WorldWideScience

Sample records for nonlinear steady-state solutions

  1. Simulating nonlinear steady-state traveling waves on the falling liquid film entrained by a gas flow

    International Nuclear Information System (INIS)

    Yu Tsvelodub, O

    2016-01-01

    The article is devoted to the simulation of nonlinear waves on a liquid film flowing under gravity in the known stress field at the interface. In the case of small Reynolds numbers the problem is reduced to the consideration of solutions of the nonlinear integral-differential equation for film thickness deviation from the undisturbed level. Weakly nonlinear steady-state traveling solutions of the equation with wave numbers in a vicinity of neutral wave numbers are constructed analytically. The nature of the wave branching from the undisturbed solution is investigated. Steady-state traveling solutions, whose wave numbers within the instability area are far from neutral wave numbers, are found numerically. (paper)

  2. Simulating nonlinear steady-state traveling waves on the falling liquid film entrained by a gas flow

    Science.gov (United States)

    Tsvelodub, O. Yu; Bocharov, A. A.

    2017-09-01

    The article is devoted to the simulation of nonlinear waves on a liquid film flowing under gravity in the known stress field at the interface. The paper studies nonlinear waves on a liquid film, flowing under the action of gravity in a known stress field at the interface. In the case of small Reynolds numbers the problem is reduced to the consideration of solutions of the nonlinear integral-differential equation for film thickness deviation from the undisturbed level. The periodic and soliton steady-state traveling solutions of this equation have been numerically found. The analysis of branching of new families of steady-state traveling solutions has been performed. In particular, it is shown that this model equation has solutions in the form of solitons-humps.

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

    Science.gov (United States)

    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.

  4. Dynamical approach study of spurious steady-state numerical solutions of nonlinear differential equations. Part 1: The ODE connection and its implications for algorithm development in computational fluid dynamics

    Science.gov (United States)

    Yee, H. C.; Sweby, P. K.; Griffiths, D. F.

    1990-01-01

    Spurious stable as well as unstable steady state numerical solutions, spurious asymptotic numerical solutions of higher period, and even stable chaotic behavior can occur when finite difference methods are used to solve nonlinear differential equations (DE) numerically. The occurrence of spurious asymptotes is independent of whether the DE possesses a unique steady state or has additional periodic solutions and/or exhibits chaotic phenomena. The form of the nonlinear DEs and the type of numerical schemes are the determining factor. In addition, the occurrence of spurious steady states is not restricted to the time steps that are beyond the linearized stability limit of the scheme. In many instances, it can occur below the linearized stability limit. Therefore, it is essential for practitioners in computational sciences to be knowledgeable about the dynamical behavior of finite difference methods for nonlinear scalar DEs before the actual application of these methods to practical computations. It is also important to change the traditional way of thinking and practices when dealing with genuinely nonlinear problems. In the past, spurious asymptotes were observed in numerical computations but tended to be ignored because they all were assumed to lie beyond the linearized stability limits of the time step parameter delta t. As can be seen from the study, bifurcations to and from spurious asymptotic solutions and transitions to computational instability not only are highly scheme dependent and problem dependent, but also initial data and boundary condition dependent, and not limited to time steps that are beyond the linearized stability limit.

  5. Bifurcation of positive solutions to scalar reaction-diffusion equations with nonlinear boundary condition

    Science.gov (United States)

    Liu, Ping; Shi, Junping

    2018-01-01

    The bifurcation of non-trivial steady state solutions of a scalar reaction-diffusion equation with nonlinear boundary conditions is considered using several new abstract bifurcation theorems. The existence and stability of positive steady state solutions are proved using a unified approach. The general results are applied to a Laplace equation with nonlinear boundary condition and bistable nonlinearity, and an elliptic equation with superlinear nonlinearity and sublinear boundary conditions.

  6. Solution of generalized control system equations at steady state

    International Nuclear Information System (INIS)

    Vilim, R.B.

    1987-01-01

    Although a number of reactor systems codes feature generalized control system models, none of the models offer a steady-state solution finder. Indeed, if a transient is to begin from steady-state conditions, the user must provide estimates for the control system initial conditions and run a null transient until the plant converges to steady state. Several such transients may have to be run before values for control system demand signals are found that produce the desired plant steady state. The intent of this paper is (a) to present the control system equations assumed in the SASSYS reactor systems code and to identify the appropriate set of initial conditions, (b) to describe the generalized block diagram approach used to represent these equations, and (c) to describe a solution method and algorithm for computing these initial conditions from the block diagram. The algorithm has been installed in the SASSYS code for use with the code's generalized control system model. The solution finder greatly enhances the effectiveness of the code and the efficiency of the user in running it

  7. Transient and Steady-State Responses of an Asymmetric Nonlinear Oscillator

    Directory of Open Access Journals (Sweden)

    Alex Elías-Zúñiga

    2013-01-01

    oscillator that describes the motion of a damped, forced system supported symmetrically by simple shear springs on a smooth inclined bearing surface. We also use the percentage overshoot value to study the influence of damping and nonlinearity on the transient and steady-state oscillatory amplitudes.

  8. Spurious Solutions Of Nonlinear Differential Equations

    Science.gov (United States)

    Yee, H. C.; Sweby, P. K.; Griffiths, D. F.

    1992-01-01

    Report utilizes nonlinear-dynamics approach to investigate possible sources of errors and slow convergence and non-convergence of steady-state numerical solutions when using time-dependent approach for problems containing nonlinear source terms. Emphasizes implications for development of algorithms in CFD and computational sciences in general. Main fundamental conclusion of study is that qualitative features of nonlinear differential equations cannot be adequately represented by finite-difference method and vice versa.

  9. Stress evaluation of metallic material under steady state based on nonlinear critically refracted longitudinal wave

    Science.gov (United States)

    Mao, Hanling; Zhang, Yuhua; Mao, Hanying; Li, Xinxin; Huang, Zhenfeng

    2018-06-01

    This paper presents the study of applying the nonlinear ultrasonic wave to evaluate the stress state of metallic materials under steady state. The pre-stress loading method is applied to guarantee components with steady stress. Three kinds of nonlinear ultrasonic experiments based on critically refracted longitudinal wave are conducted on components which the critically refracted longitudinal wave propagates along x, x1 and x2 direction. Experimental results indicate the second and third order relative nonlinear coefficients monotonically increase with stress, and the normalized relationship is consistent with simplified dislocation models, which indicates the experimental result is logical. The combined ultrasonic nonlinear parameter is proposed, and three stress evaluation models at x direction are established based on three ultrasonic nonlinear parameters, which the estimation error is below 5%. Then two stress detection models at x1 and x2 direction are built based on combined ultrasonic nonlinear parameter, the stress synthesis method is applied to calculate the magnitude and direction of principal stress. The results show the prediction error is within 5% and the angle deviation is within 1.5°. Therefore the nonlinear ultrasonic technique based on LCR wave could be applied to nondestructively evaluate the stress of metallic materials under steady state which the magnitude and direction are included.

  10. Instabilities in fluid layers and in reaction-diffusion systems: Steady states, time-periodic solutions, non-periodic attractors, and related convective and otherwise non-linear phenomena

    Energy Technology Data Exchange (ETDEWEB)

    Garcia Velarde, M

    1977-07-01

    Thermo convective instabilities in horizontal fluid layers are discussed with emphasis on the Rayleigh-Bernard model problem. Steady solutions and time-dependent phenomena (relaxation oscillations and transition to turbulence) are studied within the nonlinear Boussinesq-Oberbeck approximation. Homogeneous steady solutions, limit cycles, and inhomogeneous (ordered) spatial structures are also studied in simple reaction-diffusion systems. Lastly, the non-periodic attractor that appears at large Rayleigh numbers in the truncated Boussinesq-Oberbeck model of Lorenz, is constructed, and a discussion of turbulent behavior is given. (Author) 105 refs.

  11. Instabilities in fluid layers and in reaction-diffusion systems: Steady states, time-periodic solutions, non-periodic attractors, and related convective and otherwise non-linear phenomena

    International Nuclear Information System (INIS)

    Garcia Velarde, M.

    1977-01-01

    Thermoconvective instabilities in horizontal fluid layers are discussed with emphasis on the Rayleigh-Benard model problem. Steady solutions and time-dependent phenomena (relaxation oscillations and transition to turbulence) are studied within the nonlinear Boussinesq-Oberbeck approximation. Homogeneous steady solutions, limit cycles, and inhomogeneous (ordered) spatial structures are also studied in simple reaction-diffusion systems. Lastly, the non-periodic attractor that appears at large Rayleigh numbers in the truncated Boussinesq-Oberbeck model of Lorenz, is constructed, and a discussion of turbulent behavior is given. (author) [es

  12. Instabilities in fluid layers and in reaction-diffusion systems: Steady states, time-periodic solutions, non-periodic attractors, and related convective and otherwise non-linear phenomena

    International Nuclear Information System (INIS)

    Garcia Velarde, M.

    1977-01-01

    Thermo convective instabilities in horizontal fluid layers are discussed with emphasis on the Rayleigh-Bernard model problem. Steady solutions and time-dependent phenomena (relaxation oscillations and transition to turbulence) are studied within the nonlinear Boussinesq-Oberbeck approximation. Homogeneous steady solutions, limit cycles, and inhomogeneous (ordered) spatial structures are also studied in simple reaction-diffusion systems. Lastly, the non-periodic attractor that appears at large Rayleigh numbers in the truncated Boussinesq-Oberbeck model of Lorenz, is constructed, and a discussion of turbulent behavior is given. (Author) 105 refs

  13. Use of wiener nonlinear MPC to control a CSTR with multiple steady state

    OpenAIRE

    Lusson Cervantes, A.; Agamennoni, O.E.; Figueroa, J.L.

    2003-01-01

    In this paper a Nonlinear Model Predictive Control based on a Wiener Model with a Piecewise Linear gain is presented. The major advantages of this algorithm is that it retains all the interesting properties of the classical linear MPC and the computations are easy to solve due to the canonical structure of the nonlinear gain. The proposed control scheme is applied to a nonlinear CSTR that presents multiple steady states.

  14. Adaptive solution of some steady-state fluid-structure interaction problems

    International Nuclear Information System (INIS)

    Etienne, S.; Pelletier, D.

    2003-01-01

    This paper presents a general integrated and coupled formulation for modeling the steady-state interaction of a viscous incompressible flow with an elastic structure undergoing large displacements (geometric non-linearities). This constitutes an initial step towards developing a sensitivity analysis formulation for this class of problems. The formulation uses velocity and pressures as unknowns in a flow domain and displacements in the structural components. An interface formulation is presented that leads to clear and simple finite element implementation of the equilibrium conditions at the fluid-solid interface. Issues of error estimation and mesh adaptation are discussed. The adaptive formulation is verified on a problem with a closed form solution. It is then applied to a sample case for which the structure undergoes large displacements induced by the flow. (author)

  15. Chaotic and steady state behaviour of a nonlinear controlled gyro subjected to harmonic disturbances

    International Nuclear Information System (INIS)

    Perez Polo, Manuel F.; Perez Molina, Manuel

    2007-01-01

    Chaotic and steady state motions of a nonlinear controlled gimbals suspension gyro used to stabilize an external body are studied in this paper. The equations of the gyro without nonlinear control are deduced from the Euler-Lagrange equations by using the nutation theory. The equations of the system show that a cyclic variable appears. Its elimination allows us to find an auxiliary nonlinear system from which it is possible to deduce a nonlinear control law in order to obtain a desired equilibrium point. From the analysis of the nonlinear control law it is possible to show that due to both harmonic disturbances in the platform of the gyro and in the body to stabilize, regular and chaotic motions can appear. The chaotic motion is researched by means of chaos maps, bifurcation diagrams, sensitivity to initial conditions, Lyapunov exponents and Fourier spectrum density. The transition from chaotic to steady state motion by eliminating the harmonic disturbances from the modification of the initial nonlinear control law is also researched. Next, the paper shows how to use the chaotic motion in order to obtain small input signals so that the desired equilibrium state of the gyro can be reached. The developed methodology and its compared performance are evaluated through analytical methods and numerical simulations

  16. Chaotic and steady state behaviour of a nonlinear controlled gyro subjected to harmonic disturbances

    Energy Technology Data Exchange (ETDEWEB)

    Perez Polo, Manuel F. [Department of Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Escuela Politecnica Superior, Campus de San Vicente, 03071 Alicante (Spain)]. E-mail: manolo@dfists.ua.es; Perez Molina, Manuel [Facultad de Ciencias Matematicas, Universidad Nacional de Educacion a Distancia, UNED, C/Boyero 12-1A, Alicante 03007 (Spain)]. E-mail: ma_perez_m@hotmail.com

    2007-07-15

    Chaotic and steady state motions of a nonlinear controlled gimbals suspension gyro used to stabilize an external body are studied in this paper. The equations of the gyro without nonlinear control are deduced from the Euler-Lagrange equations by using the nutation theory. The equations of the system show that a cyclic variable appears. Its elimination allows us to find an auxiliary nonlinear system from which it is possible to deduce a nonlinear control law in order to obtain a desired equilibrium point. From the analysis of the nonlinear control law it is possible to show that due to both harmonic disturbances in the platform of the gyro and in the body to stabilize, regular and chaotic motions can appear. The chaotic motion is researched by means of chaos maps, bifurcation diagrams, sensitivity to initial conditions, Lyapunov exponents and Fourier spectrum density. The transition from chaotic to steady state motion by eliminating the harmonic disturbances from the modification of the initial nonlinear control law is also researched. Next, the paper shows how to use the chaotic motion in order to obtain small input signals so that the desired equilibrium state of the gyro can be reached. The developed methodology and its compared performance are evaluated through analytical methods and numerical simulations.

  17. Singular perturbation solutions of steady-state Poisson-Nernst-Planck systems.

    Science.gov (United States)

    Wang, Xiang-Sheng; He, Dongdong; Wylie, Jonathan J; Huang, Huaxiong

    2014-02-01

    We study the Poisson-Nernst-Planck (PNP) system with an arbitrary number of ion species with arbitrary valences in the absence of fixed charges. Assuming point charges and that the Debye length is small relative to the domain size, we derive an asymptotic formula for the steady-state solution by matching outer and boundary layer solutions. The case of two ionic species has been extensively studied, the uniqueness of the solution has been proved, and an explicit expression for the solution has been obtained. However, the case of three or more ions has received significantly less attention. Previous work has indicated that the solution may be nonunique and that even obtaining numerical solutions is a difficult task since one must solve complicated systems of nonlinear equations. By adopting a methodology that preserves the symmetries of the PNP system, we show that determining the outer solution effectively reduces to solving a single scalar transcendental equation. Due to the simple form of the transcendental equation, it can be solved numerically in a straightforward manner. Our methodology thus provides a standard procedure for solving the PNP system and we illustrate this by solving some practical examples. Despite the fact that for three ions, previous studies have indicated that multiple solutions may exist, we show that all except for one of these solutions are unphysical and thereby prove the existence and uniqueness for the three-ion case.

  18. Steady state solution of the Poisson-Nernst-Planck equations

    International Nuclear Information System (INIS)

    Golovnev, A.; Trimper, S.

    2010-01-01

    The exact steady state solution of the Poisson-Nernst-Planck equations (PNP) is given in terms of Jacobi elliptic functions. A more tractable approximate solution is derived which can be used to compare the results with experimental observations in binary electrolytes. The breakdown of the PNP for high concentration and high applied voltage is discussed.

  19. Multiple solutions of steady-state Poisson–Nernst–Planck equations with steric effects

    International Nuclear Information System (INIS)

    Lin, Tai-Chia; Eisenberg, Bob

    2015-01-01

    Experiments measuring currents through single protein channels show unstable currents. Channels switch between ‘open’ or ‘closed’ states in a spontaneous stochastic process called gating. Currents are either (nearly) zero or at a definite level, characteristic of each type of protein, independent of time, once the channel is open. The steady state Poisson–Nernst–Planck equations with steric effects (PNP-steric equations) describe steady current through the open channel quite well, in a wide variety of conditions. Here we study the existence of multiple solutions of steady state PNP-steric equations to see if they themselves, without modification or augmentation, can describe two levels of current. We prove that there are two steady state solutions of PNP-steric equations for (a) three types of ion species (two types of cations and one type of anion) with a positive constant permanent charge, and (b) four types of ion species (two types of cations and their counter-ions) with a constant permanent charge but no sign condition. The excess currents (due to steric effects) associated with these two steady state solutions are derived and expressed as two distinct formulas. Our results indicate that PNP-steric equations may become a useful model to study spontaneous gating of ion channels. Spontaneous gating is thought to involve small structural changes in the channel protein that perhaps produce large changes in the profiles of free energy that determine ion flow. Gating is known to be modulated by external structures. Both can be included in future extensions of our present analysis. (paper)

  20. Stabilizing the border steady-state solution of two interacting ...

    African Journals Online (AJOL)

    In this paper, we have successfully developed a feedback control which has been used to stabilize an unstable steady-state solution (0, 3.3534). This convergence has occurred when the values of the final time are 190, 200, 210 and 220 which corresponds to the scenario when the value of the step length of our simulation ...

  1. Nonlinear steady-state coupling of LH waves

    International Nuclear Information System (INIS)

    Ko, K.; Krapchev, V.B.

    1981-02-01

    The coupling of lower hybrid waves at the plasma edge by a two waveguide array with self-consistent density modulation is solved numerically. For a linear density profile, the governing nonlinear Klein-Gordon equation for the electric field can be written as a system of nonlinearly modified Airy equations in Fourier k/sub z/-space. Numerical solutions to the nonlinear system satisfying radiation condition are obtained. Spectra broadening and modifications to resonance cone trajectories are observed with increase of incident power

  2. Algorithm for determining two-periodic steady-states in AC machines directly in time domain

    Directory of Open Access Journals (Sweden)

    Sobczyk Tadeusz J.

    2016-09-01

    Full Text Available This paper describes an algorithm for finding steady states in AC machines for the cases of their two-periodic nature. The algorithm enables to specify the steady-state solution identified directly in time domain despite of the fact that two-periodic waveforms are not repeated in any finite time interval. The basis for such an algorithm is a discrete differential operator that specifies the temporary values of the derivative of the two-periodic function in the selected set of points on the basis of the values of that function in the same set of points. It allows to develop algebraic equations defining the steady state solution reached in a chosen point set for the nonlinear differential equations describing the AC machines when electrical and mechanical equations should be solved together. That set of those values allows determining the steady state solution at any time instant up to infinity. The algorithm described in this paper is competitive with respect to the one known in literature an approach based on the harmonic balance method operated in frequency domain.

  3. Dissipative dark matter halos: The steady state solution

    Science.gov (United States)

    Foot, R.

    2018-02-01

    Dissipative dark matter, where dark matter particle properties closely resemble familiar baryonic matter, is considered. Mirror dark matter, which arises from an isomorphic hidden sector, is a specific and theoretically constrained scenario. Other possibilities include models with more generic hidden sectors that contain massless dark photons [unbroken U (1 ) gauge interactions]. Such dark matter not only features dissipative cooling processes but also is assumed to have nontrivial heating sourced by ordinary supernovae (facilitated by the kinetic mixing interaction). The dynamics of dissipative dark matter halos around rotationally supported galaxies, influenced by heating as well as cooling processes, can be modeled by fluid equations. For a sufficiently isolated galaxy with a stable star formation rate, the dissipative dark matter halos are expected to evolve to a steady state configuration which is in hydrostatic equilibrium and where heating and cooling rates locally balance. Here, we take into account the major cooling and heating processes, and numerically solve for the steady state solution under the assumptions of spherical symmetry, negligible dark magnetic fields, and that supernova sourced energy is transported to the halo via dark radiation. For the parameters considered, and assumptions made, we were unable to find a physically realistic solution for the constrained case of mirror dark matter halos. Halo cooling generally exceeds heating at realistic halo mass densities. This problem can be rectified in more generic dissipative dark matter models, and we discuss a specific example in some detail.

  4. On the physical solutions to the heat equation subjected to nonlinear boundary conditions

    International Nuclear Information System (INIS)

    Gama, R.M.S. da.

    1990-01-01

    This work consists of a discussion on the physical solutions to the steady-state heat transfer equation, when it is subjected to nonlinear boundary conditions. It will be presented a functional, whose minimum occurs for the (unique) physical solution to the condidered heat transfer problem, suitable for a large class of typical (nonlinear) boundary conditions (representing the radiative/convective loss from the body to the environment). It will be demonstrated that these problems admit-always one, and only one, physical solution (which represents the absolute temperature). (author)

  5. Dissipative dark matter halos: The steady state solution. II.

    Science.gov (United States)

    Foot, R.

    2018-05-01

    Within the mirror dark matter model and dissipative dark matter models in general, halos around galaxies with active star formation (including spirals and gas-rich dwarfs) are dynamical: they expand and contract in response to heating and cooling processes. Ordinary type II supernovae (SNe) can provide the dominant heat source, which is possible if kinetic mixing interaction exists with strength ɛ ˜10-9- 10-10 . Dissipative dark matter halos can be modeled as a fluid governed by Euler's equations. Around sufficiently isolated and unperturbed galaxies the halo can relax to a steady state configuration, where heating and cooling rates locally balance and hydrostatic equilibrium prevails. These steady state conditions can be solved to derive the physical properties, including the halo density and temperature profiles, for model galaxies. Here, we consider idealized spherically symmetric galaxies within the mirror dark particle model, as in our earlier paper [Phys. Rev. D 97, 043012 (2018), 10.1103/PhysRevD.97.043012], but we assume that the local halo heating in the SN vicinity dominates over radiative sources. With this assumption, physically interesting steady state solutions arise which we compute for a representative range of model galaxies. The end result is a rather simple description of the dark matter halo around idealized spherically symmetric systems, characterized in principle by only one parameter, with physical properties that closely resemble the empirical properties of disk galaxies.

  6. Parallel shooting methods for finding steady state solutions to engine simulation models

    DEFF Research Database (Denmark)

    Andersen, Stig Kildegård; Thomsen, Per Grove; Carlsen, Henrik

    2007-01-01

    Parallel single- and multiple shooting methods were tested for finding periodic steady state solutions to a Stirling engine model. The model was used to illustrate features of the methods and possibilities for optimisations. Performance was measured using simulation of an experimental data set...

  7. Spurious Numerical Solutions Of Differential Equations

    Science.gov (United States)

    Lafon, A.; Yee, H. C.

    1995-01-01

    Paper presents detailed study of spurious steady-state numerical solutions of differential equations that contain nonlinear source terms. Main objectives of this study are (1) to investigate how well numerical steady-state solutions of model nonlinear reaction/convection boundary-value problem mimic true steady-state solutions and (2) to relate findings of this investigation to implications for interpretation of numerical results from computational-fluid-dynamics algorithms and computer codes used to simulate reacting flows.

  8. Natural equilibria in steady-state neutron diffusion with temperature feedback

    International Nuclear Information System (INIS)

    Pounders, J. M.; Ingram, R.

    2013-01-01

    The critical diffusion equation with feedback is investigated within the context of steady-state multiphysics. It is proposed that for critical configurations there is no need to include the multiplication factor k in the formulation of the diffusion equation. This is notable because exclusion of k from the coupled system of equations precludes the mathematically tenuous notion of a nonlinear eigenvalue problem. On the other hand, it is shown that if the factor k is retained in the diffusion equation, as is currently common practice, then the resulting problem is equivalent to the constrained minimization of a functional representing the critical equilibrium of neutron and temperature distributions. The unconstrained solution corresponding to k = 1 represents the natural equilibrium of a critical system at steady-state. Computational methods for solving the constrained problem (with k) are briefly reviewed from the literature and a method for the unconstrained problem (without k) is outlined. A numerical example is studied to examine the effects of the constraint in the nonlinear system. (authors)

  9. Steady-state mechanical squeezing and ground-state cooling of a Duffing anharmonic oscillator in an optomechanical cavity assisted by a nonlinear medium

    Science.gov (United States)

    Momeni, F.; Naderi, M. H.

    2018-05-01

    In this paper, we study theoretically a hybrid optomechanical system consisting of a degenerate optical parametric amplifier inside a driven optical cavity with a moving end mirror which is modeled as a stiffening Duffing-like anharmonic quantum mechanical oscillator. By providing analytical expressions for the critical values of the system parameters corresponding to the emergence of the multistability behavior in the steady-state response of the system, we show that the stiffening mechanical Duffing anharmonicity reduces the width of the multistability region while the optical parametric nonlinearity can be exploited to drive the system toward the multistability region. We also show that for appropriate values of the mechanical anharmonicity strength the steady-state mechanical squeezing and the ground-state cooling of the mechanical resonator can be achieved. Moreover, we find that the presence of the nonlinear gain medium can lead to the improvement of the mechanical anharmonicity-induced cooling of the mechanical motion, as well as to the mechanical squeezing beyond the standard quantum limit of 3 dB.

  10. Transient and Steady-State Analysis of Nonlinear RF and Microwave Circuits

    Directory of Open Access Journals (Sweden)

    Zhu Lei(Lana

    2006-01-01

    Full Text Available This paper offers a review of simulation methods currently available for the transient and steady-state analysis of nonlinear RF and microwave circuits. The most general method continues to be the time-marching approach used in Spice, but more recent methods based on multiple time dimensions are particularly effective for RF and microwave circuits. We derive nodal formulations for the most widely used multiple time dimension methods. We put special emphasis on methods for the analysis of oscillators based in the warped multitime partial differential equations (WaMPDE approach. Case studies of a Colpitts oscillator and a voltage controlled Clapp-Gouriet oscillator are presented and discussed. The accuracy of the amplitude and phase of these methods is investigated. It is shown that the exploitation of frequency-domain latency reduces the computational effort.

  11. Noise-Induced Modulation of the Relaxation Kinetics around a Non-Equilibrium Steady State of Non-Linear Chemical Reaction Networks

    OpenAIRE

    Ramaswamy, Rajesh; Sbalzarini, Ivo F; González-Segredo, Nélido

    2011-01-01

    Stochastic effects from correlated noise non-trivially modulate the kinetics of non-linear chemical reaction networks. This is especially important in systems where reactions are confined to small volumes and reactants are delivered in bursts. We characterise how the two noise sources confinement and burst modulate the relaxation kinetics of a non-linear reaction network around a non-equilibrium steady state. We find that the lifetimes of species change with burst input and confinement. Confi...

  12. Stability of periodic steady-state solutions to a non-isentropic Euler-Poisson system

    Science.gov (United States)

    Liu, Cunming; Peng, Yue-Jun

    2017-06-01

    We study the stability of periodic smooth solutions near non-constant steady-states for a non-isentropic Euler-Poisson system without temperature damping term. The system arises in the theory of semiconductors for which the doping profile is a given smooth function. In this stability problem, there are no special restrictions on the size of the doping profile, but only on the size of the perturbation. We prove that small perturbations of periodic steady-states are exponentially stable for large time. For this purpose, we introduce new variables and choose a non-diagonal symmetrizer of the full Euler equations to recover dissipation estimates. This also allows to make the proof of the stability result very simple and concise.

  13. The steady state solutions of radiatively driven stellar winds for a non-Sobolev, pure absorption model

    International Nuclear Information System (INIS)

    Poe, C.H.; Owocki, S.P.; Castor, J.I.

    1990-01-01

    The steady state solution topology for absorption line-driven flows is investigated for the condition that the Sobolev approximation is not used to compute the line force. The solution topology near the sonic point is of the nodal type with two positive slope solutions. The shallower of these slopes applies to reasonable lower boundary conditions and realistic ion thermal speed v(th) and to the Sobolev limit of zero of the usual Castor, Abbott, and Klein model. At finite v(th), this solution consists of a family of very similar solutions converging on the sonic point. It is concluded that a non-Sobolev, absorption line-driven flow with a realistic values of v(th) has no uniquely defined steady state. To the extent that a pure absorption model of the outflow of stellar winds is applicable, radiatively driven winds should be intrinsically variable. 34 refs

  14. Analysis of the magnetohydrodynamic equations and study of the nonlinear solution bifurcations

    International Nuclear Information System (INIS)

    Morros Tosas, J.

    1989-05-01

    The nonlinear saturation of a plasma magnetohydrodynamic instabilities is studied, by means of a bifurcation theory. The work includes: an accurate mathematical method to study the MHD equations, in which the physical content is clear; and the study of the nonlinear solutions of the branch bifurcations, applied to different unstable plasma models. A scalar function representation is proposed for the MHD equations. This representation is characterized by a reference steady magnetic field and by a velocity field, which allow to write the equations for the scalar functions. An approximation method, leading to the obtention of the reduced equations applied in the instability study, is given. The cylindrical or toroidal plasmas are studied by using the nonlinear solutions bifurcation. Concerning the cylindrical plasma, the representation leads to a reduced system which enables the analytical calculations: two different steady bifurcation solutions are obtained. In the case of the toroidal plasma, an appropriate reduced equations system, is obtained. A qualitative approach of the Kink-type steady solution bifurcation, in a toroidal geometry, is performed [fr

  15. Analytical solution and simplified analysis of coupled parent-daughter steady-state transport with multirate mass transfer

    Science.gov (United States)

    R. Haggerty

    2013-01-01

    In this technical note, a steady-state analytical solution of concentrations of a parent solute reacting to a daughter solute, both of which are undergoing transport and multirate mass transfer, is presented. Although the governing equations are complicated, the resulting solution can be expressed in simple terms. A function of the ratio of concentrations, In (daughter...

  16. Analytical Solutions to Nonlinear Conservative Oscillator with Fifth-Order Nonlinearity

    DEFF Research Database (Denmark)

    Sfahania, M. G.; Ganji, S. S.; Barari, Amin

    2010-01-01

    This paper describes analytical and numerical methods to analyze the steady state periodic response of an oscillator with symmetric elastic and inertia nonlinearity. A new implementation of the homotopy perturbation method (HPM) and an ancient Chinese method called the max-min approach are presen...

  17. Quantum thermodynamics of nanoscale steady states far from equilibrium

    Science.gov (United States)

    Taniguchi, Nobuhiko

    2018-04-01

    We develop an exact quantum thermodynamic description for a noninteracting nanoscale steady state that couples strongly with multiple reservoirs. We demonstrate that there exists a steady-state extension of the thermodynamic function that correctly accounts for the multiterminal Landauer-Büttiker formula of quantum transport of charge, energy, or heat via the nonequilibrium thermodynamic relations. Its explicit form is obtained for a single bosonic or fermionic level in the wide-band limit, and corresponding thermodynamic forces (affinities) are identified. Nonlinear generalization of the Onsager reciprocity relations are derived. We suggest that the steady-state thermodynamic function is also capable of characterizing the heat current fluctuations of the critical transport where the thermal fluctuations dominate. Also, the suggested nonequilibrium steady-state thermodynamic relations seemingly persist for a spin-degenerate single level with local interaction.

  18. On the analytic solution of the steady flow of a fourth grade fluid

    International Nuclear Information System (INIS)

    Sajid, M.; Hayat, T.; Asghar, S.

    2006-01-01

    The steady flow of a fourth grade fluid is a problem belonging to non-Newtonian fluid mechanics and deserves to be more widely studied than it has been to date. In the non-linear regime the literature is scarce. We develop a formulation suitable for solution of hydrodynamic equation containing non-linear rheological effects of fourth grade fluids. The homotopy analysis method (HAM) is used to investigate the flow of a fourth grade fluid past a porous plate. Explicit analytic solution is given. The non-linear effects on the velocity distribution is shown and discussed. Comparison of the present analysis is also made with the existing results in the literature

  19. Stochastic Galerkin methods for the steady-state Navier–Stokes equations

    Energy Technology Data Exchange (ETDEWEB)

    Sousedík, Bedřich, E-mail: sousedik@umbc.edu [Department of Mathematics and Statistics, University of Maryland, Baltimore County, 1000 Hilltop Circle, Baltimore, MD 21250 (United States); Elman, Howard C., E-mail: elman@cs.umd.edu [Department of Computer Science and Institute for Advanced Computer Studies, University of Maryland, College Park, MD 20742 (United States)

    2016-07-01

    We study the steady-state Navier–Stokes equations in the context of stochastic finite element discretizations. Specifically, we assume that the viscosity is a random field given in the form of a generalized polynomial chaos expansion. For the resulting stochastic problem, we formulate the model and linearization schemes using Picard and Newton iterations in the framework of the stochastic Galerkin method, and we explore properties of the resulting stochastic solutions. We also propose a preconditioner for solving the linear systems of equations arising at each step of the stochastic (Galerkin) nonlinear iteration and demonstrate its effectiveness for solving a set of benchmark problems.

  20. Solving Nonlinear Coupled Differential Equations

    Science.gov (United States)

    Mitchell, L.; David, J.

    1986-01-01

    Harmonic balance method developed to obtain approximate steady-state solutions for nonlinear coupled ordinary differential equations. Method usable with transfer matrices commonly used to analyze shaft systems. Solution to nonlinear equation, with periodic forcing function represented as sum of series similar to Fourier series but with form of terms suggested by equation itself.

  1. Ground state solutions for diffusion system with superlinear nonlinearity

    Directory of Open Access Journals (Sweden)

    Zhiming Luo

    2015-03-01

    where $z=(u,v\\colon\\mathbb{R}\\times\\mathbb{R}^{N}\\rightarrow\\mathbb{R}^{2}$, $b\\in C^{1}(\\mathbb{R}\\times\\mathbb{R}^{N}, \\mathbb{R}^{N}$ and $V(x\\in C(\\mathbb{R}^{N},\\mathbb{R}$. Under suitable assumptions on the nonlinearity, we establish the existence of ground state solutions by the generalized Nehari manifold method developed recently by Szulkin and Weth.

  2. Improved Dyson series expansion for steady-state quantum transport beyond the weak coupling limit: Divergences and resolution

    International Nuclear Information System (INIS)

    Thingna, Juzar; Zhou, Hangbo; Wang, Jian-Sheng

    2014-01-01

    We present a general theory to calculate the steady-state heat and electronic currents for nonlinear systems using a perturbative expansion in the system-bath coupling. We explicitly demonstrate that using the truncated Dyson-series leads to divergences in the steady-state limit, thus making it impossible to be used for actual applications. In order to resolve the divergences, we propose a unique choice of initial condition for the reduced density matrix, which removes the divergences at each order. Our approach not only allows us to use the truncated Dyson-series, with a reasonable choice of initial condition, but also gives the expected result that the steady-state solutions should be independent of initial preparations. Using our improved Dyson series we evaluate the heat and electronic currents up to fourth-order in system-bath coupling, a considerable improvement over the standard quantum master equation techniques. We then numerically corroborate our theory for archetypal settings of linear systems using the exact nonequilibrium Green's function approach. Finally, to demonstrate the advantage of our approach, we deal with the nonlinear spin-boson model to evaluate heat current up to fourth-order and find signatures of cotunnelling process

  3. Steady-state solution growth of microcrystalline silicon on nanocrystalline seed layers on glass

    Science.gov (United States)

    Bansen, R.; Ehlers, C.; Teubner, Th.; Boeck, T.

    2016-09-01

    The growth of polycrystalline silicon layers on glass from tin solutions at low temperatures is presented. This approach is based on the steady-state solution growth of Si crystallites on nanocrystalline seed layers, which are prepared in a preceding process step. Scanning electron microscopy and atomic force microscopy investigations reveal details about the seed layer surfaces, which consist of small hillocks, as well as about Sn inclusions and gaps along the glass substrate after solution growth. The successful growth of continuous microcrystalline Si layers with grain sizes up to several ten micrometers shows the feasibility of the process and makes it interesting for photovoltaics. Project supported by the German Research Foundation (DFG) (No. BO 1129/5-1).

  4. Nonlinear oscillatory rheology and structure of wormlike micellar solutions and colloidal suspensions

    Science.gov (United States)

    Gurnon, Amanda Kate

    this constitutive model are tested by comparison with experiments on model WLM solutions. Further comparisons to the nonlinear oscillatory shear responses measured from colloidal suspensions establishes this analysis as a promising, quantitative method for understanding the underlying mechanisms responsible for the nonlinear dynamic response of complex fluids. A new experimental technique is developed to measure the microstructure of complex fluids during steady and transient shear flow using small-angle neutron scattering (SANS). The Flow-SANS experimental method is now available to the broader user communities at the NIST Center for Neutron Research, Gaithersburg, MD and the Institut Laue-Langevin, Grenoble, France. Using this new method, a model shear banding WLM solution is interrogated under steady and oscillatory shear. For the first time, the flow-SANS methods identify new metastable states for shear banding WLM solutions, thus establishing the method as capable of probing new states not accessible using traditional steady or linear oscillatory shear methods. The flow-induced three-dimensional microstructure of a colloidal suspension under steady and dynamic oscillatory shear is also measured using these rheo- and flow-SANS methods. A new structure state is identified in the shear thickening regime that proves critical for defining the "hydrocluster" microstructure state of the suspension that is responsible for shear thickening. For both the suspensions and the WLM solutions, stress-SANS rules with the measured microstructures define the individual stress components arising separately from conservative and hydrodynamic forces and these are compared with the macroscopic rheology. Analysis of these results defines the crucial length- and time-scales of the transient microstructure response. The novel dynamic microstructural measurements presented in this dissertation provide new insights into the complexities of shear thickening and shear banding flow phenomena

  5. Steady State Analysis of Stochastic Systems with Multiple Time Delays

    Science.gov (United States)

    Xu, W.; Sun, C. Y.; Zhang, H. Q.

    In this paper, attention is focused on the steady state analysis of a class of nonlinear dynamic systems with multi-delayed feedbacks driven by multiplicative correlated Gaussian white noises. The Fokker-Planck equations for delayed variables are at first derived by Novikov's theorem. Then, under small delay assumption, the approximate stationary solutions are obtained by the probability density approach. As a special case, the effects of multidelay feedbacks and the correlated additive and multiplicative Gaussian white noises on the response of a bistable system are considered. It is shown that the obtained analytical results are in good agreement with experimental results in Monte Carlo simulations.

