the multivariable structural eigenvalue problem in terms of a single positive-valued parameter. The resulting equations yield first-order approximations to changes in the eigenvalues and the eigenvectors associated with the repeated eigenvalue problem. This work also presents a numerical technique that facilitates the definition of an eigenvector derivative for the case of repeated eigenvalues with repeated eigenvalue derivatives (of all orders). Examples are given which demonstrate the application of such equations for sensitivity and approximate analysis. Emphasis is placed on the application of sensitivity analysis to large-scale structural and controls-structures optimization problems.

Spectral iterative method and convergence analysis for solving nonlinear fractional differential equation

NASA Astrophysics Data System (ADS)

Yarmohammadi, M.; Javadi, S.; Babolian, E.

2018-04-01

In this study a new spectral iterative method (SIM) based on fractional interpolation is presented for solving nonlinear fractional differential equations (FDEs) involving Caputo derivative. This method is equipped with a pre-algorithm to find the singularity index of solution of the problem. This pre-algorithm gives us a real parameter as the index of the fractional interpolation basis, for which the SIM achieves the highest order of convergence. In comparison with some recent results about the error estimates for fractional approximations, a more accurate convergence rate has been attained. We have also proposed the order of convergence for fractional interpolation error under the L2-norm. Finally, general error analysis of SIM has been considered. The numerical results clearly demonstrate the capability of the proposed method.

An improved large signal model of InP HEMTs

NASA Astrophysics Data System (ADS)

Li, Tianhao; Li, Wenjun; Liu, Jun

2018-05-01

An improved large signal model for InP HEMTs is proposed in this paper. The channel current and charge model equations are constructed based on the Angelov model equations. Both the equations for channel current and gate charge models were all continuous and high order drivable, and the proposed gate charge model satisfied the charge conservation. For the strong leakage induced barrier reduction effect of InP HEMTs, the Angelov current model equations are improved. The channel current model could fit DC performance of devices. A 2 × 25 μm × 70 nm InP HEMT device is used to demonstrate the extraction and validation of the model, in which the model has predicted the DC I–V, C–V and bias related S parameters accurately. Project supported by the National Natural Science Foundation of China (No. 61331006).

Equation of state and critical point behavior of hard-core double-Yukawa fluids.

PubMed

Montes, J; Robles, M; López de Haro, M

2016-02-28

A theoretical study on the equation of state and the critical point behavior of hard-core double-Yukawa fluids is presented. Thermodynamic perturbation theory, restricted to first order in the inverse temperature and having the hard-sphere fluid as the reference system, is used to derive a relatively simple analytical equation of state of hard-core multi-Yukawa fluids. Using such an equation of state, the compressibility factor and phase behavior of six representative hard-core double-Yukawa fluids are examined and compared with available simulation results. The effect of varying the parameters of the hard-core double-Yukawa intermolecular potential on the location of the critical point is also analyzed using different perspectives. The relevance of this analysis for fluids whose molecules interact with realistic potentials is also pointed out.

Comparison between Smoluchowski and Boltzmann approaches for self-propelled rods.

PubMed

Bertin, Eric; Baskaran, Aparna; Chaté, Hugues; Marchetti, M Cristina

2015-10-01

Considering systems of self-propelled polar particles with nematic interactions ("rods"), we compare the continuum equations describing the evolution of polar and nematic order parameters, derived either from Smoluchowski or Boltzmann equations. Our main goal is to understand the discrepancies between the continuum equations obtained so far in both frameworks. We first show that, in the simple case of point-like particles with only alignment interactions, the continuum equations obtained have the same structure in both cases. We further study, in the Smoluchowski framework, the case where an interaction force is added on top of the aligning torque. This clarifies the origin of the additional terms obtained in previous works. Our observations lead us to emphasize the need for a more involved closure scheme than the standard normal form of the distribution when dealing with active systems.

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

NASA Astrophysics Data System (ADS)

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

2013-09-01

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

First-order curvature corrections to the surface tension of multicomponent systems.

PubMed

Boltachev, Grey Sh; Baidakov, Vladimir G; Schmelzer, Jürn W P

2003-08-01

The dependence of surface tension on curvature is investigated for the case of an equilibrium phase coexistence in multicomponent systems. Employing Gibbs's method of description of heterogeneous systems, an equation is derived to determine the dependence of surface tension on curvature for widely arbitrary paths of variation of the independent thermodynamic parameters. It is supposed hereby merely that the temperature is kept constant and that the variations of the different molar fractions are such that the radius of the dividing surface varies monotonically in dependence on the change of the state parameters of the ambient phase along any of the chosen paths. In the analysis, an approach developed by Blokhuis and Bedeaux for one-component systems is utilized. It relies on the expansion of the surface free energy on curvature of the dividing surface. An equation is derived that connects the first-order correction term in the expansion with the interaction potential of the particles in the multicomponent solution and with the two-particle distribution functions in the planar interfacial layer between the two phases coexisting in equilibrium at planar interfaces. The connection of the first-order curvature correction to the surface tension and the first moment of the pressure tensor at a planar interface is analyzed as well.

A well-posed and stable stochastic Galerkin formulation of the incompressible Navier–Stokes equations with random data

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

Pettersson, Per, E-mail: per.pettersson@uib.no; Nordström, Jan, E-mail: jan.nordstrom@liu.se; Doostan, Alireza, E-mail: alireza.doostan@colorado.edu

2016-02-01

We present a well-posed stochastic Galerkin formulation of the incompressible Navier–Stokes equations with uncertainty in model parameters or the initial and boundary conditions. The stochastic Galerkin method involves representation of the solution through generalized polynomial chaos expansion and projection of the governing equations onto stochastic basis functions, resulting in an extended system of equations. A relatively low-order generalized polynomial chaos expansion is sufficient to capture the stochastic solution for the problem considered. We derive boundary conditions for the continuous form of the stochastic Galerkin formulation of the velocity and pressure equations. The resulting problem formulation leads to an energy estimatemore » for the divergence. With suitable boundary data on the pressure and velocity, the energy estimate implies zero divergence of the velocity field. Based on the analysis of the continuous equations, we present a semi-discretized system where the spatial derivatives are approximated using finite difference operators with a summation-by-parts property. With a suitable choice of dissipative boundary conditions imposed weakly through penalty terms, the semi-discrete scheme is shown to be stable. Numerical experiments in the laminar flow regime corroborate the theoretical results and we obtain high-order accurate results for the solution variables and the velocity divergence converges to zero as the mesh is refined.« less

Dynamic phase transitions of the Blume-Emery-Griffiths model under an oscillating external magnetic field by the path probability method

NASA Astrophysics Data System (ADS)

Ertaş, Mehmet; Keskin, Mustafa

2015-03-01

By using the path probability method (PPM) with point distribution, we study the dynamic phase transitions (DPTs) in the Blume-Emery-Griffiths (BEG) model under an oscillating external magnetic field. The phases in the model are obtained by solving the dynamic equations for the average order parameters and a disordered phase, ordered phase and four mixed phases are found. We also investigate the thermal behavior of the dynamic order parameters to analyze the nature dynamic transitions as well as to obtain the DPT temperatures. The dynamic phase diagrams are presented in three different planes in which exhibit the dynamic tricritical point, double critical end point, critical end point, quadrupole point, triple point as well as the reentrant behavior, strongly depending on the values of the system parameters. We compare and discuss the dynamic phase diagrams with dynamic phase diagrams that were obtained within the Glauber-type stochastic dynamics based on the mean-field theory.

Pulse-coupled mixed-mode oscillators: Cluster states and extreme noise sensitivity

NASA Astrophysics Data System (ADS)

Karamchandani, Avinash J.; Graham, James N.; Riecke, Hermann

2018-04-01

Motivated by rhythms in the olfactory system of the brain, we investigate the synchronization of all-to-all pulse-coupled neuronal oscillators exhibiting various types of mixed-mode oscillations (MMOs) composed of sub-threshold oscillations (STOs) and action potentials ("spikes"). We focus particularly on the impact of the delay in the interaction. In the weak-coupling regime, we reduce the system to a Kuramoto-type equation with non-sinusoidal phase coupling and the associated Fokker-Planck equation. Its linear stability analysis identifies the appearance of various cluster states. Their type depends sensitively on the delay and the width of the pulses. Interestingly, long delays do not imply slow population rhythms, and the number of emerging clusters only loosely depends on the number of STOs. Direct simulations of the oscillator equations reveal that for quantitative agreement of the weak-coupling theory the coupling strength and the noise have to be extremely small. Even moderate noise leads to significant skipping of STO cycles, which can enhance the diffusion coefficient in the Fokker-Planck equation by two orders of magnitude. Introducing an effective diffusion coefficient extends the range of agreement significantly. Numerical simulations of the Fokker-Planck equation reveal bistability and solutions with oscillatory order parameters that result from nonlinear mode interactions. These are confirmed in simulations of the full spiking model.