  6. The Analysis of Nonlinear Vibrations of Top-Tensioned Cantilever Pipes Conveying Pressurized Steady Two-Phase Flow under Thermal Loading

    Directory of Open Access Journals (Sweden)

    Adeshina S. Adegoke

    2017-11-01

    Full Text Available This paper studied the nonlinear vibrations of top-tensioned cantilevered pipes conveying pressurized steady two-phase flow under thermal loading. The coupled axial and transverse governing partial differential equations of motion of the system were derived based on Hamilton’s mechanics, with the centerline assumed to be extensible. Using the multiple-scale perturbation technique, natural frequencies, mode shapes, and first order approximate solutions of the steady-state response of the pipes were obtained. The multiple-scale assessment reveals that at some frequencies the system is uncoupled, while at some frequencies a 1:2 coupling exists between the axial and the transverse frequencies of the pipe. Nonlinear frequencies versus the amplitude displacement of the cantilever pipe, conveying two-phase flow at super-critical mixture velocity for the uncoupled scenario, exhibit a nonlinear hardening behavior; an increment in the void fractions of the two-phase flow results in a reduction in the pipe’s transverse vibration frequencies and the coupled amplitude of the system. However, increases in the temperature difference, pressure, and the presence of top tension were observed to increase the pipe’s transverse vibration frequencies without a significant change in the coupled amplitude of the system.

  7. Implicit unified gas-kinetic scheme for steady state solutions in all flow regimes

    Science.gov (United States)

    Zhu, Yajun; Zhong, Chengwen; Xu, Kun

    2016-06-01

    This paper presents an implicit unified gas-kinetic scheme (UGKS) for non-equilibrium steady state flow computation. The UGKS is a direct modeling method for flow simulation in all regimes with the updates of both macroscopic flow variables and microscopic gas distribution function. By solving the macroscopic equations implicitly, a predicted equilibrium state can be obtained first through iterations. With the newly predicted equilibrium state, the evolution equation of the gas distribution function and the corresponding collision term can be discretized in a fully implicit way for fast convergence through iterations as well. The lower-upper symmetric Gauss-Seidel (LU-SGS) factorization method is implemented to solve both macroscopic and microscopic equations, which improves the efficiency of the scheme. Since the UGKS is a direct modeling method and its physical solution depends on the mesh resolution and the local time step, a physical time step needs to be fixed before using an implicit iterative technique with a pseudo-time marching step. Therefore, the physical time step in the current implicit scheme is determined by the same way as that in the explicit UGKS for capturing the physical solution in all flow regimes, but the convergence to a steady state speeds up through the adoption of a numerical time step with large CFL number. Many numerical test cases in different flow regimes from low speed to hypersonic ones, such as the Couette flow, cavity flow, and the flow passing over a cylinder, are computed to validate the current implicit method. The overall efficiency of the implicit UGKS can be improved by one or two orders of magnitude in comparison with the explicit one.

  8. Assessing Quasi-Steady State in Evaporation of Sessile Drops by Diffusion Models

    Science.gov (United States)

    Martin, Cameron; Nguyen, Hoa; Kelly-Zion, Peter; Pursell, Chris

    2017-11-01

    The vapor distributions surrounding sessile drops of methanol are modeled as the solutions of the steady-state and transient diffusion equations using Matlab's PDE Toolbox. The goal is to determine how quickly the transient diffusive transport reaches its quasi-steady state as the droplet geometry is varied between a Weber's disc, a real droplet shape, and a spherical cap with matching thickness or contact angle. We assume that the only transport mechanism at work is diffusion. Quasi-steady state is defined using several metrics, such as differences between the transient and steady-state solutions, and change in the transient solution over time. Knowing the vapor distribution, the gradient is computed to evaluate the diffusive flux. The flux is integrated along the surface of a control volume surrounding the drop to obtain the net rate of diffusion out of the volume. Based on the differences between the transient and steady-state diffusive fluxes at the discrete points along the control-volume surface, the time to reach quasi-steady state evaporation is determined and is consistent with other proposed measurements. By varying the dimensions of the control volume, we can also assess what regimes have equivalent or different quasi-steady states for different droplet geometries. Petroleum Research Fund.

  9. Analysis of the magnetohydrodynamic equations and study of the nonlinear solution bifurcations

    International Nuclear Information System (INIS)

    Morros Tosas, J.

    1989-01-01

    The nonlinear problems related to the plasma magnetohydrodynamic instabilities are studied. A bifurcation theory is applied and a general magnetohydrodynamic equation is proposed. Scalar functions, a steady magnetic field and a new equation for the velocity field are taken into account. A method allowing the obtention of suitable reduced equations for the instabilities study is described. Toroidal and cylindrical configuration plasmas are studied. In the cylindrical configuration case, analytical calculations are performed and two steady bifurcated solutions are found. In the toroidal configuration case, a suitable reduced equation system is obtained; a qualitative approach of a steady solution bifurcation on a toroidal Kink type geometry is carried out [fr

  10. Efficient steady-state solver for hierarchical quantum master equations

    Science.gov (United States)

    Zhang, Hou-Dao; Qiao, Qin; Xu, Rui-Xue; Zheng, Xiao; Yan, YiJing

    2017-07-01

    Steady states play pivotal roles in many equilibrium and non-equilibrium open system studies. Their accurate evaluations call for exact theories with rigorous treatment of system-bath interactions. Therein, the hierarchical equations-of-motion (HEOM) formalism is a nonperturbative and non-Markovian quantum dissipation theory, which can faithfully describe the dissipative dynamics and nonlinear response of open systems. Nevertheless, solving the steady states of open quantum systems via HEOM is often a challenging task, due to the vast number of dynamical quantities involved. In this work, we propose a self-consistent iteration approach that quickly solves the HEOM steady states. We demonstrate its high efficiency with accurate and fast evaluations of low-temperature thermal equilibrium of a model Fenna-Matthews-Olson pigment-protein complex. Numerically exact evaluation of thermal equilibrium Rényi entropies and stationary emission line shapes is presented with detailed discussion.

  11. Advances in dynamic relaxation techniques for nonlinear finite element analysis

    International Nuclear Information System (INIS)

    Sauve, R.G.; Metzger, D.R.

    1995-01-01

    Traditionally, the finite element technique has been applied to static and steady-state problems using implicit methods. When nonlinearities exist, equilibrium iterations must be performed using Newton-Raphson or quasi-Newton techniques at each load level. In the presence of complex geometry, nonlinear material behavior, and large relative sliding of material interfaces, solutions using implicit methods often become intractable. A dynamic relaxation algorithm is developed for inclusion in finite element codes. The explicit nature of the method avoids large computer memory requirements and makes possible the solution of large-scale problems. The method described approaches the steady-state solution with no overshoot, a problem which has plagued researchers in the past. The method is included in a general nonlinear finite element code. A description of the method along with a number of new applications involving geometric and material nonlinearities are presented. They include: (1) nonlinear geometric cantilever plate; (2) moment-loaded nonlinear beam; and (3) creep of nuclear fuel channel assemblies

  12. Noise-induced modulation of the relaxation kinetics around a non-equilibrium steady state of non-linear chemical reaction networks.

    Science.gov (United States)

    Ramaswamy, Rajesh; Sbalzarini, Ivo F; González-Segredo, Nélido

    2011-01-28

    Stochastic effects from correlated noise non-trivially modulate the kinetics of non-linear chemical reaction networks. This is especially important in systems where reactions are confined to small volumes and reactants are delivered in bursts. We characterise how the two noise sources confinement and burst modulate the relaxation kinetics of a non-linear reaction network around a non-equilibrium steady state. We find that the lifetimes of species change with burst input and confinement. Confinement increases the lifetimes of all species that are involved in any non-linear reaction as a reactant. Burst monotonically increases or decreases lifetimes. Competition between burst-induced and confinement-induced modulation may hence lead to a non-monotonic modulation. We quantify lifetime as the integral of the time autocorrelation function (ACF) of concentration fluctuations around a non-equilibrium steady state of the reaction network. Furthermore, we look at the first and second derivatives of the ACF, each of which is affected in opposite ways by burst and confinement. This allows discriminating between these two noise sources. We analytically derive the ACF from the linear Fokker-Planck approximation of the chemical master equation in order to establish a baseline for the burst-induced modulation at low confinement. Effects of higher confinement are then studied using a partial-propensity stochastic simulation algorithm. The results presented here may help understand the mechanisms that deviate stochastic kinetics from its deterministic counterpart. In addition, they may be instrumental when using fluorescence-lifetime imaging microscopy (FLIM) or fluorescence-correlation spectroscopy (FCS) to measure confinement and burst in systems with known reaction rates, or, alternatively, to correct for the effects of confinement and burst when experimentally measuring reaction rates.

  13. Steady State Dynamic Operating Behavior of Universal Motor

    Directory of Open Access Journals (Sweden)

    Muhammad Khan Burdi

    2015-01-01

    Full Text Available A detailed investigation of the universal motor is developed and used for various dynamic steady state and transient operating conditions of loads. In the investigation, output torque, motor speed, input current, input/output power and efficiency are computed, compared and analyzed for different loads. While this paper discusses the steady-state behavior of the universal motor, another companion paper, ?Transient dynamic behavior of universal motor?, will discuss its transient behavior in detail. A non-linear generalized electric machine model of the motor is considered for the analysis. This study was essential to investigate effect of output load on input current, power, speed and efficiency of the motor during operations. Previously such investigation is not known

  14. Steady state neutral beam injector

    International Nuclear Information System (INIS)

    Mattoo, S.K.; Bandyopadhyay, M.; Baruah, U.K.; Bisai, N.; Chakbraborty, A.K.; Chakrapani, Ch.; Jana, M.R.; Bajpai, M.; Jaykumar, P.K.; Patel, D.; Patel, G.; Patel, P.J.; Prahlad, V.; Rao, N.V.M.; Rotti, C.; Singh, N.P.; Sridhar, B.

    2000-01-01

    Learning from operational reliability of neutral beam injectors in particular and various heating schemes including RF in general on TFTR, JET, JT-60, it has become clear that neutral beam injectors may find a greater role assigned to them for maintaining the plasma in steady state devices under construction. Many technological solutions, integrated in the present day generation of injectors have given rise to capability of producing multimegawatt power at many tens of kV. They have already operated for integrated time >10 5 S without deterioration in the performance. However, a new generation of injectors for steady state devices have to address to some basic issues. They stem from material erosion under particle bombardment, heat transfer > 10 MW/m 2 , frequent regeneration of cryopanels, inertial power supplies, data acquisition and control of large volume of data. Some of these engineering issues have been addressed to in the proposed neutral beam injector for SST-1 at our institute; the remaining shall have to wait for the inputs of the database generated from the actual experience with steady state injectors. (author)

  15. Viscoelasticity and nonlinear simple shear flow behavior of an entangled asymmetric exact comb polymer solution

    KAUST Repository

    Snijkers, F.; Kirkwood, K. M.; Vlassopoulos, D.; Leal, L. G.; Nikopoulou, A.; Hadjichristidis, Nikolaos; Coppola, S.

    2016-01-01

    We report upon the characterization of the steady-state shear stresses and first normal stress differences as a function of shear rate using mechanical rheometry (both with a standard cone and plate and with a cone partitioned plate) and optical rheometry (with a flow-birefringence setup) of an entangled solution of asymmetric exact combs. The combs are polybutadienes (1,4-addition) consisting of an H-skeleton with an additional off-center branch on the backbone. We chose to investigate a solution in order to obtain reliable nonlinear shear data in overlapping dynamic regions with the two different techniques. The transient measurements obtained by cone partitioned plate indicated the appearance of overshoots in both the shear stress and the first normal stress difference during start-up shear flow. Interestingly, the overshoots in the start-up normal stress difference started to occur only at rates above the inverse stretch time of the backbone, when the stretch time of the backbone was estimated in analogy with linear chains including the effects of dynamic dilution of the branches but neglecting the effects of branch point friction, in excellent agreement with the situation for linear polymers. Flow-birefringence measurements were performed in a Couette geometry, and the extracted steady-state shear and first normal stress differences were found to agree well with the mechanical data, but were limited to relatively low rates below the inverse stretch time of the backbone. Finally, the steady-state properties were found to be in good agreement with model predictions based on a nonlinear multimode tube model developed for linear polymers when the branches are treated as solvent.

  16. Viscoelasticity and nonlinear simple shear flow behavior of an entangled asymmetric exact comb polymer solution

    KAUST Repository

    Snijkers, F.

    2016-03-31

    We report upon the characterization of the steady-state shear stresses and first normal stress differences as a function of shear rate using mechanical rheometry (both with a standard cone and plate and with a cone partitioned plate) and optical rheometry (with a flow-birefringence setup) of an entangled solution of asymmetric exact combs. The combs are polybutadienes (1,4-addition) consisting of an H-skeleton with an additional off-center branch on the backbone. We chose to investigate a solution in order to obtain reliable nonlinear shear data in overlapping dynamic regions with the two different techniques. The transient measurements obtained by cone partitioned plate indicated the appearance of overshoots in both the shear stress and the first normal stress difference during start-up shear flow. Interestingly, the overshoots in the start-up normal stress difference started to occur only at rates above the inverse stretch time of the backbone, when the stretch time of the backbone was estimated in analogy with linear chains including the effects of dynamic dilution of the branches but neglecting the effects of branch point friction, in excellent agreement with the situation for linear polymers. Flow-birefringence measurements were performed in a Couette geometry, and the extracted steady-state shear and first normal stress differences were found to agree well with the mechanical data, but were limited to relatively low rates below the inverse stretch time of the backbone. Finally, the steady-state properties were found to be in good agreement with model predictions based on a nonlinear multimode tube model developed for linear polymers when the branches are treated as solvent.

  17. The behavior of steady quasisolitons near the limit cases of third-order nonlinear Schrödinger equation

    DEFF Research Database (Denmark)

    Karpman, V.I.; Shagalov, A.G.; Juul Rasmussen, J.

    2002-01-01

    The behavior of steady quasisoliton solutions to the extended third-order nonlinear Schrodinger (NLS) equation is studied in two cases: (i) when the coefficients in the equation approach the Hirota conditions, and (ii) near the limit of the regular NLS equation. (C) 2002 Published by Elsevier...

  18. On the validity of travel-time based nonlinear bioreactive transport models in steady-state flow.

    Science.gov (United States)

    Sanz-Prat, Alicia; Lu, Chuanhe; Finkel, Michael; Cirpka, Olaf A

    2015-01-01

    conceptualization of nonlinear bioreactive transport in complex multidimensional domains by quasi 1-D travel-time models is valid for steady-state flow fields if the reactants are introduced over a wide cross-section, flow is at quasi steady state, and dispersive mixing is adequately parametrized. Copyright © 2015 Elsevier B.V. All rights reserved.

  19. Application of non-linear discretetime feedback regulators with assignable closed-loop dynamics

    Directory of Open Access Journals (Sweden)

    Dubljević Stevan

    2003-01-01

    Full Text Available In the present work the application of a new approach is demonstrated to a discrete-time state feedback regulator synthesis with feedback linearization and pole-placement for non-linear discrete-time systems. Under the simultaneous implementation of a non-linear coordinate transformation and a non-linear state feedback law computed through the solution of a system of non-linear functional equations, both the feedback linearization and pole-placement design objectives were accomplished. The non-linear state feedback regulator synthesis method was applied to a continuous stirred tank reactor (CSTR under non-isothermal operating conditions that exhibits steady-state multiplicity. The control objective was to regulate the reactor at the middle unstable steady state by manipulating the rate of input heat in the reactor. Simulation studies were performed to evaluate the performance of the proposed non-linear state feedback regulator, as it was shown a non-linear state feedback regulator clearly outperformed a standard linear one, especially in the presence of adverse disturbance under which linear regulation at the unstable steady state was not feasible.

  20. Analytical steady-state solutions for water-limited cropping systems using saline irrigation water

    Science.gov (United States)

    Skaggs, T. H.; Anderson, R. G.; Corwin, D. L.; Suarez, D. L.

    2014-12-01

    Due to the diminishing availability of good quality water for irrigation, it is increasingly important that irrigation and salinity management tools be able to target submaximal crop yields and support the use of marginal quality waters. In this work, we present a steady-state irrigated systems modeling framework that accounts for reduced plant water uptake due to root zone salinity. Two explicit, closed-form analytical solutions for the root zone solute concentration profile are obtained, corresponding to two alternative functional forms of the uptake reduction function. The solutions express a general relationship between irrigation water salinity, irrigation rate, crop salt tolerance, crop transpiration, and (using standard approximations) crop yield. Example applications are illustrated, including the calculation of irrigation requirements for obtaining targeted submaximal yields, and the generation of crop-water production functions for varying irrigation waters, irrigation rates, and crops. Model predictions are shown to be mostly consistent with existing models and available experimental data. Yet the new solutions possess advantages over available alternatives, including: (i) the solutions were derived from a complete physical-mathematical description of the system, rather than based on an ad hoc formulation; (ii) the analytical solutions are explicit and can be evaluated without iterative techniques; (iii) the solutions permit consideration of two common functional forms of salinity induced reductions in crop water uptake, rather than being tied to one particular representation; and (iv) the utilized modeling framework is compatible with leading transient-state numerical models.

  1. Noise-induced modulation of the relaxation kinetics around a non-equilibrium steady state of non-linear chemical reaction networks.

    Directory of Open Access Journals (Sweden)

    Rajesh Ramaswamy

    2011-01-01

    Full Text Available Stochastic effects from correlated noise non-trivially modulate the kinetics of non-linear chemical reaction networks. This is especially important in systems where reactions are confined to small volumes and reactants are delivered in bursts. We characterise how the two noise sources confinement and burst modulate the relaxation kinetics of a non-linear reaction network around a non-equilibrium steady state. We find that the lifetimes of species change with burst input and confinement. Confinement increases the lifetimes of all species that are involved in any non-linear reaction as a reactant. Burst monotonically increases or decreases lifetimes. Competition between burst-induced and confinement-induced modulation may hence lead to a non-monotonic modulation. We quantify lifetime as the integral of the time autocorrelation function (ACF of concentration fluctuations around a non-equilibrium steady state of the reaction network. Furthermore, we look at the first and second derivatives of the ACF, each of which is affected in opposite ways by burst and confinement. This allows discriminating between these two noise sources. We analytically derive the ACF from the linear Fokker-Planck approximation of the chemical master equation in order to establish a baseline for the burst-induced modulation at low confinement. Effects of higher confinement are then studied using a partial-propensity stochastic simulation algorithm. The results presented here may help understand the mechanisms that deviate stochastic kinetics from its deterministic counterpart. In addition, they may be instrumental when using fluorescence-lifetime imaging microscopy (FLIM or fluorescence-correlation spectroscopy (FCS to measure confinement and burst in systems with known reaction rates, or, alternatively, to correct for the effects of confinement and burst when experimentally measuring reaction rates.

  2. A gradual update method for simulating the steady-state solution of stiff differential equations in metabolic circuits.

    Science.gov (United States)

    Shiraishi, Emi; Maeda, Kazuhiro; Kurata, Hiroyuki

    2009-02-01

    Numerical simulation of differential equation systems plays a major role in the understanding of how metabolic network models generate particular cellular functions. On the other hand, the classical and technical problems for stiff differential equations still remain to be solved, while many elegant algorithms have been presented. To relax the stiffness problem, we propose new practical methods: the gradual update of differential-algebraic equations based on gradual application of the steady-state approximation to stiff differential equations, and the gradual update of the initial values in differential-algebraic equations. These empirical methods show a high efficiency for simulating the steady-state solutions for the stiff differential equations that existing solvers alone cannot solve. They are effective in extending the applicability of dynamic simulation to biochemical network models.

  3. A semi-analytical solution to accelerate spin-up of a coupled carbon and nitrogen land model to steady state

    Directory of Open Access Journals (Sweden)

    J. Y. Xia

    2012-10-01

    Full Text Available The spin-up of land models to steady state of coupled carbon–nitrogen processes is computationally so costly that it becomes a bottleneck issue for global analysis. In this study, we introduced a semi-analytical solution (SAS for the spin-up issue. SAS is fundamentally based on the analytic solution to a set of equations that describe carbon transfers within ecosystems over time. SAS is implemented by three steps: (1 having an initial spin-up with prior pool-size values until net primary productivity (NPP reaches stabilization, (2 calculating quasi-steady-state pool sizes by letting fluxes of the equations equal zero, and (3 having a final spin-up to meet the criterion of steady state. Step 2 is enabled by averaged time-varying variables over one period of repeated driving forcings. SAS was applied to both site-level and global scale spin-up of the Australian Community Atmosphere Biosphere Land Exchange (CABLE model. For the carbon-cycle-only simulations, SAS saved 95.7% and 92.4% of computational time for site-level and global spin-up, respectively, in comparison with the traditional method (a long-term iterative simulation to achieve the steady states of variables. For the carbon–nitrogen coupled simulations, SAS reduced computational cost by 84.5% and 86.6% for site-level and global spin-up, respectively. The estimated steady-state pool sizes represent the ecosystem carbon storage capacity, which was 12.1 kg C m−2 with the coupled carbon–nitrogen global model, 14.6% lower than that with the carbon-only model. The nitrogen down-regulation in modeled carbon storage is partly due to the 4.6% decrease in carbon influx (i.e., net primary productivity and partly due to the 10.5% reduction in residence times. This steady-state analysis accelerated by the SAS method can facilitate comparative studies of structural differences in determining the ecosystem carbon storage capacity among biogeochemical models. Overall, the

  4. Implications of steady-state operation on divertor design

    International Nuclear Information System (INIS)

    Sevier, D.L.; Reis, E.E.; Baxi, C.B.; Silke, G.W.; Wong, C.P.C.; Hill, D.N.

    1996-01-01

    As fusion experiments progress towards long pulse or steady state operation, plasma facing components are undergoing a significant change in their design. This change represents the transition from inertially cooled pulsed systems to steady state designs of significant power handling capacity. A limited number of Plasma Facing Component (PFC) systems are in operation or planning to address this steady state challenge at low heat flux. However in most divertor designs components are required to operate at heat fluxes at 5 MW/m 2 or above. The need for data in this area has resulted in a significant amount of thermal/hydraulic and thermal fatigue testing being done on prototypical elements. Short pulse design solutions are not adequate for longer pulse experiments and the areas of thermal design, structural design, material selection, maintainability, and lifetime prediction are undergoing significant changes. A prudent engineering approach will guide us through the transitional phase of divertor design to steady-state power plant components. This paper reviews the design implications in this transition to steady state machines and the status of the community efforts to meet evolving design requirements. 54 refs., 5 figs., 2 tabs

  5. NESTLE: Few-group neutron diffusion equation solver utilizing the nodal expansion method for eigenvalue, adjoint, fixed-source steady-state and transient problems

    International Nuclear Information System (INIS)

    Turinsky, P.J.; Al-Chalabi, R.M.K.; Engrand, P.; Sarsour, H.N.; Faure, F.X.; Guo, W.

    1994-06-01

    NESTLE is a FORTRAN77 code that solves the few-group neutron diffusion equation utilizing the Nodal Expansion Method (NEM). NESTLE can solve the eigenvalue (criticality); eigenvalue adjoint; external fixed-source steady-state; or external fixed-source. or eigenvalue initiated transient problems. The code name NESTLE originates from the multi-problem solution capability, abbreviating Nodal Eigenvalue, Steady-state, Transient, Le core Evaluator. The eigenvalue problem allows criticality searches to be completed, and the external fixed-source steady-state problem can search to achieve a specified power level. Transient problems model delayed neutrons via precursor groups. Several core properties can be input as time dependent. Two or four energy groups can be utilized, with all energy groups being thermal groups (i.e. upscatter exits) if desired. Core geometries modelled include Cartesian and Hexagonal. Three, two and one dimensional models can be utilized with various symmetries. The non-linear iterative strategy associated with the NEM method is employed. An advantage of the non-linear iterative strategy is that NSTLE can be utilized to solve either the nodal or Finite Difference Method representation of the few-group neutron diffusion equation

  6. Links between soil properties and steady-state solute transport through cultivated topsoil at the field scale

    DEFF Research Database (Denmark)

    Koestel, J. K.; Nørgaard, Trine; Loung, N. M.

    2013-01-01

    It is known that solute transport through soil is heterogeneous at all spatial scales. However, little data are available to allow quantification of these heterogeneities at the field scale or larger. In this study, we investigated the spatial patterns of soil properties, hydrologic state variables......, and tracer breakthrough curves (BTCs) at the field scale for the inert solute transport under a steady-state irrigation rate which produced near-saturated conditions. Sixty-five undisturbed soil columns approximately 20 cm in height and diameter were sampled from the loamy topsoil of an agricultural field...... to larger water saturation and the activation of larger macropores. Our study provides further evidence that it should be possible to estimate solute transport properties from soil properties such as soil texture or bulk density. We also demonstrated that estimation approaches established for the column...

  7. Computational multiple steady states for enzymatic esterification of ethanol and oleic acid in an isothermal CSTR.

    Science.gov (United States)

    Ho, Pang-Yen; Chuang, Guo-Syong; Chao, An-Chong; Li, Hsing-Ya

    2005-05-01

    The capacity of complex biochemical reaction networks (consisting of 11 coupled non-linear ordinary differential equations) to show multiple steady states, was investigated. The system involved esterification of ethanol and oleic acid by lipase in an isothermal continuous stirred tank reactor (CSTR). The Deficiency One Algorithm and the Subnetwork Analysis were applied to determine the steady state multiplicity. A set of rate constants and two corresponding steady states are computed. The phenomena of bistability, hysteresis and bifurcation are discussed. Moreover, the capacity of steady state multiplicity is extended to the family of the studied reaction networks.

  8. Computing multiple periodic solutions of nonlinear vibration problems using the harmonic balance method and Groebner bases

    Science.gov (United States)

    Grolet, Aurelien; Thouverez, Fabrice

    2015-02-01

    This paper is devoted to the study of vibration of mechanical systems with geometric nonlinearities. The harmonic balance method is used to derive systems of polynomial equations whose solutions give the frequency component of the possible steady states. Groebner basis methods are used for computing all solutions of polynomial systems. This approach allows to reduce the complete system to an unique polynomial equation in one variable driving all solutions of the problem. In addition, in order to decrease the number of variables, we propose to first work on the undamped system, and recover solution of the damped system using a continuation on the damping parameter. The search for multiple solutions is illustrated on a simple system, where the influence of the retained number of harmonic is studied. Finally, the procedure is applied on a simple cyclic system and we give a representation of the multiple states versus frequency.

  9. Basin stability measure of different steady states in coupled oscillators

    Science.gov (United States)

    Rakshit, Sarbendu; Bera, Bidesh K.; Majhi, Soumen; Hens, Chittaranjan; Ghosh, Dibakar

    2017-04-01

    In this report, we investigate the stabilization of saddle fixed points in coupled oscillators where individual oscillators exhibit the saddle fixed points. The coupled oscillators may have two structurally different types of suppressed states, namely amplitude death and oscillation death. The stabilization of saddle equilibrium point refers to the amplitude death state where oscillations are ceased and all the oscillators converge to the single stable steady state via inverse pitchfork bifurcation. Due to multistability features of oscillation death states, linear stability theory fails to analyze the stability of such states analytically, so we quantify all the states by basin stability measurement which is an universal nonlocal nonlinear concept and it interplays with the volume of basins of attractions. We also observe multi-clustered oscillation death states in a random network and measure them using basin stability framework. To explore such phenomena we choose a network of coupled Duffing-Holmes and Lorenz oscillators which are interacting through mean-field coupling. We investigate how basin stability for different steady states depends on mean-field density and coupling strength. We also analytically derive stability conditions for different steady states and confirm by rigorous bifurcation analysis.

  10. Steady states of a diode with counterstreaming electron and positron beams

    Energy Technology Data Exchange (ETDEWEB)

    Ender, A. Ya.; Kuznetsov, V. I., E-mail: victor.kuznetsov@mail.ioffe.ru; Gruzdev, A. A. [Russian Academy of Sciences, Ioffe Institute (Russian Federation)

    2016-10-15

    Steady states of a plasma layer with counterstreaming beams of oppositely charged particles moving without collisions in a self-consistent electric field are analyzed. The study is aimed at clarifying the mechanism of generation and reconstruction of pulsar radiation. Such a layer also models the processes occurring in Knudsen plasma diodes with counterstreaming electron and ion beams. The steady-state solutions are exhaustively classified. The existence of several solutions at the same external parameters is established.

  11. Numerical study on the convergence to steady state solutions of a new class of high order WENO schemes

    Science.gov (United States)

    Zhu, Jun; Shu, Chi-Wang

    2017-11-01

    A new class of high order weighted essentially non-oscillatory (WENO) schemes (Zhu and Qiu, 2016, [50]) is applied to solve Euler equations with steady state solutions. It is known that the classical WENO schemes (Jiang and Shu, 1996, [23]) might suffer from slight post-shock oscillations. Even though such post-shock oscillations are small enough in magnitude and do not visually affect the essentially non-oscillatory property, they are truly responsible for the residue to hang at a truncation error level instead of converging to machine zero. With the application of this new class of WENO schemes, such slight post-shock oscillations are essentially removed and the residue can settle down to machine zero in steady state simulations. This new class of WENO schemes uses a convex combination of a quartic polynomial with two linear polynomials on unequal size spatial stencils in one dimension and is extended to two dimensions in a dimension-by-dimension fashion. By doing so, such WENO schemes use the same information as the classical WENO schemes in Jiang and Shu (1996) [23] and yield the same formal order of accuracy in smooth regions, yet they could converge to steady state solutions with very tiny residue close to machine zero for our extensive list of test problems including shocks, contact discontinuities, rarefaction waves or their interactions, and with these complex waves passing through the boundaries of the computational domain.

  12. New Modeling of Steady-State Modes of Complex Electrical Grids of Power Systems

    Directory of Open Access Journals (Sweden)

    Akhmetbayev Arman

    2018-01-01

    Full Text Available Classical methods for modeling the steady-state modes of complex electrical networks and systems are based on the application of nonlinear node equations. Nonlinear equations are solved by iterative methods, which are connected by known difficulties. To a certain extent, these difficulties can be weakened by applying topological methods. In this paper, we outline the theoretical foundations for the formation of the inverse form of nodal stress equations based on the topology of electrical networks and systems. A new topological method for calculating the distribution coefficients of node currents is proposed based on all possible trees of a directed graph of a complex electrical network. A complex program for calculating current distribution coefficients and forming steady-state parameters in the MATLAB environment has been developed.

  13. Steady states and outbreaks of two-phase nonlinear age-structured model of population dynamics with discrete time delay.

    Science.gov (United States)

    Akimenko, Vitalii; Anguelov, Roumen

    2017-12-01

    In this paper we study the nonlinear age-structured model of a polycyclic two-phase population dynamics including delayed effect of population density growth on the mortality. Both phases are modelled as a system of initial boundary values problem for semi-linear transport equation with delay and initial problem for nonlinear delay ODE. The obtained system is studied both theoretically and numerically. Three different regimes of population dynamics for asymptotically stable states of autonomous systems are obtained in numerical experiments for the different initial values of population density. The quasi-periodical travelling wave solutions are studied numerically for the autonomous system with the different values of time delays and for the system with oscillating death rate and birth modulus. In both cases it is observed three types of travelling wave solutions: harmonic oscillations, pulse sequence and single pulse.

  14. Effect of state-dependent delay on a weakly damped nonlinear oscillator.

    Science.gov (United States)

    Mitchell, Jonathan L; Carr, Thomas W

    2011-04-01

    We consider a weakly damped nonlinear oscillator with state-dependent delay, which has applications in models for lasers, epidemics, and microparasites. More generally, the delay-differential equations considered are a predator-prey system where the delayed term is linear and represents the proliferation of the predator. We determine the critical value of the delay that causes the steady state to become unstable to periodic oscillations via a Hopf bifurcation. Using asymptotic averaging, we determine how the system's behavior is influenced by the functional form of the state-dependent delay. Specifically, we determine whether the branch of periodic solutions will be either sub- or supercritical as well as an accurate estimation of the amplitude. Finally, we choose a few examples of state-dependent delay to test our analytical results by comparing them to numerical continuation.

  15. ATC calculation with steady-state security constraints using Benders decomposition

    International Nuclear Information System (INIS)

    Shaaban, M.; Yan, Z.; Ni, Y.; Wu, F.; Li, W.; Liu, H.

    2003-01-01

    Available transfer capability (ATC) is an important indicator of the usable amount of transmission capacity accessible by assorted parties for commercial trading, ATC calculation is nontrivial when steady-state security constraints are included. In hie paper, Benders decomposition method is proposed to partition the AC problem with steady-state security constraints into a base case master problem and a series of subproblems relevant to various contingencies to include their impacts on ATC. The mathematical model is formulated and the two solution schemes are presented. Computer testing on the 4-bus system and IEEE 30-bus system shows the effectiveness of the proposed method and the solution schemes. (Author)

  16. Local and global nonlinear dynamics of a parametrically excited rectangular symmetric cross-ply laminated composite plate

    International Nuclear Information System (INIS)

    Ye Min; Lu Jing; Zhang Wei; Ding Qian

    2005-01-01

    The present investigation deals with nonlinear dynamic behavior of a parametrically excited simply supported rectangular symmetric cross-ply laminated composite thin plate for the first time. The governing equation of motion for rectangular symmetric cross-ply laminated composite thin plate is derived by using von Karman equation. The geometric nonlinearity and nonlinear damping are included in the governing equations of motion. The Galerkin approach is used to obtain a two-degree-of-freedom nonlinear system under parametric excitation. The method of multiple scales is utilized to transform the second-order non-autonomous differential equations to the first-order averaged equations. Using numerical method, the averaged equations are analyzed to obtain the steady state bifurcation responses. The analysis of stability for steady state bifurcation responses in laminated composite thin plate is also given. Under certain conditions laminated composite thin plate may have two or multiple steady state bifurcation solutions. Jumping phenomenon occurs in the steady state bifurcation solutions. The chaotic motions of rectangular symmetric cross-ply laminated composite thin plate are also found by using numerical simulation. The results obtained here demonstrate that the periodic, quasi-periodic and chaotic motions coexist for a parametrically excited fore-edge simply supported rectangular symmetric cross-ply laminated composite thin plate under certain conditions

  17. Multiple solutions and stability of the steady transonic small-disturbance equation

    Directory of Open Access Journals (Sweden)

    Ya Liu

    2017-09-01

    Full Text Available Numerical solutions of the steady transonic small-disturbance (TSD potential equation are computed using the conservative Murman−Cole scheme. Multiple solutions are discovered and mapped out for the Mach number range at zero angle of attack and the angle of attack range at Mach number 0.85 for the NACA 0012 airfoil. We present a linear stability analysis method by directly assembling and evaluating the Jacobian matrix of the nonlinear finite-difference equation of the TSD equation. The stability of all the discovered multiple solutions are then determined by the proposed eigen analysis. The relation of stability to convergence of the iterative method for solving the TSD equation is discussed. Computations and the stability analysis demonstrate the possibility of eliminating the multiple solutions and stabilizing the remaining unique solution by adding a sufficiently long splitter plate downstream the airfoil trailing edge. Finally, instability of the solution of the TSD equation is shown to be closely connected to the onset of transonic buffet by comparing with experimental data.

  18. Steady-state oxygen-solubility in niobium

    International Nuclear Information System (INIS)

    Schulze, K.; Jehn, H.

    1977-01-01

    During annealing of niobium in oxygen in certain temperature and pressure ranges steady states are established between the absorption of molecular oxygen and the evaporation of volatile oxides. The oxygen concentration in the niobium-oxygen α-solid solution is a function of oxygen pressure and temperature and has been redetermined in the ranges 10 -5 - 10 -2 Pa O 2 and 2,070 - 2,470 K. It follows differing from former results the equation csub(o) = 9.1 x 10 -6 x sub(po2) x exp (502000/RT) with csub(o) in at.-ppm, sub(po2) in Pa, T in K, R = 8.31 J x mol -1 x K -1 . The existence of steady states is limited to a temperature range from 1870 to 2470 K and to oxygen concentrations below the solubility limit given by solidus and solvus lines in the T-c diagram. In the experiments high-purity niobium wires with a specific electrical ratio rho (273 K)/rho(4.2 K) > 5,000 have been gassed under isothermal-isobaric conditions until the steady state has been reached. The oxygen concentration has been determined analytically by vacuum fusion extraction with platinum-flux technique as well as by electrical residual resistivity measurements at 4.2 K. (orig.) [de

  19. Steady-state solidification of aqueous ammonium chloride

    Science.gov (United States)

    Peppin, S. S. L.; Huppert, Herbert E.; Worster, M. Grae

    We report on a series of experiments in which a Hele-Shaw cell containing aqueous solutions of NH4Cl was translated at prescribed rates through a steady temperature gradient. The salt formed the primary solid phase of a mushy layer as the solution solidified, with the salt-depleted residual fluid driving buoyancy-driven convection and the development of chimneys in the mushy layer. Depending on the operating conditions, several morphological transitions occurred. A regime diagram is presented quantifying these transitions as a function of freezing rate and the initial concentration of the solution. In general, for a given concentration, increasing the freezing rate caused the steady-state system to change from a convecting mushy layer with chimneys to a non-convecting mushy layer below a relatively quiescent liquid, and then to a much thinner mushy layer separated from the liquid by a region of active secondary nucleation. At higher initial concentrations the second of these states did not occur. At lower concentrations, but still above the eutectic, the mushy layer disappeared. A simple mathematical model of the system is developed which compares well with the experimental measurements of the intermediate, non-convecting state and serves as a benchmark against which to understand some of the effects of convection. Movies are available with the online version of the paper.