Kinetics of Polydomain Ordering at Second-Order Phase Transitions (by the Example of the AuCu3 Alloy)

NASA Astrophysics Data System (ADS)

Feldman, E. P.; Stefanovich, L. I.; Gumennyk, K. V.

2008-08-01

Kinetics of polydomain spinodal ordering is studied in alloys of AuCu3 type. We introduce four non-conserved long-range order parameters whose sum, however, is conserved and, using the statistical approach, follow the temporal evolution of their random spatial distribution after a rapid temperature quench. A system of nonlinear differential equations for correlators of second and third order is derived. Asymptotical analysis of this system allows to investigate the scaling regime, which develops on the late stages of evolution and to extract additional information concerning the rate of decrease of the specific volume of disordered regions and the rate of decrease of the average thickness of antiphase boundaries. Comparison of these results to experimental data is given. The quench below the spinodal and the onset of long-range order may be separated by the incubation time, whose origin is different from that in first-order phase transitions. Numerical integration of equations for correlators shows also, that it is possible to prepare a sample in such a way that its further evolution will go with formation of transient kinetically slowed polydomain structures different from the final L12 structure.

Classes of exact Einstein Maxwell solutions

NASA Astrophysics Data System (ADS)

Komathiraj, K.; Maharaj, S. D.

2007-12-01

We find new classes of exact solutions to the Einstein Maxwell system of equations for a charged sphere with a particular choice of the electric field intensity and one of the gravitational potentials. The condition of pressure isotropy is reduced to a linear, second order differential equation which can be solved in general. Consequently we can find exact solutions to the Einstein Maxwell field equations corresponding to a static spherically symmetric gravitational potential in terms of hypergeometric functions. It is possible to find exact solutions which can be written explicitly in terms of elementary functions, namely polynomials and product of polynomials and algebraic functions. Uncharged solutions are regainable with our choice of electric field intensity; in particular we generate the Einstein universe for particular parameter values.

Solving differential equations for Feynman integrals by expansions near singular points

NASA Astrophysics Data System (ADS)

Lee, Roman N.; Smirnov, Alexander V.; Smirnov, Vladimir A.

2018-03-01

We describe a strategy to solve differential equations for Feynman integrals by powers series expansions near singular points and to obtain high precision results for the corresponding master integrals. We consider Feynman integrals with two scales, i.e. non-trivially depending on one variable. The corresponding algorithm is oriented at situations where canonical form of the differential equations is impossible. We provide a computer code constructed with the help of our algorithm for a simple example of four-loop generalized sunset integrals with three equal non-zero masses and two zero masses. Our code gives values of the master integrals at any given point on the real axis with a required accuracy and a given order of expansion in the regularization parameter ɛ.

Statefinder diagnostic for modified Chaplygin gas cosmology in f(R,T) gravity with particle creation

NASA Astrophysics Data System (ADS)

Singh, J. K.; Nagpal, Ritika; Pacif, S. K. J.

In this paper, we have studied flat Friedmann-Lemaître-Robertson-Walker (FLRW) model with modified Chaplygin gas (MCG) having equation of state pm = Aρ ‑ B ργ, where 0 ≤ A ≤ 1, 0 ≤ γ ≤ 1 and B is any positive constant in f(R,T) gravity with particle creation. We have considered a simple parametrization of the Hubble parameter H in order to solve the field equations and discussed the time evolution of different cosmological parameters for some obtained models showing unique behavior of scale factor. We have also discussed the statefinder diagnostic pair {r,s} that characterizes the evolution of obtained models and explore their stability. The physical consequences of the models and their kinematic behaviors have also been scrutinized here in some detail.

Meshless Solution of the Problem on the Static Behavior of Thin and Thick Laminated Composite Beams

NASA Astrophysics Data System (ADS)

Xiang, S.; Kang, G. W.

2018-03-01

For the first time, the static behavior of laminated composite beams is analyzed using the meshless collocation method based on a thin-plate-spline radial basis function. In the approximation of a partial differential equation by using a radial basis function, the shape parameter has an important role in ensuring the numerical accuracy. The choice of a shape parameter in the thin plate spline radial basis function is easier than in other radial basis functions. The governing differential equations are derived based on Reddy's third-order shear deformation theory. Numerical results are obtained for symmetric cross-ply laminated composite beams with simple-simple and cantilever boundary conditions under a uniform load. The results found are compared with available published ones and demonstrate the accuracy of the present method.

Basic research and data analysis for the National Geodetic Satellite program and for the Earth Surveys program

NASA Technical Reports Server (NTRS)

1972-01-01

Current research is reported on precise and accurate descriptions of the earth's surface and gravitational field and on time variations of geophysical parameters. A new computer program was written in connection with the adjustment of the BC-4 worldwide geometric satellite triangulation net. The possibility that an increment to accuracy could be transferred from a super-control net to the basic geodetic (first-order triangulation) was investigated. Coordinates of the NA9 solution were computed and were transformed to the NAD datum, based on GEOS 1 observations. Normal equations from observational data of several different systems and constraint equations were added and a single solution was obtained for the combined systems. Transformation parameters with constraints were determined, and the impact of computers on surveying and mapping is discussed.

Effect of thermal radiation and suction on convective heat transfer of nanofluid along a wedge in the presence of heat generation/absorption

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

Kasmani, Ruhaila Md; Bhuvaneswari, M.; Sivasankaran, S.

2015-10-22

An analysis is presented to find the effects of thermal radiation and heat generation/absorption on convection heat transfer of nanofluid past a wedge in the presence of wall suction. The governing partial differential equations are transformed into a system of ordinary differential equations using similarity transformation. The resulting system is solved numerically using a fourth-order Runge–Kutta method with shooting technique. Numerical computations are carried out for different values of dimensionless parameters to predict the effects of wedge angle, thermophoresis, Brownian motion, heat generation/absorption, thermal radiation and suction. It is found that the temperature increases significantly when the value of themore » heat generation/absorption parameter increases. But the opposite observation is found for the effect of thermal radiation.« less

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

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

Rogue waves in the multicomponent Mel'nikov system and multicomponent Schrödinger-Boussinesq system

NASA Astrophysics Data System (ADS)

Sun, Baonan; Lian, Zhan

2018-02-01

By virtue of the bilinear method and the KP hierarchy reduction technique, exact explicit rational solutions of the multicomponent Mel'nikov equation and the multicomponent Schrödinger-Boussinesq equation are constructed, which contain multicomponent short waves and single-component long wave. For the multicomponent Mel'nikov equation, the fundamental rational solutions possess two different behaviours: lump and rogue wave. It is shown that the fundamental (simplest) rogue waves are line localised waves which arise from the constant background with a line profile and then disappear into the constant background again. The fundamental line rogue waves can be classified into three: bright, intermediate and dark line rogue waves. Two subclasses of non-fundamental rogue waves, i.e., multirogue waves and higher-order rogue waves are discussed. The multirogue waves describe interaction of several fundamental line rogue waves, in which interesting wave patterns appear in the intermediate time. Higher-order rogue waves exhibit dynamic behaviours that the wave structures start from lump and then retreat back to it. Moreover, by taking the parameter constraints further, general higher-order rogue wave solutions for the multicomponent Schrödinger-Boussinesq system are generated.

Removal of Congo Red from Aqueous Solution by Anion Exchange Membrane (EBTAC): Adsorption Kinetics and Themodynamics.

PubMed

Khan, Muhammad Imran; Akhtar, Shahbaz; Zafar, Shagufta; Shaheen, Aqeela; Khan, Muhammad Ali; Luque, Rafael; Rehman, Aziz Ur

2015-07-08

The adsorption behavior of anionic dye congo red (CR) from aqueous solutions using an anion exchange membrane (EBTAC) has been investigated at room temperature. The effect of several factors including contact time, membrane dosage, ionic strength and temperature were studied. Kinetic models, namely pseudo-first-order and pseudo-second-order, liquid film diffusion and Elovich models as well as Bangham and modified freundlich Equations, were employed to evaluate the experimental results. Parameters such as adsorption capacities, rate constant and related correlation coefficients for every model were calculated and discussed. The adsorption of CR on anion exchange membranes followed pseudo-second-order Kinetics. Thermodynamic parameters, namely changes in Gibbs free energy ( ∆G° ), enthalpy ( ∆H° ) and entropy ( ∆S° ) were calculated for the adsorption of congo red, indicating an exothermic process.