  20. An implicit steady-state initialization package for the RELAP5 computer code

    International Nuclear Information System (INIS)

    Paulsen, M.P.; Peterson, C.E.; Odar, F.

    1995-08-01

    A direct steady-state initialization (DSSI) method has been developed and implemented in the RELAP5 hydrodynamic analysis program. It provides a means for users to specify a small set of initial conditions which are then propagated through the remainder of the system. The DSSI scheme utilizes the steady-state form of the RELAP5 balance equations for nonequilibrium two-phase flow. It also employs the RELAP5 component models and constitutive model packages for wall-to-phase and interphase momentum and heat exchange. A fully implicit solution of the linearized hydrodynamic equations is implemented. An implicit coupling scheme is used to augment the standard steady-state heat conduction solution for steam generator use. It solves the primary-side tube region energy equations, heat conduction equations, wall heat flux boundary conditions, and overall energy balance equation as a coupled system of equations and improves convergence. The DSSI method for initializing RELAP5 problems to steady-state conditions has been compared with the transient solution scheme using a suite of test problems including; adiabatic single-phase liquid and vapor flow through channels with and without healing and area changes; a heated two-phase test bundle representative of BWR core conditions; and a single-loop PWR model

  1. The steady-state tokamak program

    International Nuclear Information System (INIS)

    Politzer, D.A.; Nevins, W.M.

    1992-01-01

    This paper reports on a steady-state tokamak experiment (STE) needed to develop the technology and physics data base required for construction of a steady-state fusion power demonstration reactor in the early 21st century. The STE will provide an integrated facility for the development and demonstration of steady-state and particle handling, low-activation high-heat-flux components and materials, efficient current drive, and continuous plasma performance in steady-state, with reactor-like plasma conditions under severe conditions of heat and particle bombardment of the wall. The STE facility will also be used to develop operation and control scenarios for ITER

  2. Series Solution for Steady Three-Dimensional Flow due to Spraying on Inclined Spinning Disk by Homotopy Perturbation Method

    Directory of Open Access Journals (Sweden)

    Saeed Dinarvand

    2012-01-01

    Full Text Available The steady three-dimensional flow of condensation or spraying on inclined spinning disk is studied analytically. The governing nonlinear equations and their associated boundary conditions are transformed into the system of nonlinear ordinary differential equations. The series solution of the problem is obtained by utilizing the homotopy perturbation method (HPM. The velocity and temperature profiles are shown and the influence of Prandtl number on the heat transfer and Nusselt number is discussed in detail. The validity of our solutions is verified by the numerical results. Unlike free surface flows on an incline, this through flow is highly affected by the spray rate and the rotation of the disk.

  3. Exact Solutions to Several Nonlinear Cases of Generalized Grad-Shafranov Equation for Ideal Magnetohydrodynamic Flows in Axisymmetric Domain

    Science.gov (United States)

    Adem, Abdullahi Rashid; Moawad, Salah M.

    2018-05-01

    In this paper, the steady-state equations of ideal magnetohydrodynamic incompressible flows in axisymmetric domains are investigated. These flows are governed by a second-order elliptic partial differential equation as a type of generalized Grad-Shafranov equation. The problem of finding exact equilibria to the full governing equations in the presence of incompressible mass flows is considered. Two different types of constraints on position variables are presented to construct exact solution classes for several nonlinear cases of the governing equations. Some of the obtained results are checked for their applications to magnetic confinement plasma. Besides, they cover many previous configurations and include new considerations about the nonlinearity of magnetic flux stream variables.

  4. Feasibility study for improved steady-state initialization algorithms for the RELAP5 computer code

    International Nuclear Information System (INIS)

    Paulsen, M.P.; Peterson, C.E.; Katsma, K.R.

    1993-04-01

    A design for a new steady-state initialization method is presented that represents an improvement over the current method used in RELAP5. Current initialization methods for RELAP5 solve the transient fluidflow balance equations simulating a transient to achieve steady-state conditions. Because the transient solution is used, the initial conditions may change from the desired values requiring the use of controllers and long transient running times to obtain steady-state conditions for system problems. The new initialization method allows the user to fix thermal-hydraulic values in volumes and junctions where the conditions are best known and have the code compute the initial conditions in other areas of the system. The steady-state balance equations and solution methods are presented. The constitutive, component, and specialpurpose models are reviewed with respect to modifications required for the new steady-state initialization method. The requirements for user input are defined and the feasibility of the method is demonstrated with a testbed code by initializing some simple channel problems. The initialization of the sample problems using, the old and the new methods are compared

  5. Toroidal visco-resistive magnetohydrodynamic steady states contain vortices

    International Nuclear Information System (INIS)

    Bates, J.W.; Montgomery, D.C.

    1998-01-01

    Poloidal velocity fields seem to be a fundamental feature of resistive toroidal magnetohydrodynamic (MHD) steady states. They are a consequence of force balance in toroidal geometry, do not require any kind of instability, and disappear in the open-quotes straight cylinderclose quotes (infinite aspect ratio) limit. If a current density j results from an axisymmetric toroidal electric field that is irrotational inside a torus, it leads to a magnetic field B such that ∇x(jxB) is nonvanishing, so that the Lorentz force cannot be balanced by the gradient of any scalar pressure in the equation of motion. In a steady state, finite poloidal velocity fields and toroidal vorticity must exist. Their calculation is difficult, but explicit solutions can be found in the limit of low Reynolds number. Here, existing calculations are generalized to the more realistic case of no-slip boundary conditions on the velocity field and a circular toroidal cross section. The results of this paper strongly suggest that discussions of confined steady states in toroidal MHD must include flows from the outset. copyright 1998 American Institute of Physics

  6. Exact steady state manifold of a boundary driven spin-1 Lai–Sutherland chain

    International Nuclear Information System (INIS)

    Ilievski, Enej; Prosen, Tomaž

    2014-01-01

    We present an explicit construction of a family of steady state density matrices for an open integrable spin-1 chain with bilinear and biquadratic interactions, also known as the Lai–Sutherland model, driven far from equilibrium by means of two oppositely polarizing Markovian dissipation channels localized at the boundary. The steady state solution exhibits n+1 fold degeneracy, for a chain of length n, due to existence of (strong) Liouvillian U(1) symmetry. The latter can be exploited to introduce a chemical potential and define a grand canonical nonequilibrium steady state ensemble. The matrix product form of the solution entails an infinitely-dimensional representation of a non-trivial Lie algebra (semidirect product of sl 2 and a non-nilpotent radical) and hints to a novel Yang–Baxter integrability structure

  7. Exact steady state manifold of a boundary driven spin-1 Lai–Sutherland chain

    Energy Technology Data Exchange (ETDEWEB)

    Ilievski, Enej; Prosen, Tomaž

    2014-05-15

    We present an explicit construction of a family of steady state density matrices for an open integrable spin-1 chain with bilinear and biquadratic interactions, also known as the Lai–Sutherland model, driven far from equilibrium by means of two oppositely polarizing Markovian dissipation channels localized at the boundary. The steady state solution exhibits n+1 fold degeneracy, for a chain of length n, due to existence of (strong) Liouvillian U(1) symmetry. The latter can be exploited to introduce a chemical potential and define a grand canonical nonequilibrium steady state ensemble. The matrix product form of the solution entails an infinitely-dimensional representation of a non-trivial Lie algebra (semidirect product of sl{sub 2} and a non-nilpotent radical) and hints to a novel Yang–Baxter integrability structure.

  8. Accuracy Improvement of the Method of Multiple Scales for Nonlinear Vibration Analyses of Continuous Systems with Quadratic and Cubic Nonlinearities

    Directory of Open Access Journals (Sweden)

    Akira Abe

    2010-01-01

    and are the driving and natural frequencies, respectively. The application of Galerkin's procedure to the equation of motion yields nonlinear ordinary differential equations with quadratic and cubic nonlinear terms. The steady-state responses are obtained by using the discretization approach of the MMS in which the definition of the detuning parameter, expressing the relationship between the natural frequency and the driving frequency, is changed in an attempt to improve the accuracy of the solutions. The validity of the solutions is discussed by comparing them with solutions of the direct approach of the MMS and the finite difference method.

  9. Cnoidal waves as solutions of the nonlinear liquid drop model

    International Nuclear Information System (INIS)

    Ludu, Andrei; Sandulescu, Aureliu; Greiner Walter

    1997-01-01

    By introducing in the hydrodynamic model, i.e. in the hydrodynamic equation and the corresponding boundary conditions, the higher order terms in the deviation of the shape, we obtain in the second order the Korteweg de Vries equations (KdV). The same equation is obtained by introducing in the liquid drop model (LDM), i.e. in the kinetic, surface and Coulomb terms, the higher terms in the second order. The KdV equation has the cnoidal waves as steady-state solutions. These waves could describe the small anharmonic vibrations of spherical nuclei up to the solitary waves. The solitons could describe the preformation of clusters on the nuclear surface. We apply this nonlinear liquid drop model to the alpha formation in heavy nuclei. We find an additional minimum in the total energy of such systems, corresponding to the solitons as clusters on the nuclear surface. By introducing the shell effects we choose this minimum to be degenerated with the ground state. The spectroscopic factor is given by ratio of the square amplitudes in the two minima. (authors)

  10. Nonlinear dynamics and numerical uncertainties in CFD

    Science.gov (United States)

    Yee, H. C.; Sweby, P. K.

    1996-01-01

    The application of nonlinear dynamics to improve the understanding of numerical uncertainties in computational fluid dynamics (CFD) is reviewed. Elementary examples in the use of dynamics to explain the nonlinear phenomena and spurious behavior that occur in numerics are given. The role of dynamics in the understanding of long time behavior of numerical integrations and the nonlinear stability, convergence, and reliability of using time-marching, approaches for obtaining steady-state numerical solutions in CFD is explained. The study is complemented with spurious behavior observed in CFD computations.

  11. Reliable and Efficient Procedure for Steady-State Analysis of Nonautonomous and Autonomous Systems

    Directory of Open Access Journals (Sweden)

    J. Dobes

    2012-04-01

    Full Text Available The majority of contemporary design tools do not still contain steady-state algorithms, especially for the autonomous systems. This is mainly caused by insufficient accuracy of the algorithm for numerical integration, but also by unreliable steady-state algorithms themselves. Therefore, in the paper, a very stable and efficient procedure for the numerical integration of nonlinear differential-algebraic systems is defined first. Afterwards, two improved methods are defined for finding the steady state, which use this integration algorithm in their iteration loops. The first is based on the idea of extrapolation, and the second utilizes nonstandard time-domain sensitivity analysis. The two steady-state algorithms are compared by analyses of a rectifier and a C-class amplifier, and the extrapolation algorithm is primarily selected as a more reliable alternative. Finally, the method based on the extrapolation naturally cooperating with the algorithm for solving the differential-algebraic systems is thoroughly tested on various electronic circuits: Van der Pol and Colpitts oscillators, fragment of a large bipolar logical circuit, feedback and distributed microwave oscillators, and power amplifier. The results confirm that the extrapolation method is faster than a classical plain numerical integration, especially for larger circuits with complicated transients.

  12. On the application of finite element method in the solution of steady state diffusion equation

    International Nuclear Information System (INIS)

    Ono, S.

    1982-01-01

    The solution of the steady state neutron diffusion equation is obtained by using the finite element method. Specifically the variational approach is used for one dimensional problems and the weighted residual method (Galerkin) for one and two dimensional problems. The spatial domain is divided into retangular elements and the neutron flux is approximated by linear (one dimensional case), and bilinear (two-dimensional case) functions. Numerical results are obtained with a FORTRAN IV computer program and compared with those obtained by the finite difference CITATION code. The results show that linear or bilinear functions, do not satisfactorily describe the differential parameters in highly heterogeneous reactor cases, but provide good results for integral parameters such as multiplication factor. (Author) [pt

  13. Tailored parameter optimization methods for ordinary differential equation models with steady-state constraints.

    Science.gov (United States)

    Fiedler, Anna; Raeth, Sebastian; Theis, Fabian J; Hausser, Angelika; Hasenauer, Jan

    2016-08-22

    analysis of the dataset for Raf/MEK/ERK signaling provides novel biological insights regarding the existence of feedback regulation. Many optimization problems considered in systems and computational biology are subject to steady-state constraints. While most optimization methods have convergence problems if these steady-state constraints are highly nonlinear, the methods presented recover the convergence properties of optimizers which can exploit an analytical expression for the parameter-dependent steady state. This renders them an excellent alternative to methods which are currently employed in systems and computational biology.

  14. Evaluation of postural steadiness before and after sedation: comparison of four nonlinear and three conventional measures

    International Nuclear Information System (INIS)

    Tietäväinen, A; Hæggström, E; Mandel, J E

    2014-01-01

    Sedative drugs decrease postural steadiness and increase the risk of injury from falls and accidents. The recovery rate is individual, making it hard to predict the patient's steadiness and hence safe discharge time. 103 outpatients sedated with midazolam and fentanyl were measured posturographically, before (PRE) and after (POST) endoscopy. The ability of conventional and nonlinear sway measures to separate the PRE and POST conditions were compared, and the area under the receiver operating characteristics curve (AUC) was used to quantify the significance of the separation. A nonlinear measure, fuzzy sample entropy, scored the largest AUC (AUC FSE  = 0.83, p < 0.0001). While the AUC FSE  was not significantly larger than the AUCs of conventional sway measures which offer easy quantification of postural steadiness, nonlinear measures provide more insight into the structure of postural control, which may help understand the effect of sedation on postural steadiness. This study is a step toward developing a tester that indicates a safe discharge time. (paper)

  15. Steady-state equations of even flux and scattering

    International Nuclear Information System (INIS)

    Verwaerde, D.

    1985-11-01

    Some mathematical properties of steady-state equation of even flux are shown in variational formalism. This theoretical frame allows to study the existence of a solution and its asymptotical behavior in opaque media (i.e. the relation with scattering equation). At last it allows to qualify the convergence velocity of resolution iterative processes used practically [fr

  16. Optimal control of transitions between nonequilibrium steady states.

    Directory of Open Access Journals (Sweden)

    Patrick R Zulkowski

    Full Text Available Biological systems fundamentally exist out of equilibrium in order to preserve organized structures and processes. Many changing cellular conditions can be represented as transitions between nonequilibrium steady states, and organisms have an interest in optimizing such transitions. Using the Hatano-Sasa Y-value, we extend a recently developed geometrical framework for determining optimal protocols so that it can be applied to systems driven from nonequilibrium steady states. We calculate and numerically verify optimal protocols for a colloidal particle dragged through solution by a translating optical trap with two controllable parameters. We offer experimental predictions, specifically that optimal protocols are significantly less costly than naive ones. Optimal protocols similar to these may ultimately point to design principles for biological energy transduction systems and guide the design of artificial molecular machines.

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

    Science.gov (United States)

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

    2018-05-01

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

  18. Some Aspects of Nonlinear Dynamics and CFD

    Science.gov (United States)

    Yee, Helen C.; Merriam, Marshal (Technical Monitor)

    1996-01-01

    The application of nonlinear dynamics to improve the understanding of numerical uncertainties in computational fluid dynamics (CFD) is reviewed. Elementary examples in the use of dynamics to explain the nonlinear phenomena and spurious behavior that occur in numerics are given. The role of dynamics in the understanding of long time behavior of numerical integrations and the nonlinear stability, convergence, and reliability of using time-marching approaches for obtaining steady-state numerical solutions in CFD is explained. The study is complemented with examples of spurious behavior observed in CFD computations.

  19. A closed-form solution for steady-state coupled phloem/xylem flow using the Lambert-W function.

    Science.gov (United States)

    Hall, A J; Minchin, P E H

    2013-12-01

    A closed-form solution for steady-state coupled phloem/xylem flow is presented. This incorporates the basic Münch flow model of phloem transport, the cohesion model of xylem flow, and local variation in the xylem water potential and lateral water flow along the transport pathway. Use of the Lambert-W function allows this solution to be obtained under much more general and realistic conditions than has previously been possible. Variation in phloem resistance (i.e. viscosity) with solute concentration, and deviations from the Van't Hoff expression for osmotic potential are included. It is shown that the model predictions match those of the equilibrium solution of a numerical time-dependent model based upon the same mechanistic assumptions. The effect of xylem flow upon phloem flow can readily be calculated, which has not been possible in any previous analytical model. It is also shown how this new analytical solution can handle multiple sources and sinks within a complex architecture, and can describe competition between sinks. The model provides new insights into Münch flow by explicitly including interactions with xylem flow and water potential in the closed-form solution, and is expected to be useful as a component part of larger numerical models of entire plants. © 2013 John Wiley & Sons Ltd.

  20. A steady-state fluid model of the coaxial plasma gun

    International Nuclear Information System (INIS)

    Herziger, G.; Krompholz, H.; Schneider, W.; Schoenbach, K.

    1979-01-01

    The plasma layer in a coaxial plasma gun is considered as a shock front driven by expanding magnetic fields. Analytical steady-state solutions of the fluid equations yield the plasma properties, allowing the scaling of plasma focus devices. (Auth.)

  1. Energy management in multi stage evaporator through a steady and dynamic state analysis

    Energy Technology Data Exchange (ETDEWEB)

    Verma, Om Prakash; Manik, Gaurav; Mohammed, Toufiq Haji [Indian Institute of Technology Roorkee, Roorkee (India)

    2017-10-15

    Increasing energy demand, high cost of energy and global warming issues across the globe require energy intensive industries, such as paper mills to improve energy efficiency. Multi-stage evaporators used to concentrate the black liquor in such mills form its most energy consuming unit and require a strong understanding of steady and unsteady state behavior to ensure energy savings. The modeling of nonlinear heptads’ effect system yielded a set of complex nonlinear algebraic and differential equations that are analyzed using Interior-point method and state space representation. Dynamic response of product concentration and system vapor temperatures along with system stability and controllability have been explored by disturbing the flow rate, concentration and temperature of feed, and fresh steam flow rate. Simulations predict that steam flow rate, feed flow rate and its concentration invariably are major controlling factors (in decreasing order) of vapor temperature and product concentration. The interactive behavior between different effects translates into slower responses of the effects with increasing separation from disturbance source. This steady state and transient study opens many new explanations to this relatively less explored area and helps to propose and implement industrial PID controllers to reduce steam consumption and control product quality.

  2. Existence of non-unique steady state solutions to the RMF current drive equations

    Energy Technology Data Exchange (ETDEWEB)

    Hugrass, W N [Flinders Univ. of South Australia, Bedford Park. School of Physical Sciences

    1985-05-04

    It is shown that the value of the d.c. current driven in a plasma cylinder by means of a rotating magnetic field (RMF) is not unique for R/delta >= 6 and eBsub(..omega..)/..nu..sub(ei)m approx.R/delta, where R is the radius of the plasma cylinder, delta is the classical skin depth, ..nu..sub(ei) is the electron-ion momentum transfer collision frequency, Bsub(..omega..) is the magnitude of the rotating magnetic field, e is the electron charge and m is the electron mass. This effect is predicted using three distinct approaches: (i) a steady state anaysis which ignores the second and higher harmonics of the fields and currents; (ii) a qualitative model which utilizes the analogy between the RMF current drive technique and the operation of the induction motor; (iii) a solution of the initial boundary value equations describing the RMF current drive in cylindrical plasmas.

  3. The non-local Fisher–KPP equation: travelling waves and steady states

    International Nuclear Information System (INIS)

    Berestycki, Henri; Nadin, Grégoire; Perthame, Benoit; Ryzhik, Lenya

    2009-01-01

    We consider the Fisher–KPP equation with a non-local saturation effect defined through an interaction kernel φ(x) and investigate the possible differences with the standard Fisher–KPP equation. Our first concern is the existence of steady states. We prove that if the Fourier transform φ-circumflex(ξ) is positive or if the length σ of the non-local interaction is short enough, then the only steady states are u ≡ 0 and u ≡ 1. Next, we study existence of the travelling waves. We prove that this equation admits travelling wave solutions that connect u = 0 to an unknown positive steady state u ∞ (x), for all speeds c ≥ c * . The travelling wave connects to the standard state u ∞ (x) ≡ 1 under the aforementioned conditions: φ-circumflex(ξ) > 0 or σ is sufficiently small. However, the wave is not monotonic for σ large

  4. Numerical solution of non-linear dual-phase-lag bioheat transfer equation within skin tissues.

    Science.gov (United States)

    Kumar, Dinesh; Kumar, P; Rai, K N

    2017-11-01

    This paper deals with numerical modeling and simulation of heat transfer in skin tissues using non-linear dual-phase-lag (DPL) bioheat transfer model under periodic heat flux boundary condition. The blood perfusion is assumed temperature-dependent which results in non-linear DPL bioheat transfer model in order to predict more accurate results. A numerical method of line which is based on finite difference and Runge-Kutta (4,5) schemes, is used to solve the present non-linear problem. Under specific case, the exact solution has been obtained and compared with the present numerical scheme, and we found that those are in good agreement. A comparison based on model selection criterion (AIC) has been made among non-linear DPL models when the variation of blood perfusion rate with temperature is of constant, linear and exponential type with the experimental data and it has been found that non-linear DPL model with exponential variation of blood perfusion rate is closest to the experimental data. In addition, it is found that due to absence of phase-lag phenomena in Pennes bioheat transfer model, it achieves steady state more quickly and always predict higher temperature than thermal and DPL non-linear models. The effect of coefficient of blood perfusion rate, dimensionless heating frequency and Kirchoff number on dimensionless temperature distribution has also been analyzed. The whole analysis is presented in dimensionless form. Copyright © 2017 Elsevier Inc. All rights reserved.

  5. Basis adaptation and domain decomposition for steady-state partial differential equations with random coefficients

    Energy Technology Data Exchange (ETDEWEB)

    Tipireddy, R.; Stinis, P.; Tartakovsky, A. M.

    2017-12-01

    We present a novel approach for solving steady-state stochastic partial differential equations (PDEs) with high-dimensional random parameter space. The proposed approach combines spatial domain decomposition with basis adaptation for each subdomain. The basis adaptation is used to address the curse of dimensionality by constructing an accurate low-dimensional representation of the stochastic PDE solution (probability density function and/or its leading statistical moments) in each subdomain. Restricting the basis adaptation to a specific subdomain affords finding a locally accurate solution. Then, the solutions from all of the subdomains are stitched together to provide a global solution. We support our construction with numerical experiments for a steady-state diffusion equation with a random spatially dependent coefficient. Our results show that highly accurate global solutions can be obtained with significantly reduced computational costs.

  6. Nonlinear modal analysis in NPP dynamics: a proposal

    International Nuclear Information System (INIS)

    Suarez Antola, R.

    2005-07-01

    We propose and briefly suggest how to apply the analytical tools of nonlinear modal analysis (NMA) to problems of nuclear reactor kinetics, NPP dynamics, and NPP instrumentation and control. The proposed method is closely related with recent approaches by modal analysis using the reactivity matrix with feedbacks to couple neutron kinetics with thermal hydraulics in the reactors core. A nonlinear system of ordinary differential equations for mode amplitudes is obtained, projecting the dynamic equations of a model of NPP onto the eigenfunctions of a suitable adjoint operator. A steady state solution of the equations is taken as a reference, and the behaviour of transient solutions in some neighbourhood of the steady state solution is studied by an extension of Liapunov's First Method that enables to cope directly with the non-linear terms in the dynamics. In NPP dynamics these differential equations for the mode amplitudes are of polynomial type of low degree A few dominant modes can usually be identified. These mode amplitudes evolve almost independently of the other modes, more slowly and tending to slave the other mode amplitudes. Using asymptotic methods, it is possible to calculate a closed form analytical approximation to the response to finite amplitude perturbations from the given steady spatial pattern (the origin of the space of mode amplitudes).When there is finite amplitude instability, the method allows us to calculate the threshold amplitude as a well defined function of system's parameters. This is a most significant accomplishment that the other methods cannot afford

  7. steadystate performance of induction and transfer state

    African Journals Online (AJOL)

    eobe

    This paper presents paper presents paper presents the steady the steady the steady–state performance state performance state performance comparison comparison comparison between polyphase induction motor and polyphase between polyphase induction motor and polyphase. TF motor operating in. TF motor ...

  8. Green's theorem and Green's functions for the steady-state cosmic-ray equation of transport

    International Nuclear Information System (INIS)

    Webb, G.M.; Gleeson, L.J.

    1977-01-01

    Green's Theorem is developed for the spherically-symmetric steady-state cosmic-ray equation of transport in interplanetary space. By means of it the momentum distribution function F 0 (r,p), (r=heliocentric distance, p=momentum) can be determined in a region rsub(a) 0 . Examples of Green's functions are given for the case rsub(a)=0, rsub(b)=infinity and derived for the cases of finite rsub(a) and rsub(b). The diffusion coefficient kappa is assumed of the form kappa=kappa 0 (p)rsup(b). The treatment systematizes the development of all analytic solutions for steady-state solar and galactic cosmic-ray propagation and previous solutions form a subset of the present solutions. (Auth.)

  9. Steady-state and pre-steady-state kinetic analysis of halopropane conversion by a Rhodococcus haloalkane dehalogenase

    NARCIS (Netherlands)

    Bosma, T; Pikkemaat, MG; Kingma, Jacob; Dijk, J; Janssen, DB

    2003-01-01

    Haloalkane dehalogenase from Rhodococcus rhodochrous NCIMB 13064 (DhaA) catalyzes the hydrolysis of carbon-halogen bonds in a wide range of haloalkanes. We examined the steady-state and pre-steady-state kinetics of halopropane conversion by DhaA to illuminate mechanistic details of the

  10. Pseudo Steady-State Free Precession for MR-Fingerprinting.

    Science.gov (United States)

    Assländer, Jakob; Glaser, Steffen J; Hennig, Jürgen

    2017-03-01

    This article discusses the signal behavior in the case the flip angle in steady-state free precession sequences is continuously varied as suggested for MR-fingerprinting sequences. Flip angle variations prevent the establishment of a steady state and introduce instabilities regarding to magnetic field inhomogeneities and intravoxel dephasing. We show how a pseudo steady state can be achieved, which restores the spin echo nature of steady-state free precession. Based on geometrical considerations, relationships between the flip angle, repetition and echo time are derived that suffice to the establishment of a pseudo steady state. The theory is tested with Bloch simulations as well as phantom and in vivo experiments. A typical steady-state free precession passband can be restored with the proposed conditions. The stability of the pseudo steady state is demonstrated by comparing the evolution of the signal of a single isochromat to one resulting from a spin ensemble. As confirmed by experiments, magnetization in a pseudo steady state can be described with fewer degrees of freedom compared to the original fingerprinting and the pseudo steady state results in more reliable parameter maps. The proposed conditions restore the spin-echo-like signal behavior typical for steady-state free precession in fingerprinting sequences, making this approach more robust to B 0 variations. Magn Reson Med 77:1151-1161, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicine.

  11. Existence and instability of steady states for a triangular cross-diffusion system: A computer-assisted proof

    Science.gov (United States)

    Breden, Maxime; Castelli, Roberto

    2018-05-01

    In this paper, we present and apply a computer-assisted method to study steady states of a triangular cross-diffusion system. Our approach consist in an a posteriori validation procedure, that is based on using a fixed point argument around a numerically computed solution, in the spirit of the Newton-Kantorovich theorem. It allows to prove the existence of various non homogeneous steady states for different parameter values. In some situations, we obtain as many as 13 coexisting steady states. We also apply the a posteriori validation procedure to study the linear stability of the obtained steady states, proving that many of them are in fact unstable.

  12. Chemical-specific screening criteria for interpretation of biomonitoring data for volatile organic compounds (VOCs)--application of steady-state PBPK model solutions.

    Science.gov (United States)

    Aylward, Lesa L; Kirman, Chris R; Blount, Ben C; Hays, Sean M

    2010-10-01

    The National Health and Nutrition Examination Survey (NHANES) generates population-representative biomonitoring data for many chemicals including volatile organic compounds (VOCs) in blood. However, no health or risk-based screening values are available to evaluate these data from a health safety perspective or to use in prioritizing among chemicals for possible risk management actions. We gathered existing risk assessment-based chronic exposure reference values such as reference doses (RfDs), reference concentrations (RfCs), tolerable daily intakes (TDIs), cancer slope factors, etc. and key pharmacokinetic model parameters for 47 VOCs. Using steady-state solutions to a generic physiologically-based pharmacokinetic (PBPK) model structure, we estimated chemical-specific steady-state venous blood concentrations across chemicals associated with unit oral and inhalation exposure rates and with chronic exposure at the identified exposure reference values. The geometric means of the slopes relating modeled steady-state blood concentrations to steady-state exposure to a unit oral dose or unit inhalation concentration among 38 compounds with available pharmacokinetic parameters were 12.0 microg/L per mg/kg-d (geometric standard deviation [GSD] of 3.2) and 3.2 microg/L per mg/m(3) (GSD=1.7), respectively. Chemical-specific blood concentration screening values based on non-cancer reference values for both oral and inhalation exposure range from 0.0005 to 100 microg/L; blood concentrations associated with cancer risk-specific doses at the 1E-05 risk level ranged from 5E-06 to 6E-02 microg/L. The distribution of modeled steady-state blood concentrations associated with unit exposure levels across VOCs may provide a basis for estimating blood concentration screening values for VOCs that lack chemical-specific pharmacokinetic data. The screening blood concentrations presented here provide a tool for risk assessment-based evaluation of population biomonitoring data for VOCs and

  13. Multimode optical fibers: steady state mode exciter.

    Science.gov (United States)

    Ikeda, M; Sugimura, A; Ikegami, T

    1976-09-01

    The steady state mode power distribution of the multimode graded index fiber was measured. A simple and effective steady state mode exciter was fabricated by an etching technique. Its insertion loss was 0.5 dB for an injection laser. Deviation in transmission characteristics of multimode graded index fibers can be avoided by using the steady state mode exciter.

  14. New solutions of a nonlinear classical field theory

    International Nuclear Information System (INIS)

    Marques, G.C.; Ventura, I.

    1975-01-01

    New solutions of a relativistic, classical, field theoretical model having logarithmic nonlinearities are obtained. Some of these solutions correspond to field not bounded in time but having finite energy and charge. There are no bounded solutions (bound states and resonances in particular) if the charge exceeds a certain value. This effect is due to the existance of a 'charge barrier' in this field theoretical model. All calculations are performed in a number of spatial dimensions [pt

  15. Analytical solutions of steady-state conjugate heat transfer in ducts with turbulent flow

    International Nuclear Information System (INIS)

    Cerqueira, Djane R.; Jian Su

    2007-01-01

    In this work, we present an approximate analytical solution of the steady-state conjugate heat transfer of turbulent forced convection in a circular pipe with wall axial heat conduction and external convective boundary conditions. Improved lumped differential approach based on two points Hermite approximation for integrals was applied to reduce the heat conduction equation in the solid into a second-order ordinary differential equation for the radially averaged solid temperature. The energy equation in the fluid was solved by applying the generalized integral transform technique (GITT). The Sturm-Lioville eigenproblem for fluid energy equation in the cylindrical coordinate system was solved by the sign-count method. The truncated system of N ordinary differential equations for transformed potentials of the fluid temperature and the second-order ordinary differential equation for radially averaged solid temperature formed a homogeneous system of N+2 ordinary differential equations, which was solved analytically. The effects of the fluid-solid thermal conductivity ratio on the Nusselt number, the average fluid and solid temperatures, and the fluid-solid interface temperature were investigated. (author)

  16. Bifurcation of steady tearing states

    International Nuclear Information System (INIS)

    Saramito, B.; Maschke, E.K.

    1985-10-01

    We apply the bifurcation theory for compact operators to the problem of the nonlinear solutions of the 3-dimensional incompressible visco-resistive MHD equations. For the plane plasma slab model we compute branches of nonlinear tearing modes, which are stationary for the range of parameters investigated up to now

  17. Links between soil properties and steady-state solute transport through cultivated topsoil at the field scale

    Science.gov (United States)

    Koestel, J. K.; Norgaard, T.; Luong, N. M.; Vendelboe, A. L.; Moldrup, P.; Jarvis, N. J.; Lamandé, M.; Iversen, B. V.; Wollesen de Jonge, L.

    2013-02-01

    It is known that solute transport through soil is heterogeneous at all spatial scales. However, little data are available to allow quantification of these heterogeneities at the field scale or larger. In this study, we investigated the spatial patterns of soil properties, hydrologic state variables, and tracer breakthrough curves (BTCs) at the field scale for the inert solute transport under a steady-state irrigation rate which produced near-saturated conditions. Sixty-five undisturbed soil columns approximately 20 cm in height and diameter were sampled from the loamy topsoil of an agricultural field site in Silstrup (Denmark) at a sampling distance of approximately 15 m (with a few exceptions), covering an area of approximately 1 ha (60 m × 165 m). For 64 of the 65 investigated soil columns, we observed BTC shapes indicating a strong preferential transport. The strength of preferential transport was positively correlated with the bulk density and the degree of water saturation. The latter suggests that preferential macropore transport was the dominating transport process. Increased bulk densities were presumably related with a decrease in near-saturated hydraulic conductivities and as a consequence to larger water saturation and the activation of larger macropores. Our study provides further evidence that it should be possible to estimate solute transport properties from soil properties such as soil texture or bulk density. We also demonstrated that estimation approaches established for the column scale have to be upscaled when applied to the field scale or larger.

  18. Limitations of steady state solutions to a two-state model of population oscillations and hole burning

    International Nuclear Information System (INIS)

    Payne, M. G.; Deng, L.; Jiang, K. J.

    2006-01-01

    We consider a two-state system driven by an on-resonance, continuous wave pump laser and a much weaker pulsed probe laser that is slightly detuned from the pump laser frequency (usually this detuning is about ω p -ω P =Δ≅1 kHz). The upper state population is assumed to be slowly decaying, but the off-diagonal element of the density matrix decays rapidly due to homogeneous broadening. This model has been solved by others in rare-earth-element-doped fibers and crystals in a usual steady state approximation for slow optical wave propagation. We show that in general the usual steady state approximation does not apply unless either Δτ>>1 or (2S+1)γ 2 τ>>1 where γ 2 is the decay rate of the excited state population, τ is the pulse length of the probe field, and 2S is the saturation parameter. Both conditions, however, are not satisfied in many population-oscillation- and corresponding group-velocity-reduction-related studies. Our theory and corresponding numerical simulations have indicated that for probe pulses that are much shorter than the lifetime of the upper state, there is no analytical theory for the amplitude, pulse shape, and group velocity of the probe field. In addition, there is no reason to assume that the group velocity remains small when γ 2 τ<<1 and there is no reason to believe that many pulse length decays can be obtained for such short pulses

  19. Steady-State Creep of Asphalt Concrete

    Directory of Open Access Journals (Sweden)

    Alibai Iskakbayev

    2017-02-01

    Full Text Available This paper reports the experimental investigation of the steady-state creep process for fine-grained asphalt concrete at a temperature of 20 ± 2 °С and under stress from 0.055 to 0.311 MPa under direct tension and was found to occur at a constant rate. The experimental results also determined the start, the end point, and the duration of the steady-state creep process. The dependence of these factors, in addition to the steady-state creep rate and viscosity of the asphalt concrete on stress is satisfactorily described by a power function. Furthermore, it showed that stress has a great impact on the specific characteristics of asphalt concrete: stress variation by one order causes their variation by 3–4.5 orders. The described relations are formulated for the steady-state of asphalt concrete in a complex stressed condition. The dependence is determined between stress intensity and strain rate intensity.

  20. Reactor kinetics - pulse and steady state

    Energy Technology Data Exchange (ETDEWEB)

    Estes, B F; Morris, F M [Sandia Laboratories (United States)

    1974-07-01

    An analytical model has been developed which couples the nuclear and thermal characteristics of the Annular Core Pulse Reactor (ACPR) into a solution which describes both the neutron kinetics of the reactor and the temperature behavior of a fuel-moderator element. The model describes both pulse and steady state operations. This paper describes the important aspects of the reactor, the fuel- moderator elements, the neutron kinetic equations of the reactor, and the time-temperature behavior of a fuel-moderator element that is being subjected to the maximum power density in the core. The parameters which are utilized in the equations are divided into two classes, those that can be measured directly and those that are assumed to be known (each is described briefly). Some of the solutions which demonstrate the versatility of the analytical model are described. (author)

  1. Effects of quadratic and cubic nonlinearities on a perfectly tuned parametric amplifier

    DEFF Research Database (Denmark)

    Neumeyer, Stefan; Sorokin, Vladislav; Thomsen, Jon Juel

    2016-01-01

    We consider the performance of a parametric amplifier with perfect tuning (two-to-one ratio between the parametric and direct excitation frequencies) and quadratic and cubic nonlinearities. A forced Duffing–Mathieu equation with appended quadratic nonlinearity is considered as the model system......, and approximate analytical steady-state solutions and corresponding stabilities are obtained by the method of varying amplitudes. Some general effects of pure quadratic, and mixed quadratic and cubic nonlinearities on parametric amplification are shown. In particular, the effects of mixed quadratic and cubic...... nonlinearities may generate additional amplitude–frequency solutions. In this case an increased response and a more phase sensitive amplitude (phase between excitation frequencies) is obtained, as compared to the case with either pure quadratic or cubic nonlinearity. Furthermore, jumps and bi...

  2. Theory of steady state plasma flow and confinement in a periodic magnetic field

    International Nuclear Information System (INIS)

    Brown, M.G.

    1981-02-01

    The steady flow of plasmas through spatially periodic magnetic fields is examined, and a theoretical model is developed for the case of axisymmetric geometry. The externally applied magnetic fields can be cusps or mirrors joined end to end; electrons are then localised by these fields because of their small Larmor radius, while the ions can traverse the magnetic mirrors. The properties of the model equations are studied and dimensionless parameters which appear are interpreted. Numerical methods used in steady flow applications are reviewed, and some techniques of solution for the model equations are discussed. A solution method involving numerical integration of time-dependent equations is described, which approaches the steady state asymptotically; results from this method are presented and compared with the results from perturbation theory. (author)

  3. Steady State Turbulent Transport in Magnetic Fusion Plasmas

    International Nuclear Information System (INIS)

    Lee, W.W.; Ethier, S.; Kolesnikov, R.; Wang, W.X.; Tang, W.M.

    2007-01-01

    For more than a decade, the study of microturbulence, driven by ion temperature gradient (ITG) drift instabilities in tokamak devices, has been an active area of research in magnetic fusion science for both experimentalists and theorists alike. One of the important impetus for this avenue of research was the discovery of the radial streamers associated the ITG modes in the early nineties using a Particle-In-Cell (PIC) code. Since then, ITG simulations based on the codes with increasing realism have become possible with the dramatic increase in computing power. The notable examples were the demonstration of the importance of nonlinearly generated zonal flows in regulating ion thermal transport and the transition from Bohm to GyroBoham scaling with increased device size. In this paper, we will describe another interesting nonlinear physical process associated with the parallel acceleration of the ions, that is found to play an important role for the steady state turbulent transport. Its discovery is again through the use of the modern massively parallel supercomputers

  4. Quasi-exact solutions of nonlinear differential equations

    OpenAIRE

    Kudryashov, Nikolay A.; Kochanov, Mark B.

    2014-01-01

    The concept of quasi-exact solutions of nonlinear differential equations is introduced. Quasi-exact solution expands the idea of exact solution for additional values of parameters of differential equation. These solutions are approximate solutions of nonlinear differential equations but they are close to exact solutions. Quasi-exact solutions of the the Kuramoto--Sivashinsky, the Korteweg--de Vries--Burgers and the Kawahara equations are founded.

  5. Exact solutions of a nonpolynomially nonlinear Schrodinger equation

    International Nuclear Information System (INIS)

    Parwani, R.; Tan, H.S.

    2007-01-01

    A nonlinear generalisation of Schrodinger's equation had previously been obtained using information-theoretic arguments. The nonlinearities in that equation were of a nonpolynomial form, equivalent to the occurrence of higher-derivative nonlinear terms at all orders. Here we construct some exact solutions to that equation in 1+1 dimensions. On the half-line, the solutions resemble (exponentially damped) Bloch waves even though no external periodic potential is included. The solutions are nonperturbative as they do not reduce to solutions of the linear theory in the limit that the nonlinearity parameter vanishes. An intriguing feature of the solutions is their infinite degeneracy: for a given energy, there exists a very large arbitrariness in the normalisable wavefunctions. We also consider solutions to a q-deformed version of the nonlinear equation and discuss a natural discretisation implied by the nonpolynomiality. Finally, we contrast the properties of our solutions with other solutions of nonlinear Schrodinger equations in the literature and suggest some possible applications of our results in the domains of low-energy and high-energy physics

  6. Minimal gain marching schemes: searching for unstable steady-states with unsteady solvers

    Science.gov (United States)

    de S. Teixeira, Renan; S. de B. Alves, Leonardo

    2017-12-01

    Reference solutions are important in several applications. They are used as base states in linear stability analyses as well as initial conditions and reference states for sponge zones in numerical simulations, just to name a few examples. Their accuracy is also paramount in both fields, leading to more reliable analyses and efficient simulations, respectively. Hence, steady-states usually make the best reference solutions. Unfortunately, standard marching schemes utilized for accurate unsteady simulations almost never reach steady-states of unstable flows. Steady governing equations could be solved instead, by employing Newton-type methods often coupled with continuation techniques. However, such iterative approaches do require large computational resources and very good initial guesses to converge. These difficulties motivated the development of a technique known as selective frequency damping (SFD) (Åkervik et al. in Phys Fluids 18(6):068102, 2006). It adds a source term to the unsteady governing equations that filters out the unstable frequencies, allowing a steady-state to be reached. This approach does not require a good initial condition and works well for self-excited flows, where a single nonzero excitation frequency is selected by either absolute or global instability mechanisms. On the other hand, it seems unable to damp stationary disturbances. Furthermore, flows with a broad unstable frequency spectrum might require the use of multiple filters, which delays convergence significantly. Both scenarios appear in convectively, absolutely or globally unstable flows. An alternative approach is proposed in the present paper. It modifies the coefficients of a marching scheme in such a way that makes the absolute value of its linear gain smaller than one within the required unstable frequency spectra, allowing the respective disturbance amplitudes to decay given enough time. These ideas are applied here to implicit multi-step schemes. A few chosen test cases

  7. Modeling and Analysis of a Nonlinear Age-Structured Model for Tumor Cell Populations with Quiescence

    Science.gov (United States)

    Liu, Zijian; Chen, Jing; Pang, Jianhua; Bi, Ping; Ruan, Shigui

    2018-05-01

    We present a nonlinear first-order hyperbolic partial differential equation model to describe age-structured tumor cell populations with proliferating and quiescent phases at the avascular stage in vitro. The division rate of the proliferating cells is assumed to be nonlinear due to the limitation of the nutrient and space. The model includes a proportion of newborn cells that enter directly the quiescent phase with age zero. This proportion can reflect the effect of treatment by drugs such as erlotinib. The existence and uniqueness of solutions are established. The local and global stabilities of the trivial steady state are investigated. The existence and local stability of the positive steady state are also analyzed. Numerical simulations are performed to verify the results and to examine the impacts of parameters on the nonlinear dynamics of the model.

  8. Linear superposition solutions to nonlinear wave equations

    International Nuclear Information System (INIS)

    Liu Yu

    2012-01-01

    The solutions to a linear wave equation can satisfy the principle of superposition, i.e., the linear superposition of two or more known solutions is still a solution of the linear wave equation. We show in this article that many nonlinear wave equations possess exact traveling wave solutions involving hyperbolic, triangle, and exponential functions, and the suitable linear combinations of these known solutions can also constitute linear superposition solutions to some nonlinear wave equations with special structural characteristics. The linear superposition solutions to the generalized KdV equation K(2,2,1), the Oliver water wave equation, and the k(n, n) equation are given. The structure characteristic of the nonlinear wave equations having linear superposition solutions is analyzed, and the reason why the solutions with the forms of hyperbolic, triangle, and exponential functions can form the linear superposition solutions is also discussed

  9. Practical steady-state enzyme kinetics.

    Science.gov (United States)

    Lorsch, Jon R

    2014-01-01

    Enzymes are key components of most biological processes. Characterization of enzymes is therefore frequently required during the study of biological systems. Steady-state kinetics provides a simple and rapid means of assessing the substrate specificity of an enzyme. When combined with site-directed mutagenesis (see Site-Directed Mutagenesis), it can be used to probe the roles of particular amino acids in the enzyme in substrate recognition and catalysis. Effects of interaction partners and posttranslational modifications can also be assessed using steady-state kinetics. This overview explains the general principles of steady-state enzyme kinetics experiments in a practical, rather than theoretical, way. Any biochemistry textbook will have a section on the theory of Michaelis-Menten kinetics, including derivations of the relevant equations. No specific enzymatic assay is described here, although a method for monitoring product formation or substrate consumption over time (an assay) is required to perform the experiments described. © 2014 Elsevier Inc. All rights reserved.

  10. Steady state magnetic field configurations for the earth's magnetotail

    Science.gov (United States)

    Hau, L.-N.; Wolf, R. A.; Voigt, G.-H.; Wu, C. C.

    1989-01-01

    A two-dimensional, force-balance magnetic field model is presented. The theoretical existence of a steady state magnetic field configuration that is force-balanced and consistent with slow, lossless, adiabatic, earthward convection within the limit of the ideal MHD is demonstrated. A numerical solution is obtained for a two-dimensional magnetosphere with a rectangular magnetopause and nonflaring tail. The results are consistent with the convection time sequences reported by Erickson (1985).

  11. Generalized solutions of nonlinear partial differential equations

    CERN Document Server

    Rosinger, EE

    1987-01-01

    During the last few years, several fairly systematic nonlinear theories of generalized solutions of rather arbitrary nonlinear partial differential equations have emerged. The aim of this volume is to offer the reader a sufficiently detailed introduction to two of these recent nonlinear theories which have so far contributed most to the study of generalized solutions of nonlinear partial differential equations, bringing the reader to the level of ongoing research.The essence of the two nonlinear theories presented in this volume is the observation that much of the mathematics concernin

  12. Stochastic theory of nonequilibrium steady states and its applications. Part I

    International Nuclear Information System (INIS)

    Zhang Xuejuan; Qian Hong; Qian Min

    2012-01-01

    The concepts of equilibrium and nonequilibrium steady states are introduced in the present review as mathematical concepts associated with stationary Markov processes. For both discrete stochastic systems with master equations and continuous diffusion processes with Fokker–Planck equations, the nonequilibrium steady state (NESS) is characterized in terms of several key notions which are originated from nonequilibrium physics: time irreversibility, breakdown of detailed balance, free energy dissipation, and positive entropy production rate. After presenting this NESS theory in pedagogically accessible mathematical terms that require only a minimal amount of prerequisites in nonlinear differential equations and the theory of probability, it is applied, in Part I, to two widely studied problems: the stochastic resonance (also known as coherent resonance) and molecular motors (also known as Brownian ratchet). Although both areas have advanced rapidly on their own with a vast amount of literature, the theory of NESS provides them with a unifying mathematical foundation. Part II of this review contains applications of the NESS theory to processes from cellular biochemistry, ranging from enzyme catalyzed reactions, kinetic proofreading, to zeroth-order ultrasensitivity.

  13. Steady state drift vortices in plasmas with shear flow in equilibrium

    DEFF Research Database (Denmark)

    Chakrabarti, N.

    1999-01-01

    The Hasegawa-Mima equation in the presence of sheared poloidal flow is solved for two-dimensional steady state vortex. It is shown that when the phase velocity of the vortex is the same as the diamagnetic drift velocity, an exact solution in the form of counter-rotating vortices may appear...

  14. Quasi-steady state thermal performances of a solar air heater with ...

    African Journals Online (AJOL)

    Quasi-steady state thermal performance of a solar air heater with a combined absorber is studied. The whole energy balance equations related to the system were articulated as a linear system of temperature equations. Solutions to this linear system were assessed from program based on an iterative process. The mean ...

  15. Steady-State Performance of Kalman Filter for DPLL

    Institute of Scientific and Technical Information of China (English)

    QIAN Yi; CUI Xiaowei; LU Mingquan; FENG Zhenming

    2009-01-01

    For certain system models, the structure of the Kalman filter is equivalent to a second-order vari-able gain digital phase-locked loop (DPLL). To apply the knowledge of DPLLs to the design of Kalman filters, this paper studies the steady-state performance of Kalman filters for these system models. The results show that the steady-state Kalman gain has the same form as the DPLL gain. An approximate simple form for the steady-state Kalman gain is used to derive an expression for the equivalent loop bandwidth of the Kalman filter as a function of the process and observation noise variances. These results can be used to analyze the steady-state performance of a Kalman filter with DPLL theory or to design a Kalman filter model with the same steady-state performance as a given DPLL.

  16. Global stability and exact solution of an arbitrary-solute nonlinear cellular mass transport system.

    Science.gov (United States)

    Benson, James D

    2014-12-01

    The prediction of the cellular state as a function of extracellular concentrations and temperatures has been of interest to physiologists for nearly a century. One of the most widely used models in the field is one where mass flux is linearly proportional to the concentration difference across the membrane. These fluxes define a nonlinear differential equation system for the intracellular state, which when coupled with appropriate initial conditions, define the intracellular state as a function of the extracellular concentrations of both permeating and nonpermeating solutes. Here we take advantage of a reparametrization scheme to extend existing stability results to a more general setting and to a develop analytical solutions to this model for an arbitrary number of extracellular solutes. Copyright © 2014 Elsevier Inc. All rights reserved.

  17. Steady state magnetic field configurations for the earth's magnetotail

    International Nuclear Information System (INIS)

    Hau, L.N.; Wolf, R.A.; Voigt, G.H.; Wu, C.C.

    1989-01-01

    The authors present a two-dimensional, force-balanced magnetic field model in which flux tubes have constant pVγ throughout an extended region of the nightside plasma sheet, between approximately 36 R E geocentric distance and the region of the inner edge of the plasma sheet. They have thus demonstrated the theoretical existence of a steady state magnetic field configuration that is force-balanced and also consistent with slow, lossless, adiabatic, earthward convection within the limit of the ideal MHD (isotropic pressure, perfect conductivity). The numerical solution was constructed for a two-dimensional magnetosphere with a rectangular magnetopause and nonflaring tail. The primary characteristics of the steady state convection solution are (1) a pressure maximum just tailward of the inner edge of the plasma sheet and (2) a deep, broad minimum in equatorial magnetic field strength B ze , also just tailward of the inner edge. The results are consistent with Erickson's (1985) convection time sequences, which exhibited analogous pressure peaks and B ze minima. Observations do not indicate the existence of a B ze minimum, on the average. They suggest that the configurations with such deep minima in B ze may be tearing-mode unstable, thus leading to substorm onset in the inner plasma sheet

  18. Nonlinear vibrations of an inclined beam subjected to a moving load

    International Nuclear Information System (INIS)

    Mamandi, A; Kargarnovin, M H; Younesian, D

    2009-01-01

    In this paper, the nonlinear dynamic responses of an inclined pinned-pinned Euler-Bernoulli beam with a constant cross section and finite length subjected to a concentrated vertical force traveling with constant velocity is investigated by using the mode summation method. Frequency analysis of the PDE's governing equations of motion for steady-state response is studied by applying multiple scales method. The nonlinear dynamic deflections of the beam are obtained by solving two coupled nonlinear PDE's governing equations of planar motion for both longitudinal and transverse oscillations of the beam. The dynamic magnification factor and normalized time histories of mid-point of the beam are obtained for various load velocity ratios and the numerical results are compared with those obtained from traditional linear solution. It is found that quadratic nonlinearity renders the softening effect on the dynamic response of the beam under the act of traveling load. Also stability analysis of the steady-state response for the modes equations having quadratic nonlinearity is carried out and it is observed from the amplitude response curves that for the case of internal-external primary resonance, both saturation phenomenon and jump phenomenon are predicted for the longitudinal excitation.

  19. Multiple Long-Time Solutions for Intermediate Reynolds Number Flow past a Circular Cylinder with a Nonlinear Inertial and Dissipative Attachment

    Science.gov (United States)

    Blanchard, Antoine B. E.; Bergman, Lawrence A.; Vakakis, Alexander F.; Pearlstein, Arne J.

    2016-11-01

    We consider two-dimensional flow past a linearly-sprung cylinder allowed to undergo rectilinear motion normal to the mean flow, with an attached "nonlinear energy sink" consisting of a mass allowed to rotate about the cylinder axis, and whose rotational motion is linearly damped by a viscous damper. For Re fluid density, dimensionless damping coefficient, and ratio of the rotating mass to the total mass, we find that different inlet transients lead to different long-time solutions, including solutions that are steady and symmetric (with a motionless cylinder), time-periodic, quasi-periodic, and chaotic. The results show that over a wide range of the parameters, the steady symmetric motionless-cylinder solution is locally, but not globally, stable. Supported by NSF Grant CMMI-1363231.

  20. Polynomial solutions of nonlinear integral equations

    International Nuclear Information System (INIS)

    Dominici, Diego

    2009-01-01

    We analyze the polynomial solutions of a nonlinear integral equation, generalizing the work of Bender and Ben-Naim (2007 J. Phys. A: Math. Theor. 40 F9, 2008 J. Nonlinear Math. Phys. 15 (Suppl. 3) 73). We show that, in some cases, an orthogonal solution exists and we give its general form in terms of kernel polynomials

  1. Polynomial solutions of nonlinear integral equations

    Energy Technology Data Exchange (ETDEWEB)

    Dominici, Diego [Department of Mathematics, State University of New York at New Paltz, 1 Hawk Dr. Suite 9, New Paltz, NY 12561-2443 (United States)], E-mail: dominicd@newpaltz.edu

    2009-05-22

    We analyze the polynomial solutions of a nonlinear integral equation, generalizing the work of Bender and Ben-Naim (2007 J. Phys. A: Math. Theor. 40 F9, 2008 J. Nonlinear Math. Phys. 15 (Suppl. 3) 73). We show that, in some cases, an orthogonal solution exists and we give its general form in terms of kernel polynomials.

  2. A asymptotic numerical method for the steady-state convection diffusion equation

    International Nuclear Information System (INIS)

    Wu Qiguang

    1988-01-01

    In this paper, A asymptotic numerical method for the steady-state Convection diffusion equation is proposed, which need not take very fine mesh size in the neighbourhood of the boundary layer. Numerical computation for model problem show that we can obtain the numerical solution in the boundary layer with moderate step size

  3. Lower bounds for ballistic current and noise in non-equilibrium quantum steady states

    Directory of Open Access Journals (Sweden)

    Benjamin Doyon

    2015-03-01

    Full Text Available Let an infinite, homogeneous, many-body quantum system be unitarily evolved for a long time from a state where two halves are independently thermalized. One says that a non-equilibrium steady state emerges if there are nonzero steady currents in the central region. In particular, their presence is a signature of ballistic transport. We analyze the consequences of the current observable being a conserved density; near equilibrium this is known to give rise to linear wave propagation and a nonzero Drude peak. Using the Lieb–Robinson bound, we derive, under a certain regularity condition, a lower bound for the non-equilibrium steady-state current determined by equilibrium averages. This shows and quantifies the presence of ballistic transport far from equilibrium. The inequality suggests the definition of “nonlinear sound velocities”, which specialize to the sound velocity near equilibrium in non-integrable models, and “generalized sound velocities”, which encode generalized Gibbs thermalization in integrable models. These are bounded by the Lieb–Robinson velocity. The inequality also gives rise to a bound on the energy current noise in the case of pure energy transport. We show that the inequality is satisfied in many models where exact results are available, and that it is saturated at one-dimensional criticality.

  4. Dynamical interactions between solute and solvent studied by nonlinear infrared spectroscopy

    International Nuclear Information System (INIS)

    Ohta, K.; Tominaga, K.

    2006-01-01

    Interactions between solute and solvent play an important role in chemical reaction dynamics and in many relaxation processes in condensed phases. Recently third-order nonlinear infrared (IR) spectroscopy has shown to be useful to investigate solute-solvent interaction and dynamics of the vibrational transition. These studies provide detailed information on the energy relaxation of the vibrationally excited state, and the time scale and the magnitude of the time correlation functions of the vibrational frequency fluctuations. In this work we have studied vibrational energy relaxation (VER) of solutions and molecular complexes by nonlinear IR spectroscopy, especially IR pump-probe method, to understand the microscopic interactions in liquids. (authors)

  5. New Tore Supra steady state operating scenario

    International Nuclear Information System (INIS)

    Martin, G.; Parlange, F.; van Houtte, D.; Wijnands, T.

    1995-01-01

    This document deals with plasma control in steady state conditions. A new plasma control systems enabling feedback control of global plasma equilibrium parameters has been developed. It also enables to operate plasma discharge in steady state regime. (TEC). 4 refs., 5 figs

  6. High-precision numerical simulation with autoadaptative grid technique in nonlinear thermal diffusion

    International Nuclear Information System (INIS)

    Chambarel, A.; Pumborios, M.

    1992-01-01

    This paper reports that many engineering problems concern the determination of a steady state solution in the case with strong thermal gradients, and results obtained using the finite-element technique are sometimes inaccurate, particularly for nonlinear problems with unadapted meshes. Building on previous results in linear problems, we propose an autoadaptive technique for nonlinear cases that uses quasi-Newtonian iterations to reevaluate an interpolation error estimation. The authors perfected an automatic refinement technique to solve the nonlinear thermal problem of temperature calculus in a cast-iron cylinder head of a diesel engine

  7. Some Considerations on the Fundamentals of Chemical Kinetics: Steady State, Quasi-Equilibrium, and Transition State Theory

    Science.gov (United States)

    Perez-Benito, Joaquin F.

    2017-01-01

    The elementary reaction sequence A ? I ? Products is the simplest mechanism for which the steady-state and quasi-equilibrium kinetic approximations can be applied. The exact integrated solutions for this chemical system allow inferring the conditions that must fulfill the rate constants for the different approximations to hold. A graphical…

  8. Measurement of non-steady-state free fatty acid turnover

    International Nuclear Information System (INIS)

    Jensen, M.D.; Heiling, V.; Miles, J.M.

    1990-01-01

    The accuracy of non-steady-state equations for measuring changes in free fatty acid rate of appearance (Ra) is unknown. In the present study, endogenous lipolysis (traced with [ 14 C]-linoleate) was pharmacologically suppressed in six conscious mongrel dogs. A computer-responsive infusion pump was then used to deliver an intravenous oleic acid emulsion in both constant and linear gradient infusion modes. Both non-steady-state equations with various effective volumes of distribution (V) and steady-state equations were used to measure oleate Ra [( 14 C]oleate). Endogenous lipolysis did not change during the experiment. When oleate Ra increased in a linear gradient fashion, only non-steady-state equations with a large (150 ml/kg) V resulted in erroneous values (9% overestimate, P less than 0.05). In contrast, when oleate Ra decreased in a similar fashion, steady-state and standard non-steady-state equations (V = plasma volume = 50 ml/kg) overestimated total oleate Ra (18 and 7%, P less than 0.001 and P less than 0.05, respectively). Overall, non-steady-state equations with an effective V of 90 ml/kg (1.8 x plasma volume) allowed the most accurate estimates of oleate Ra

  9. Quantized gauge invariant periodic TDHF solutions

    International Nuclear Information System (INIS)

    Kan, K.-K.; Griffin, J.J.; Lichtner, P.C.; Dworzecka, M.

    1979-01-01

    Time-dependent Hartree-Fock (TDHF) is used to study steady state large amplitude nuclear collective motions, such as vibration and rotation. As is well known the small amplitude TDHF leads to the RPA equation. The analysis of periodicity in TDHF is not trivial because TDHF is a nonlinear theory and it is not known under what circumstances a nonlinear theory can support periodic solutions. It is also unknown whether such periodic solution, if they exist, form a continuous or a discrete set. But, these properties may be important in obtaining the energy spectrum of the collective states from the TDHF description. The periodicity and Gauge Invariant Periodicity of solutions are investigated for that class of models whose TDHF solutions depend on time through two parameters. In such models TDHF supports a continuous family of periodic solutions, but only a discrete subset of these is gauge invariant. These discrete Gauge Invariant Periodic solutions obey the Bohr-Summerfeld quantization rule. The energy spectrum of the Gauge Invariant Periodic solutions is compared with the exact eigenergies in one specific example

  10. Symmetry and exact solutions of nonlinear spinor equations

    International Nuclear Information System (INIS)

    Fushchich, W.I.; Zhdanov, R.Z.

    1989-01-01

    This review is devoted to the application of algebraic-theoretical methods to the problem of constructing exact solutions of the many-dimensional nonlinear systems of partial differential equations for spinor, vector and scalar fields widely used in quantum field theory. Large classes of nonlinear spinor equations invariant under the Poincare group P(1, 3), Weyl group (i.e. Poincare group supplemented by a group of scale transformations), and the conformal group C(1, 3) are described. Ansaetze invariant under the Poincare and the Weyl groups are constructed. Using these we reduce the Poincare-invariant nonlinear Dirac equations to systems of ordinary differential equations and construct large families of exact solutions of the nonlinear Dirac-Heisenberg equation depending on arbitrary parameters and functions. In a similar way we have obtained new families of exact solutions of the nonlinear Maxwell-Dirac and Klein-Gordon-Dirac equations. The obtained solutions can be used for quantization of nonlinear equations. (orig.)

  11. Analysis of the Multiple-Solution Response of a Flexible Rotor Supported on Non-Linear Squeeze Film Dampers

    Science.gov (United States)

    ZHU, C. S.; ROBB, D. A.; EWINS, D. J.

    2002-05-01

    The multiple-solution response of rotors supported on squeeze film dampers is a typical non-linear phenomenon. The behaviour of the multiple-solution response in a flexible rotor supported on two identical squeeze film dampers with centralizing springs is studied by three methods: synchronous circular centred-orbit motion solution, numerical integration method and slow acceleration method using the assumption of a short bearing and cavitated oil film; the differences of computational results obtained by the three different methods are compared in this paper. It is shown that there are three basic forms for the multiple-solution response in the flexible rotor system supported on the squeeze film dampers, which are the resonant, isolated bifurcation and swallowtail bifurcation multiple solutions. In the multiple-solution speed regions, the rotor motion may be subsynchronous, super-subsynchronous, almost-periodic and even chaotic, besides synchronous circular centred, even if the gravity effect is not considered. The assumption of synchronous circular centred-orbit motion for the journal and rotor around the static deflection line can be used only in some special cases; the steady state numerical integration method is very useful, but time consuming. Using the slow acceleration method, not only can the multiple-solution speed regions be detected, but also the non-synchronous response regions.

  12. Solution of continuous nonlinear PDEs through order completion

    CERN Document Server

    Oberguggenberger, MB

    1994-01-01

    This work inaugurates a new and general solution method for arbitrary continuous nonlinear PDEs. The solution method is based on Dedekind order completion of usual spaces of smooth functions defined on domains in Euclidean spaces. However, the nonlinear PDEs dealt with need not satisfy any kind of monotonicity properties. Moreover, the solution method is completely type independent. In other words, it does not assume anything about the nonlinear PDEs, except for the continuity of their left hand term, which includes the unkown function. Furthermore the right hand term of such nonlinear PDEs can in fact be given any discontinuous and measurable function.

  13. Differential equation methods for simulation of GFP kinetics in non-steady state experiments.

    Science.gov (United States)

    Phair, Robert D

    2018-03-15

    Genetically encoded fluorescent proteins, combined with fluorescence microscopy, are widely used in cell biology to collect kinetic data on intracellular trafficking. Methods for extraction of quantitative information from these data are based on the mathematics of diffusion and tracer kinetics. Current methods, although useful and powerful, depend on the assumption that the cellular system being studied is in a steady state, that is, the assumption that all the molecular concentrations and fluxes are constant for the duration of the experiment. Here, we derive new tracer kinetic analytical methods for non-steady state biological systems by constructing mechanistic nonlinear differential equation models of the underlying cell biological processes and linking them to a separate set of differential equations governing the kinetics of the fluorescent tracer. Linking the two sets of equations is based on a new application of the fundamental tracer principle of indistinguishability and, unlike current methods, supports correct dependence of tracer kinetics on cellular dynamics. This approach thus provides a general mathematical framework for applications of GFP fluorescence microscopy (including photobleaching [FRAP, FLIP] and photoactivation to frequently encountered experimental protocols involving physiological or pharmacological perturbations (e.g., growth factors, neurotransmitters, acute knockouts, inhibitors, hormones, cytokines, and metabolites) that initiate mechanistically informative intracellular transients. When a new steady state is achieved, these methods automatically reduce to classical steady state tracer kinetic analysis. © 2018 Phair. This article is distributed by The American Society for Cell Biology under license from the author(s). Two months after publication it is available to the public under an Attribution–Noncommercial–Share Alike 3.0 Unported Creative Commons License (http://creativecommons.org/licenses/by-nc-sa/3.0).

  14. Restitution slope is principally determined by steady-state action potential duration.

    Science.gov (United States)

    Shattock, Michael J; Park, Kyung Chan; Yang, Hsiang-Yu; Lee, Angela W C; Niederer, Steven; MacLeod, Kenneth T; Winter, James

    2017-06-01

    The steepness of the action potential duration (APD) restitution curve and local tissue refractoriness are both thought to play important roles in arrhythmogenesis. Despite this, there has been little recognition of the apparent association between steady-state APD and the slope of the restitution curve. The objective of this study was to test the hypothesis that restitution slope is determined by APD and to examine the relationship between restitution slope, refractoriness and susceptibility to VF. Experiments were conducted in isolated hearts and ventricular myocytes from adult guinea pigs and rabbits. Restitution curves were measured under control conditions and following intervention to prolong (clofilium, veratridine, bretylium, low [Ca]e, chronic transverse aortic constriction) or shorten (catecholamines, rapid pacing) ventricular APD. Despite markedly differing mechanisms of action, all interventions that prolonged the action potential led to a steepening of the restitution curve (and vice versa). Normalizing the restitution curve as a % of steady-state APD abolished the difference in restitution curves with all interventions. Effects on restitution were preserved when APD was modulated by current injection in myocytes pre-treated with the calcium chelator BAPTA-AM - to abolish the intracellular calcium transient. The non-linear relation between APD and the rate of repolarization of the action potential is shown to underpin the common influence of APD on the slope of the restitution curve. Susceptibility to VF was found to parallel changes in APD/refractoriness, rather than restitution slope. Steady-state APD is the principal determinant of the slope of the ventricular electrical restitution curve. In the absence of post-repolarization refractoriness, factors that prolong the action potential would be expected to steepen the restitution curve. However, concomitant changes in tissue refractoriness act to reduce susceptibility to sustained VF. Dependence on

  15. Nonlinear reaction-diffusion equations with delay: some theorems, test problems, exact and numerical solutions

    Science.gov (United States)

    Polyanin, A. D.; Sorokin, V. G.

    2017-12-01

    The paper deals with nonlinear reaction-diffusion equations with one or several delays. We formulate theorems that allow constructing exact solutions for some classes of these equations, which depend on several arbitrary functions. Examples of application of these theorems for obtaining new exact solutions in elementary functions are provided. We state basic principles of construction, selection, and use of test problems for nonlinear partial differential equations with delay. Some test problems which can be suitable for estimating accuracy of approximate analytical and numerical methods of solving reaction-diffusion equations with delay are presented. Some examples of numerical solutions of nonlinear test problems with delay are considered.

  16. Exact solutions for the higher-order nonlinear Schoerdinger equation in nonlinear optical fibres

    International Nuclear Information System (INIS)

    Liu Chunping

    2005-01-01

    First, by using the generally projective Riccati equation method, many kinds of exact solutions for the higher-order nonlinear Schoerdinger equation in nonlinear optical fibres are obtained in a unified way. Then, some relations among these solutions are revealed

  17. Generation and growth rates of nonlinear distortions in a traveling wave tube

    International Nuclear Information System (INIS)

    Woehlbier, John G.; Dobson, Ian; Booske, John H.

    2002-01-01

    The structure of a steady state multifrequency model of a traveling wave tube amplifier is exploited to describe the generation of intermodulation frequencies and calculate their growth rates. The model describes the evolution of Fourier coefficients of circuit and electron beam quantities and has the form of differential equations with quadratic nonlinearities. Intermodulation frequencies are sequentially generated by the quadratic nonlinearities in a series solution of the differential equations. A formula for maximum intermodulation growth rates is derived and compared to simulation results

  18. Comparison of Numerical Approaches to a Steady-State Landscape Equation

    Science.gov (United States)

    Bachman, S.; Peckham, S.

    2008-12-01

    A mathematical model of an idealized fluvial landscape has been developed, in which a land surface will evolve to preserve dendritic channel networks as the surface is lowered. The physical basis for this model stems from the equations for conservation of mass for water and sediment. These equations relate the divergence of the 2D vector fields showing the unit-width discharge of water and sediment to the excess rainrate and tectonic uplift on the land surface. The 2D flow direction is taken to be opposite to the water- surface gradient vector. These notions are combined with a generalized Manning-type flow resistance formula and a generalized sediment transport law to give a closed mathematical system that can, in principle, be solved for all variables of interest: discharge of water and sediment, land surface height, vertically- averaged flow velocity, water depth, and shear stress. The hydraulic geometry equations (Leopold et. al, 1964, 1995) are used to incorporate width, depth, velocity, and slope of river channels as powers of the mean-annual river discharge. Combined, they give the unit- width discharge of the stream as a power, γ, of the water surface slope. The simplified steady-state model takes into account three components among those listed above: conservation of mass for water, flow opposite the gradient, and a slope-discharge exponent γ = -1 to reflect mature drainage networks. The mathematical representation of this model appears as a second-order hyperbolic partial differential equation (PDE) where the diffusivity is inversely proportional to the square of the local surface slope. The highly nonlinear nature of this PDE has made it very difficult to solve both analytically and numerically. We present simplistic analytic solutions to this equation which are used to test the validity of the numerical algorithms. We also present three such numerical approaches which have been used in solving the differential equation. The first is based on a

  19. New exact travelling wave solutions of nonlinear physical models

    International Nuclear Information System (INIS)

    Bekir, Ahmet; Cevikel, Adem C.

    2009-01-01

    In this work, we established abundant travelling wave solutions for some nonlinear evolution equations. This method was used to construct travelling wave solutions of nonlinear evolution equations. The travelling wave solutions are expressed by the hyperbolic functions, the trigonometric functions and the rational functions. The ((G ' )/G )-expansion method presents a wider applicability for handling nonlinear wave equations.

  20. On the relationship of steady states of continuous and discrete models arising from biology.

    Science.gov (United States)

    Veliz-Cuba, Alan; Arthur, Joseph; Hochstetler, Laura; Klomps, Victoria; Korpi, Erikka

    2012-12-01

    For many biological systems that have been modeled using continuous and discrete models, it has been shown that such models have similar dynamical properties. In this paper, we prove that this happens in more general cases. We show that under some conditions there is a bijection between the steady states of continuous and discrete models arising from biological systems. Our results also provide a novel method to analyze certain classes of nonlinear models using discrete mathematics.

  1. Nonlinear dynamics of semiclassical coherent states in periodic potentials

    International Nuclear Information System (INIS)

    Carles, Rémi; Sparber, Christof

    2012-01-01

    We consider nonlinear Schrödinger equations with either local or nonlocal nonlinearities. In addition, we include periodic potentials as used, for example, in matter wave experiments in optical lattices. By considering the corresponding semiclassical scaling regime, we construct asymptotic solutions, which are concentrated both in space and in frequency around the effective semiclassical phase-space flow induced by Bloch’s spectral problem. The dynamics of these generalized coherent states is governed by a nonlinear Schrödinger model with effective mass. In the case of nonlocal nonlinearities, we establish a novel averaging-type result in the critical case. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Coherent states: mathematical and physical aspects’. (paper)

  2. Determination of kinetic parameters of Fe sup 3+ reduction mediated by a polyaniline film using steady-state and impedance methods

    Energy Technology Data Exchange (ETDEWEB)

    Deslouis, C. (LP15 du CNRS, Physique des Liquides et Electrochimie, Lab. de l' Univ. Pierre et Marie Curie, 75252 Paris Cedex 05 (FR)); Musiani, M.M.; Pagura, C.; Tribollet, C. (Inst. di Polarografia de Elettrochimica Preparativa del CNR, Corso Stati Uniti, 4, 35020 Camin, Padova (IT))

    1991-09-01

    This paper discusses the Fe{sup 3+} reduction reaction studied at Pt and polyaniline rotating disk electrodes by steady-state and impedance methods with the aim of testing the possibility of achieving the charge transfer resistance (R{sub ts}) of a redox reaction mediated by a conducting polymer film by ac impedance R{sub ts} was obtained as a function of electrode potential and rotation rate by nonlinear least squares fitting of a previously developed kinetic equation to the experimental data. These R{sub ts} values were combined with steady-state ones to calculate b{sub c} and k{sup 0}.

  3. Exact analytical solutions for nonlinear reaction-diffusion equations

    International Nuclear Information System (INIS)

    Liu Chunping

    2003-01-01

    By using a direct method via the computer algebraic system of Mathematica, some exact analytical solutions to a class of nonlinear reaction-diffusion equations are presented in closed form. Subsequently, the hyperbolic function solutions and the triangular function solutions of the coupled nonlinear reaction-diffusion equations are obtained in a unified way

  4. Data system design considerations for a pseudo-steady-state device

    International Nuclear Information System (INIS)

    Wing, W.R.

    1981-01-01

    The Advanced Toroidal Facility is being designed to run in a steady state. This places stringent requirements on a data system, since it must provide steady-state support that is equivalent to the support users are accustomed to from pulsed experiments; i.e., enough capacity to reduce diagnostic data for live presentation. Parameters such as density, position, and temperature must be presented live (i.e., within 0.1 s). Quantities such as plasma shape or internal structure should be available with a minimum of delay. The traditional solution to providing such capabilities is to use distributed processing to off-load data acquisition from the analysis computers. However, this suffers in a real-time environment because of the necessity of moving large quantities of data from acquisition to analysis. We expect to solve the problem by using a pipelined design that will acquire data directly into shared memory, where any one of four CPU's (VAX 11/780's) can proceed with analysis

  5. Exact solutions of the two-dimensional discrete nonlinear Schrodinger equation with saturable nonlinearity

    DEFF Research Database (Denmark)

    Khare, A.; Rasmussen, K. O.; Samuelsen, Mogens Rugholm

    2010-01-01

    We show that the two-dimensional, nonlinear Schrodinger lattice with a saturable nonlinearity admits periodic and pulse-like exact solutions. We establish the general formalism for the stability considerations of these solutions and give examples of stability diagrams. Finally, we show that the e...

  6. Steady-State Process Modelling

    DEFF Research Database (Denmark)

    Cameron, Ian; Gani, Rafiqul

    2011-01-01

    illustrate the “equation oriented” approach as well as the “sequential modular” approach to solving complex flowsheets for steady state applications. The applications include the Williams-Otto plant, the hydrodealkylation (HDA) of toluene, conversion of ethylene to ethanol and a bio-ethanol process....

  7. Nonlinear thermal reduced model for Microwave Circuit Analysis

    OpenAIRE

    Chang, Christophe; Sommet, Raphael; Quéré, Raymond; Dueme, Ph.

    2004-01-01

    With the constant increase of transistor power density, electro thermal modeling is becoming a necessity for accurate prediction of device electrical performances. For this reason, this paper deals with a methodology to obtain a precise nonlinear thermal model based on Model Order Reduction of a three dimensional thermal Finite Element (FE) description. This reduced thermal model is based on the Ritz vector approach which ensure the steady state solution in every case. An equi...