Removal of Congo Red from Aqueous Solution by Anion Exchange Membrane (EBTAC): Adsorption Kinetics and Themodynamics

PubMed Central

Khan, Muhammad Imran; Akhtar, Shahbaz; Zafar, Shagufta; Shaheen, Aqeela; Khan, Muhammad Ali; Luque, Rafael; ur Rehman, Aziz

2015-01-01

The adsorption behavior of anionic dye congo red (CR) from aqueous solutions using an anion exchange membrane (EBTAC) has been investigated at room temperature. The effect of several factors including contact time, membrane dosage, ionic strength and temperature were studied. Kinetic models, namely pseudo-first-order and pseudo-second-order, liquid film diffusion and Elovich models as well as Bangham and modified freundlich Equations, were employed to evaluate the experimental results. Parameters such as adsorption capacities, rate constant and related correlation coefficients for every model were calculated and discussed. The adsorption of CR on anion exchange membranes followed pseudo-second-order Kinetics. Thermodynamic parameters, namely changes in Gibbs free energy (∆G°), enthalpy (∆H°) and entropy (∆S°) were calculated for the adsorption of congo red, indicating an exothermic process. PMID:28793430

A second-order shock-expansion method applicable to bodies of revolution near zero lift

NASA Technical Reports Server (NTRS)

1957-01-01

A second-order shock-expansion method applicable to bodies of revolution is developed by the use of the predictions of the generalized shock-expansion method in combination with characteristics theory. Equations defining the zero-lift pressure distributions and the normal-force and pitching-moment derivatives are derived. Comparisons with experimental results show that the method is applicable at values of the similarity parameter, the ratio of free-stream Mach number to nose fineness ratio, from about 0.4 to 2.

Scaled equation of state parameters for gases in the critical region

NASA Technical Reports Server (NTRS)

Sengers, J. M. H. L.; Greer, W. L.; Sengers, J. V.

1976-01-01

In the light of recent theoretical developments, the paper presents an accurate characterization of anomalous thermodynamic behavior of xenon, helium 4, helium 3, carbon dioxide, steam and oxygen in the critical region. This behavior is associated with long range fluctuations in the system and the physical properties depend primarily on a single variable, namely, the correlation length. A description of the thermodynamic behavior of fluids in terms of scaling laws is formulated, and the two successfully used scaled equations of state (NBS equation and Linear Model parametric equation) are compared. Methods for fitting both equations to experimental equation of state data are developed and formulated, and the optimum fit for each of the two scaled equations of the above gases are presented and the results are compared. By extending the experimental data for the above one-component fluids to partially miscible binary liquids, superfluid liquid helium, ferromagnets and solids exhibiting order-disorder transitions, the principle of universality is concluded. Finally by using this principle, the critical regions for nine additional fluids are described.

On the integrability of some generalized Lotka-Volterra systems

NASA Astrophysics Data System (ADS)

Bier, M.; Hijmans, J.; Bountis, T. C.

1983-08-01

Several integrable systems of nonlinear ordinary differential equations of the Lotka-Volterra type are identified by the Painleveproperty and completely integrated. One such integrable case of N first order ode's is found, with N-2 free parameters and N arbitrary. The concept of integrability of a general dynamical system, not necessarily derived from a Hamiltonian, is also discussed.

Slip Effects On MHD Three Dimensional Flow Of Casson Fluid Over An Exponentially Stretching Surface

NASA Astrophysics Data System (ADS)

Madhusudhana Rao, B.; Krishna Murthy, M.; Sivakumar, N.; Rushi Kumar, B.; Raju, C. S. K.

2018-04-01

Heat and mass transfer effects on MHD three dimensional flow of Casson fluid over an exponentially stretching surface with slip conditions is examined. The similarity transformations are used to convert the governing equations into a set of nonlinear ordinary differential equations and are solved numerically using fourth order Runge-Kutta method along with shooting technique. The effects of Casson parameter, Hartmann number, heat source/sink,chemical reaction and slip factors on velocity, temperature and concentration are shown graphically. The skin friction coefficient and the Nusselt number are examined numerically.

Equations for normal-mode statistics of sound scattering by a rough elastic boundary in an underwater waveguide, including backscattering.

PubMed

Morozov, Andrey K; Colosi, John A

2017-09-01

Underwater sound scattering by a rough sea surface, ice, or a rough elastic bottom is studied. The study includes both the scattering from the rough boundary and the elastic effects in the solid layer. A coupled mode matrix is approximated by a linear function of one random perturbation parameter such as the ice-thickness or a perturbation of the surface position. A full two-way coupled mode solution is used to derive the stochastic differential equation for the second order statistics in a Markov approximation.

The Renormalization-Group Method in the Problem on Calculation of the Spectral Energy Density of Fluid Turbulence

NASA Astrophysics Data System (ADS)

Teodorovich, E. V.

2018-03-01

In order to find the shape of energy spectrum within the framework of the model of stationary homogeneous isotropic turbulence, the renormalization-group equations, which reflect the Markovian nature of the mechanism of energy transfer along the wavenumber spectrum, are used in addition to the dimensional considerations and the energy balance equation. For the spectrum, the formula depends on three parameters, namely, the wavenumber, which determines the upper boundary of the range of the turbulent energy production, the spectral flux through this boundary, and the fluid kinematic viscosity.

Controllable optical rogue waves via nonlinearity management.

PubMed

Yang, Zhengping; Zhong, Wei-Ping; Belić, Milivoj; Zhang, Yiqi

2018-03-19

Using a similarity transformation, we obtain analytical solutions to a class of nonlinear Schrödinger (NLS) equations with variable coefficients in inhomogeneous Kerr media, which are related to the optical rogue waves of the standard NLS equation. We discuss the dynamics of such optical rogue waves via nonlinearity management, i.e., by selecting the appropriate nonlinearity coefficients and integration constants, and presenting the solutions. In addition, we investigate higher-order rogue waves by suitably adjusting the nonlinearity coefficient and the rogue wave parameters, which could help in realizing complex but controllable optical rogue waves in properly engineered fibers and other photonic materials.

Painlevé equations, topological type property and reconstruction by the topological recursion

NASA Astrophysics Data System (ADS)

Iwaki, K.; Marchal, O.; Saenz, A.

2018-01-01

In this article we prove that Lax pairs associated with ħ-dependent six Painlevé equations satisfy the topological type property proposed by Bergère, Borot and Eynard for any generic choice of the monodromy parameters. Consequently we show that one can reconstruct the formal ħ-expansion of the isomonodromic τ-function and of the determinantal formulas by applying the so-called topological recursion to the spectral curve attached to the Lax pair in all six Painlevé cases. Finally we illustrate the former results with the explicit computations of the first orders of the six τ-functions.

Numerical simulations for tumor and cellular immune system interactions in lung cancer treatment

NASA Astrophysics Data System (ADS)

Kolev, M.; Nawrocki, S.; Zubik-Kowal, B.

2013-06-01

We investigate a new mathematical model that describes lung cancer regression in patients treated by chemotherapy and radiotherapy. The model is composed of nonlinear integro-differential equations derived from the so-called kinetic theory for active particles and a new sink function is investigated according to clinical data from carcinoma planoepitheliale. The model equations are solved numerically and the data are utilized in order to find their unknown parameters. The results of the numerical experiments show a good correlation between the predicted and clinical data and illustrate that the mathematical model has potential to describe lung cancer regression.

Maximum likelihood clustering with dependent feature trees

NASA Technical Reports Server (NTRS)

Chittineni, C. B. (Principal Investigator)

1981-01-01

The decomposition of mixture density of the data into its normal component densities is considered. The densities are approximated with first order dependent feature trees using criteria of mutual information and distance measures. Expressions are presented for the criteria when the densities are Gaussian. By defining different typs of nodes in a general dependent feature tree, maximum likelihood equations are developed for the estimation of parameters using fixed point iterations. The field structure of the data is also taken into account in developing maximum likelihood equations. Experimental results from the processing of remotely sensed multispectral scanner imagery data are included.

Constraints on a generalized deceleration parameter from cosmic chronometers

NASA Astrophysics Data System (ADS)

Mamon, Abdulla Al

2018-04-01

In this paper, we have proposed a generalized parametrization for the deceleration parameter q in order to study the evolutionary history of the universe. We have shown that the proposed model can reproduce three well known q-parametrized models for some specific values of the model parameter α. We have used the latest compilation of the Hubble parameter measurements obtained from the cosmic chronometer (CC) method (in combination with the local value of the Hubble constant H0) and the Type Ia supernova (SNIa) data to place constraints on the parameters of the model for different values of α. We have found that the resulting constraints on the deceleration parameter and the dark energy equation of state support the ΛCDM model within 1σ confidence level at the present epoch.