  8. On the steady-state structure of shock waves in elastic media and dielectrics

    International Nuclear Information System (INIS)

    Kulikovskii, A. G.; Chugainova, A. P.

    2010-01-01

    A simplified system of equations describing small-amplitude nonlinear quasi-transverse waves in an elastic weakly anisotropic medium with complicated dissipation and dispersion is considered. A simplified system of equations derived for describing the propagation and evolution of one-dimensional weakly nonlinear electromagnetic waves in a weakly anisotropic dielectric is found to be of the same type as the system of equations for quasi-transverse waves in an elastic medium. The steady-state structure of small-amplitude quasi-transverse discontinuities and a large number of admissible discontinuity types is studied using this system of equations. Viscous dissipation is traditionally assumed to be described in terms of the next differentiation order as compared to those constituting the hyperbolic system describing long waves, while the terms responsible for dispersion have an even higher differentiation order.

  9. Do's and don'ts in Fourier analysis of steady-state potentials.

    Science.gov (United States)

    Bach, M; Meigen, T

    1999-01-01

    Fourier analysis is a powerful tool in signal analysis that can be very fruitfully applied to steady-state evoked potentials (flicker ERG, pattern ERG, VEP, etc.). However, there are some inherent assumptions in the underlying discrete Fourier transform (DFT) that are not necessarily fulfilled in typical electrophysiological recording and analysis conditions. Furthermore, engineering software-packages may be ill-suited and/or may not fully exploit the information of steady-state recordings. Specifically: * In the case of steady-state stimulation we know more about the stimulus than in standard textbook situations (exact frequency, phase stability), so 'windowing' and calculation of the 'periodogram' are not necessary. * It is mandatory to choose an integer relationship between sampling rate and frame rate when employing a raster-based CRT stimulator. * The analysis interval must comprise an exact integer number (e.g., 10) of stimulus periods. * The choice of the number of stimulus periods per analysis interval needs a wise compromise: A high number increases the frequency resolution, but makes artifact removal difficult; a low number 'spills' noise into the response frequency. * There is no need to feel tied to a power-of-two number of data points as required by standard FFT, 'resampling' is an easy and efficient alternative. * Proper estimates of noise-corrected Fourier magnitude and statistical significance can be calculated that take into account the non-linear superposition of signal and noise. These aspects are developed in an intuitive approach with examples using both simulations and recordings. Proper use of Fourier analysis of our electrophysiological records will reduce recording time and/or increase the reliability of physiologic or pathologic interpretations.

  10. Exact Solutions for Nonlinear Differential Difference Equations in Mathematical Physics

    Directory of Open Access Journals (Sweden)

    Khaled A. Gepreel

    2013-01-01

    Full Text Available We modified the truncated expansion method to construct the exact solutions for some nonlinear differential difference equations in mathematical physics via the general lattice equation, the discrete nonlinear Schrodinger with a saturable nonlinearity, the quintic discrete nonlinear Schrodinger equation, and the relativistic Toda lattice system. Also, we put a rational solitary wave function method to find the rational solitary wave solutions for some nonlinear differential difference equations. The proposed methods are more effective and powerful to obtain the exact solutions for nonlinear difference differential equations.

  11. Exact Solution of a Generalized Nonlinear Schrodinger Equation Dimer

    DEFF Research Database (Denmark)

    Christiansen, Peter Leth; Maniadis, P.; Tsironis, G.P.

    1998-01-01

    We present exact solutions for a nonlinear dimer system defined throught a discrete nonlinear Schrodinger equation that contains also an integrable Ablowitz-Ladik term. The solutions are obtained throught a transformation that maps the dimer into a double Sine-Gordon like ordinary nonlinear...... differential equation....

  12. Wall locking and multiple nonlinear states of magnetic islands

    International Nuclear Information System (INIS)

    Persson, Mikael; Australian National Univ., Canberra, ACT

    1994-01-01

    The nonlinear evolution of magnetic islands is analysed in configurations with multiple resonant magnetic surfaces. The existence of multiple nonlinear steady states, is discussed. These are shown to be associated with states where the dynamics around the different rational surfaces are coupled or decoupled and in the presence of a wall of finite resistivity may correspond wall-locked or non-wall-locked magnetic islands. For the case of strong wall stabilization the locking is shown to consist of two different phases. During the first phase the locking of the plasma at the different rational surfaces occurs. Only when the outermost resonant magnetic surface has locked to the inner surfaces can the actual wall locking process take place. Consequently, wall locking, of a global mode, involving more than one rational surface, can be prevented by the decoupling of the resonant magnetic surfaces by plasma rotation. Possible implications on tokamak experiments are discussed. (author)

  13. Exact Solutions to Nonlinear Schroedinger Equation and Higher-Order Nonlinear Schroedinger Equation

    International Nuclear Information System (INIS)

    Ren Ji; Ruan Hangyu

    2008-01-01

    We study solutions of the nonlinear Schroedinger equation (NLSE) and higher-order nonlinear Schroedinger equation (HONLSE) with variable coefficients. By considering all the higher-order effect of HONLSE as a new dependent variable, the NLSE and HONLSE can be changed into one equation. Using the generalized Lie group reduction method (GLGRM), the abundant solutions of NLSE and HONLSE are obtained

  14. Solution of linear and nonlinear matrix systems. Application to a nonlinear diffusion equation

    International Nuclear Information System (INIS)

    Bonnet, M.; Meurant, G.

    1978-01-01

    Different methods of solution of linear and nonlinear algebraic systems are applied to the nonlinear system obtained by discretizing a nonlinear diffusion equation. For linear systems, methods in general use of alternating directions type or Gauss Seidel's methods are compared to more recent ones of the type of generalized conjugate gradient; the superiority of the latter is shown by numerical examples. For nonlinear systems, a method on nonlinear conjugate gradient is studied as also Newton's method and some of its variants. It should be noted, however that Newton's method is found to be more efficient when coupled with a good method for solution of the linear system. To conclude, such methods are used to solve a nonlinear diffusion problem and the numerical results obtained are to be compared [fr

  15. BR2 reactor core steady state transient modeling

    International Nuclear Information System (INIS)

    Makarenko, A.; Petrova, T.

    2000-01-01

    A coupled neutronics/hydraulics/heat-conduction model of the BR2 reactor core is under development at SCK-CEN. The neutron transport phenomenon has been implemented as steady state and time dependent nodal diffusion. The non-linear heat conduction equation in-side fuel elements is solved with a time dependent finite element method. To allow coupling between functional modules and to simulate subcooled regimes, a simple single-phase hydraulics has been introduced, while the two-phase hydraulics is under development. Multiple tests, general benchmark cases as well as calculation/experiment comparisons demonstrated a good accuracy of both neutronic and thermal hydraulic models, numerical reliability and full code portability. A refinement methodology has been developed and tested for better neutronic representation in hexagonal geometry. Much effort is still needed to complete the development of an extended cross section library with kinetic data and two-phase flow representation. (author)

  16. Pellet injectors for steady state plasma fuelling

    International Nuclear Information System (INIS)

    Vinyar, I.; Geraud, A.; Yamada, H.; Lukin, A.; Sakamoto, R.; Skoblikov, S.; Umov, A.; Oda, Y.; Gros, G.; Krasilnikov, I.; Reznichenko, P.; Panchenko, V.

    2005-01-01

    Successful steady state operation of a fusion reactor should be supported by repetitive pellet injection of solidified hydrogen isotopes in order to produce high performance plasmas. This paper presents pneumatic pellet injectors and its implementation for long discharge on the LHD and TORE SUPRA, and a new centrifuge pellet injector test results. All injectors are fitted with screw extruders well suited for steady state operation

  17. Asymptotics of steady states of a selection–mutation equation for small mutation rate

    KAUST Repository

    Calsina, Àngel

    2013-12-01

    We consider a selection-mutation equation for the density of individuals with respect to a continuous phenotypic evolutionary trait. We assume that the competition term for an individual with a given trait depends on the traits of all the other individuals, therefore giving an infinite-dimensional nonlinearity. Mutations are modelled by means of an integral operator. We prove existence of steady states and show that, when the mutation rate goes to zero, the asymptotic profile of the population is a Cauchy distribution. © Royal Society of Edinburgh 2013.

  18. Asymptotics of steady states of a selection–mutation equation for small mutation rate

    KAUST Repository

    Calsina, À ngel; Cuadrado, Sí lvia; Desvillettes, Laurent; Raoul, Gaë l

    2013-01-01

    We consider a selection-mutation equation for the density of individuals with respect to a continuous phenotypic evolutionary trait. We assume that the competition term for an individual with a given trait depends on the traits of all the other individuals, therefore giving an infinite-dimensional nonlinearity. Mutations are modelled by means of an integral operator. We prove existence of steady states and show that, when the mutation rate goes to zero, the asymptotic profile of the population is a Cauchy distribution. © Royal Society of Edinburgh 2013.

  19. Steady state analysis of Boolean molecular network models via model reduction and computational algebra.

    Science.gov (United States)

    Veliz-Cuba, Alan; Aguilar, Boris; Hinkelmann, Franziska; Laubenbacher, Reinhard

    2014-06-26

    A key problem in the analysis of mathematical models of molecular networks is the determination of their steady states. The present paper addresses this problem for Boolean network models, an increasingly popular modeling paradigm for networks lacking detailed kinetic information. For small models, the problem can be solved by exhaustive enumeration of all state transitions. But for larger models this is not feasible, since the size of the phase space grows exponentially with the dimension of the network. The dimension of published models is growing to over 100, so that efficient methods for steady state determination are essential. Several methods have been proposed for large networks, some of them heuristic. While these methods represent a substantial improvement in scalability over exhaustive enumeration, the problem for large networks is still unsolved in general. This paper presents an algorithm that consists of two main parts. The first is a graph theoretic reduction of the wiring diagram of the network, while preserving all information about steady states. The second part formulates the determination of all steady states of a Boolean network as a problem of finding all solutions to a system of polynomial equations over the finite number system with two elements. This problem can be solved with existing computer algebra software. This algorithm compares favorably with several existing algorithms for steady state determination. One advantage is that it is not heuristic or reliant on sampling, but rather determines algorithmically and exactly all steady states of a Boolean network. The code for the algorithm, as well as the test suite of benchmark networks, is available upon request from the corresponding author. The algorithm presented in this paper reliably determines all steady states of sparse Boolean networks with up to 1000 nodes. The algorithm is effective at analyzing virtually all published models even those of moderate connectivity. The problem for

  20. Nonlinear observer output-feedback MPC treatment scheduling for HIV

    Directory of Open Access Journals (Sweden)

    Zurakowski Ryan

    2011-05-01

    Full Text Available Abstract Background Mathematical models of the immune response to the Human Immunodeficiency Virus demonstrate the potential for dynamic schedules of Highly Active Anti-Retroviral Therapy to enhance Cytotoxic Lymphocyte-mediated control of HIV infection. Methods In previous work we have developed a model predictive control (MPC based method for determining optimal treatment interruption schedules for this purpose. In this paper, we introduce a nonlinear observer for the HIV-immune response system and an integrated output-feedback MPC approach for implementing the treatment interruption scheduling algorithm using the easily available viral load measurements. We use Monte-Carlo approaches to test robustness of the algorithm. Results The nonlinear observer shows robust state tracking while preserving state positivity both for continuous and discrete measurements. The integrated output-feedback MPC algorithm stabilizes the desired steady-state. Monte-Carlo testing shows significant robustness to modeling error, with 90% success rates in stabilizing the desired steady-state with 15% variance from nominal on all model parameters. Conclusions The possibility of enhancing immune responsiveness to HIV through dynamic scheduling of treatment is exciting. Output-feedback Model Predictive Control is uniquely well-suited to solutions of these types of problems. The unique constraints of state positivity and very slow sampling are addressable by using a special-purpose nonlinear state estimator, as described in this paper. This shows the possibility of using output-feedback MPC-based algorithms for this purpose.

  1. Topological soliton solutions for some nonlinear evolution equations

    Directory of Open Access Journals (Sweden)

    Ahmet Bekir

    2014-03-01

    Full Text Available In this paper, the topological soliton solutions of nonlinear evolution equations are obtained by the solitary wave ansatz method. Under some parameter conditions, exact solitary wave solutions are obtained. Note that it is always useful and desirable to construct exact solutions especially soliton-type (dark, bright, kink, anti-kink, etc. envelope for the understanding of most nonlinear physical phenomena.

  2. A Novel ARX-Based Approach for the Steady-State Identification Analysis of Industrial Depropanizer Column Datasets

    Directory of Open Access Journals (Sweden)

    Franklin D. Rincón

    2015-04-01

    Full Text Available This paper introduces a novel steady-state identification (SSI method based on the auto-regressive model with exogenous inputs (ARX. This method allows the SSI with reduced tuning by analyzing the identifiability properties of the system. In particular, the singularity of the model matrices is used as an index for steady-state determination. In this contribution, the novel SSI method is compared to other available techniques, namely the F-like test, wavelet transform and a polynomial-based approach. These methods are implemented for SSI of three different case studies. In the first case, a simulated dataset is used for calibrating the output-based SSI methods. The second case corresponds to a literature nonlinear continuous stirred-tank reactor (CSTR example running at different steady states in which the ARX-based approach is tuned with the available input-output data. Finally, an industrial case with real data of a depropanizer column from PETROBRAS S.A. considering different pieces of equipment is analyzed. The results for a reflux drum case indicate that the wavelet and the F-like test can satisfactorily detect the steady-state periods after careful tuning and when respecting their hypothesis, i.e., smooth data for the wavelet method and the presence of variance in the data for the F-like test. Through a heat exchanger case with different measurement frequencies, we demonstrate the advantages of using the ARX-based method over the other techniques, which include the aspect of online implementation.

  3. Finite element solution of quasistationary nonlinear magnetic field

    International Nuclear Information System (INIS)

    Zlamal, Milos

    1982-01-01

    The computation of quasistationary nonlinear two-dimensional magnetic field leads to the following problem. There is given a bounded domain OMEGA and an open nonempty set R included in OMEGA. We are looking for the magnetic vector potential u(x 1 , x 2 , t) which satisifies: 1) a certain nonlinear parabolic equation and an initial condition in R: 2) a nonlinear elliptic equation in S = OMEGA - R which is the stationary case of the above mentioned parabolic equation; 3) a boundary condition on delta OMEGA; 4) u as well as its conormal derivative are continuous accross the common boundary of R and S. This problem is formulated in two equivalent abstract ways. There is constructed an approximate solution completely discretized in space by a generalized Galerkin method (straight finite elements are a special case) and by backward A-stable differentiation methods in time. Existence and uniqueness of a weak solution is proved as well as a weak and strong convergence of the approximate solution to this solution. There are also derived error bounds for the solution of the two-dimensional nonlinear magnetic field equations under the assumption that the exact solution is sufficiently smooth

  4. Steady state compact toroidal plasma production

    Science.gov (United States)

    Turner, William C.

    1986-01-01

    Apparatus and method for maintaining steady state compact toroidal plasmas. A compact toroidal plasma is formed by a magnetized coaxial plasma gun and held in close proximity to the gun electrodes by applied magnetic fields or magnetic fields produced by image currents in conducting walls. Voltage supply means maintains a constant potential across the electrodes producing an increasing magnetic helicity which drives the plasma away from a minimum energy state. The plasma globally relaxes to a new minimum energy state, conserving helicity according to Taylor's relaxation hypothesis, and injecting net helicity into the core of the compact toroidal plasma. Controlling the voltage so as to inject net helicity at a predetermined rate based on dissipative processes maintains or increases the compact toroidal plasma in a time averaged steady state mode.

  5. Steady-state and dynamic models for particle engulfment during solidification

    Science.gov (United States)

    Tao, Yutao; Yeckel, Andrew; Derby, Jeffrey J.

    2016-06-01

    Steady-state and dynamic models are developed to study the physical mechanisms that determine the pushing or engulfment of a solid particle at a moving solid-liquid interface. The mathematical model formulation rigorously accounts for energy and momentum conservation, while faithfully representing the interfacial phenomena affecting solidification phase change and particle motion. A numerical solution approach is developed using the Galerkin finite element method and elliptic mesh generation in an arbitrary Lagrangian-Eulerian implementation, thus allowing for a rigorous representation of forces and dynamics previously inaccessible by approaches using analytical approximations. We demonstrate that this model accurately computes the solidification interface shape while simultaneously resolving thin fluid layers around the particle that arise from premelting during particle engulfment. We reinterpret the significance of premelting via the definition an unambiguous critical velocity for engulfment from steady-state analysis and bifurcation theory. We also explore the complicated transient behaviors that underlie the steady states of this system and posit the significance of dynamical behavior on engulfment events for many systems. We critically examine the onset of engulfment by comparing our computational predictions to those obtained using the analytical model of Rempel and Worster [29]. We assert that, while the accurate calculation of van der Waals repulsive forces remains an open issue, the computational model developed here provides a clear benefit over prior models for computing particle drag forces and other phenomena needed for the faithful simulation of particle engulfment.

  6. The generalized approximation method and nonlinear heat transfer equations

    Directory of Open Access Journals (Sweden)

    Rahmat Khan

    2009-01-01

    Full Text Available Generalized approximation technique for a solution of one-dimensional steady state heat transfer problem in a slab made of a material with temperature dependent thermal conductivity, is developed. The results obtained by the generalized approximation method (GAM are compared with those studied via homotopy perturbation method (HPM. For this problem, the results obtained by the GAM are more accurate as compared to the HPM. Moreover, our (GAM generate a sequence of solutions of linear problems that converges monotonically and rapidly to a solution of the original nonlinear problem. Each approximate solution is obtained as the solution of a linear problem. We present numerical simulations to illustrate and confirm the theoretical results.

  7. New compacton solutions and solitary wave solutions of fully nonlinear generalized Camassa-Holm equations

    International Nuclear Information System (INIS)

    Tian Lixin; Yin Jiuli

    2004-01-01

    In this paper, we introduce the fully nonlinear generalized Camassa-Holm equation C(m,n,p) and by using four direct ansatzs, we obtain abundant solutions: compactons (solutions with the absence of infinite wings), solitary patterns solutions having infinite slopes or cups, solitary waves and singular periodic wave solutions and obtain kink compacton solutions and nonsymmetry compacton solutions. We also study other forms of fully nonlinear generalized Camassa-Holm equation, and their compacton solutions are governed by linear equations

  8. On modulated complex non-linear dynamical systems

    International Nuclear Information System (INIS)

    Mahmoud, G.M.; Mohamed, A.A.; Rauh, A.

    1999-01-01

    This paper is concerned with the development of an approximate analytical method to investigate periodic solutions and their stability in the case of modulated non-linear dynamical systems whose equation of motion is describe. Such differential equations appear, for example, in problems of colliding particle beams in high-energy accelerators or one-mass systems with two or more degrees of freedom, e.g. rotors. The significance of periodic solutions lies on the fact that all non-periodic responses, if convergent, would approach to periodic solutions at the steady-state conditions. The example shows a good agreement between numerical and analytical results for small values of ε. The effect of the periodic modulation on the stability of the 2π-periodic solutions is discussed

  9. Mathematical Modeling and Simulation of the Dehydrogenation of Ethyl Benzene to Form Styrene Using Steady-State Fixed Bed Reactor

    Directory of Open Access Journals (Sweden)

    Zaidon M. Shakoor

    2013-05-01

    Full Text Available In this research, two models are developed to simulate the steady state fixed bed reactor used for styrene production by ethylbenzene dehydrogenation. The first is one-dimensional model, considered axial gradient only while the second is two-dimensional model considered axial and radial gradients for same variables.The developed mathematical models consisted of nonlinear simultaneous equations in multiple dependent variables. A complete description of the reactor bed involves partial, ordinary differential and algebraic equations (PDEs, ODEs and AEs describing the temperatures, concentrations and pressure drop across the reactor was given. The model equations are solved by finite differences method. The reactor models were coded with Mat lab 6.5 program and various numerical techniques were used to obtain the desired solution.The simulation data for both models were validated with industrial reactor results with a very good concordance.

  10. STEADY STATE AND PSEUDO-TRANSIENT ELECTRIC POTENTIAL USING THE POISSONBOLTZMANN EQUATION

    Directory of Open Access Journals (Sweden)

    L. C. dos Santos

    2015-03-01

    Full Text Available A method for analysis of the electric potential profile in saline solutions was developed for systems with one or two infinite flat plates. A modified Poisson-Boltzmann equation, taking into account nonelectrostatic interactions between ions and surfaces, was used. To solve the stated problem in the steady-state approach the finite-difference method was used. For the formulated pseudo-transient problem, we solved the set of ordinary differential equations generated from the algebraic equations of the stationary case. A case study was also carried out in relation to temperature, solution concentration, surface charge and salt-type. The results were validated by the stationary problem solution, which had also been used to verify the ionic specificity for different salts. The pseudo-transient approach allowed a better understanding of the dynamic behavior of the ion-concentration profile and other properties due to the surface charge variation.

  11. Steady State Shift Damage Localization

    DEFF Research Database (Denmark)

    Sekjær, Claus; Bull, Thomas; Markvart, Morten Kusk

    2017-01-01

    The steady state shift damage localization (S3DL) method localizes structural deterioration, manifested as either a mass or stiffness perturbation, by interrogating the damage-induced change in the steady state vibration response with damage patterns cast from a theoretical model. Damage is, thus...... the required accuracy when examining complex structures, an extensive amount of degrees of freedom (DOF) must often be utilized. Since the interrogation matrix for each damage pattern depends on the size of the system matrices constituting the FE-model, the computational time quickly becomes of first......-order importance. The present paper investigates two sub-structuring approaches, in which the idea is to employ Craig-Bampton super-elements to reduce the amount of interrogation distributions while still providing an acceptable localization resolution. The first approach operates on a strict super-element level...

  12. Light diffusion in N-layered turbid media: steady-state domain.

    Science.gov (United States)

    Liemert, André; Kienle, Alwin

    2010-01-01

    We deal with light diffusion in N-layered turbid media. The steady-state diffusion equation is solved for N-layered turbid media having a finite or an infinitely thick N'th layer. Different refractive indices are considered in the layers. The Fourier transform formalism is applied to derive analytical solutions of the fluence rate in Fourier space. The inverse Fourier transform is calculated using four different methods to test their performance and accuracy. Further, to avoid numerical errors, approximate formulas in Fourier space are derived. Fast solutions for calculation of the spatially resolved reflectance and transmittance from the N-layered turbid media ( approximately 10 ms) with small relative differences (<10(-7)) are found. Additionally, the solutions of the diffusion equation are compared to Monte Carlo simulations for turbid media having up to 20 layers.

  13. Quantum and classical nonlinear dynamics in a microwave cavity

    Energy Technology Data Exchange (ETDEWEB)

    Meaney, Charles H.; Milburn, Gerard J. [The University of Queensland, Department of Physics, St Lucia, QLD (Australia); Nha, Hyunchul [Texas A and M University at Qatar, Department of Physics, PO Box 23874, Doha (Qatar); Duty, Timothy [The University of New South Wales, Department of Physics, Kensington, NSW (Australia)

    2014-12-01

    We consider a quarter wave coplanar microwave cavity terminated to ground via a superconducting quantum interference device. By modulating the flux through the loop, the cavity frequency is modulated. The flux is varied at twice the cavity frequency implementing a parametric driving of the cavity field. The cavity field also exhibits a large effective nonlinear susceptibility modelled as an effective Kerr nonlinearity, and is also driven by a detuned linear drive. We show that the semi-classical model corresponding to this system exhibits a fixed point bifurcation at a particular threshold of parametric pumping power. We show the quantum signature of this bifurcation in the dissipative quantum system. We further linearise about the below threshold classical steady state and consider it to act as a bifurcation amplifier, calculating gain and noise spectra for the corresponding small signal regime. Furthermore, we use a phase space technique to analytically solve for the exact quantum steady state. We use this solution to calculate the exact small signal gain of the amplifier. (orig.)

  14. Steady State Analysis of LCLC Resonant Converter with Capacitive Output Filter

    Directory of Open Access Journals (Sweden)

    Navid Shafiyi

    2010-01-01

    Full Text Available This paper presents the mathematical analysis and modeling of a 4th order LCLC resonant converter with capacitive output filter in steady-state condition. Due to the nonlinearity of the LCLC resonant circuit with capacitive output filter, the conventional modeling procedure cannot thoroughly describe the behavior of the converter. In this paper, a mathematical model is proposed that can accommodate the absence of the output inductor and predict the converter performance for a wide range of operating conditions. A 2.25KW prototype converter is provided to evaluate the accuracy of the proposed model. Experimental results show that the proposed model can precisely predict the behavior of the converter for a wide range of operating conditions.

  15. Finite element solution of nonlinear eddy current problems with periodic excitation and its industrial applications.

    Science.gov (United States)

    Bíró, Oszkár; Koczka, Gergely; Preis, Kurt

    2014-05-01

    An efficient finite element method to take account of the nonlinearity of the magnetic materials when analyzing three-dimensional eddy current problems is presented in this paper. The problem is formulated in terms of vector and scalar potentials approximated by edge and node based finite element basis functions. The application of Galerkin techniques leads to a large, nonlinear system of ordinary differential equations in the time domain. The excitations are assumed to be time-periodic and the steady-state periodic solution is of interest only. This is represented either in the frequency domain as a finite Fourier series or in the time domain as a set of discrete time values within one period for each finite element degree of freedom. The former approach is the (continuous) harmonic balance method and, in the latter one, discrete Fourier transformation will be shown to lead to a discrete harmonic balance method. Due to the nonlinearity, all harmonics, both continuous and discrete, are coupled to each other. The harmonics would be decoupled if the problem were linear, therefore, a special nonlinear iteration technique, the fixed-point method is used to linearize the equations by selecting a time-independent permeability distribution, the so-called fixed-point permeability in each nonlinear iteration step. This leads to uncoupled harmonics within these steps. As industrial applications, analyses of large power transformers are presented. The first example is the computation of the electromagnetic field of a single-phase transformer in the time domain with the results compared to those obtained by traditional time-stepping techniques. In the second application, an advanced model of the same transformer is analyzed in the frequency domain by the harmonic balance method with the effect of the presence of higher harmonics on the losses investigated. Finally a third example tackles the case of direct current (DC) bias in the coils of a single-phase transformer.

  16. Computing stationary solutions of the two-dimensional Gross-Pitaevskii equation with deflated continuation

    Science.gov (United States)

    Charalampidis, E. G.; Kevrekidis, P. G.; Farrell, P. E.

    2018-01-01

    In this work we employ a recently proposed bifurcation analysis technique, the deflated continuation algorithm, to compute steady-state solitary waveforms in a one-component, two-dimensional nonlinear Schrödinger equation with a parabolic trap and repulsive interactions. Despite the fact that this system has been studied extensively, we discover a wide variety of previously unknown branches of solutions. We analyze the stability of the newly discovered branches and discuss the bifurcations that relate them to known solutions both in the near linear (Cartesian, as well as polar) and in the highly nonlinear regimes. While deflated continuation is not guaranteed to compute the full bifurcation diagram, this analysis is a potent demonstration that the algorithm can discover new nonlinear states and provide insights into the energy landscape of complex high-dimensional Hamiltonian dynamical systems.

  17. Riccati-parameter solutions of nonlinear second-order ODEs

    International Nuclear Information System (INIS)

    Reyes, M A; Rosu, H C

    2008-01-01

    It has been proven by Rosu and Cornejo-Perez (Rosu and Cornejo-Perez 2005 Phys. Rev. E 71 046607, Cornejo-Perez and Rosu 2005 Prog. Theor. Phys. 114 533) that for some nonlinear second-order ODEs it is a very simple task to find one particular solution once the nonlinear equation is factorized with the use of two first-order differential operators. Here, it is shown that an interesting class of parametric solutions is easy to obtain if the proposed factorization has a particular form, which happily turns out to be the case in many problems of physical interest. The method that we exemplify with a few explicitly solved cases consists in using the general solution of the Riccati equation, which contributes with one parameter to this class of parametric solutions. For these nonlinear cases, the Riccati parameter serves as a 'growth' parameter from the trivial null solution up to the particular solution found through the factorization procedure

  18. HEXNOD23, 2-D, 3-D Coarse Mesh Solution of Steady State Diffusion Equation in Hexagonal Geometry

    International Nuclear Information System (INIS)

    Grundmann, Ulrich

    1986-01-01

    1 - Description of program or function: Two- or three dimensional coarse mesh solution of steady state two group neutron diffusion equation in arrays of regular hexagons or hexagonal subassemblies. 2 - Method of solution: The neutron flux in a hexagonal node is expanded in a series of Bessel functions in the hexagonal plane. Polynomials up to the 4. order are used for the approximation of neutron flux in axial direction of three dimensional cases. Resulting relations between node averaged fluxes and mean partial currents of node faces in connection with the neutron balance of nodes are used to calculate the eigenvalue Keff, mean fluxes and mean powers of nodes. The iterations process is divided into inner and outer iterations. The iterations are accelerated by Ljusternik and Tschebyscheff extrapolation schemes. The power densities in the nodes and subassembly powers are computed for given reactor power in three dimensional cases. 30 degree reflectional, 60 and 120 degree rotational core symmetry and the whole core can be treated. 3 - Restrictions on the complexity of the problem: If the problem size designated by LIAR and LRAR exceeds 3000 and 50000 respectively, the lengths of the working array MIAR and MRAR in the main program can be increased. External sources are not permitted

  19. Steady states in conformal theories

    CERN Multimedia

    CERN. Geneva

    2015-01-01

    A novel conjecture regarding the steady state behavior of conformal field theories placed between two heat baths will be presented. Some verification of the conjecture will be provided in the context of fluid dynamics and holography.

  20. A procedure to construct exact solutions of nonlinear evolution ...

    Indian Academy of Sciences (India)

    Exact solutions; the functional variable method; nonlinear wave equations. PACS Nos 02.30. ... computer science, directly searching for solutions of nonlinear differential equations has become more and ... Right after this pioneer work, this ...

  1. Cumulants of heat transfer across nonlinear quantum systems

    Science.gov (United States)

    Li, Huanan; Agarwalla, Bijay Kumar; Li, Baowen; Wang, Jian-Sheng

    2013-12-01

    We consider thermal conduction across a general nonlinear phononic junction. Based on two-time observation protocol and the nonequilibrium Green's function method, heat transfer in steady-state regimes is studied, and practical formulas for the calculation of the cumulant generating function are obtained. As an application, the general formalism is used to study anharmonic effects on fluctuation of steady-state heat transfer across a single-site junction with a quartic nonlinear on-site pinning potential. An explicit nonlinear modification to the cumulant generating function exact up to the first order is given, in which the Gallavotti-Cohen fluctuation symmetry is found still valid. Numerically a self-consistent procedure is introduced, which works well for strong nonlinearity.

  2. Nonlinear vibrations of thin arbitrarily laminated composite plates subjected to harmonic excitations using DKT elements

    Science.gov (United States)

    Chiang, C. K.; Xue, David Y.; Mei, Chuh

    1993-04-01

    A finite element formulation is presented for determining the large-amplitude free and steady-state forced vibration response of arbitrarily laminated anisotropic composite thin plates using the Discrete Kirchhoff Theory (DKT) triangular elements. The nonlinear stiffness and harmonic force matrices of an arbitrarily laminated composite triangular plate element are developed for nonlinear free and forced vibration analyses. The linearized updated-mode method with nonlinear time function approximation is employed for the solution of the system nonlinear eigenvalue equations. The amplitude-frequency relations for convergence with gridwork refinement, triangular plates, different boundary conditions, lamination angles, number of plies, and uniform versus concentrated loads are presented.

  3. Differences between automatically detected and steady-state fractional flow reserve.

    Science.gov (United States)

    Härle, Tobias; Meyer, Sven; Vahldiek, Felix; Elsässer, Albrecht

    2016-02-01

    Measurement of fractional flow reserve (FFR) has become a standard diagnostic tool in the catheterization laboratory. FFR evaluation studies were based on pressure recordings during steady-state maximum hyperemia. Commercially available computer systems detect the lowest Pd/Pa ratio automatically, which might not always be measured during steady-state hyperemia. We sought to compare the automatically detected FFR and true steady-state FFR. Pressure measurement traces of 105 coronary lesions from 77 patients with intermediate coronary lesions or multivessel disease were reviewed. In all patients, hyperemia had been achieved by intravenous adenosine administration using a dosage of 140 µg/kg/min. In 42 lesions (40%) automatically detected FFR was lower than true steady-state FFR. Mean bias was 0.009 (standard deviation 0.015, limits of agreement -0.02, 0.037). In 4 lesions (3.8%) both methods lead to different treatment recommendations, in all 4 cases instantaneous wave-free ratio confirmed steady-state FFR. Automatically detected FFR was slightly lower than steady-state FFR in more than one-third of cases. Consequently, interpretation of automatically detected FFR values closely below the cutoff value requires special attention.

  4. Nonlinear Forced Vibration of a Viscoelastic Buckled Beam with 2 : 1 Internal Resonance

    Directory of Open Access Journals (Sweden)

    Liu-Yang Xiong

    2014-01-01

    Full Text Available Nonlinear dynamics of a viscoelastic buckled beam subjected to primary resonance in the presence of internal resonance is investigated for the first time. For appropriate choice of system parameters, the natural frequency of the second mode is approximately twice that of the first providing the condition for 2 : 1 internal resonance. The ordinary differential equations of the two mode shapes are established using the Galerkin method. The problem is replaced by two coupled second-order differential equations with quadratic and cubic nonlinearities. The multiple scales method is applied to derive the modulation-phase equations. Steady-state solutions of the system as well as their stability are examined. The frequency-amplitude curves exhibit the steady-state response in the directly excited and indirectly excited modes due to modal interaction. The double-jump, the saturation phenomenon, and the nonperiodic region phenomena are observed illustrating the influence of internal resonance. The validity range of the analytical approximations is assessed by comparing the analytical approximate results with a numerical solution by the Runge-Kutta method. The unstable regions in the internal resonance are explored via numerical simulations.

  5. Exact solutions of nonlinear generalizations of the Klein Gordon and Schrodinger equations

    International Nuclear Information System (INIS)

    Burt, P.B.

    1978-01-01

    Exact solutions of sine Gordon and multiple sine Gordon equations are constructed in terms of solutions of a linear base equation, the Klein Gordon equation and also in terms of nonlinear base equations where the nonlinearity is polynomial in the dependent variable. Further, exact solutions of nonlinear generalizations of the Schrodinger equation and of additional nonlinear generalizations of the Klein Gordon equation are constructed in terms of solutions of linear base equations. Finally, solutions with spherical symmetry, of nonlinear Klein Gordon equations are given. 14 references

  6. Iterative Observer-based Estimation Algorithms for Steady-State Elliptic Partial Differential Equation Systems

    KAUST Repository

    Majeed, Muhammad Usman

    2017-07-19

    Steady-state elliptic partial differential equations (PDEs) are frequently used to model a diverse range of physical phenomena. The source and boundary data estimation problems for such PDE systems are of prime interest in various engineering disciplines including biomedical engineering, mechanics of materials and earth sciences. Almost all existing solution strategies for such problems can be broadly classified as optimization-based techniques, which are computationally heavy especially when the problems are formulated on higher dimensional space domains. However, in this dissertation, feedback based state estimation algorithms, known as state observers, are developed to solve such steady-state problems using one of the space variables as time-like. In this regard, first, an iterative observer algorithm is developed that sweeps over regular-shaped domains and solves boundary estimation problems for steady-state Laplace equation. It is well-known that source and boundary estimation problems for the elliptic PDEs are highly sensitive to noise in the data. For this, an optimal iterative observer algorithm, which is a robust counterpart of the iterative observer, is presented to tackle the ill-posedness due to noise. The iterative observer algorithm and the optimal iterative algorithm are then used to solve source localization and estimation problems for Poisson equation for noise-free and noisy data cases respectively. Next, a divide and conquer approach is developed for three-dimensional domains with two congruent parallel surfaces to solve the boundary and the source data estimation problems for the steady-state Laplace and Poisson kind of systems respectively. Theoretical results are shown using a functional analysis framework, and consistent numerical simulation results are presented for several test cases using finite difference discretization schemes.

  7. Steady State versus Pulsed Tokamak DEMO

    Energy Technology Data Exchange (ETDEWEB)

    Orsitto, F.P., E-mail: francesco.orsitto@enea.it [Associazione EURATOM-ENEA Unita Tecnica Fusione, Frascati (Italy); Todd, T. [CCFE/Fusion Association, Culham Science Centre, Abingdon (United Kingdom)

    2012-09-15

    Full text: The present report deals with a Review of problems for a Steady state(SS) DEMO, related argument is treated about the models and the present status of comparison between the characteristics of DEMO pulsed versus a Steady state device.The studied SS DEMO Models (SLIM CS, PPCS model C EU-DEMO, ARIES-RS) are analyzed from the point of view of the similarity scaling laws and critical issues for a steady state DEMO. A comparison between steady state and pulsed DEMO is therefore carried out: in this context a new set of parameters for a pulsed (6 - 8 hours pulse) DEMO is determined working below the density limit, peak temperature of 20 keV, and requiring a modest improvement in the confinement factor(H{sub IPBy2} = 1.1) with respect to the H-mode. Both parameters density and confinement parameter are lower than the DEMO models presently considered. The concept of partially non-inductive pulsed DEMO is introduced since a pulsed DEMO needs heating and current drive tools for plasma stability and burn control. The change of the main parameter design for a DEMO working at high plasma peak temperatures T{sub e} {approx} 35 keV is analyzed: in this range the reactivity increases linearly with temperature, and a device with smaller major radius (R = 7.5 m) is compatible with high temperature. Increasing temperature is beneficial for current drive efficiency and heat load on divertor, being the synchrotron radiation one of the relevant components of the plasma emission at high temperatures and current drive efficiency increases with temperature. Technology and engineering problems are examined including efficiency and availability R&D issues for a high temperature DEMO. Fatigue and creep-fatigue effects of pulsed operations on pulsed DEMO components are considered in outline to define the R&D needed for DEMO development. (author)

  8. The multi-order envelope periodic solutions to the nonlinear Schrodinger equation and cubic nonlinear Schrodinger equation

    International Nuclear Information System (INIS)

    Xiao Yafeng; Xue Haili; Zhang Hongqing

    2011-01-01

    Based on Jacobi elliptic function and the Lame equation, the perturbation method is applied to get the multi-order envelope periodic solutions of the nonlinear Schrodinger equation and cubic nonlinear Schrodinger equation. These multi-order envelope periodic solutions can degenerate into the different envelope solitary solutions. (authors)

  9. A family of analytical solutions of a nonlinear diffusion-convection equation

    Science.gov (United States)

    Hayek, Mohamed

    2018-01-01

    Despite its popularity in many engineering fields, the nonlinear diffusion-convection equation has no general analytical solutions. This work presents a family of closed-form analytical traveling wave solutions for the nonlinear diffusion-convection equation with power law nonlinearities. This kind of equations typically appears in nonlinear problems of flow and transport in porous media. The solutions that are addressed are simple and fully analytical. Three classes of analytical solutions are presented depending on the type of the nonlinear diffusion coefficient (increasing, decreasing or constant). It has shown that the structure of the traveling wave solution is strongly related to the diffusion term. The main advantage of the proposed solutions is that they are presented in a unified form contrary to existing solutions in the literature where the derivation of each solution depends on the specific values of the diffusion and convection parameters. The proposed closed-form solutions are simple to use, do not require any numerical implementation, and may be implemented in a simple spreadsheet. The analytical expressions are also useful to mathematically analyze the structure and properties of the solutions.

  10. Active ideal sedimentation: exact two-dimensional steady states.

    Science.gov (United States)

    Hermann, Sophie; Schmidt, Matthias

    2018-02-28

    We consider an ideal gas of active Brownian particles that undergo self-propelled motion and both translational and rotational diffusion under the influence of gravity. We solve analytically the corresponding Smoluchowski equation in two space dimensions for steady states. The resulting one-body density is given as a series, where each term is a product of an orientation-dependent Mathieu function and a height-dependent exponential. A lower hard wall is implemented as a no-flux boundary condition. Numerical evaluation of the suitably truncated analytical solution shows the formation of two different spatial regimes upon increasing Peclet number. These regimes differ in their mean particle orientation and in their variation of the orientation-averaged density with height.

  11. Dynamical and technological consequences of multiple isolas of steady states in a catalytic fluidised-bed reactor

    Directory of Open Access Journals (Sweden)

    Bizon Katarzyna

    2017-09-01

    Full Text Available Steady-state characteristics of a catalytic fluidised bed reactor and its dynamical consequences are analyzed. The occurrence of an untypical steady-state structure manifesting in a form of multiple isolas is described. A two-phase bubbling bed model is used for a quantitative description of the bed of catalyst. The influence of heat exchange intensity and a fluidisation ratio onto the generation of isolated solution branches is presented for two kinetic schemes. Dynamical consequences of the coexistence of such untypical branches of steady states are presented. The impact of linear growth of the fluidisation ratio and step change of the cooling medium temperature onto the desired product yield is analyzed. The results presented in this study confirm that the identification of a region of the occurrence of multiple isolas is important due to their strong impact both on the process start-up and its control.

  12. LANSCE steady state unperturbed thermal neutron fluxes at 100 μA

    International Nuclear Information System (INIS)

    Russell, G.J.

    1989-01-01

    The ''maximum'' unperturbed, steady state thermal neutron flux for LANSCE is calculated to be 2 /times/ 10 13 n/cm 2 -s for 100 μA of 800-MeV protons. This LANSCE neutron flux is a comparable entity to a steady state reactor thermal neutron flux. LANSCE perturbed steady state thermal neutron fluxes have also been calculated. Because LANSCE is a pulsed neutron source, much higher ''peak'' (in time) neutron fluxes can be generated than at a steady state reactor source. 5 refs., 5 figs

  13. The Asymptotic Solution for the Steady Variable-Viscosity Free ...

    African Journals Online (AJOL)

    Under an arbitrary time-dependent heating of an infinite vertical plate (or wall), the steady viscosity-dependent free convection flow of a viscous incompressible fluid is investigated. Using the asymptotic method of solution on the governing equations of motion and energy, the resulting Ordinary differential equations were ...

  14. STEADY STATE DUST DISTRIBUTIONS IN DISK VORTICES: OBSERVATIONAL PREDICTIONS AND APPLICATIONS TO TRANSITIONAL DISKS

    International Nuclear Information System (INIS)

    Lyra, Wladimir; Lin, Min-Kai

    2013-01-01

    The Atacama Large Millimeter Array has returned images of transitional disks in which large asymmetries are seen in the distribution of millimeter sized dust in the outer disk. The explanation in vogue borrows from the vortex literature and suggests that these asymmetries are the result of dust trapping in giant vortices, excited via Rossby wave instabilities at planetary gap edges. Due to the drag force, dust trapped in vortices will accumulate in the center and diffusion is needed to maintain a steady state over the lifetime of the disk. While previous work derived semi-analytical models of the process, in this paper we provide analytical steady-steady solutions. Exact solutions exist for certain vortex models. The solution is determined by the vortex rotation profile, the gas scale height, the vortex aspect ratio, and the ratio of dust diffusion to gas-dust friction. In principle, all of these quantities can be derived from observations, which would validate the model and also provide constrains on the strength of the turbulence inside the vortex core. Based on our solution, we derive quantities such as the gas-dust contrast, the trapped dust mass, and the dust contrast at the same orbital location. We apply our model to the recently imaged Oph IRS 48 system, finding values within the range of the observational uncertainties

  15. Jacobi Elliptic Solutions for Nonlinear Differential Difference Equations in Mathematical Physics

    Directory of Open Access Journals (Sweden)

    Khaled A. Gepreel

    2012-01-01

    Full Text Available We put a direct new method to construct the rational Jacobi elliptic solutions for nonlinear differential difference equations which may be called the rational Jacobi elliptic functions method. We use the rational Jacobi elliptic function method to construct many new exact solutions for some nonlinear differential difference equations in mathematical physics via the lattice equation and the discrete nonlinear Schrodinger equation with a saturable nonlinearity. The proposed method is more effective and powerful to obtain the exact solutions for nonlinear differential difference equations.

  16. Pseudo-transient Continuation Based Variable Relaxation Solve in Nonlinear Magnetohydrodynamic Simulations

    International Nuclear Information System (INIS)

    Chen, Jin

    2009-01-01

    Efficient and robust Variable Relaxation Solver, based on pseudo-transient continuation, is developed to solve nonlinear anisotropic thermal conduction arising from fusion plasma simulations. By adding first and/or second order artificial time derivatives to the system, this type of method advances the resulting time-dependent nonlinear PDEs to steady state, which is the solution to be sought. In this process, only the stiffness matrix itself is involved so that the numerical complexity and errors can be greatly reduced. In fact, this work is an extension of integrating efficient linear elliptic solvers for fusion simulation on Cray XIE. Two schemes are derived in this work, first and second order Variable Relaxations. Four factors are observed to be critical for efficiency and preservation of solution's symmetric structure arising from periodic boundary condition: refining meshes in different coordinate directions, initializing nonlinear process, varying time steps in both temporal and spatial directions, and accurately generating nonlinear stiffness matrix. First finer mesh scale should be taken in strong transport direction; Next the system is carefully initialized by the solution with linear conductivity; Third, time step and relaxation factor are vertex-based varied and optimized at each time step; Finally, the nonlinear stiffness matrix is updated by just scaling corresponding linear one with the vector generated from nonlinear thermal conductivity.

  17. Calculation analysis on steady state natural circulation characteristics

    International Nuclear Information System (INIS)

    Wang Fei; Nie Changhua; Huang Yanping

    2005-01-01

    The calculation results of single-phase steady state natural circulation characteristics by using Retran02 code have been presented, good agreement is achieved between the verified calculation result and the experimental data which were conducted at a test facility. Based on the calculation model, some sensibility analyses were made and much deeper understanding for single-phase steady state natural circulation characteristics was obtained. (author)

  18. Selection of steady states in planar Darcy convection

    International Nuclear Information System (INIS)

    Tsybulin, V.G.; Karasoezen, B.; Ergenc, T.

    2006-01-01

    The planar natural convection of an incompressible fluid in a porous medium is considered. We study the selection of steady states under temperature perturbations on the boundary. A selection map is introduced in order to analyze the selection of a steady state from a continuous family of equilibria which exists under zero boundary conditions. The results of finite-difference modeling for a rectangular enclosure are presented

  19. Analytical exact solution of the non-linear Schroedinger equation

    International Nuclear Information System (INIS)

    Martins, Alisson Xavier; Rocha Filho, Tarcisio Marciano da

    2011-01-01

    Full text: In this work we present how to classify and obtain analytical solutions of the Schroedinger equation with a generic non-linearity in 1+1 dimensions. Our approach is based on the determination of Lie symmetry transformation mapping solutions into solutions, and non-classical symmetry transformations, mapping a given solution into itself. From these symmetries it is then possible to reduce the equation to a system of ordinary differential equations which can then be solved using standard methods. The generic non-linearity is handled by considering it as an additional unknown in the determining equations for the symmetry transformations. This results in an over-determined system of non-linear partial differential equations. Its solution can then be determined in some cases by reducing it to the so called involutive (triangular) form, and then solved. This reduction is very tedious and can only performed using a computer algebra system. Once the determining system is solved, we obtain the explicit form for the non-linearity admitting a Lie or non-classical symmetry. The analytical solutions are then derived by solving the reduced ordinary differential equations. The non-linear determining system for the non-classical symmetry transformations and Lie symmetry generators are obtaining using the computer algebra package SADE (symmetry analysis of differential equations), developed at our group. (author)

  20. Steady-state entanglement activation in optomechanical cavities

    Science.gov (United States)

    Farace, Alessandro; Ciccarello, Francesco; Fazio, Rosario; Giovannetti, Vittorio

    2014-02-01

    Quantum discord, and related indicators, are raising a relentless interest as a novel paradigm of nonclassical correlations beyond entanglement. Here, we discover a discord-activated mechanism yielding steady-state entanglement production in a realistic continuous-variable setup. This comprises two coupled optomechanical cavities, where the optical modes (OMs) communicate through a fiber. We first use a simplified model to highlight the creation of steady-state discord between the OMs. We show next that such discord improves the level of stationary optomechanical entanglement attainable in the system, making it more robust against temperature and thermal noise.

  1. Two-Dimensional Steady-State Boundary Shape Inversion of CGM-SPSO Algorithm on Temperature Information

    Directory of Open Access Journals (Sweden)

    Shoubin Wang

    2017-01-01

    Full Text Available Addressing the problem of two-dimensional steady-state thermal boundary recognition, a hybrid algorithm of conjugate gradient method and social particle swarm optimization (CGM-SPSO algorithm is proposed. The global search ability of particle swarm optimization algorithm and local search ability of gradient algorithm are effectively combined, which overcomes the shortcoming that the conjugate gradient method tends to converge to the local solution and relies heavily on the initial approximation of the iterative process. The hybrid algorithm also avoids the problem that the particle swarm optimization algorithm requires a large number of iterative steps and a lot of time. The experimental results show that the proposed algorithm is feasible and effective in solving the problem of two-dimensional steady-state thermal boundary shape.

  2. Steady state in a gas of inelastic rough spheres heated by a uniform stochastic force

    Energy Technology Data Exchange (ETDEWEB)

    Vega Reyes, Francisco, E-mail: fvega@unex.es; Santos, Andrés, E-mail: andres@unex.es [Departamento de Física and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, 06071 Badajoz (Spain)

    2015-11-15

    We study here the steady state attained in a granular gas of inelastic rough spheres that is subject to a spatially uniform random volume force. The stochastic force has the form of the so-called white noise and acts by adding impulse to the particle translational velocities. We work out an analytical solution of the corresponding velocity distribution function from a Sonine polynomial expansion that displays energy non-equipartition between the translational and rotational modes, translational and rotational kurtoses, and translational-rotational velocity correlations. By comparison with a numerical solution of the Boltzmann kinetic equation (by means of the direct simulation Monte Carlo method), we show that our analytical solution provides a good description that is quantitatively very accurate in certain ranges of inelasticity and roughness. We also find three important features that make the forced granular gas steady state very different from the homogeneous cooling state (attained by an unforced granular gas). First, the marginal velocity distributions are always close to a Maxwellian. Second, there is a continuous transition to the purely smooth limit (where the effects of particle rotations are ignored). And third, the angular translational-rotational velocity correlations show a preference for a quasiperpendicular mutual orientation (which is called “lifted-tennis-ball” behavior)

  3. Steady-State Ion Beam Modeling with MICHELLE

    Science.gov (United States)

    Petillo, John

    2003-10-01

    There is a need to efficiently model ion beam physics for ion implantation, chemical vapor deposition, and ion thrusters. Common to all is the need for three-dimensional (3D) simulation of volumetric ion sources, ion acceleration, and optics, with the ability to model charge exchange of the ion beam with a background neutral gas. The two pieces of physics stand out as significant are the modeling of the volumetric source and charge exchange. In the MICHELLE code, the method for modeling the plasma sheath in ion sources assumes that the electron distribution function is a Maxwellian function of electrostatic potential over electron temperature. Charge exchange is the process by which a neutral background gas with a "fast" charged particle streaming through exchanges its electron with the charged particle. An efficient method for capturing this is essential, and the model presented is based on semi-empirical collision cross section functions. This appears to be the first steady-state 3D algorithm of its type to contain multiple generations of charge exchange, work with multiple species and multiple charge state beam/source particles simultaneously, take into account the self-consistent space charge effects, and track the subsequent fast neutral particles. The solution used by MICHELLE is to combine finite element analysis with particle-in-cell (PIC) methods. The basic physics model is based on the equilibrium steady-state application of the electrostatic particle-in-cell (PIC) approximation employing a conformal computational mesh. The foundation stems from the same basic model introduced in codes such as EGUN. Here, Poisson's equation is used to self-consistently include the effects of space charge on the fields, and the relativistic Lorentz equation is used to integrate the particle trajectories through those fields. The presentation will consider the complexity of modeling ion thrusters.

  4. Towards exact solutions of the non-linear Heisenberg-Pauli-Weyl spinor equation

    International Nuclear Information System (INIS)

    Mielke, E.W.

    1980-03-01

    In ''color geometrodynamics'' fundamental spinor fields are assumed to obey a GL(2f,C) x GL(2c,C) gauge-invariant nonlinear spinor equation of the Heisenberg-Pauli-Weyl type. Quark confinement, assimilating a scheme of Salam and Strathdee, is (partially) mediated by the tensor ''gluons'' of strong gravity. This hypothesis is incorporated into the model by considering the nonlinear Dirac equation in a curved space-time of hadronic dimensions. Disregarding internal degrees of freedom, it is then feasible, for a particular background space-time, to obtain exact solutions of the spherical bound-state problem. Finally, these solutions are tentatively interpreted as droplet-type solitons and remarks on their interrelation with Wheeler's geon construction are made. (author)

  5. Numerical method for three dimensional steady-state two-phase flow calculations

    International Nuclear Information System (INIS)

    Raymond, P.; Toumi, I.

    1992-01-01

    This paper presents the numerical scheme which was developed for the FLICA-4 computer code to calculate three dimensional steady state two phase flows. This computer code is devoted to steady state and transient thermal hydraulics analysis of nuclear reactor cores 1,3 . The first section briefly describes the FLICA-4 flow modelling. Then in order to introduce the numerical method for steady state computations, some details are given about the implicit numerical scheme based upon an approximate Riemann solver which was developed for calculation of flow transients. The third section deals with the numerical method for steady state computations, which is derived from this previous general scheme and its optimization. We give some numerical results for steady state calculations and comparisons on required CPU time and memory for various meshing and linear system solvers

  6. Development of synchronous generator saturation model from steady-state operating data

    Energy Technology Data Exchange (ETDEWEB)

    Jadric, Martin; Despalatovic, Marin; Terzic, Bozo [FESB University of Split, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, Split (Croatia)

    2010-11-15

    A new method to estimate and model the saturated synchronous reactances of hydroturbine generators from operating data is presented. For the estimation process, measurements of only the generator steady-state variables are required. First, using a specific procedure, the field to armature turns ratio is estimated from measured steady-state variables at constant power generation and various excitation conditions. Subsequently, for each set of steady-state operating data, saturated synchronous reactances are identified. Fitting surfaces, defined as polynomial functions in two variables, are later used to model these saturated reactances. It is shown that the simpler polynomial functions may be used to model saturation at the steady-state than at the dynamic conditions. The developed steady-state model is validated with measurements performed on the 34 MVA hydroturbine generator. (author)

  7. Analytical solution of strongly nonlinear Duffing oscillators

    OpenAIRE

    El-Naggar, A.M.; Ismail, G.M.

    2016-01-01

    In this paper, a new perturbation technique is employed to solve strongly nonlinear Duffing oscillators, in which a new parameter α=α(ε)α=α(ε) is defined such that the value of α is always small regardless of the magnitude of the original parameter εε. Therefore, the strongly nonlinear Duffing oscillators with large parameter ε are transformed into a small parameter system with respect to αα. Approximate solution obtained by the present method is compared with the solution of energy balance m...

  8. Periodic solutions of nonlinear vibrating beams

    Directory of Open Access Journals (Sweden)

    J. Berkovits

    2003-01-01

    Full Text Available The aim of this paper is to prove new existence and multiplicity results for periodic semilinear beam equation with a nonlinear time-independent perturbation in case the period is not prescribed. Since the spectrum of the linear part varies with the period, the solvability of the equation depends crucially on the period which can be chosen as a free parameter. Since the period of the external forcing is generally unknown a priori, we consider the following natural problem. For a given time-independent nonlinearity, find periods T for which the equation is solvable for any T-periodic forcing. We will also deal with the existence of multiple solutions when the nonlinearity interacts with the spectrum of the linear part. We show that under certain conditions multiple solutions do exist for any small forcing term with suitable period T. The results are obtained via generalized Leray-Schauder degree and reductions to invariant subspaces.

  9. Steady state and transient critical heat flux examinations

    International Nuclear Information System (INIS)

    Szabados, L.

    1978-02-01

    In steady state conditions within the P.W.R. parameter range the critical heat flux correlations based on local parameters reproduce the experimental data with less deviations than those based on system parameters. The transient experiments were restricted for the case of power transients. A data processing method for critical heat flux measurements has been developed and the applicability of quasi steady state calculation has been verified. (D.P.)

  10. A simplified method for power-law modelling of metabolic pathways from time-course data and steady-state flux profiles.

    Science.gov (United States)

    Kitayama, Tomoya; Kinoshita, Ayako; Sugimoto, Masahiro; Nakayama, Yoichi; Tomita, Masaru

    2006-07-17

    In order to improve understanding of metabolic systems there have been attempts to construct S-system models from time courses. Conventionally, non-linear curve-fitting algorithms have been used for modelling, because of the non-linear properties of parameter estimation from time series. However, the huge iterative calculations required have hindered the development of large-scale metabolic pathway models. To solve this problem we propose a novel method involving power-law modelling of metabolic pathways from the Jacobian of the targeted system and the steady-state flux profiles by linearization of S-systems. The results of two case studies modelling a straight and a branched pathway, respectively, showed that our method reduced the number of unknown parameters needing to be estimated. The time-courses simulated by conventional kinetic models and those described by our method behaved similarly under a wide range of perturbations of metabolite concentrations. The proposed method reduces calculation complexity and facilitates the construction of large-scale S-system models of metabolic pathways, realizing a practical application of reverse engineering of dynamic simulation models from the Jacobian of the targeted system and steady-state flux profiles.

  11. A simplified method for power-law modelling of metabolic pathways from time-course data and steady-state flux profiles

    Directory of Open Access Journals (Sweden)

    Sugimoto Masahiro

    2006-07-01

    Full Text Available Abstract Background In order to improve understanding of metabolic systems there have been attempts to construct S-system models from time courses. Conventionally, non-linear curve-fitting algorithms have been used for modelling, because of the non-linear properties of parameter estimation from time series. However, the huge iterative calculations required have hindered the development of large-scale metabolic pathway models. To solve this problem we propose a novel method involving power-law modelling of metabolic pathways from the Jacobian of the targeted system and the steady-state flux profiles by linearization of S-systems. Results The results of two case studies modelling a straight and a branched pathway, respectively, showed that our method reduced the number of unknown parameters needing to be estimated. The time-courses simulated by conventional kinetic models and those described by our method behaved similarly under a wide range of perturbations of metabolite concentrations. Conclusion The proposed method reduces calculation complexity and facilitates the construction of large-scale S-system models of metabolic pathways, realizing a practical application of reverse engineering of dynamic simulation models from the Jacobian of the targeted system and steady-state flux profiles.

  12. Characteristics of steady vibration in a rotating hub-beam system

    Science.gov (United States)

    Zhao, Zhen; Liu, Caishan; Ma, Wei

    2016-02-01

    A rotating beam features a puzzling character in which its frequencies and modal shapes may vary with the hub's inertia and its rotating speed. To highlight the essential nature behind the vibration phenomena, we analyze the steady vibration of a rotating Euler-Bernoulli beam with a quasi-steady-state stretch. Newton's law is used to derive the equations governing the beam's elastic motion and the hub's rotation. A combination of these equations results in a nonlinear partial differential equation (PDE) that fully reflects the mutual interaction between the two kinds of motion. Via the Fourier series expansion within a finite interval of time, we reduce the PDE into an infinite system of a nonlinear ordinary differential equation (ODE) in spatial domain. We further nondimensionalize the ODE and discretize it via a difference method. The frequencies and modal shapes of a general rotating beam are then determined numerically. For a low-speed beam where the ignorance of geometric stiffening is feasible, the beam's vibration characteristics are solved analytically. We validate our numerical method and the analytical solutions by comparing with either the past experiments or the past numerical findings reported in existing literature. Finally, systematic simulations are performed to demonstrate how the beam's eigenfrequencies vary with the hub's inertia and rotating speed.

  13. Perturbation Solutions of the Quintic Duffing Equation with Strong Nonlinearities

    Directory of Open Access Journals (Sweden)

    Mehmet Pakdemirli

    Full Text Available The quintic Duffing equation with strong nonlinearities is considered. Perturbation solutions are constructed using two different techniques: The classical multiple scales method (MS and the newly developed multiple scales Lindstedt Poincare method (MSLP. The validity criteria for admissible solutions are derived. Both approximate solutions are contrasted with the numerical solutions. It is found that MSLP provides compatible solution with the numerical solution for strong nonlinearities whereas MS solution fail to produce physically acceptable solution for large perturbation parameters.

  14. The Markov process admits a consistent steady-state thermodynamic formalism

    Science.gov (United States)

    Peng, Liangrong; Zhu, Yi; Hong, Liu

    2018-01-01

    The search for a unified formulation for describing various non-equilibrium processes is a central task of modern non-equilibrium thermodynamics. In this paper, a novel steady-state thermodynamic formalism was established for general Markov processes described by the Chapman-Kolmogorov equation. Furthermore, corresponding formalisms of steady-state thermodynamics for the master equation and Fokker-Planck equation could be rigorously derived in mathematics. To be concrete, we proved that (1) in the limit of continuous time, the steady-state thermodynamic formalism for the Chapman-Kolmogorov equation fully agrees with that for the master equation; (2) a similar one-to-one correspondence could be established rigorously between the master equation and Fokker-Planck equation in the limit of large system size; (3) when a Markov process is restrained to one-step jump, the steady-state thermodynamic formalism for the Fokker-Planck equation with discrete state variables also goes to that for master equations, as the discretization step gets smaller and smaller. Our analysis indicated that general Markov processes admit a unified and self-consistent non-equilibrium steady-state thermodynamic formalism, regardless of underlying detailed models.

  15. Nonlinear stability of spin-flip excitations

    International Nuclear Information System (INIS)

    Arunasalam, V.

    1975-01-01

    A rather complete discussion of the nonlinear electrodynamic behavior of a negative-temperature spin system is presented. The method presented here is based on a coupled set of master equations, one describing the time evolution of the photon (i.e., the spin-flip excitation) distribution function and the other describing the time evolution of the particle distribution function. It is found that the initially unstable (i.e., growing) spin-flip excitations grow to such a large amplitude that their nonlinear reaction on the particle distribution function becomes important. It is then shown that the initially totally inverted two-level spin system evolves rapidly (through this nonlinear photon-particle coupling) towards a quasilinear steady state where the populations of the spin-up and the spin-down states are equal to each other. Explicit expressions for the time taken to reach this quasilinear steady state and the energy in the spin-flip excitations at this state are also presented

  16. Steady-state global optimization of metabolic non-linear dynamic models through recasting into power-law canonical models.

    Science.gov (United States)

    Pozo, Carlos; Marín-Sanguino, Alberto; Alves, Rui; Guillén-Gosálbez, Gonzalo; Jiménez, Laureano; Sorribas, Albert

    2011-08-25

    Design of newly engineered microbial strains for biotechnological purposes would greatly benefit from the development of realistic mathematical models for the processes to be optimized. Such models can then be analyzed and, with the development and application of appropriate optimization techniques, one could identify the modifications that need to be made to the organism in order to achieve the desired biotechnological goal. As appropriate models to perform such an analysis are necessarily non-linear and typically non-convex, finding their global optimum is a challenging task. Canonical modeling techniques, such as Generalized Mass Action (GMA) models based on the power-law formalism, offer a possible solution to this problem because they have a mathematical structure that enables the development of specific algorithms for global optimization. Based on the GMA canonical representation, we have developed in previous works a highly efficient optimization algorithm and a set of related strategies for understanding the evolution of adaptive responses in cellular metabolism. Here, we explore the possibility of recasting kinetic non-linear models into an equivalent GMA model, so that global optimization on the recast GMA model can be performed. With this technique, optimization is greatly facilitated and the results are transposable to the original non-linear problem. This procedure is straightforward for a particular class of non-linear models known as Saturable and Cooperative (SC) models that extend the power-law formalism to deal with saturation and cooperativity. Our results show that recasting non-linear kinetic models into GMA models is indeed an appropriate strategy that helps overcoming some of the numerical difficulties that arise during the global optimization task.

  17. Steady-state global optimization of metabolic non-linear dynamic models through recasting into power-law canonical models

    Directory of Open Access Journals (Sweden)

    Sorribas Albert

    2011-08-01

    Full Text Available Abstract Background Design of newly engineered microbial strains for biotechnological purposes would greatly benefit from the development of realistic mathematical models for the processes to be optimized. Such models can then be analyzed and, with the development and application of appropriate optimization techniques, one could identify the modifications that need to be made to the organism in order to achieve the desired biotechnological goal. As appropriate models to perform such an analysis are necessarily non-linear and typically non-convex, finding their global optimum is a challenging task. Canonical modeling techniques, such as Generalized Mass Action (GMA models based on the power-law formalism, offer a possible solution to this problem because they have a mathematical structure that enables the development of specific algorithms for global optimization. Results Based on the GMA canonical representation, we have developed in previous works a highly efficient optimization algorithm and a set of related strategies for understanding the evolution of adaptive responses in cellular metabolism. Here, we explore the possibility of recasting kinetic non-linear models into an equivalent GMA model, so that global optimization on the recast GMA model can be performed. With this technique, optimization is greatly facilitated and the results are transposable to the original non-linear problem. This procedure is straightforward for a particular class of non-linear models known as Saturable and Cooperative (SC models that extend the power-law formalism to deal with saturation and cooperativity. Conclusions Our results show that recasting non-linear kinetic models into GMA models is indeed an appropriate strategy that helps overcoming some of the numerical difficulties that arise during the global optimization task.

  18. Exact partial solution to the steady-state, compressible fluid flow problems of jet formation and jet penetration

    International Nuclear Information System (INIS)

    Karpp, R.R.

    1980-10-01

    This report treats analytically the problem of the symmetric impact of two compressible fluid streams. The flow is assumed to be steady, plane, inviscid, and subsonic and that the compressible fluid is of the Chaplygin (tangent gas) type. In the analysis, the governing equations are first transformed to the hodograph plane where an exact, closed-form solution is obtained by standard techniques. The distributions of fluid properties along the plane of symmetry as well as the shapes of the boundary streamlines are exactly determined by transforming the solution back to the physical plane. The problem of a compressible fluid jet penetrating into an infinite target of similar material is also exactly solved by considering a limiting case of this solution. This new compressible flow solution reduces to the classical result of incompressible flow theory when the sound speed of the fluid is allowed to approach infinity. Several illustrations of the differences between compressible and incompressible flows of the type considered are presented

  19. A study on the steady-state solutions of a relativistic Bursian diode in the presence of a transverse magnetic field

    Energy Technology Data Exchange (ETDEWEB)

    Pramanik, Sourav; Chakrabarti, Nikhil [Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata 700 064 (India); Kuznetsov, V. I.; Bakaleinikov, L. A. [Ioffe Institute, St. Petersburg 194021 (Russian Federation)

    2016-08-15

    A comprehensive study on the steady states of a planar vacuum diode driven by a cold relativistic electron beam in the presence of an external transverse magnetic field is presented. The regimes, where no electrons are turned around by the external magnetic field and where they are reflected back to the emitter by the magnetic field, are both considered in a generalized way. The problem is solved by two methods: with the Euler and the Lagrange formulation. Taking non-relativistic limit, the solutions are compared with the similar ones which were obtained for the Bursian diode with a non-relativistic electron beam in previous work [Pramanik et al., Phys. Plasmas 22, 112108 (2015)]. It is shown that, at a moderate value of the relativistic factor of the injected beam, the region of the ambiguous solutions located to the right of the SCL bifurcation point (space charge limit) in the non-relativistic regime disappears. In addition, the dependencies of the characteristic bifurcation points and the transmitted current on the Larmor frequency as well as on the relativistic factor are explored.

  20. Contour analysis of steady state tokamak reactor performance

    International Nuclear Information System (INIS)

    Devoto, R.S.; Fenstermacher, M.E.

    1990-01-01

    A new method of analysis for presenting the possible operating space for steady state, non-ignited tokamak reactors is proposed. The method uses contours of reactor performance and plasma characteristics, fusion power gain, wall neutron flux, current drive power, etc., plotted on a two-dimensional grid, the axes of which are the plasma current I p and the normalized beta, β n = β/(I p /aB 0 ), to show possible operating points. These steady state operating contour plots are called SOPCONS. This technique is illustrated in an application to a design for the International Thermonuclear Experimental Reactor (ITER) with neutral beam, lower hybrid and bootstrap current drive. The utility of the SOPCON plots for pointing out some of the non-intuitive considerations in steady state reactor design is shown. (author). Letter-to-the-editor. 16 refs, 3 figs, 1 tab

  1. CROSS DIFFUSION AND NONLINEAR DIFFUSION PREVENTING BLOW UP IN THE KELLER–SEGEL MODEL

    KAUST Repository

    CARRILLO, JOSÉ ANTONIO

    2012-12-01

    A parabolic-parabolic (Patlak-)Keller-Segel model in up to three space dimensions with nonlinear cell diffusion and an additional nonlinear cross-diffusion term is analyzed. The main feature of this model is that there exists a new entropy functional, yielding gradient estimates for the cell density and chemical concentration. For arbitrarily small cross-diffusion coefficients and for suitable exponents of the nonlinear diffusion terms, the global-in-time existence of weak solutions is proved, thus preventing finite-time blow up of the cell density. The global existence result also holds for linear and fast diffusion of the cell density in a certain parameter range in three dimensions. Furthermore, we show L∞ bounds for the solutions to the parabolic-elliptic system. Sufficient conditions leading to the asymptotic stability of the constant steady state are given for a particular choice of the nonlinear diffusion exponents. Numerical experiments in two and three space dimensions illustrate the theoretical results. © 2012 World Scientific Publishing Company.

  2. Exact solutions for the quintic nonlinear Schroedinger equation with time and space modulated nonlinearities and potentials

    International Nuclear Information System (INIS)

    Belmonte-Beitia, Juan; Calvo, Gabriel F.

    2009-01-01

    In this Letter, by means of similarity transformations, we construct explicit solutions to the quintic nonlinear Schroedinger equation with potentials and nonlinearities depending both on time and on the spatial coordinates. We present the general approach and use it to study some examples and find nontrivial explicit solutions such as periodic (breathers), quasiperiodic and bright and dark soliton solutions

  3. Nonlinear MHD-equations: symmetries, solutions and conservation laws

    International Nuclear Information System (INIS)

    Samokhin, A.V.

    1985-01-01

    To investigate stability and nonlinear effects in a high-temperature plasma the system of two scalar nonlinear equations is considered. The algebra of classical symmetries of this system and a certain natural part of its conservation laws are described. It is shown that first, with symmetries one can derive invariant (self-similar) solutions, second, acting with symmetry on the known solution the latter can be included into parametric family

  4. On the solution of the nonlinear Schrodinger equation

    International Nuclear Information System (INIS)

    Zayed, E.M.E.; Zedan, Hassan A.

    2003-01-01

    In this paper we study the nonlinear Schrodinger equation with respect to the unknown function S(x,t). New dimensional reduction and exact solution for a nonlinear Schrodinger equation are presented and a complete group classification is given with respect to the function S(x,t). Moreover, specializing the potential function S(x,t), new classes of invariant solution and group classification are obtained in the cases of physical interest

  5. Bound state solution of the Grassmannian nonlinear sigma model with fermions

    International Nuclear Information System (INIS)

    Abdalla, E.; Lima-Santos, A.

    1987-11-01

    We construct the s matrix for bound state (gauge-invariant) scattering for nonlinear sigma models defined on the manifold SU(N)/S(U(p)x (lower casex)U(n-p)) with fermions. It is not possible to compute gauge non-singlet matrix elements. In the present language they are not submitted to sufficiently many constraints derived from higher conservation laws. (author) [pt

  6. Spike-layer solutions to nonlinear fractional Schrodinger equations with almost optimal nonlinearities

    Directory of Open Access Journals (Sweden)

    Jinmyoung Seok

    2015-07-01

    Full Text Available In this article, we are interested in singularly perturbed nonlinear elliptic problems involving a fractional Laplacian. Under a class of nonlinearity which is believed to be almost optimal, we construct a positive solution which exhibits multiple spikes near any given local minimum components of an exterior potential of the problem.

  7. Steady-state spheromak reactor studies

    International Nuclear Information System (INIS)

    Krakowski, R.A.; Hagenson, R.L.

    1985-01-01

    After summarizing the essential elements of a gun-sustained spheromak, the potential for a steady-state is explored by means of a comprehensive physics/engineering/costing model. A range of cost-optimized reactor design points is presented, and the sensitivity of cost to key physics, engineering, and operational variables is reported

  8. Application of quasi-steady state methods to molecular motor transport on microtubules in fungal hyphae.

    Science.gov (United States)

    Dauvergne, Duncan; Edelstein-Keshet, Leah

    2015-08-21

    We consider bidirectional transport of cargo by molecular motors dynein and kinesin that walk along microtubules, and/or diffuse in the cell. The motors compete to transport cargo in opposite directions with respect to microtubule polarity (towards the plus or minus end of the microtubule). In recent work, Gou et al. (2014) used a hierarchical set of models, each consisting of continuum transport equations to track the evolution of motors and their cargo (early endosomes) in the specific case of the fungus Ustilago maydis. We complement their work using a framework of quasi-steady state analysis developed by Newby and Bressloff (2010) and Bressloff and Newby (2013) to reduce the models to an approximating steady state Fokker-Plank equation. This analysis allows us to find analytic approximations to the steady state solutions in many cases where the full models are not easily solved. Consequently, we can make predictions about parameter dependence of the resulting spatial distributions. We also characterize the overall rates of bulk transport and diffusion, and how these are related to state transition parameters, motor speeds, microtubule polarity distribution, and specific assumptions made. Copyright © 2015 Elsevier Ltd. All rights reserved.

  9. Bifurcation topology transfer in nonlinear nanocantilever arrays subject to parametric and internal resonances

    Directory of Open Access Journals (Sweden)

    Souayeh Saoussen

    2014-01-01

    Full Text Available The collective nonlinear dynamics of a coupled array of nanocantilevers is investigated while taking into account the main sources of nonlinearities. The amplitude and phase equations of this device, subject to parametric and internal resonances, are analytically derived by means of a multi-modal Galerkin discretization coupled with a multiscale analysis. Based on the steady-state solutions of these equations, the frequency responses are numerically computed for a two-beam array. The effects of different parameters are investigated and several dynamical aspects are confirmed by numerical simulations. Particularly, we have demonstrated that the bifurcation topology transfer is imposed by the first nanocantilever and it can be general to the collective nonlinear dynamics of the NEMS array.

  10. Coupled Particle Transport and Pattern Formation in a Nonlinear Leaky-Box Model

    Science.gov (United States)

    Barghouty, A. F.; El-Nemr, K. W.; Baird, J. K.

    2009-01-01

    Effects of particle-particle coupling on particle characteristics in nonlinear leaky-box type descriptions of the acceleration and transport of energetic particles in space plasmas are examined in the framework of a simple two-particle model based on the Fokker-Planck equation in momentum space. In this model, the two particles are assumed coupled via a common nonlinear source term. In analogy with a prototypical mathematical system of diffusion-driven instability, this work demonstrates that steady-state patterns with strong dependence on the magnetic turbulence but a rather weak one on the coupled particles attributes can emerge in solutions of a nonlinearly coupled leaky-box model. The insight gained from this simple model may be of wider use and significance to nonlinearly coupled leaky-box type descriptions in general.