A rigorous multiple independent binding site model for determining cell-based equilibrium dissociation constants.

PubMed

Drake, Andrew W; Klakamp, Scott L

2007-01-10

A new 4-parameter nonlinear equation based on the standard multiple independent binding site model (MIBS) is presented for fitting cell-based ligand titration data in order to calculate the ligand/cell receptor equilibrium dissociation constant and the number of receptors/cell. The most commonly used linear (Scatchard Plot) or nonlinear 2-parameter model (a single binding site model found in commercial programs like Prism(R)) used for analysis of ligand/receptor binding data assumes only the K(D) influences the shape of the titration curve. We demonstrate using simulated data sets that, depending upon the cell surface receptor expression level, the number of cells titrated, and the magnitude of the K(D) being measured, this assumption of always being under K(D)-controlled conditions can be erroneous and can lead to unreliable estimates for the binding parameters. We also compare and contrast the fitting of simulated data sets to the commonly used cell-based binding equation versus our more rigorous 4-parameter nonlinear MIBS model. It is shown through these simulations that the new 4-parameter MIBS model, when used for cell-based titrations under optimal conditions, yields highly accurate estimates of all binding parameters and hence should be the preferred model to fit cell-based experimental nonlinear titration data.

Quasi-Newton methods for parameter estimation in functional differential equations

NASA Technical Reports Server (NTRS)

Brewer, Dennis W.

1988-01-01

A state-space approach to parameter estimation in linear functional differential equations is developed using the theory of linear evolution equations. A locally convergent quasi-Newton type algorithm is applied to distributed systems with particular emphasis on parameters that induce unbounded perturbations of the state. The algorithm is computationally implemented on several functional differential equations, including coefficient and delay estimation in linear delay-differential equations.

Dynamic interaction of monowheel inclined vehicle-vibration platform coupled system with quadratic and cubic nonlinearities

NASA Astrophysics Data System (ADS)

Zhou, Shihua; Song, Guiqiu; Sun, Maojun; Ren, Zhaohui; Wen, Bangchun

2018-01-01

In order to analyze the nonlinear dynamics and stability of a novel design for the monowheel inclined vehicle-vibration platform coupled system (MIV-VPCS) with intermediate nonlinearity support subjected to a harmonic excitation, a multi-degree of freedom lumped parameter dynamic model taking into account the dynamic interaction of the MIV-VPCS with quadratic and cubic nonlinearities is presented. The dynamical equations of the coupled system are derived by applying the displacement relationship, interaction force relationship at the contact position and Lagrange's equation, which are further discretized into a set of nonlinear ordinary differential equations with coupled terms by Galerkin's truncation. Based on the mathematical model, the coupled multi-body nonlinear dynamics of the vibration system is investigated by numerical method, and the parameters influences of excitation amplitude, mass ratio and inclined angle on the dynamic characteristics are precisely analyzed and discussed by bifurcation diagram, Largest Lyapunov exponent and 3-D frequency spectrum. Depending on different ranges of system parameters, the results show that the different motions and jump discontinuity appear, and the coupled system enters into chaotic behavior through different routes (period-doubling bifurcation, inverse period-doubling bifurcation, saddle-node bifurcation and Hopf bifurcation), which are strongly attributed to the dynamic interaction of the MIV-VPCS. The decreasing excitation amplitude and inclined angle could reduce the higher order bifurcations, and effectively control the complicated nonlinear dynamic behaviors under the perturbation of low rotational speed. The first bifurcation and chaotic motion occur at lower value of inclined angle, and the chaotic behavior lasts for larger intervals with higher rotational speed. The investigation results could provide a better understanding of the nonlinear dynamic behaviors for the dynamic interaction of the MIV-VPCS.

High-Order Energy Stable WENO Schemes

NASA Technical Reports Server (NTRS)

Yamaleev, Nail K.; Carpenter, Mark H.

2009-01-01

A third-order Energy Stable Weighted Essentially Non-Oscillatory (ESWENO) finite difference scheme developed by Yamaleev and Carpenter was proven to be stable in the energy norm for both continuous and discontinuous solutions of systems of linear hyperbolic equations. Herein, a systematic approach is presented that enables 'energy stable' modifications for existing WENO schemes of any order. The technique is demonstrated by developing a one-parameter family of fifth-order upwind-biased ESWENO schemes; ESWENO schemes up to eighth order are presented in the appendix. New weight functions are also developed that provide (1) formal consistency, (2) much faster convergence for smooth solutions with an arbitrary number of vanishing derivatives, and (3) improved resolution near strong discontinuities.

Spatio-temporal dynamics induced by competing instabilities in two asymmetrically coupled nonlinear evolution equations

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

Schüler, D.; Alonso, S.; Bär, M.

2014-12-15

Pattern formation often occurs in spatially extended physical, biological, and chemical systems due to an instability of the homogeneous steady state. The type of the instability usually prescribes the resulting spatio-temporal patterns and their characteristic length scales. However, patterns resulting from the simultaneous occurrence of instabilities cannot be expected to be simple superposition of the patterns associated with the considered instabilities. To address this issue, we design two simple models composed by two asymmetrically coupled equations of non-conserved (Swift-Hohenberg equations) or conserved (Cahn-Hilliard equations) order parameters with different characteristic wave lengths. The patterns arising in these systems range from coexistingmore » static patterns of different wavelengths to traveling waves. A linear stability analysis allows to derive a two parameter phase diagram for the studied models, in particular, revealing for the Swift-Hohenberg equations, a co-dimension two bifurcation point of Turing and wave instability and a region of coexistence of stationary and traveling patterns. The nonlinear dynamics of the coupled evolution equations is investigated by performing accurate numerical simulations. These reveal more complex patterns, ranging from traveling waves with embedded Turing patterns domains to spatio-temporal chaos, and a wide hysteretic region, where waves or Turing patterns coexist. For the coupled Cahn-Hilliard equations the presence of a weak coupling is sufficient to arrest the coarsening process and to lead to the emergence of purely periodic patterns. The final states are characterized by domains with a characteristic length, which diverges logarithmically with the coupling amplitude.« less

Diffusion of non-Gaussianity in heavy ion collisions

NASA Astrophysics Data System (ADS)

Kitazawa, Masakiyo; Asakawa, Masayuki; Ono, Hirosato

2014-05-01

We investigate the time evolution of higher order cumulants of bulk fluctuations of conserved charges in the hadronic stage in relativistic heavy ion collisions. The dynamical evolution of non-Gaussian fluctuations is modeled by the diffusion master equation. Using this model we predict that the fourth-order cumulant of net-electric charge is suppressed compared with the recently observed second-order one at ALICE for a reasonable parameter range. Significance of the measurements of various cumulants as functions of rapidity window to probe dynamical history of the hot medium created by heavy ion collisions is emphasized.

Novel third-order Lovelock wormhole solutions

NASA Astrophysics Data System (ADS)

Mehdizadeh, Mohammad Reza; Lobo, Francisco S. N.

2016-06-01

In this work, we consider wormhole geometries in third-order Lovelock gravity and investigate the possibility that these solutions satisfy the energy conditions. In this framework, by applying a specific equation of state, we obtain exact wormhole solutions, and by imposing suitable values for the parameters of the theory, we find that these geometries satisfy the weak energy condition in the vicinity of the throat, due to the presence of higher-order curvature terms. Finally, we trace out a numerical analysis, by assuming a specific redshift function, and find asymptotically flat solutions that satisfy the weak energy condition throughout the spacetime.

A distributed parameter electromechanical model for bimorph piezoelectric energy harvesters based on the refined zigzag theory

NASA Astrophysics Data System (ADS)

Chen, Chung-De

2018-04-01

In this paper, a distributed parameter electromechanical model for bimorph piezoelectric energy harvesters based on the refined zigzag theory (RZT) is developed. In this model, the zigzag function is incorporated into the axial displacement, and the zigzag distribution of the displacement between the adjacent layers of the bimorph structure can be considered. The governing equations, including three equations of motions and one equation of circuit, are derived using Hamilton’s principle. The natural frequency, its corresponding modal function and the steady state response of the base excitation motion are given in exact forms. The presented results are benchmarked with the finite element method and two beam theories, the first-order shear deformation theory and the classical beam theory. Comparing examples shows that the RZT provides predictions of output voltage and generated power at high accuracy, especially for the case of a soft middle layer. Variation of the parameters, such as the beam thickness, excitation frequencies and the external electrical loads, is investigated and its effects on the performance of the energy harvesters are studied by using the RZT developed in this paper. Based on this refined theory, analysts and engineers can capture more details on the electromechanical behavior of piezoelectric harvesters.