  11. Steady state of tapped granular polygons

    International Nuclear Information System (INIS)

    Carlevaro, Carlos M; Pugnaloni, Luis A

    2011-01-01

    The steady state packing fraction of a tapped granular bed is studied for different grain shapes via a discrete element method. Grains are monosized regular polygons, from triangles to icosagons. Comparisons with disc packings show that the steady state packing fraction as a function of the tapping intensity presents the same general trends in polygon packings. However, better packing fractions are obtained, as expected, for shapes that can tessellate the plane (triangles, squares and hexagons). In addition, we find a sharp transition for packings of polygons with more than 13 vertices signaled by a discontinuity in the packing fraction at a particular tapping intensity. Density fluctuations for most shapes are consistent with recent experimental findings in disc packing; however, a peculiar behavior is found for triangles and squares

  12. Nonlinear differential equations with exact solutions expressed via the Weierstrass function

    NARCIS (Netherlands)

    Kudryashov, NA

    2004-01-01

    A new problem is studied, that is to find nonlinear differential equations with special solutions expressed via the Weierstrass function. A method is discussed to construct nonlinear ordinary differential equations with exact solutions. The main step of our method is the assumption that nonlinear

  13. Accelerated solution of non-linear flow problems using Chebyshev iteration polynomial based RK recursions

    Energy Technology Data Exchange (ETDEWEB)

    Lorber, A.A.; Carey, G.F.; Bova, S.W.; Harle, C.H. [Univ. of Texas, Austin, TX (United States)

    1996-12-31

    The connection between the solution of linear systems of equations by iterative methods and explicit time stepping techniques is used to accelerate to steady state the solution of ODE systems arising from discretized PDEs which may involve either physical or artificial transient terms. Specifically, a class of Runge-Kutta (RK) time integration schemes with extended stability domains has been used to develop recursion formulas which lead to accelerated iterative performance. The coefficients for the RK schemes are chosen based on the theory of Chebyshev iteration polynomials in conjunction with a local linear stability analysis. We refer to these schemes as Chebyshev Parameterized Runge Kutta (CPRK) methods. CPRK methods of one to four stages are derived as functions of the parameters which describe an ellipse {Epsilon} which the stability domain of the methods is known to contain. Of particular interest are two-stage, first-order CPRK and four-stage, first-order methods. It is found that the former method can be identified with any two-stage RK method through the correct choice of parameters. The latter method is found to have a wide range of stability domains, with a maximum extension of 32 along the real axis. Recursion performance results are presented below for a model linear convection-diffusion problem as well as non-linear fluid flow problems discretized by both finite-difference and finite-element methods.

  14. Analytical solution of strongly nonlinear Duffing oscillators

    Directory of Open Access Journals (Sweden)

    A.M. El-Naggar

    2016-06-01

    Full Text Available In this paper, a new perturbation technique is employed to solve strongly nonlinear Duffing oscillators, in which a new parameter α=α(ε is defined such that the value of α is always small regardless of the magnitude of the original parameter ε. Therefore, the strongly nonlinear Duffing oscillators with large parameter ε are transformed into a small parameter system with respect to α. Approximate solution obtained by the present method is compared with the solution of energy balance method, homotopy perturbation method, global error minimization method and lastly numerical solution. We observe from the results that this method is very simple, easy to apply, and gives a very good accuracy not only for small parameter εbut also for large values of ε.

  15. State-dependent differential Riccati equation to track control of time-varying systems with state and control nonlinearities.

    Science.gov (United States)

    Korayem, M H; Nekoo, S R

    2015-07-01

    This work studies an optimal control problem using the state-dependent Riccati equation (SDRE) in differential form to track for time-varying systems with state and control nonlinearities. The trajectory tracking structure provides two nonlinear differential equations: the state-dependent differential Riccati equation (SDDRE) and the feed-forward differential equation. The independence of the governing equations and stability of the controller are proven along the trajectory using the Lyapunov approach. Backward integration (BI) is capable of solving the equations as a numerical solution; however, the forward solution methods require the closed-form solution to fulfill the task. A closed-form solution is introduced for SDDRE, but the feed-forward differential equation has not yet been obtained. Different ways of solving the problem are expressed and analyzed. These include BI, closed-form solution with corrective assumption, approximate solution, and forward integration. Application of the tracking problem is investigated to control robotic manipulators possessing rigid or flexible joints. The intention is to release a general program for automatic implementation of an SDDRE controller for any manipulator that obeys the Denavit-Hartenberg (D-H) principle when only D-H parameters are received as input data. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

  16. Nontrivial Periodic Solutions for Nonlinear Second-Order Difference Equations

    Directory of Open Access Journals (Sweden)

    Tieshan He

    2011-01-01

    Full Text Available This paper is concerned with the existence of nontrivial periodic solutions and positive periodic solutions to a nonlinear second-order difference equation. Under some conditions concerning the first positive eigenvalue of the linear equation corresponding to the nonlinear second-order equation, we establish the existence results by using the topological degree and fixed point index theories.

  17. Three dimensional nonlinear magnetic AdS solutions through topological defects

    International Nuclear Information System (INIS)

    Hendi, S.H.; Panah, B.E.; Momennia, M.; Panahiyan, S.

    2015-01-01

    Inspired by large applications of topological defects in describing different phenomena in physics, and considering the importance of three dimensional solutions in AdS/CFT correspondence, in this paper we obtain magnetic anti-de Sitter solutions of nonlinear electromagnetic fields. We take into account three classes of nonlinear electrodynamic models; first two classes are the well-known Born-Infeld like models including logarithmic and exponential forms and third class is known as the power Maxwell invariant nonlinear electrodynamics. We investigate the effects of these nonlinear sources on three dimensional magnetic solutions. We show that these asymptotical AdS solutions do not have any curvature singularity and horizon. We also generalize the static metric to the case of rotating solutions and find that the value of the electric charge depends on the rotation parameter. Finally, we consider the quadratic Maxwell invariant as a correction of Maxwell theory and we investigate the effects of nonlinearity as a correction. We study the behavior of the deficit angle in presence of these theories of nonlinearity and compare them with each other. We also show that some cases with negative deficit angle exists which are representing objects with different geometrical structure. We also show that in case of the static only magnetic field exists whereas by boosting the metric to rotating one, electric field appears too. (orig.)

  18. Steady-state propagation of interface corner crack

    DEFF Research Database (Denmark)

    Veluri, Badrinath; Jensen, Henrik Myhre

    2013-01-01

    Steady-state propagation of interface cracks close to three-dimensional corners has been analyzed. Attention was focused on modeling the shape of the interface crack front and calculating the critical stress for steady-state propagation of the crack. The crack propagation was investigated...... on the finite element method with iterative adjustment of the crack front to estimate the critical delamination stresses as a function of the fracture criterion and corner angles. The implication of the results on the delamination is discussed in terms of crack front profiles and the critical stresses...... for propagation and the angle of intersection of the crack front with the free edge....

  19. Steady-state leaching of tritiated water from silica gel

    DEFF Research Database (Denmark)

    Das, H.A.; Hou, Xiaolin

    2009-01-01

    Aqueous leaching of tritium from silica gel, loaded by absorption of water vapor, makes part of reactor de-commissioning. It is found to follow the formulation of steady-state diffusion.......Aqueous leaching of tritium from silica gel, loaded by absorption of water vapor, makes part of reactor de-commissioning. It is found to follow the formulation of steady-state diffusion....

  20. Superposition of elliptic functions as solutions for a large number of nonlinear equations

    International Nuclear Information System (INIS)

    Khare, Avinash; Saxena, Avadh

    2014-01-01

    For a large number of nonlinear equations, both discrete and continuum, we demonstrate a kind of linear superposition. We show that whenever a nonlinear equation admits solutions in terms of both Jacobi elliptic functions cn(x, m) and dn(x, m) with modulus m, then it also admits solutions in terms of their sum as well as difference. We have checked this in the case of several nonlinear equations such as the nonlinear Schrödinger equation, MKdV, a mixed KdV-MKdV system, a mixed quadratic-cubic nonlinear Schrödinger equation, the Ablowitz-Ladik equation, the saturable nonlinear Schrödinger equation, λϕ 4 , the discrete MKdV as well as for several coupled field equations. Further, for a large number of nonlinear equations, we show that whenever a nonlinear equation admits a periodic solution in terms of dn 2 (x, m), it also admits solutions in terms of dn 2 (x,m)±√(m) cn (x,m) dn (x,m), even though cn(x, m)dn(x, m) is not a solution of these nonlinear equations. Finally, we also obtain superposed solutions of various forms for several coupled nonlinear equations

  1. Quasi steady-state aerodynamic model development for race vehicle simulations

    Science.gov (United States)

    Mohrfeld-Halterman, J. A.; Uddin, M.

    2016-01-01

    Presented in this paper is a procedure to develop a high fidelity quasi steady-state aerodynamic model for use in race car vehicle dynamic simulations. Developed to fit quasi steady-state wind tunnel data, the aerodynamic model is regressed against three independent variables: front ground clearance, rear ride height, and yaw angle. An initial dual range model is presented and then further refined to reduce the model complexity while maintaining a high level of predictive accuracy. The model complexity reduction decreases the required amount of wind tunnel data thereby reducing wind tunnel testing time and cost. The quasi steady-state aerodynamic model for the pitch moment degree of freedom is systematically developed in this paper. This same procedure can be extended to the other five aerodynamic degrees of freedom to develop a complete six degree of freedom quasi steady-state aerodynamic model for any vehicle.

  2. Computational issues of solving the 1D steady gradually varied flow equation

    Directory of Open Access Journals (Sweden)

    Artichowicz Wojciech

    2014-09-01

    Full Text Available In this paper a problem of multiple solutions of steady gradually varied flow equation in the form of the ordinary differential energy equation is discussed from the viewpoint of its numerical solution. Using the Lipschitz theorem dealing with the uniqueness of solution of an initial value problem for the ordinary differential equation it was shown that the steady gradually varied flow equation can have more than one solution. This fact implies that the nonlinear algebraic equation approximating the ordinary differential energy equation, which additionally coincides with the wellknown standard step method usually applied for computing of the flow profile, can have variable number of roots. Consequently, more than one alternative solution corresponding to the same initial condition can be provided. Using this property it is possible to compute the water flow profile passing through the critical stage.

  3. Realizing steady-state tokamak operation for fusion energy

    International Nuclear Information System (INIS)

    Luce, T. C.

    2011-01-01

    Continuous operation of a tokamak for fusion energy has clear engineering advantages but requires conditions beyond those sufficient for a burning plasma. The fusion reactions and external sources must support both the pressure and the current equilibrium without inductive current drive, leading to demands on stability, confinement, current drive, and plasma-wall interactions that exceed those for pulsed tokamaks. These conditions have been met individually, and significant progress has been made in the past decade to realize scenarios where the required conditions are obtained simultaneously. Tokamaks are operated routinely without disruptions near pressure limits, as needed for steady-state operation. Fully noninductive sustainment with more than half of the current from intrinsic currents has been obtained for a resistive time with normalized pressure and confinement approaching those needed for steady-state conditions. One remaining challenge is handling the heat and particle fluxes expected in a steady-state tokamak without compromising the core plasma performance.

  4. Improving the steady-state loading margin to voltage collapse in the North-West Control Area of the Mexican Power System

    Energy Technology Data Exchange (ETDEWEB)

    Calderon-Guizar, J.G.; Inda-Ruiz, G.A.; Tovar, G.E. [Gerencia de Analisis de Redes, Temixco, Morelos (Mexico). Inst. de Investigaciones Eleectricas

    2003-10-01

    This paper reports the application of a static approach for assessing the steady-state loading margin to voltage collapse of the North-West Control Area (NWCA) of the Mexican Power System. The approach uses both optimal load flow (OLF) and conventional load flow (LF) solutions, and singular value decomposition of the load flow Jacobian matrix (J). Additionally, the approach allows to determine suitable locations for corrective actions such as, the addition of new equipment or load shedding. The results shows that the combination of OLF and LF resulted in a steady-state loading margin to voltage collapse of the NWCA 7.2% higher than the case when only conventional load flow solutions were considered. (author)

  5. Steady State Advanced Tokamak (SSAT): The mission and the machine

    International Nuclear Information System (INIS)

    Thomassen, K.; Goldston, R.; Nevins, B.; Neilson, H.; Shannon, T.; Montgomery, B.

    1992-03-01

    Extending the tokamak concept to the steady state regime and pursuing advances in tokamak physics are important and complementary steps for the magnetic fusion energy program. The required transition away from inductive current drive will provide exciting opportunities for advances in tokamak physics, as well as important impetus to drive advances in fusion technology. Recognizing this, the Fusion Policy Advisory Committee and the US National Energy Strategy identified the development of steady state tokamak physics and technology, and improvements in the tokamak concept, as vital elements in the magnetic fusion energy development plan. Both called for the construction of a steady state tokamak facility to address these plan elements. Advances in physics that produce better confinement and higher pressure limits are required for a similar unit size reactor. Regimes with largely self-driven plasma current are required to permit a steady-state tokamak reactor with acceptable recirculating power. Reliable techniques of disruption control will be needed to achieve the availability goals of an economic reactor. Thus the central role of this new tokamak facility is to point the way to a more attractive demonstration reactor (DEMO) than the present data base would support. To meet the challenges, we propose a new ''Steady State Advanced Tokamak'' (SSAT) facility that would develop and demonstrate optimized steady state tokamak operating mode. While other tokamaks in the world program employ superconducting toroidal field coils, SSAT would be the first major tokamak to operate with a fully superconducting coil set in the elongated, divertor geometry planned for ITER and DEMO

  6. Pseudo-transient Continuation Based Variable Relaxation Solve in Nonlinear Magnetohydrodynamic Simulations

    Energy Technology Data Exchange (ETDEWEB)

    Jin Chen

    2009-12-07

    Efficient and robust Variable Relaxation Solver, based on pseudo-transient continuation, is developed to solve nonlinear anisotropic thermal conduction arising from fusion plasma simulations. By adding first and/or second order artificial time derivatives to the system, this type of method advances the resulting time-dependent nonlinear PDEs to steady state, which is the solution to be sought. In this process, only the stiffness matrix itself is involved so that the numerical complexity and errors can be greatly reduced. In fact, this work is an extension of integrating efficient linear elliptic solvers for fusion simulation on Cray XIE. Two schemes are derived in this work, first and second order Variable Relaxations. Four factors are observed to be critical for efficiency and preservation of solution's symmetric structure arising from periodic boundary condition: refining meshes in different coordinate directions, initializing nonlinear process, varying time steps in both temporal and spatial directions, and accurately generating nonlinear stiffness matrix. First finer mesh scale should be taken in strong transport direction; Next the system is carefully initialized by the solution with linear conductivity; Third, time step and relaxation factor are vertex-based varied and optimized at each time step; Finally, the nonlinear stiffness matrix is updated by just scaling corresponding linear one with the vector generated from nonlinear thermal conductivity.

  7. Two Ways to Examine Differential Constitutive Equations: Initiated on Steady or Initiated on Unsteady (LAOS Shear Characteristics

    Directory of Open Access Journals (Sweden)

    Jana Zelenkova

    2017-06-01

    Full Text Available The exponential Phan–Tien and Tanner (PTT, Giesekus, Leonov, and modified extended Pom–Pom (mXPP differential constitutive models are evaluated in two ways: with regard to steady shear characteristics and with regard to large amplitude oscillatory shear characteristics of a solution of poly(ethylene oxide in dimethyl sulfoxide. Efficiency of the models with nonlinear parameters optimized with respect to steady shear measurements is evaluated by their ability to describe large amplitude oscillatory shear (LAOS characteristics. The reciprocal problem is also analyzed: The nonlinear parameters are optimized with respect to the LAOS measurements, and the models are confronted with the steady shear characteristics. In this case, optimization is based on the LAOS measurements and equal emphasis is placed on both real and imaginary parts of the stress amplitude. The results show that the chosen models are not adequately able to fit the LAOS characteristics if the optimization of nonlinear parameters is based on steady shear measurements. It follows that the optimization of nonlinear parameters is much more responsible if it is carried out with respect to the LAOS data. In this case, when the optimized parameters are used for a description of steady shear characteristics, efficiency of the individual models as documented differs.

  8. Nonlinear theory for the parametric instability with comparable electron and ion temperatures

    International Nuclear Information System (INIS)

    Oberman, C.

    1972-01-01

    The basic linear theory of the parametric instability driven by a pump E 0 sin ω 0 t oscillating near the electron plasma frequency is reviewed. An expression is derived for the temporal nonlinear development of the fluctuation spectrum of the excited waves. For plasma with comparable electron and ion temperatures nonlinear Landau damping of electron plasma waves on ions provides the dominant nonlinearity. The steady state solutions are examined both analytically and numerically in the limit when the spontaneous emission term is small. The characteristics of the plasma wave spectrum agrees well with the general features of ionospheric observations. The enhanced dissipation rate of the pump due to the presence of the fluctuations agrees with laboratory observations. (U.S.)

  9. Steady-State Diffusion of Water through Soft-Contact LensMaterials

    Energy Technology Data Exchange (ETDEWEB)

    Fornasiero, Francesco; Krull, Florian; Radke, Clayton J.; Prausnitz, JohnM.

    2005-01-31

    Water transport through soft contact lenses (SCL) is important for acceptable performance on the human eye. Chemical-potential gradient-driven diffusion rates of water through soft-contact-lens materials are measured with an evaporation-cell technique. Water is evaporated from the bottom surface of a lens membrane by impinging air at controlled flow rate and humidity. The resulting weight loss of a water reservoir covering the top surface of the contact-lens material is recorded as a function of time. New results are reported for a conventional hydrogel material (SofLens{trademark} One Day, hilafilcon A, water content at saturation W{sub 10} = 70 weight %) and a silicone hydrogel material (PureVision{trademark}, balafilcon A, W{sub 10} = 36 %), with and without surface oxygen plasma treatment. Also, previously reported data for a conventional HEMA-SCL (W{sub 10} = 38 %) hydrogel are reexamined and compared with those for SofLens{trademark} One Day and PureVision{trademark} hydrogels. Measured steady-state water fluxes are largest for SofLens{trademark} One Day, followed by PureVision{trademark} and HEMA. In some cases, the measured steady-state water fluxes increase with rising relative air humidity. This increase, due to an apparent mass-transfer resistance at the surface (trapping skinning), is associated with formation of a glassy skin at the air/membrane interface when the relative humidity is below 55-75%. Steady-state water-fluxes are interpreted through an extended Maxwell-Stefan diffusion model for a mixture of species starkly different in size. Thermodynamic nonideality is considered through Flory-Rehner polymer-solution theory. Shrinking/swelling is self-consistently modeled by conservation of the total polymer mass. Fitted Maxwell-Stefan diffusivities increase significantly with water concentration in the contact lens.

  10. Exact solutions for a system of nonlinear plasma fluid equations

    International Nuclear Information System (INIS)

    Prahovic, M.G.; Hazeltine, R.D.; Morrison, P.J.

    1991-04-01

    A method is presented for constructing exact solutions to a system of nonlinear plasma fluid equations that combines the physics of reduced magnetohydrodynamics and the electrostatic drift-wave description of the Charney-Hasegawa-Mima equation. The system has nonlinearities that take the form of Poisson brackets involving the fluid field variables. The method relies on modifying a class of simple equilibrium solutions, but no approximations are made. A distinguishing feature is that the original nonlinear problem is reduced to the solution of two linear partial differential equations, one fourth-order and the other first-order. The first-order equation has Hamiltonian characteristics and is easily integrated, supplying information about the general structure of solutions. 6 refs

  11. Computer simulation of the steam--graphite reaction under isothermal and steady-state conditions

    International Nuclear Information System (INIS)

    Joy, D.S.; Stem, S.C.

    1975-05-01

    A mathematical model was formulated to describe the isothermal, steady-state diffusion and reaction of steam in a graphite matrix. A generalized Langmuir-Hinshelwood equation is used to represent the steam-graphite reaction rate. The model also includes diffusion in the gas phase adjacent to the graphite matrix. A computer program, written to numerically integrate the resulting differential equations, is described. The coupled nonlinear differential equations in the graphite phase are solved using the IBM Continuous System Modeling Program. Classical finite difference techniques are used for the gas-phase calculations. An iterative procedure is required to couple the two sets of calculations. Several sample problems are presented to demonstrate the utility of the model. (U.S.)

  12. VARI-QUIR-3, 2-D Multigroup Steady-State Neutron Diffusion in X-Y R-Z or R-Theta Geometry

    International Nuclear Information System (INIS)

    Collier, George

    1984-01-01

    1 - Nature of physical problem solved: The steady-state, multigroup, two-dimensional neutron diffusion equations are solved in x-y, r-z, and r-theta geometry. 2 - Method of solution: A Gauss-Seidel type of solution with inner and outer iterations is used. The source is held constant during the inner iterations

  13. Nonlinear Plasma Response to Resonant Magnetic Perturbation in Rutherford Regime

    Science.gov (United States)

    Zhu, Ping; Yan, Xingting; Huang, Wenlong

    2017-10-01

    Recently a common analytic relation for both the locked mode and the nonlinear plasma response in the Rutherford regime has been developed based on the steady-state solution to the coupled dynamic system of magnetic island evolution and torque balance equations. The analytic relation predicts the threshold and the island size for the full penetration of resonant magnetic perturbation (RMP). It also rigorously proves a screening effect of the equilibrium toroidal flow. In this work, we test the theory by solving for the nonlinear plasma response to a single-helicity RMP of a circular-shaped limiter tokamak equilibrium with a constant toroidal flow, using the initial-value, full MHD simulation code NIMROD. Time evolution of the parallel flow or ``slip frequency'' profile and its asymptotic approach to steady state obtained from the NIMROD simulations qualitatively agree with the theory predictions. Further comparisons are carried out for the saturated island size, the threshold for full mode penetration, as well as the screening effects of equilibrium toroidal flow in order to understand the physics of nonlinear plasma response in the Rutherford regime. Supported by National Magnetic Confinement Fusion Science Program of China Grants 2014GB124002 and 2015GB101004, the 100 Talent Program of the Chinese Academy of Sciences, and U.S. Department of Energy Grants DE-FG02-86ER53218 and DE-FC02-08ER54975.

  14. Nonlinear instability and convection in a vertically vibrated granular bed

    NARCIS (Netherlands)

    Shukla, P.; Ansari, I.H.; van der Meer, Roger M.; Lohse, Detlef; Alam, M.

    2014-01-01

    The nonlinear instability of the density-inverted granular Leidenfrost state and the resulting convective motion in strongly shaken granular matter are analysed via a weakly nonlinear analysis of the hydrodynamic equations. The base state is assumed to be quasi-steady and the effect of harmonic

  15. Solitonlike solutions of the generalized discrete nonlinear Schrödinger equation

    DEFF Research Database (Denmark)

    Rasmussen, Kim; Henning, D.; Gabriel, H.

    1996-01-01

    We investigate the solution properties oi. a generalized discrete nonlinear Schrodinger equation describing a nonlinear lattice chain. The generalized equation interpolates between the integrable discrete Ablowitz-Ladik equation and the nonintegrable discrete Schrodinger equation. Special interes...... nonlinear Schrodinger equation. In this way eve are able to construct coherent solitonlike structures of profile determined by the map parameters.......We investigate the solution properties oi. a generalized discrete nonlinear Schrodinger equation describing a nonlinear lattice chain. The generalized equation interpolates between the integrable discrete Ablowitz-Ladik equation and the nonintegrable discrete Schrodinger equation. Special interest...

  16. Computation of Value Functions in Nonlinear Differential Games with State Constraints

    KAUST Repository

    Botkin, Nikolai; Hoffmann, Karl-Heinz; Mayer, Natalie; Turova, Varvara

    2013-01-01

    Finite-difference schemes for the computation of value functions of nonlinear differential games with non-terminal payoff functional and state constraints are proposed. The solution method is based on the fact that the value function is a

  17. Qualitative analysis and traveling wave solutions for the perturbed nonlinear Schroedinger's equation with Kerr law nonlinearity

    International Nuclear Information System (INIS)

    Zhang Zaiyun; Liu Zhenhai; Miao Xiujin; Chen Yuezhong

    2011-01-01

    In this Letter, we investigate the perturbed nonlinear Schroedinger's equation (NLSE) with Kerr law nonlinearity. All explicit expressions of the bounded traveling wave solutions for the equation are obtained by using the bifurcation method and qualitative theory of dynamical systems. These solutions contain bell-shaped solitary wave solutions, kink-shaped solitary wave solutions and Jacobi elliptic function periodic solutions. Moreover, we point out the region which these periodic wave solutions lie in. We present the relation between the bounded traveling wave solution and the energy level h. We find that these periodic wave solutions tend to the corresponding solitary wave solutions as h increases or decreases. Finally, for some special selections of the energy level h, it is shown that the exact periodic solutions evolute into solitary wave solution.

  18. Dynamics and non-equilibrium steady state in a system of coupled harmonic oscillators

    Energy Technology Data Exchange (ETDEWEB)

    Ghesquière, Anne, E-mail: Anne.Ghesquiere@nithep.ac.za; Sinayskiy, Ilya, E-mail: sinayskiy@ukzn.ac.za; Petruccione, Francesco, E-mail: petruccione@ukzn.ac.za

    2013-10-15

    A system of two coupled oscillators, each of them coupled to an independent reservoir, is analysed. The analytical solution of the non-rotating wave master equation is obtained in the high-temperature and weak coupling limits. No thermal entanglement is found in the high-temperature limit. In the weak coupling limit the system converges to an entangled non-equilibrium steady state. A critical temperature for the appearance of quantum correlations is found.

  19. Stability of racemic and chiral steady states in open and closed chemical systems

    Energy Technology Data Exchange (ETDEWEB)

    Ribo, Josep M. [Departament de Quimica Organica, Universitat de Barcelona, c. Marti i Franques 1, Barcelona (Spain); Hochberg, David [Centro de Astrobiologia (CSIC-INTA), Ctra. Ajalvir Km. 4, 28850 Torrejon de Ardoz, Madrid (Spain)], E-mail: hochbergd@inta.es

    2008-12-22

    The stability properties of models of spontaneous mirror symmetry breaking in chemistry are characterized algebraically. The models considered here all derive either from the Frank model or from autocatalysis with limited enantioselectivity. Emphasis is given to identifying the critical parameter controlling the chiral symmetry breaking transition from racemic to chiral steady-state solutions. This parameter is identified in each case, and the constraints on the chemical rate constants determined from dynamic stability are derived.

  20. Stability of racemic and chiral steady states in open and closed chemical systems

    International Nuclear Information System (INIS)

    Ribo, Josep M.; Hochberg, David

    2008-01-01

    The stability properties of models of spontaneous mirror symmetry breaking in chemistry are characterized algebraically. The models considered here all derive either from the Frank model or from autocatalysis with limited enantioselectivity. Emphasis is given to identifying the critical parameter controlling the chiral symmetry breaking transition from racemic to chiral steady-state solutions. This parameter is identified in each case, and the constraints on the chemical rate constants determined from dynamic stability are derived

  1. An implicit scheme with memory reduction technique for steady state solutions of DVBE in all flow regimes

    Science.gov (United States)

    Yang, L. M.; Shu, C.; Yang, W. M.; Wu, J.

    2018-04-01

    High consumption of memory and computational effort is the major barrier to prevent the widespread use of the discrete velocity method (DVM) in the simulation of flows in all flow regimes. To overcome this drawback, an implicit DVM with a memory reduction technique for solving a steady discrete velocity Boltzmann equation (DVBE) is presented in this work. In the method, the distribution functions in the whole discrete velocity space do not need to be stored, and they are calculated from the macroscopic flow variables. As a result, its memory requirement is in the same order as the conventional Euler/Navier-Stokes solver. In the meantime, it is more efficient than the explicit DVM for the simulation of various flows. To make the method efficient for solving flow problems in all flow regimes, a prediction step is introduced to estimate the local equilibrium state of the DVBE. In the prediction step, the distribution function at the cell interface is calculated by the local solution of DVBE. For the flow simulation, when the cell size is less than the mean free path, the prediction step has almost no effect on the solution. However, when the cell size is much larger than the mean free path, the prediction step dominates the solution so as to provide reasonable results in such a flow regime. In addition, to further improve the computational efficiency of the developed scheme in the continuum flow regime, the implicit technique is also introduced into the prediction step. Numerical results showed that the proposed implicit scheme can provide reasonable results in all flow regimes and increase significantly the computational efficiency in the continuum flow regime as compared with the existing DVM solvers.

  2. Steady state theta pinch concept for slow formation of FRC

    International Nuclear Information System (INIS)

    Hirano, K.

    1987-05-01

    A steady state high beta plasma flow through a channel along the magnetic field increasing downstream can be regarded as a ''steady state theta pinch'', because if we see the plasma riding on the flow we should observe very similar process taking place in a theta pinch. Anticipating to produce an FRC without using very high voltage technics such as the ones required in a conventional theta pinch, we have studied after the analogy a ''steady state reversed field theta pinch'' which is brought about by steady head-on collision of counter plasma streams along the channel as ejected from two identical co-axial plasma sources mounted at the both ends of the apparatus. The ideal Poisson and shock adiabatic flow models are employed for the analysis of the steady colliding process. It is demonstrated that an FRC involving large numbers of particles is produced only by the weak shock mode which is achieved in case energetic plasma flow is decelerated almost to be stagnated through Poisson adiabatic process before the streams are collided. (author)

  3. A new perspective on steady-state cosmology: from Einstein to Hoyle

    OpenAIRE

    O'Raifeartaigh, Cormac; Mitton, Simon

    2015-01-01

    We recently reported the discovery of an unpublished manuscript by Albert Einstein in which he attempted a 'steady-state' model of the universe, i.e., a cosmic model in which the expanding universe remains essentially unchanged due to a continuous formation of matter from empty space. The manuscript was apparently written in early 1931, many years before the steady-state models of Fred Hoyle, Hermann Bondi and Thomas Gold. We compare Einstein’s steady-state cosmology with that of Hoyle, Bondi...

  4. Modified harmonic balance method for the solution of nonlinear jerk equations

    Science.gov (United States)

    Rahman, M. Saifur; Hasan, A. S. M. Z.

    2018-03-01

    In this paper, a second approximate solution of nonlinear jerk equations (third order differential equation) can be obtained by using modified harmonic balance method. The method is simpler and easier to carry out the solution of nonlinear differential equations due to less number of nonlinear equations are required to solve than the classical harmonic balance method. The results obtained from this method are compared with those obtained from the other existing analytical methods that are available in the literature and the numerical method. The solution shows a good agreement with the numerical solution as well as the analytical methods of the available literature.

  5. Analytical construction of peaked solutions for the nonlinear ...

    African Journals Online (AJOL)

    These results demonstrate the existence of peaked pulses propagating through a pair plasma. The algebraic decay rate of the pulses are determined analytically, as well. The method discussed here can be applied to approximate solutions to similar nonlinear partial differential equations of nonlinear Schrödinger type.

  6. New travelling wave solutions for nonlinear stochastic evolution

    Indian Academy of Sciences (India)

    The nonlinear stochastic evolution equations have a wide range of applications in physics, chemistry, biology, economics and finance from various points of view. In this paper, the (′/)-expansion method is implemented for obtaining new travelling wave solutions of the nonlinear (2 + 1)-dimensional stochastic ...

  7. An efficient nonlinear relaxation technique for the three-dimensional, Reynolds-averaged Navier-Stokes equations

    Science.gov (United States)

    Edwards, Jack R.; Mcrae, D. S.

    1993-01-01

    An efficient implicit method for the computation of steady, three-dimensional, compressible Navier-Stokes flowfields is presented. A nonlinear iteration strategy based on planar Gauss-Seidel sweeps is used to drive the solution toward a steady state, with approximate factorization errors within a crossflow plane reduced by the application of a quasi-Newton technique. A hybrid discretization approach is employed, with flux-vector splitting utilized in the streamwise direction and central differences with artificial dissipation used for the transverse fluxes. Convergence histories and comparisons with experimental data are presented for several 3-D shock-boundary layer interactions. Both laminar and turbulent cases are considered, with turbulent closure provided by a modification of the Baldwin-Barth one-equation model. For the problems considered (175,000-325,000 mesh points), the algorithm provides steady-state convergence in 900-2000 CPU seconds on a single processor of a Cray Y-MP.

  8. Explicit analytical solution of the nonlinear Vlasov Poisson system

    International Nuclear Information System (INIS)

    Skarka, V.; Mahajan, S.M.; Fijalkow, E.

    1993-10-01

    In order to describe the time evolution of an inhomogeneous collisionless plasma the nonlinear Vlasov equation is solved perturbatively, using the subdynamics approach and the diagrammatic techniques. The solution is given in terms of a double perturbation series, one with respect to the nonlinearities and the other with respect to the interaction between particles. The infinite sum of interaction terms can be performed exactly due to the property of dynamical factorization. Following the methodology, the exact solution in each order with respect to nonlinearities is computed. For a choice of initial perturbation the first order exact solution is numerically integrated in order to find the local density excess. The approximate analytical solution is found to be in excellent agreement with exact numerical integration as well as with ab initio numerical simulations. Analytical computation gives a better insight into the problem and it has the advantage to be simpler, and also accessible in some range of parameters where it is difficult to find numerical solutions. (author). 27 refs, 12 figs

  9. Global solutions of nonlinear Schrödinger equations

    CERN Document Server

    Bourgain, J

    1999-01-01

    This volume presents recent progress in the theory of nonlinear dispersive equations, primarily the nonlinear Schrödinger (NLS) equation. The Cauchy problem for defocusing NLS with critical nonlinearity is discussed. New techniques and results are described on global existence and properties of solutions with large Cauchy data. Current research in harmonic analysis around Strichartz's inequalities and its relevance to nonlinear PDE is presented. Several topics in NLS theory on bounded domains are reviewed. Using the NLS as an example, the book offers comprehensive insight on current research r

  10. A new solution method for wheel/rail rolling contact.

    Science.gov (United States)

    Yang, Jian; Song, Hua; Fu, Lihua; Wang, Meng; Li, Wei

    2016-01-01

    To solve the problem of wheel/rail rolling contact of nonlinear steady-state curving, a three-dimensional transient finite element (FE) model is developed by the explicit software ANSYS/LS-DYNA. To improve the solving speed and efficiency, an explicit-explicit order solution method is put forward based on analysis of the features of implicit and explicit algorithm. The solution method was first applied to calculate the pre-loading of wheel/rail rolling contact with explicit algorithm, and then the results became the initial conditions in solving the dynamic process of wheel/rail rolling contact with explicit algorithm as well. Simultaneously, the common implicit-explicit order solution method is used to solve the FE model. Results show that the explicit-explicit order solution method has faster operation speed and higher efficiency than the implicit-explicit order solution method while the solution accuracy is almost the same. Hence, the explicit-explicit order solution method is more suitable for the wheel/rail rolling contact model with large scale and high nonlinearity.

  11. Transient and steady-state currents in epoxy resin

    International Nuclear Information System (INIS)

    Guillermin, Christophe; Rain, Pascal; Rowe, Stephen W

    2006-01-01

    Charging and discharging currents have been measured in a diglycidyl ether of bisphenol-A epoxy resin with and without silica fillers, below and above its glass transition temperature T g = 65 deg. C. Both transient and steady-state current densities have been analysed. The average applied fields ranged from 3 to 35 kV mm -1 with a sample thickness of 0.5 mm. Above T g , transient currents suggested a phenomenon of charge injection forming trapped space charges even at low fields. Steady-state currents confirmed that the behaviour was not Ohmic and suggested Schottky-type injection. Below T g , the current is not controlled by the metal-dielectric interface but by the conduction in the volume: the current is Ohmic at low fields and both transient and steady-state currents suggest a phenomenon of space-charge limited currents at high fields. The field threshold is similar in the filler-free and the filled resin. Values in the range 12-17 kV mm -1 have been measured

  12. Transient and steady-state currents in epoxy resin

    Energy Technology Data Exchange (ETDEWEB)

    Guillermin, Christophe [Schneider Electric Industries S.A.S., 37 quai Paul-Louis Merlin, 38050 Grenoble Cedex 9 (France); Rain, Pascal [Laboratoire d' Electrostatique et de Materiaux Dielectriques (LEMD), CNRS, 25 avenue des Martyrs, 38042 Grenoble Cedex 9 (France); Rowe, Stephen W [Schneider Electric Industries S.A.S., 37 quai Paul-Louis Merlin, 38050 Grenoble Cedex 9 (France)

    2006-02-07

    Charging and discharging currents have been measured in a diglycidyl ether of bisphenol-A epoxy resin with and without silica fillers, below and above its glass transition temperature T{sub g} = 65 deg. C. Both transient and steady-state current densities have been analysed. The average applied fields ranged from 3 to 35 kV mm{sup -1} with a sample thickness of 0.5 mm. Above T{sub g}, transient currents suggested a phenomenon of charge injection forming trapped space charges even at low fields. Steady-state currents confirmed that the behaviour was not Ohmic and suggested Schottky-type injection. Below T{sub g}, the current is not controlled by the metal-dielectric interface but by the conduction in the volume: the current is Ohmic at low fields and both transient and steady-state currents suggest a phenomenon of space-charge limited currents at high fields. The field threshold is similar in the filler-free and the filled resin. Values in the range 12-17 kV mm{sup -1} have been measured.

  13. Multiple normalized solutions for a planar gauged nonlinear Schrödinger equation

    Science.gov (United States)

    Luo, Xiao

    2018-06-01

    We study the existence, multiplicity, quantitative property and asymptotic behavior of normalized solutions for a gauged nonlinear Schrödinger equation arising from the Chern-Simons theory Δ u + ω u +|x|^2u+ λ ( {{h^2}(| x | )}/{{{| x | ^2}}} + \\int \\limits _{| x | }^{ + ∞} {{h(s)}/s} {u^2}(s)ds) u = {| u | ^{p - 2}}u,\\quad x\\in R^2, where ω \\in R, λ >0, p>4 and h(s) = 1/2\\int \\limits _0^s {r{u^2}(r)dr} . Combining constraint minimization method and minimax principle, we prove that the problem possesses at least two normalized solutions: One is a ground state and the other is an excited state. Furthermore, the asymptotic behavior and quantitative property of the ground state are analyzed.