Nonlinear programming extensions to rational function approximations of unsteady aerodynamics

NASA Technical Reports Server (NTRS)

Tiffany, Sherwood H.; Adams, William M., Jr.

1987-01-01

This paper deals with approximating unsteady generalized aerodynamic forces in the equations of motion of a flexible aircraft. Two methods of formulating these approximations are extended to include both the same flexibility in constraining them and the same methodology in optimizing nonlinear parameters as another currently used 'extended least-squares' method. Optimal selection of 'nonlinear' parameters is made in each of the three methods by use of the same nonlinear (nongradient) optimizer. The objective of the nonlinear optimization is to obtain rational approximations to the unsteady aerodynamics whose state-space realization is of lower order than that required when no optimization of the nonlinear terms is performed. The free 'linear' parameters are determined using least-squares matrix techniques on a Lagrange multiplier formulation of an objective function which incorporates selected linear equality constraints. State-space mathematical models resulting from the different approaches are described, and results are presented which show comparative evaluations from application of each of the extended methods to a numerical example. The results obtained for the example problem show a significant (up to 63 percent) reduction in the number of differential equations used to represent the unsteady aerodynamic forces in linear time-invariant equations of motion as compared to a conventional method in which nonlinear terms are not optimized.

Estimating Soil Hydraulic Parameters using Gradient Based Approach

NASA Astrophysics Data System (ADS)

Rai, P. K.; Tripathi, S.

2017-12-01

The conventional way of estimating parameters of a differential equation is to minimize the error between the observations and their estimates. The estimates are produced from forward solution (numerical or analytical) of differential equation assuming a set of parameters. Parameter estimation using the conventional approach requires high computational cost, setting-up of initial and boundary conditions, and formation of difference equations in case the forward solution is obtained numerically. Gaussian process based approaches like Gaussian Process Ordinary Differential Equation (GPODE) and Adaptive Gradient Matching (AGM) have been developed to estimate the parameters of Ordinary Differential Equations without explicitly solving them. Claims have been made that these approaches can straightforwardly be extended to Partial Differential Equations; however, it has been never demonstrated. This study extends AGM approach to PDEs and applies it for estimating parameters of Richards equation. Unlike the conventional approach, the AGM approach does not require setting-up of initial and boundary conditions explicitly, which is often difficult in real world application of Richards equation. The developed methodology was applied to synthetic soil moisture data. It was seen that the proposed methodology can estimate the soil hydraulic parameters correctly and can be a potential alternative to the conventional method.

Constitutive Equation with Varying Parameters for Superplastic Flow Behavior

NASA Astrophysics Data System (ADS)

Guan, Zhiping; Ren, Mingwen; Jia, Hongjie; Zhao, Po; Ma, Pinkui

2014-03-01

In this study, constitutive equations for superplastic materials with an extra large elongation were investigated through mechanical analysis. From the view of phenomenology, firstly, some traditional empirical constitutive relations were standardized by restricting some strain paths and parameter conditions, and the coefficients in these relations were strictly given new mechanical definitions. Subsequently, a new, general constitutive equation with varying parameters was theoretically deduced based on the general mechanical equation of state. The superplastic tension test data of Zn-5%Al alloy at 340 °C under strain rates, velocities, and loads were employed for building a new constitutive equation and examining its validity. Analysis results indicated that the constitutive equation with varying parameters could characterize superplastic flow behavior in practical superplastic forming with high prediction accuracy and without any restriction of strain path or deformation condition, showing good industrial or scientific interest. On the contrary, those empirical equations have low prediction capabilities due to constant parameters and poor applicability because of the limit of special strain path or parameter conditions based on strict phenomenology.

Capacitance of a highly ordered array of nanocapacitors: Model and microscopy

NASA Astrophysics Data System (ADS)

Cortés, A.; Celedón, C.; Ulloa, P.; Kepaptsoglou, D.; Häberle, P.

2011-11-01

This manuscript describes briefly the process used to build an ordered porous array in an anodic aluminum oxide (AAO) membrane, filled with multiwall carbon nanotubes (MWCNTs). The MWCNTs were grown directly inside the membrane through chemical vapor deposition (CVD). The role of the CNTs is to provide narrow metal electrodes contact with a dielectric surface barrier, hence, forming a capacitor. This procedure allows the construction of an array of 1010 parallel nano-spherical capacitors/cm2. A central part of this contribution is the use of physical parameters obtained from processing transmission electron microscopy (TEM) images, to predict the specific capacitance of the AAOs arrays. Electrical parameters were obtained by solving Laplace's equation through finite element methods (FEMs).

Globally coupled stochastic two-state oscillators: fluctuations due to finite numbers.

PubMed

Pinto, Italo'Ivo Lima Dias; Escaff, Daniel; Harbola, Upendra; Rosas, Alexandre; Lindenberg, Katja

2014-05-01

Infinite arrays of coupled two-state stochastic oscillators exhibit well-defined steady states. We study the fluctuations that occur when the number N of oscillators in the array is finite. We choose a particular form of global coupling that in the infinite array leads to a pitchfork bifurcation from a monostable to a bistable steady state, the latter with two equally probable stationary states. The control parameter for this bifurcation is the coupling strength. In finite arrays these states become metastable: The fluctuations lead to distributions around the most probable states, with one maximum in the monostable regime and two maxima in the bistable regime. In the latter regime, the fluctuations lead to transitions between the two peak regions of the distribution. Also, we find that the fluctuations break the symmetry in the bimodal regime, that is, one metastable state becomes more probable than the other, increasingly so with increasing array size. To arrive at these results, we start from microscopic dynamical evolution equations from which we derive a Langevin equation that exhibits an interesting multiplicative noise structure. We also present a master equation description of the dynamics. Both of these equations lead to the same Fokker-Planck equation, the master equation via a 1/N expansion and the Langevin equation via standard methods of Itô calculus for multiplicative noise. From the Fokker-Planck equation we obtain an effective potential that reflects the transition from the monomodal to the bimodal distribution as a function of a control parameter. We present a variety of numerical and analytic results that illustrate the strong effects of the fluctuations. We also show that the limits N → ∞ and t → ∞ (t is the time) do not commute. In fact, the two orders of implementation lead to drastically different results.

Globally coupled stochastic two-state oscillators: Fluctuations due to finite numbers

NASA Astrophysics Data System (ADS)

Pinto, Italo'Ivo Lima Dias; Escaff, Daniel; Harbola, Upendra; Rosas, Alexandre; Lindenberg, Katja

2014-05-01

Infinite arrays of coupled two-state stochastic oscillators exhibit well-defined steady states. We study the fluctuations that occur when the number N of oscillators in the array is finite. We choose a particular form of global coupling that in the infinite array leads to a pitchfork bifurcation from a monostable to a bistable steady state, the latter with two equally probable stationary states. The control parameter for this bifurcation is the coupling strength. In finite arrays these states become metastable: The fluctuations lead to distributions around the most probable states, with one maximum in the monostable regime and two maxima in the bistable regime. In the latter regime, the fluctuations lead to transitions between the two peak regions of the distribution. Also, we find that the fluctuations break the symmetry in the bimodal regime, that is, one metastable state becomes more probable than the other, increasingly so with increasing array size. To arrive at these results, we start from microscopic dynamical evolution equations from which we derive a Langevin equation that exhibits an interesting multiplicative noise structure. We also present a master equation description of the dynamics. Both of these equations lead to the same Fokker-Planck equation, the master equation via a 1/N expansion and the Langevin equation via standard methods of Itô calculus for multiplicative noise. From the Fokker-Planck equation we obtain an effective potential that reflects the transition from the monomodal to the bimodal distribution as a function of a control parameter. We present a variety of numerical and analytic results that illustrate the strong effects of the fluctuations. We also show that the limits N →∞ and t →∞ (t is the time) do not commute. In fact, the two orders of implementation lead to drastically different results.

Theoretical regime diagrams for thermally driven flows in a beta-plane channel in the presence of variable gravity

NASA Technical Reports Server (NTRS)

Geisler, J. E.; Fowlis, W. W.

1980-01-01

The effect of a power law gravity field on baroclinic instability is examined, with a focus on the case of inverse fifth power gravity, since this is the power law produced when terrestrial gravity is simulated in spherical geometry by a dielectric force. Growth rates are obtained of unstable normal modes as a function of parameters of the problem by solving a second order differential equation numerically. It is concluded that over the range of parameter space explored, there is no significant change in the character of theoretical regime diagrams if the vertically averaged gravity is used as parameter.

Order-parameter model for unstable multilane traffic flow

NASA Astrophysics Data System (ADS)

Lubashevsky, Ihor A.; Mahnke, Reinhard

2000-11-01

We discuss a phenomenological approach to the description of unstable vehicle motion on multilane highways that explains in a simple way the observed sequence of the ``free flow <--> synchronized mode <--> jam'' phase transitions as well as the hysteresis in these transitions. We introduce a variable called an order parameter that accounts for possible correlations in the vehicle motion at different lanes. So, it is principally due to the ``many-body'' effects in the car interaction in contrast to such variables as the mean car density and velocity being actually the zeroth and first moments of the ``one-particle'' distribution function. Therefore, we regard the order parameter as an additional independent state variable of traffic flow. We assume that these correlations are due to a small group of ``fast'' drivers and by taking into account the general properties of the driver behavior we formulate a governing equation for the order parameter. In this context we analyze the instability of homogeneous traffic flow that manifested itself in the above-mentioned phase transitions and gave rise to the hysteresis in both of them. Besides, the jam is characterized by the vehicle flows at different lanes which are independent of one another. We specify a certain simplified model in order to study the general features of the car cluster self-formation under the ``free flow <--> synchronized motion'' phase transition. In particular, we show that the main local parameters of the developed cluster are determined by the state characteristics of vehicle motion only.

Equation of state of dark energy in f (R ) gravity

NASA Astrophysics Data System (ADS)

Takahashi, Kazufumi; Yokoyama, Jun'ichi

2015-04-01

f (R ) gravity is one of the simplest generalizations of general relativity, which may explain the accelerated cosmic expansion without introducing a cosmological constant. Transformed into the Einstein frame, a new scalar degree of freedom appears and it couples with matter fields. In order for f (R ) theories to pass the local tests of general relativity, it has been known that the chameleon mechanism with a so-called thin-shell solution must operate. If the thin-shell constraint is applied to a cosmological situation, it has been claimed that the equation-of-state parameter of dark energy w must be extremely close to -1 . We argue this is due to the incorrect use of the Poisson equation, which is valid only in the static case. By solving the correct Klein-Gordon equation perturbatively, we show that a thin-shell solution exists even if w deviates appreciably from -1 .

Computation of the stability derivatives via CFD and the sensitivity equations

NASA Astrophysics Data System (ADS)

Lei, Guo-Dong; Ren, Yu-Xin

2011-04-01

The method to calculate the aerodynamic stability derivates of aircrafts by using the sensitivity equations is extended to flows with shock waves in this paper. Using the newly developed second-order cell-centered finite volume scheme on the unstructured-grid, the unsteady Euler equations and sensitivity equations are solved simultaneously in a non-inertial frame of reference, so that the aerodynamic stability derivatives can be calculated for aircrafts with complex geometries. Based on the numerical results, behavior of the aerodynamic sensitivity parameters near the shock wave is discussed. Furthermore, the stability derivatives are analyzed for supersonic and hypersonic flows. The numerical results of the stability derivatives are found in good agreement with theoretical results for supersonic flows, and variations of the aerodynamic force and moment predicted by the stability derivatives are very close to those obtained by CFD simulation for both supersonic and hypersonic flows.

Atmospheric pollution history at Linfen (China) uncovered by magnetic and chemical parameters of sediments from a water reservoir.

PubMed

Ma, Mingming; Hu, Shouyun; Cao, Liwan; Appel, Erwin; Wang, Longsheng

2015-09-01

We studied magnetic and chemical parameters of sediments from sediments of a water reservoir at Linfen (China) in order to quantitatively reconstruct the atmospheric pollution history in this region. The results show that the main magnetic phases are magnetite and maghemite originating from the surrounding catchment and from anthropogenic activities, and there is a significant positive relationship between magnetic concentration parameters and heavy metals concentrations, indicating that magnetic proxies can be used to monitor the anthropogenic pollution. In order to uncover the atmospheric pollution history, we combined the known events of environmental improvement with variations of magnetic susceptibility (χ) and heavy metals along the cores to obtain a detailed chronological framework. In addition, air comprehensive pollution index (ACPI) was reconstructed from regression equation among magnetic and chemical parameters as well as atmospheric monitoring data. Based on these results, the atmospheric pollution history was successfully reconstructed. Copyright © 2015 Elsevier Ltd. All rights reserved.

Creation of Frustrated Systems by d-dot Array

NASA Astrophysics Data System (ADS)

Masahiko, Machida

2004-03-01

When a square shape dot of High-Tc superconductor is embedded in s-wave superconducting matrix, half quantized vortices are spontaneously generated at the corners of the dot. This feature gives the magnetic interactions between neighboring dots in array systems composed of sevaral dots of High-Tc superconductor and allows us to make magnetic interaction systems. We propose that we can create interesting frustrated systems like the spin-ice by setting the dots in various manners. In order to demonstrate which types of frustrated systems are possible, we perform numerical simulations for the time-dependent Ginzburg-Landau equation describing dynamics of the superconducting order parameters with d-wave and s-wave symmetries. The simulations reveal that the proposed system has two parameters originated from the magnetic interaction between emerged half vortices. We tune the parameters and show various patterns of half vortices from the Ising to the ice model.

A two-parameter family of double-power-law biorthonormal potential-density expansions

NASA Astrophysics Data System (ADS)

Lilley, Edward J.; Sanders, Jason L.; Evans, N. Wyn

2018-07-01

We present a two-parameter family of biorthonormal double-power-law potential-density expansions. Both the potential and density are given in a closed analytic form and may be rapidly computed via recurrence relations. We show that this family encompasses all the known analytic biorthonormal expansions: the Zhao expansions (themselves generalizations of ones found earlier by Hernquist & Ostriker and by Clutton-Brock) and the recently discovered Lilley et al. expansion. Our new two-parameter family includes expansions based around many familiar spherical density profiles as zeroth-order models, including the γ models and the Jaffe model. It also contains a basis expansion that reproduces the famous Navarro-Frenk-White (NFW) profile at zeroth order. The new basis expansions have been found via a systematic methodology which has wide applications in finding other new expansions. In the process, we also uncovered a novel integral transform solution to Poisson's equation.

A two-parameter family of double-power-law biorthonormal potential-density expansions

NASA Astrophysics Data System (ADS)

Lilley, Edward J.; Sanders, Jason L.; Evans, N. Wyn

2018-05-01

We present a two-parameter family of biorthonormal double-power-law potential-density expansions. Both the potential and density are given in closed analytic form and may be rapidly computed via recurrence relations. We show that this family encompasses all the known analytic biorthonormal expansions: the Zhao expansions (themselves generalizations of ones found earlier by Hernquist & Ostriker and by Clutton-Brock) and the recently discovered Lilley et al. (2017a) expansion. Our new two-parameter family includes expansions based around many familiar spherical density profiles as zeroth-order models, including the γ models and the Jaffe model. It also contains a basis expansion that reproduces the famous Navarro-Frenk-White (NFW) profile at zeroth order. The new basis expansions have been found via a systematic methodology which has wide applications in finding other new expansions. In the process, we also uncovered a novel integral transform solution to Poisson's equation.

A two-parameter family of double-power-law biorthonormal potential-density expansions

NASA Astrophysics Data System (ADS)

Lilley, Edward J.; Sanders, Jason L.; Evans, N. Wyn

2018-05-01

We present a two-parameter family of biorthonormal double-power-law potential-density expansions. Both the potential and density are given in closed analytic form and may be rapidly computed via recurrence relations. We show that this family encompasses all the known analytic biorthonormal expansions: the Zhao expansions (themselves generalizations of ones found earlier by Hernquist & Ostriker and by Clutton-Brock) and the recently discovered Lilley et al. (2018b) expansion. Our new two-parameter family includes expansions based around many familiar spherical density profiles as zeroth-order models, including the γ models and the Jaffe model. It also contains a basis expansion that reproduces the famous Navarro-Frenk-White (NFW) profile at zeroth order. The new basis expansions have been found via a systematic methodology which has wide applications in finding other new expansions. In the process, we also uncovered a novel integral transform solution to Poisson's equation.

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.

Existence and stability of dispersive solutions to the Kadomtsev-Petviashvili equation in the presence of dispersion effect

NASA Astrophysics Data System (ADS)

Das, Amiya; Ganguly, Asish

2017-07-01

The paper deals with Kadomtsev-Petviashvili (KP) equation in presence of a small dispersion effect. The nature of solutions are examined under the dispersion effect by using Lyapunov function and dynamical system theory. We prove that when dispersion is added to the KP equation, in certain regions, yet there exist bounded traveling wave solutions in the form of solitary waves, periodic and elliptic functions. The general solution of the equation with or without the dispersion effect are obtained in terms of Weirstrass ℘ functions and Jacobi elliptic functions. New form of kink-type solutions are established by exploring a new technique based on factorization method, use of functional transformation and the Abel's first order nonlinear equation. Furthermore, the stability analysis of the dispersive solutions are examined which shows that the traveling wave velocity is a bifurcation parameter which governs between different classes of waves. We use the phase plane analysis and show that at a critical velocity, the solution has a transcritical bifurcation.

Certain bright soliton interactions of the Sasa-Satsuma equation in a monomode optical fiber

NASA Astrophysics Data System (ADS)

Liu, Lei; Tian, Bo; Chai, Han-Peng; Yuan, Yu-Qiang

2017-03-01

Under investigation in this paper is the Sasa-Satsuma equation, which describes the propagation of ultrashort pulses in a monomode fiber with the third-order dispersion, self-steepening, and stimulated Raman scattering effects. Based on the known bilinear forms, through the modified expanded formulas and symbolic computation, we construct the bright two-soliton solutions. Through classifying the interactions under different parameter conditions, we reveal six cases of interactions between the two solitons via an asymptotic analysis. With the help of the analytic and graphic analysis, we find that such interactions are different from those of the nonlinear Schrödinger equation and Hirota equation. When those solitons interact with each other, the singular-I soliton is shape-preserving, while the singular-II and nonsingular solitons may be shape preserving or shape changing. Such elastic and inelastic interaction phenomena in a scalar equation might enrich the knowledge of soliton behavior, which could be expected to be experimentally observed.

Certain bright soliton interactions of the Sasa-Satsuma equation in a monomode optical fiber.

PubMed

Liu, Lei; Tian, Bo; Chai, Han-Peng; Yuan, Yu-Qiang

2017-03-01

Under investigation in this paper is the Sasa-Satsuma equation, which describes the propagation of ultrashort pulses in a monomode fiber with the third-order dispersion, self-steepening, and stimulated Raman scattering effects. Based on the known bilinear forms, through the modified expanded formulas and symbolic computation, we construct the bright two-soliton solutions. Through classifying the interactions under different parameter conditions, we reveal six cases of interactions between the two solitons via an asymptotic analysis. With the help of the analytic and graphic analysis, we find that such interactions are different from those of the nonlinear Schrödinger equation and Hirota equation. When those solitons interact with each other, the singular-I soliton is shape-preserving, while the singular-II and nonsingular solitons may be shape preserving or shape changing. Such elastic and inelastic interaction phenomena in a scalar equation might enrich the knowledge of soliton behavior, which could be expected to be experimentally observed.

Simulation of subwavelength metallic gratings using a new implementation of the recursive convolution finite-difference time-domain algorithm.

PubMed

Banerjee, Saswatee; Hoshino, Tetsuya; Cole, James B

2008-08-01

We introduce a new implementation of the finite-difference time-domain (FDTD) algorithm with recursive convolution (RC) for first-order Drude metals. We implemented RC for both Maxwell's equations for light polarized in the plane of incidence (TM mode) and the wave equation for light polarized normal to the plane of incidence (TE mode). We computed the Drude parameters at each wavelength using the measured value of the dielectric constant as a function of the spatial and temporal discretization to ensure both the accuracy of the material model and algorithm stability. For the TE mode, where Maxwell's equations reduce to the wave equation (even in a region of nonuniform permittivity) we introduced a wave equation formulation of RC-FDTD. This greatly reduces the computational cost. We used our methods to compute the diffraction characteristics of metallic gratings in the visible wavelength band and compared our results with frequency-domain calculations.

Development of reference equations for spirometry in Japanese children aged 6-18 years.

PubMed

Takase, Masato; Sakata, Hiroshi; Shikada, Masahiro; Tatara, Katsuyoshi; Fukushima, Takayoshi; Miyakawa, Tomoo

2013-01-01

Spirometry is the most widely used pulmonary function test and the measured values of spirometric parameters need to be evaluated using reference values predicted for the corresponding race, sex, age, and height. However, none of the existing reference equations for Japanese children covers the entire age range of 6-18 years. The Japanese Society of Pediatric Pulmonology had organized a working group in 2006, in order to develop a new set of national standard reference equations for commonly used spirometric parameters that are applicable through the age range of 6-18 years. Quality assured spirometric data were collected through 2006-2008, from 14 institutions in Japan. We applied multiple regression analysis, using age in years (A), square of age (A(2)), height in meters (H), square of height (H(2)), and the product of age and height (AH) as explanatory variables to predict forced vital capacity (FVC), forced expiratory volume in 1 sec (FEV(1)), peak expiratory flow (PEF), forced expiratory flow between 25% and 75% of the FVC (FEF(25-75%)), instantaneous forced expiratory flow when 50% (FEF(50%)) or 75% (FEF(75%)) of the FVC have been expired. Finally, 1,296 tests (674 boys, 622 girls) formed the reference data set. Distributions of the percent predicted values did not differ by ages, confirming excellent fit of the prediction equations throughout the entire age range from 6 to 18 years. Cut-off values (around 5 percentile points) for the parameters were also determined. We recommend the use of this new set of prediction equations together with suggested cut-off values, for assessment of spirometry in Japanese children and adolescents. Copyright © 2012 Wiley Periodicals, Inc.

Large-Scale Chaos and Fluctuations in Active Nematics

NASA Astrophysics Data System (ADS)

Ngo, Sandrine; Peshkov, Anton; Aranson, Igor S.; Bertin, Eric; Ginelli, Francesco; Chaté, Hugues

2014-07-01

We show that dry active nematics, e.g., collections of shaken elongated granular particles, exhibit large-scale spatiotemporal chaos made of interacting dense, ordered, bandlike structures in a parameter region including the linear onset of nematic order. These results are obtained from the study of both the well-known (deterministic) hydrodynamic equations describing these systems and of the self-propelled particle model they were derived from. We prove, in particular, that the chaos stems from the generic instability of the band solution of the hydrodynamic equations. Revisiting the status of the strong fluctuations and long-range correlations in the particle model, we show that the giant number fluctuations observed in the chaotic phase are a trivial consequence of density segregation. However anomalous, curvature-driven number fluctuations are present in the homogeneous quasiordered nematic phase and characterized by a nontrivial scaling exponent.

A stochastic process approach of the drake equation parameters

NASA Astrophysics Data System (ADS)

Glade, Nicolas; Ballet, Pascal; Bastien, Olivier

2012-04-01

The number N of detectable (i.e. communicating) extraterrestrial civilizations in the Milky Way galaxy is usually calculated by using the Drake equation. This equation was established in 1961 by Frank Drake and was the first step to quantifying the Search for ExtraTerrestrial Intelligence (SETI) field. Practically, this equation is rather a simple algebraic expression and its simplistic nature leaves it open to frequent re-expression. An additional problem of the Drake equation is the time-independence of its terms, which for example excludes the effects of the physico-chemical history of the galaxy. Recently, it has been demonstrated that the main shortcoming of the Drake equation is its lack of temporal structure, i.e., it fails to take into account various evolutionary processes. In particular, the Drake equation does not provides any error estimation about the measured quantity. Here, we propose a first treatment of these evolutionary aspects by constructing a simple stochastic process that will be able to provide both a temporal structure to the Drake equation (i.e. introduce time in the Drake formula in order to obtain something like N(t)) and a first standard error measure.

A generic model for a single strain mosquito-transmitted disease with memory on the host and the vector.

PubMed

Sardar, Tridip; Rana, Sourav; Bhattacharya, Sabyasachi; Al-Khaled, Kamel; Chattopadhyay, Joydev

2015-05-01

In the present investigation, three mathematical models on a common single strain mosquito-transmitted diseases are considered. The first one is based on ordinary differential equations, and other two models are based on fractional order differential equations. The proposed models are validated using published monthly dengue incidence data from two provinces of Venezuela during the period 1999-2002. We estimate several parameters of these models like the order of the fractional derivatives (in case of two fractional order systems), the biting rate of mosquito, two probabilities of infection, mosquito recruitment and mortality rates, etc., from the data. The basic reproduction number, R0, for the ODE system is estimated using the data. For two fractional order systems, an upper bound for, R0, is derived and its value is obtained using the published data. The force of infection, and the effective reproduction number, R(t), for the three models are estimated using the data. Sensitivity analysis of the mosquito memory parameter with some important responses is worked out. We use Akaike Information Criterion (AIC) to identify the best model among the three proposed models. It is observed that the model with memory in both the host, and the vector population provides a better agreement with epidemic data. Finally, we provide a control strategy for the vector-borne disease, dengue, using the memory of the host, and the vector. Copyright © 2015 Elsevier Inc. All rights reserved.

The effect of magnetohydrodynamic nano fluid flow through porous cylinder

NASA Astrophysics Data System (ADS)

Widodo, Basuki; Arif, Didik Khusnul; Aryany, Deviana; Asiyah, Nur; Widjajati, Farida Agustini; Kamiran

2017-08-01

This paper concerns about the analysis of the effect of magnetohydrodynamic nano fluid flow through horizontal porous cylinder on steady and incompressible condition. Fluid flow is assumed opposite gravity and induced by magnet field. Porous cylinder is assumed had the same depth of porous and was not absorptive. The First thing to do in this research is to build the model of fluid flow to obtain dimentional governing equations. The dimentional governing equations are consist of continuity equation, momentum equation, and energy equation. Furthermore, the dimensional governing equations are converted to non-dimensional governing equation by using non-dimensional parameters and variables. Then, the non-dimensional governing equations are transformed into similarity equations using stream function and solved using Keller-Box method. The result of numerical solution further is obtained by taking variation of magnetic parameter, Prandtl number, porosity parameter, and volume fraction. The numerical results show that velocity profiles increase and temperature profiles decrease when both of the magnetic and the porosity parameter increase. However, the velocity profiles decrease and the temperature profiles increase when both of the magnetic and the porosity parameter increase.

Experimental study on interfacial area transport in downward two-phase flow

NASA Astrophysics Data System (ADS)

Wang, Guanyi

In view of the importance of two group interfacial area transport equations and lack of corresponding accurate downward flow database that can reveal two group interfacial area transport, a systematic database for adiabatic, air-water, vertically downward two-phase flow in a round pipe with inner diameter of 25.4 mm was collected to gain an insight of interfacial structure and provide benchmarking data for two-group interfacial area transport models. A four-sensor conductivity probe was used to measure the local two phase flow parameters and data was collected with data sampling frequency much higher than conventional data sampling frequency to ensure the accuracy. Axial development of local flow parameter profiles including void fraction, interfacial area concentration, and Sauter mean diameter were presented. Drastic inter-group transfer of void fraction and interfacial area was observed at bubbly to slug transition flow. And the wall peaked interfacial area concentration profiles were observed in churn-turbulent flow. The importance of local data about these phenomenon on flow structure prediction and interfacial area transport equation benchmark was analyzed. Bedsides, in order to investigate the effect of inlet conditions, all experiments were repeated after installing the flow straightening facility, and the results were briefly analyzed. In order to check the accuracy of current data, the experiment results were cross-checked with rotameter measurement as well as drift-flux model prediction, the averaged error is less than 15%. Current models for two-group interfacial area transport equation were evaluated using these data. The results show that two-group interfacial area transport equations with current models can predict most flow conditions with error less than 20%, except some bubbly to slug transition flow conditions and some churn-turbulent flow conditions. The disagreement between models and experiments could result from underestimate of inter-group void transfer.

Exponential-fitted methods for integrating stiff systems of ordinary differential equations: Applications to homogeneous gas-phase chemical kinetics

NASA Technical Reports Server (NTRS)

Pratt, D. T.

1984-01-01

Conventional algorithms for the numerical integration of ordinary differential equations (ODEs) are based on the use of polynomial functions as interpolants. However, the exact solutions of stiff ODEs behave like decaying exponential functions, which are poorly approximated by polynomials. An obvious choice of interpolant are the exponential functions themselves, or their low-order diagonal Pade (rational function) approximants. A number of explicit, A-stable, integration algorithms were derived from the use of a three-parameter exponential function as interpolant, and their relationship to low-order, polynomial-based and rational-function-based implicit and explicit methods were shown by examining their low-order diagonal Pade approximants. A robust implicit formula was derived by exponential fitting the trapezoidal rule. Application of these algorithms to integration of the ODEs governing homogenous, gas-phase chemical kinetics was demonstrated in a developmental code CREK1D, which compares favorably with the Gear-Hindmarsh code LSODE in spite of the use of a primitive stepsize control strategy.

Modulation stability and optical soliton solutions of nonlinear Schrödinger equation with higher order dispersion and nonlinear terms and its applications

NASA Astrophysics Data System (ADS)

Arshad, Muhammad; Seadawy, Aly R.; Lu, Dianchen

2017-12-01

In optical fibers, the higher order non-linear Schrödinger equation (NLSE) with cubic quintic nonlinearity describes the propagation of extremely short pulses. We constructed bright and dark solitons, solitary wave and periodic solitary wave solutions of generalized higher order NLSE in cubic quintic non Kerr medium by applying proposed modified extended mapping method. These obtained solutions have key applications in physics and mathematics. Moreover, we have also presented the formation conditions on solitary wave parameters in which dark and bright solitons can exist for this media. We also gave graphically the movement of constructed solitary wave and soliton solutions, that helps to realize the physical phenomena's of this model. The stability of the model in normal dispersion and anomalous regime is discussed by using the modulation instability analysis, which confirms that all constructed solutions are exact and stable. Many other such types of models arising in applied sciences can also be solved by this reliable, powerful and effective method.

Instabilities and patterns in an active nematic film

NASA Astrophysics Data System (ADS)

Srivastava, Pragya; Marchetti, Cristina

2015-03-01

Experiments on microtubule bundles confined to an oil-water interface have motivated extensive theoretical studies of two-dimensional active nematics. Theoretical models taking into account the interplay between activity, flow and order have remarkably reproduced several experimentally observed features of the defect-dynamics in these ``living'' nematics. Here, we derive minimal description of a two-dimensional active nematic film confined between walls. At high friction, we eliminate the flow to obtain closed equations for the nematic order parameter, with renormalized Frank elastic constants. Active processes can render the ``Frank'' constants negative, resulting in the instability of the uniformly ordered nematic state. The minimal model yields emergent patterns of growing complexity with increasing activity, including bands and turbulent dynamics with a steady density of topological defects, as obtained with the full hydrodynamic equations. We report on the scaling of the length scales of these patterns and of the steady state number of defects with activity and system size. National Science Foundation grant DMR-1305184 and Syracuse Soft Matter Program.

Nonlinear isotherm and kinetics of adsorption of copper from aqueous solutions on bentonite

NASA Astrophysics Data System (ADS)

Sadeghalvad, Bahareh; Khosravi, Sara; Azadmehr, Amir Reza

2016-11-01

Bentonite is one of the most significant of clay minerals that has been studied extensively due to its potential applications in removal of various environmental pollutants. This ability is related to its high ionic exchange capacity and high specific surface area. Copper is one of the important elements of non-ferrous metals found in industrial waste waters. In the present work, the removal of copper from aqueous solutions with Iranian bentonite (from Birjand area, southeastern Iran) used without any chemical pretreatment, was studied. The experimental results were fitted by adsorption isotherms equations with two or three parameters, which include Langmuir, Freundlich, Dubinin-Radushkevich (D-R), Redlich-Peterson, Khan, and Toth models. The best correlation coefficient ( r 2) is 0.9879 observed for Langmuir model, maximum adsorption capacity of bentonite was 55.71 mg/g. The first-order and pseudo-second-order kinetic equations were used to describe the kinetics of adsorption. The experimental data were well fitted by the pseudo-second-order kinetics.

Deformations of a pre-stretched elastic membrane driven by non-uniform electroosmotic flow

NASA Astrophysics Data System (ADS)

Bercovici, Moran; Boyko, Evgeniy; Gat, Amir

2016-11-01

We study viscous-elastic dynamics of fluid confined between a rigid plate and a pre-stretched elastic membrane subjected to non-uniform electroosmotic flow, and focus on the case of a finite-size membrane clamped at its boundaries. Considering small deformations of a strongly pre-stretched membrane, and applying the lubrication approximation for the flow, we derive a linearized leading-order non-homogenous 4th order diffusion equation governing the deformation and pressure fields. We derive a time-dependent Green's function for a rectangular domain, and use it to obtain several basic solutions for the cases of constant and time varying electric fields. In addition, defining an asymptotic expansion where the small parameter is the ratio of the induced to prescribed tension, we obtain a set of four one-way coupled equations providing a first order correction for the deformation field. Funded by the European Research Council (ERC) under the Horizon 2020 Research and Innovation Programme, Grant agreement No. 678734 (MetamorphChip).