  14. Statics and rotational dynamics of composite beams

    CERN Document Server

    Ghorashi, Mehrdaad

    2016-01-01

    This book presents a comprehensive study of the nonlinear statics and dynamics of composite beams and consists of solutions with and without active elements embedded in the beams. The static solution provides the initial conditions for the dynamic analysis. The dynamic problems considered include the analyses of clamped (hingeless) and articulated (hinged) accelerating rotating beams. Two independent numerical solutions for the steady state and the transient responses are presented. The author illustrates that the transient solution of the nonlinear formulation of accelerating rotating beam converges to the steady state solution obtained by the shooting method. Other key areas considered include calculation of the effect of perturbing the steady state solution, coupled nonlinear flap-lag dynamics of a rotating articulated beam with hinge offset and aerodynamic damping, and static and dynamic responses of nonlinear composite beams with embedded anisotropic piezo-composite actuators. The book is intended as a t...

  15. Large-time asymptotic behaviour of solutions of non-linear Sobolev-type equations

    International Nuclear Information System (INIS)

    Kaikina, Elena I; Naumkin, Pavel I; Shishmarev, Il'ya A

    2009-01-01

    The large-time asymptotic behaviour of solutions of the Cauchy problem is investigated for a non-linear Sobolev-type equation with dissipation. For small initial data the approach taken is based on a detailed analysis of the Green's function of the linear problem and the use of the contraction mapping method. The case of large initial data is also closely considered. In the supercritical case the asymptotic formulae are quasi-linear. The asymptotic behaviour of solutions of a non-linear Sobolev-type equation with a critical non-linearity of the non-convective kind differs by a logarithmic correction term from the behaviour of solutions of the corresponding linear equation. For a critical convective non-linearity, as well as for a subcritical non-convective non-linearity it is proved that the leading term of the asymptotic expression for large times is a self-similar solution. For Sobolev equations with convective non-linearity the asymptotic behaviour of solutions in the subcritical case is the product of a rarefaction wave and a shock wave. Bibliography: 84 titles.

  16. Finding all solutions of nonlinear equations using the dual simplex method

    Science.gov (United States)

    Yamamura, Kiyotaka; Fujioka, Tsuyoshi

    2003-03-01

    Recently, an efficient algorithm has been proposed for finding all solutions of systems of nonlinear equations using linear programming. This algorithm is based on a simple test (termed the LP test) for nonexistence of a solution to a system of nonlinear equations using the dual simplex method. In this letter, an improved version of the LP test algorithm is proposed. By numerical examples, it is shown that the proposed algorithm could find all solutions of a system of 300 nonlinear equations in practical computation time.

  17. Positive Solutions for Coupled Nonlinear Fractional Differential Equations

    Directory of Open Access Journals (Sweden)

    Wenning Liu

    2014-01-01

    Full Text Available We consider the existence of positive solutions for a coupled system of nonlinear fractional differential equations with integral boundary values. Assume the nonlinear term is superlinear in one equation and sublinear in the other equation. By constructing two cones K1, K2 and computing the fixed point index in product cone K1×K2, we obtain that the system has a pair of positive solutions. It is remarkable that it is established on the Cartesian product of two cones, in which the feature of two equations can be opposite.

  18. Periodic and solitary wave solutions of cubic–quintic nonlinear ...

    Indian Academy of Sciences (India)

    Hence, most of the real nonlinear physical equations possess variable ... evolution of the system with time and second term represents the convective flux term. The ... Travelling wave solutions of nonlinear reaction-diffusion equations are.

  19. Stabilization of the potential multi-steady-state absolute instabilities in a gyrotron traveling-wave amplifier

    International Nuclear Information System (INIS)

    Du Chaohai; Liu Pukun

    2009-01-01

    The problem of spurious oscillations induced by absolute instabilities is the most challenging one that hinders the development of the millimeter-wave gyrotron traveling-wave amplifiers (gyro-TWTs). A spurious oscillation exists as a high order axial mode (HOAM) in the interaction circuit. This paper is devoted to demonstrating the complicated steady states of these HOAMs and exploring corresponding techniques to stabilize these potential multi-steady-state absolute instabilities. The stability-oriented design principle is conveyed in a start-to-end design flow of a Ka-band TE 11 mode gyro-TWT. Strong magnetic tapering near the downstream port, which is capable of cutting short the effective interaction circuit of a spurious oscillation and simultaneously boosting the amplification performance, is for the first time proposed to further improve the system stability. It is also found that an ideal prebunched electron beam in the linear stage is the necessary condition to efficient amplification in the nonlinear stage, suggesting that it is feasible to design a stable prebunching stage to replace the distributed-loss-loaded linear stage. The stability-oriented design principle provides more explicit reference for future design of a zero-drive stable gyro-TWT.

  20. Approximate Solution of Nonlinear Klein-Gordon Equation Using Sobolev Gradients

    Directory of Open Access Journals (Sweden)

    Nauman Raza

    2016-01-01

    Full Text Available The nonlinear Klein-Gordon equation (KGE models many nonlinear phenomena. In this paper, we propose a scheme for numerical approximation of solutions of the one-dimensional nonlinear KGE. A common approach to find a solution of a nonlinear system is to first linearize the equations by successive substitution or the Newton iteration method and then solve a linear least squares problem. Here, we show that it can be advantageous to form a sum of squared residuals of the nonlinear problem and then find a zero of the gradient. Our scheme is based on the Sobolev gradient method for solving a nonlinear least square problem directly. The numerical results are compared with Lattice Boltzmann Method (LBM. The L2, L∞, and Root-Mean-Square (RMS values indicate better accuracy of the proposed method with less computational effort.

  1. Impact of quadratic non-linearity on the dynamics of periodic solutions of a wave equation

    International Nuclear Information System (INIS)

    Kolesov, Andrei Yu; Rozov, Nikolai Kh

    2002-01-01

    For the non-linear telegraph equation with homogeneous Dirichlet or Neumann conditions at the end-points of a finite interval the question of the existence and the stability of time-periodic solutions bifurcating from the zero equilibrium state is considered. The dynamics of these solutions under a change of the diffusion coefficient (that is, the coefficient of the second derivative with respect to the space variable) is investigated. For the Dirichlet boundary conditions it is shown that this dynamics substantially depends on the presence - or the absence - of quadratic terms in the non-linearity. More precisely, it is shown that a quadratic non-linearity results in the occurrence, under an unbounded decrease of diffusion, of an infinite sequence of bifurcations of each periodic solution. En route, the related issue of the limits of applicability of Yu.S. Kolesov's method of quasinormal forms to the construction of self-oscillations in singularly perturbed hyperbolic boundary value problems is studied

  2. Steady state flow evaluations for passive auxiliary feedwater system of APR

    International Nuclear Information System (INIS)

    Park, Jongha; Kim, Jaeyul; Seong, Hoje; Kang, Kyoungho

    2012-01-01

    This paper briefly introduces a methodology to evaluate steady state flow of APR+ Passive Auxiliary Feedwater System (PAFS). The PAFS is being developed as a safety grade passive system to completely replace the existing active Auxiliary Feedwater System (AFWS). Natural circulation cooling can be generally classified into the single-phase, two-phase, and boiling-condensation modes. The PAF is designed to be operated in a boiling-condensation natural circulation mode. The steady-state flow rate should be equal to the steady-state boiling/condensation rate determined by the steady-state energy and momentum balances in the PAFS. The determined steady-state flow rate can be used in the design optimization for the natural circulation loop of the PAFS through the steady-state momentum balance. Since the retarding force, which is to be balanced by the driving force in the natural circulation system design depends on the reliable evaluation of the success of a natural circulation system design depends on the reliable evaluation of the pressure loss coefficients. In PAFS, the core decay heat is released by natural circulation flow between the S G secondary side and the Passive Condensation Heat Exchanger (PCHX) that is immersed in the Passive Condensation Cooling Tank (PCCT). The PCCT is located on the top of Auxiliary building The driving force is determined by the difference between the S/G (heat Source) secondary water level and condensation liquid (heat sink) level. It will overcome retarding force at flowrate in the system, which is determined by vaporization and condensation of the steam which is generated at the S/G by the latent heat in system. In this study, the theoretical method to estimate the steady state flow rate in boiling-condensation natural circulation system is developed and compared with test results

  3. SYNTH-C, Steady-State and Time-Dependent 3-D Neutron Diffusion with Thermohydraulic Feedback

    Energy Technology Data Exchange (ETDEWEB)

    Brega, E [ENEL-CRTN, Bastioni di Porta Volta 10, Milan (Italy); Salina, E [A.R.S. Spa, Viale Maino 35, Milan (Italy)

    1980-04-01

    1 - Description of problem or function: SYNTH-C-STEADY and SYNTH-C- TRANS solve respectively the steady-state and time-dependent few- group neutron diffusion equations in three dimensions x,y,z in the presence of fuel temperature and thermal-hydraulic feedback. The neutron diffusion and delayed precursor equations are approximated by a space-time (z,t) synthesis method with axially discontinuous trial functions. Three thermal-hydraulic and fuel heat transfer models are available viz. COBRA-3C/MIT model, lumped parameter (WIGL) model and adiabatic fuel heat-up model. 2 - Method of solution: The steady-state and time-dependent synthesis equations are solved respectively by the Wielandt's power method and by the theta-difference method (in time), both coupled with a block factorization technique and double precision arithmetic. The thermal-hydraulic model equations are solved by fully implicit finite differences (WIGL) or explicit-implicit difference techniques with iterations (COBRA-EC/MIT). 3 - Restrictions on the complexity of the problem: Except for the few- group limitation, the programs have no other fixed limitation so the ability to run a problem depends only on the available computer storage.

  4. Einstein's steady-state theory: an abandoned model of the cosmos

    Science.gov (United States)

    O'Raifeartaigh, Cormac; McCann, Brendan; Nahm, Werner; Mitton, Simon

    2014-09-01

    We present a translation and analysis of an unpublished manuscript by Albert Einstein in which he attempted to construct a `steady-state' model of the universe. The manuscript, which appears to have been written in early 1931, demonstrates that Einstein once explored a cosmic model in which the mean density of matter in an expanding universe is maintained constant by the continuous formation of matter from empty space. This model is very different to previously known Einsteinian models of the cosmos (both static and dynamic) but anticipates the later steady-state cosmology of Hoyle, Bondi and Gold in some ways. We find that Einstein's steady-state model contains a fundamental flaw and suggest that it was abandoned for this reason. We also suggest that he declined to explore a more sophisticated version because he found such theories rather contrived. The manuscript is of historical interest because it reveals that Einstein debated between steady-state and evolving models of the cosmos decades before a similar debate took place in the cosmological community.

  5. Numerical solution of two-dimensional non-linear partial differential ...

    African Journals Online (AJOL)

    linear partial differential equations using a hybrid method. The solution technique involves discritizing the non-linear system of partial differential equations (PDEs) to obtain a corresponding nonlinear system of algebraic difference equations to be ...

  6. Exact travelling wave solutions for some important nonlinear

    Indian Academy of Sciences (India)

    The two-dimensional nonlinear physical models and coupled nonlinear systems such as Maccari equations, Higgs equations and Schrödinger–KdV equations have been widely applied in many branches of physics. So, finding exact travelling wave solutions of such equations are very helpful in the theories and numerical ...

  7. The evolution of an unsteady translating nonlinear rossby-wave critical layer

    Science.gov (United States)

    Haynes, Peter H.; Cowley, Stephen J.

    When a monochromatic Rossby wave is forced on a flow which is slowly varying in time, the location of the critical line, where the phase speed of the wave is equal to that of the flow, also slowly changes. It is shown that this translation can play an important role in the vorticity balance near the critical line. The behavior of the translating critical layer is analyzed for various values of y, a parameter which measures the relative importance of nonlinear advection and translation. First, the vorticity equation in the critical layer is solved numerically in an important special case, where the velocity field in the critical layer is independent of the vorticity distribution and constant in time. The solutions reveal a number of new aspects of the behavior which are introduced by the translation, including the formation of a wake behind the critical layer, and the possibility of "trapping" of fluid particles in the critical layer if y exceeds a threshold value. Viewed in a frame of reference moving with the critical line the vorticity distribution may tend to a steady state, except in a "vorticity front" far downstream in the wake. If streamlines in the critical layer are open this steady state may be a predominantly inviscid one; if they are closed a steady state is possible only with non-zero dissipation. For both the unsteady and steady flows the translation allows the "logarithmic phase jump" across the critical layer, 4, to be non-zero and negative. Hence, even when the viscosity is vanishingly small, the critical layer can act as a strong "absorber" of Eliassen-Palm wave activity. Second, steady-state solutions are obtained numerically for a case when the velocity field in the critical layer is not independent of the vorticity distribution there. The interaction restricts the formation of closed streamlines, and an asymptotic open-streamline solution for large y can be found. The critical layer again acts an absorber of wave activity, but with decreasing e

  8. A solution to nonlinearity problems

    International Nuclear Information System (INIS)

    Neuffer, D.V.

    1989-01-01

    New methods of correcting dynamic nonlinearities resulting from the multipole content of a synchrotron or transport line are presented. In a simplest form, correction elements are places at the center (C) of the accelerator half-cells as well as near the focusing (F) and defocusing (D) quadrupoles. In a first approximation, the corrector strengths follow Simpson's Rule, forming an accurate quasi-local canceling approximation to the nonlinearity. The F, C, and D correctors may also be used to obtain precise control of the horizontal, coupled, and vertical motion. Correction by three or more orders of magnitude can be obtained, and simple solutions to a fundamental problem in beam transport have been obtained. 13 refs., 1 fig., 1 tab

  9. Localized solutions of non-linear Klein--Gordon equations

    International Nuclear Information System (INIS)

    Werle, J.

    1977-05-01

    Nondissipative, stationary solutions for a class of nonlinear Klein-Gordon equations for a scalar field were found explicitly. Since the field is different from zero only inside a sphere of definite radius, the solutions are called quantum droplets

  10. Simulations of KSTAR high performance steady state operation scenarios

    International Nuclear Information System (INIS)

    Na, Yong-Su; Kessel, C.E.; Park, J.M.; Yi, Sumin; Kim, J.Y.; Becoulet, A.; Sips, A.C.C.

    2009-01-01

    We report the results of predictive modelling of high performance steady state operation scenarios in KSTAR. Firstly, the capabilities of steady state operation are investigated with time-dependent simulations using a free-boundary plasma equilibrium evolution code coupled with transport calculations. Secondly, the reproducibility of high performance steady state operation scenarios developed in the DIII-D tokamak, of similar size to that of KSTAR, is investigated using the experimental data taken from DIII-D. Finally, the capability of ITER-relevant steady state operation is investigated in KSTAR. It is found that KSTAR is able to establish high performance steady state operation scenarios; β N above 3, H 98 (y, 2) up to 2.0, f BS up to 0.76 and f NI equals 1.0. In this work, a realistic density profile is newly introduced for predictive simulations by employing the scaling law of a density peaking factor. The influence of the current ramp-up scenario and the transport model is discussed with respect to the fusion performance and non-inductive current drive fraction in the transport simulations. As observed in the experiments, both the heating and the plasma current waveforms in the current ramp-up phase produce a strong effect on the q-profile, the fusion performance and also on the non-inductive current drive fraction in the current flattop phase. A criterion in terms of q min is found to establish ITER-relevant steady state operation scenarios. This will provide a guideline for designing the current ramp-up phase in KSTAR. It is observed that the transport model also affects the predictive values of fusion performance as well as the non-inductive current drive fraction. The Weiland transport model predicts the highest fusion performance as well as non-inductive current drive fraction in KSTAR. In contrast, the GLF23 model exhibits the lowest ones. ITER-relevant advanced scenarios cannot be obtained with the GLF23 model in the conditions given in this work

  11. Computation of Value Functions in Nonlinear Differential Games with State Constraints

    KAUST Repository

    Botkin, Nikolai

    2013-01-01

    Finite-difference schemes for the computation of value functions of nonlinear differential games with non-terminal payoff functional and state constraints are proposed. The solution method is based on the fact that the value function is a generalized viscosity solution of the corresponding Hamilton-Jacobi-Bellman-Isaacs equation. Such a viscosity solution is defined as a function satisfying differential inequalities introduced by M. G. Crandall and P. L. Lions. The difference with the classical case is that these inequalities hold on an unknown in advance subset of the state space. The convergence rate of the numerical schemes is given. Numerical solution to a non-trivial three-dimensional example is presented. © 2013 IFIP International Federation for Information Processing.

  12. Superconducting magnets and cryogenics for the steady state superconducting tokamak SST-1

    International Nuclear Information System (INIS)

    Saxena, Y.C.

    2000-01-01

    SST-1 is a steady state superconducting tokamak for studying the physics of the plasma processes in tokamak under steady state conditions and to learn technologies related to the steady state operation of the tokamak. SST-1 will have superconducting magnets made from NbTi based conductors operating at 4.5 K temperature. The design of the superconducting magnets and the cryogenic system of SST-1 tokamak are described. (author)

  13. Single-ion nonlinear mechanical oscillator

    International Nuclear Information System (INIS)

    Akerman, N.; Kotler, S.; Glickman, Y.; Dallal, Y.; Keselman, A.; Ozeri, R.

    2010-01-01

    We study the steady-state motion of a single trapped ion oscillator driven to the nonlinear regime. Damping is achieved via Doppler laser cooling. The ion motion is found to be well described by the Duffing oscillator model with an additional nonlinear damping term. We demonstrate here the unique ability of tuning both the linear as well as the nonlinear damping coefficients by controlling the laser-cooling parameters. Our observations pave the way for the investigation of nonlinear dynamics on the quantum-to-classical interface as well as mechanical noise squeezing in laser-cooling dynamics.

  14. Steady-state models in electrophoresis: from isotachophoresis to capillary zone electrophoresis

    NARCIS (Netherlands)

    Beckers, J.L.

    1995-01-01

    Although all electrophoretic techniques are closely allied and controlled by the same rules, we often distinguish between steady-state and dynamic models in the modeling of electrophoretic processes, whereby steady-state models are applied for isotachophoresis (ITP) and dynamic models are applied

  15. New travelling wave solutions for nonlinear stochastic evolution ...

    Indian Academy of Sciences (India)

    expansion method to look for travelling wave solutions of nonlinear partial differential equations. It is interesting to mention that, in this method the sign of the parameters can be used to judge the numbers and types of travelling wave solutions.

  16. Exact solutions for the cubic-quintic nonlinear Schroedinger equation

    International Nuclear Information System (INIS)

    Zhu Jiamin; Ma Zhengyi

    2007-01-01

    In this paper, the cubic-quintic nonlinear Schroedinger equation is solved through the extended elliptic sub-equation method. As a consequence, many types of exact travelling wave solutions are obtained which including bell and kink profile solitary wave solutions, triangular periodic wave solutions and singular solutions

  17. X-Ray Spectral Analysis of the Steady States of GRS1915+105

    Science.gov (United States)

    Peris, Charith S.; Remillard, Ronald A.; Steiner, James F.; Vrtilek, Saeqa D.; Varnière, Peggy; Rodriguez, Jerome; Pooley, Guy

    2016-05-01

    We report on the X-ray spectral behavior within the steady states of GRS1915+105. Our work is based on the full data set of the source obtained using the Proportional Counter Array (PCA) on the Rossi X-ray Timing Explorer (RXTE) and 15 GHz radio data obtained using the Ryle Telescope. The steady observations within the X-ray data set naturally separated into two regions in the color-color diagram and we refer to these regions as steady-soft and steady-hard. GRS1915+105 displays significant curvature in the coronal component in both the soft and hard data within the RXTE/PCA bandpass. A majority of the steady-soft observations displays a roughly constant inner disk radius ({R}{{in}}), while the steady-hard observations display an evolving disk truncation which is correlated to the mass accretion rate through the disk. The disk flux and coronal flux are strongly correlated in steady-hard observations and very weakly correlated in the steady-soft observations. Within the steady-hard observations, we observe two particular circumstances when there are correlations between the coronal X-ray flux and the radio flux with log slopes η ˜ 0.68+/- 0.35 and η ˜ 1.12+/- 0.13. They are consistent with the upper and lower tracks of Gallo et al. (2012), respectively. A comparison of the model parameters to the state definitions shows that almost all of the steady-soft observations match the criteria of either a thermal or steep power-law state, while a large portion of the steady-hard observations match the hard-state criteria when the disk fraction constraint is neglected.

  18. Chirped self-similar solutions of a generalized nonlinear Schroedinger equation

    Energy Technology Data Exchange (ETDEWEB)

    Fei Jin-Xi [Lishui Univ., Zhejiang (China). College of Mathematics and Physics; Zheng Chun-Long [Shaoguan Univ., Guangdong (China). School of Physics and Electromechanical Engineering; Shanghai Univ. (China). Shanghai Inst. of Applied Mathematics and Mechanics

    2011-01-15

    An improved homogeneous balance principle and an F-expansion technique are used to construct exact chirped self-similar solutions to the generalized nonlinear Schroedinger equation with distributed dispersion, nonlinearity, and gain coefficients. Such solutions exist under certain conditions and impose constraints on the functions describing dispersion, nonlinearity, and distributed gain function. The results show that the chirp function is related only to the dispersion coefficient, however, it affects all of the system parameters, which influence the form of the wave amplitude. As few characteristic examples and some simple chirped self-similar waves are presented. (orig.)

  19. Fuzzy combination of fuzzy and switching state-feedback controllers for nonlinear systems subject to parameter uncertainties.

    Science.gov (United States)

    Lam, H K; Leung, Frank H F

    2005-04-01

    This paper presents a fuzzy controller, which involves a fuzzy combination of local fuzzy and global switching state-feedback controllers, for nonlinear systems subject to parameter uncertainties with known bounds. The nonlinear system is represented by a fuzzy combined Takagi-Sugeno-Kang model, which is a fuzzy combination of the global and local fuzzy plant models. By combining the local fuzzy and global switching state-feedback controllers using fuzzy logic techniques, the advantages of both controllers can be retained and the undesirable chattering effect introduced by the global switching state-feedback controller can be eliminated. The steady-state error introduced by the global switching state-feedback controller when a saturation function is used can also be removed. Stability conditions, which are related to the system matrices of the local and global closed-loop systems, are derived to guarantee the closed-loop system stability. An application example will be given to demonstrate the merits of the proposed approach.

  20. On nonlinear differential equation with exact solutions having various pole orders

    International Nuclear Information System (INIS)

    Kudryashov, N.A.

    2015-01-01

    We consider a nonlinear ordinary differential equation having solutions with various movable pole order on the complex plane. We show that the pole order of exact solution is determined by values of parameters of the equation. Exact solutions in the form of the solitary waves for the second order nonlinear differential equation are found taking into account the method of the logistic function. Exact solutions of differential equations are discussed and analyzed

  1. New Exact Travelling Wave and Periodic Solutions of Discrete Nonlinear Schroedinger Equation

    International Nuclear Information System (INIS)

    Yang Qin; Dai Chaoqing; Zhang Jiefang

    2005-01-01

    Some new exact travelling wave and period solutions of discrete nonlinear Schroedinger equation are found by using a hyperbolic tangent function approach, which was usually presented to find exact travelling wave solutions of certain nonlinear partial differential models. Now we can further extend the new algorithm to other nonlinear differential-different models.

  2. Diffusion in coronas around clinopyroxene: modelling with local equilibrium and steady state, and a non-steady-state modification to account for zoned actinolite-hornblende

    Science.gov (United States)

    Ashworth, J. R.; Birdi, J. J.; Emmett, T. F.

    1992-01-01

    Retrograde coronas of Caledonian age, between clinopyroxene and plagioclase in the Jotun Nappe Complex, Norway, illustrate the effects of diffusion kinetics on mineral distributions among layers and on the compositions of hornblende-actinolite. One corona type comprises a symplectite of epidote + quartz adjacent to plagioclase, and a less well-organized intergrowth of amphibole + quartz replacing clinopyroxene. The observed mineral proportions imply an open-system reaction, but the similarity of Al/Si ratios in reactant plagioclase and product symplectite indicates approximate conservation of Al2O3 and SiO2. The largest inferred open-system flux is a loss of CaO, mostly derived from consumption of clinopyroxene. The approximate layer structure, Pl|Ep + Qtz|Hbl + Qtz|Act±Hbl + Qtz|Cpx, is modelled using the theory of steady-state diffusion-controlled growth with local equilibrium. To obtain a solution, it is necessary to use a reactant plagioclase composition which takes into account aluminous (epidote) inclusions. The results indicate that, in terms of Onsager diffusion coefficients L ii , Ca is more mobile than AL ( L CaCa/ L AlAl≳3.) (where ≳ means greater than or approximately equal to). This behaviour of Ca is comparable with that of Mg in previously studied coronas around olivine. Si is non-diffusing in the present modelling, because of silica saturation. Oxidation of some Fe2+ to Fe3+ occurs within the corona. Mg diffuses towards its source (clinopyroxene) to maintain local equilibrium. Other coronas consist of two layers, hornblende adjacent to plagioclase and zoned amphibole + quartz adjacent to clinopyroxene. In the zoned layer, actinolitic hornblende forms relict patches, separated from quartz blebs by more aluminous hornblende. A preliminary steady-state, local-equilibrium model of grain-boundary diffusion explains the formation of low-Al and high-Al layers as due to Al immobility. Zoning and replacement are qualitatively explained in terms of

  3. Physical design of MW-class steady-state spherical tokamak, QUEST

    International Nuclear Information System (INIS)

    Hanada, K.; Sato, K.N.; Zushi, H.; Nakamura, K.; Sakamoto, M.; Idei, H.; Hasegawa, M.; Kawasaki, S.; Nakashima, H.; Higashijima, A.; Higashizono, Y.; Yoshida, N.; Takase, Y.; Ejiri, A.; Ogawa, Y.; Ono, Y.; Yoshida, Z.; Mitarai, O.; Maekawa, T.; Kishimoto, Y.; Ishiguro, M.; Yoshinaga, T.; Igami, H.; Hirooka, Y.; Komori, A.; Motojima, O.; Sudo, S.; Yamada, H.; Ando, A.; Asakura, Nobuyuki; Matsukawa, Makoto; Ishida, A.; Ohno, N.; Peng, M.

    2008-10-01

    QUEST (R=0.68 m, a=0.4 m) focuses on the steady state operation of the spherical tokamak (ST) by controlled PWI and electron Bernstain wave (EBW) current drive (CD). The QUEST project will be developed along two phases, phase I: steady state operation with plasma current, I p =20-30 kA on open divertor configuration and phase II: steady state operation with I p = 100 kA and β of 10% in short pulse on closed divertor configuration. Feasibility of the missions on QUEST was investigated and the suitable machine size of QUEST was decided based on the physical view of plasma parameters. Electron Bernstein wave (EBW) current drive are planned to establish the maintenance of plasma current in steady state. Mode conversion efficiency to EBW was calculated and the conversion of 95% will be expected. A new type antenna for QUEST has been fabricated to excite EBW effectively. The situation of heat and particle handling is challenging, and W and high temperature wall is adopted. The start-up scenario of plasma current was investigated based on the driven current by energetic electron and the most favorable magnetic configuration for start-up is proposed. (author)

  4. Staggered and short-period solutions of the saturable discrete nonlinear Schrodinger equation

    DEFF Research Database (Denmark)

    Khare, A.; Rasmussen, K.O.; Samuelsen, Mogens Rugholm

    2009-01-01

    We point out that the nonlinear Schrodinger lattice with a saturable nonlinearity also admits staggered periodic aswell as localized pulse-like solutions. Further, the same model also admits solutions with a short period. We examine the stability of these solutions and find that the staggered as ...

  5. Stochastic theory of nonequilibrium steady states. Part II: Applications in chemical biophysics

    International Nuclear Information System (INIS)

    Ge Hao; Qian Min; Qian Hong

    2012-01-01

    The mathematical theory of nonequilibrium steady state (NESS) has a natural application in open biochemical systems which have sustained source(s) and sink(s) in terms of a difference in their chemical potentials. After a brief introduction in Section , in Part II of this review, we present the widely studied biochemical enzyme kinetics, the workhorse of biochemical dynamic modeling, in terms of the theory of NESS (Section ). We then show that several phenomena in enzyme kinetics, including a newly discovered activation–inhibition switching (Section ) and the well-known non-Michaelis–Menten-cooperativity (Section ) and kinetic proofreading (Section ), are all consequences of the NESS of driven biochemical systems with associated cycle fluxes. Section is focused on nonlinear and nonequilibrium systems of biochemical reactions. We use the phosphorylation–dephosphorylation cycle (PdPC), one of the most important biochemical signaling networks, as an example (Section ). It starts with a brief introduction of the Delbrück–Gillespie process approach to mesoscopic biochemical kinetics (Sections ). We shall discuss the zeroth-order ultrasensitivity of PdPC in terms of a new concept — the temporal cooperativity (Sections ), as well as PdPC with feedback which leads to biochemical nonlinear bistability (Section ). Also, both are nonequilibrium phenomena. PdPC with a nonlinear feedback is kinetically isomorphic to a self-regulating gene expression network, hence the theory of NESS discussed here could have wide applications to many other biochemical systems.

  6. Stability of Carotid Artery Under Steady-State and Pulsatile Blood Flow: A Fluid–Structure Interaction Study

    Science.gov (United States)

    Saeid Khalafvand, Seyed; Han, Hai-Chao

    2015-01-01

    It has been shown that arteries may buckle into tortuous shapes under lumen pressure, which in turn could alter blood flow. However, the mechanisms of artery instability under pulsatile flow have not been fully understood. The objective of this study was to simulate the buckling and post-buckling behaviors of the carotid artery under pulsatile flow using a fully coupled fluid–structure interaction (FSI) method. The artery wall was modeled as a nonlinear material with a two-fiber strain-energy function. FSI simulations were performed under steady-state flow and pulsatile flow conditions with a prescribed flow velocity profile at the inlet and different pressures at the outlet to determine the critical buckling pressure. Simulations were performed for normal (160 ml/min) and high (350 ml/min) flow rates and normal (1.5) and reduced (1.3) axial stretch ratios to determine the effects of flow rate and axial tension on stability. The results showed that an artery buckled when the lumen pressure exceeded a critical value. The critical mean buckling pressure at pulsatile flow was 17–23% smaller than at steady-state flow. For both steady-state and pulsatile flow, the high flow rate had very little effect (<5%) on the critical buckling pressure. The fluid and wall stresses were drastically altered at the location with maximum deflection. The maximum lumen shear stress occurred at the inner side of the bend and maximum tensile wall stresses occurred at the outer side. These findings improve our understanding of artery instability in vivo. PMID:25761257

  7. Stability of carotid artery under steady-state and pulsatile blood flow: a fluid-structure interaction study.

    Science.gov (United States)

    Saeid Khalafvand, Seyed; Han, Hai-Chao

    2015-06-01

    It has been shown that arteries may buckle into tortuous shapes under lumen pressure, which in turn could alter blood flow. However, the mechanisms of artery instability under pulsatile flow have not been fully understood. The objective of this study was to simulate the buckling and post-buckling behaviors of the carotid artery under pulsatile flow using a fully coupled fluid-structure interaction (FSI) method. The artery wall was modeled as a nonlinear material with a two-fiber strain-energy function. FSI simulations were performed under steady-state flow and pulsatile flow conditions with a prescribed flow velocity profile at the inlet and different pressures at the outlet to determine the critical buckling pressure. Simulations were performed for normal (160 ml/min) and high (350 ml/min) flow rates and normal (1.5) and reduced (1.3) axial stretch ratios to determine the effects of flow rate and axial tension on stability. The results showed that an artery buckled when the lumen pressure exceeded a critical value. The critical mean buckling pressure at pulsatile flow was 17-23% smaller than at steady-state flow. For both steady-state and pulsatile flow, the high flow rate had very little effect (<5%) on the critical buckling pressure. The fluid and wall stresses were drastically altered at the location with maximum deflection. The maximum lumen shear stress occurred at the inner side of the bend and maximum tensile wall stresses occurred at the outer side. These findings improve our understanding of artery instability in vivo.

  8. New Methods for Processing and Quantifying VO2 Kinetics to Steady State: VO2 Onset Kinetics

    Directory of Open Access Journals (Sweden)

    Craig R. McNulty

    2017-09-01

    Full Text Available Current methods of oxygen uptake (VO2 kinetics data handling may be too simplistic for the complex physiology involved in the underlying physiological processes. Therefore, the aim of this study was to quantify the VO2 kinetics to steady state across the full range of sub-ventilatory threshold work rates, with a particular focus on the VO2 onset kinetics. Ten healthy, moderately trained males participated in five bouts of cycling. Each bout involved 10 min at a percentage of the subject's ventilation threshold (30, 45, 60, 75, 90% from unloaded cycling. The VO2 kinetics was quantified using the conventional mono-exponential time constant (tau, τ, as well as the new methods for VO2 onset kinetics. Compared to linear modeling, non-linear modeling caused a deterioration of goodness of fit (main effect, p < 0.001 across all exercise intensities. Remainder kinetics were also improved using a modified application of the mono-exponential model (main effect, p < 0.001. Interestingly, the slope from the linear regression of the onset kinetics data is similar across all subjects and absolute exercise intensities, and thereby independent of subject fitness and τ. This could indicate that there are no functional limitations between subjects during this onset phase, with limitations occurring for the latter transition to steady state. Finally, the continuing use of mono-exponential modeling could mask important underlying physiology of more instantaneous VO2 responses to steady state. Consequently, further research should be conducted on this new approach to VO2 onset kinetics.

  9. Small-angle scattering at a pulsed neutron source: comparison with a steady-state reactor

    Energy Technology Data Exchange (ETDEWEB)

    Borso, C S; Carpenter, J M; Williamson, F S; Holmblad, G L; Mueller, M H; Faber, J Jr; Epperson, J E; Danyluk, S S [Argonne National Lab., IL (USA)

    1982-08-01

    A time-of-flight small-angle diffractometer employing seven tapered collimator elements and a two-dimensional gas proportional counter was successfully utilized to collect small-angle scattering data from a solution sample of the lipid salt cetylpyridinium chloride, C/sub 21/H/sub 38/N/sup +/.Cl/sup -/, at the Argonne National Laboratory prototype pulsed spallation neutron source, ZING-P'. Comparison of the small-angle scattering observed from the same compound at the University of Missouri Research Reactor corroborated the ZING-P' results. The results are used to compare the neutron flux available from the ZING-P' source relative to the well characterized University of Missouri source. Calculations based on experimentally determined parameters indicated the time-averaged rate of detected neutrons at the ZING-P' pulsed spallation source to have been at least 33% higher than the steady-state count rate from the same sample. Differences between time-of-flight techniques and conventional steady-state techniques are discussed.

  10. Analysis of steady-state creep of Fe-Mo alloys from the viewpoint of recovery

    International Nuclear Information System (INIS)

    Maruyama, K.; Karashima, S.; Oikawa, H.

    1979-01-01

    A theoretical equation to d evaluate the steady-state creep-rates, d epsilon/dtsub(s), based on a recovery creep model is derived: epsilonsub(s)/dt proportional to r/sigma 2 sub(a) x lambda 2 , where r is the recovery rate, which can be determined from results of stress-reduction tests, deltasub(a) the applied stress, and lambda the dislocation link-length. Two cases of recovery are considered, i.e., recovery of dislocation networks at sub-boundaries and that of three-dimensional networks within subgrains. The high-temperature steady-state creep of Fe-Mo solid solutions, creep characteristics of which have been reported to be well rationalized as viscous glide creep, is analyzed using this equation. It is shown that stress dependence of d epsilon/dtsub(s) is well explained from the viewpoint of recovery, in which the activation and the annihilation of dislocations at sub-boundaries are considered to take place. (orig.) [de

  11. A model on valence state evaluation of TRU nuclides in reprocessing solutions

    International Nuclear Information System (INIS)

    Uchiyama, Gunzo; Fujine, Sachio; Yoshida, Zenko; Maeda, Mitsuru; Motoyama, Satoshi.

    1998-02-01

    A mathematical model was developed to evaluate the valence state of TRU nuclides in reprocessing process solutions. The model consists of mass balance equations, Nernst equations, reaction rate equations and electrically neutrality equations. The model is applicable for the valence state evaluation of TRU nuclides in both steady state and transient state conditions in redox equilibrium. The valence state which is difficult to measure under high radiation and multi component conditions is calculated by the model using experimentally measured data for the TRU nuclide concentrations, nitric acid and redox reagent concentrations, electrode potential and solution temperature. (author)

  12. A mixed finite element method for nonlinear diffusion equations

    KAUST Repository

    Burger, Martin; Carrillo, José ; Wolfram, Marie-Therese

    2010-01-01

    We propose a mixed finite element method for a class of nonlinear diffusion equations, which is based on their interpretation as gradient flows in optimal transportation metrics. We introduce an appropriate linearization of the optimal transport problem, which leads to a mixed symmetric formulation. This formulation preserves the maximum principle in case of the semi-discrete scheme as well as the fully discrete scheme for a certain class of problems. In addition solutions of the mixed formulation maintain exponential convergence in the relative entropy towards the steady state in case of a nonlinear Fokker-Planck equation with uniformly convex potential. We demonstrate the behavior of the proposed scheme with 2D simulations of the porous medium equations and blow-up questions in the Patlak-Keller-Segel model. © American Institute of Mathematical Sciences.

  13. Molecular control of steady-state dendritic cell maturation and immune homeostasis.

    Science.gov (United States)

    Hammer, Gianna Elena; Ma, Averil

    2013-01-01

    Dendritic cells (DCs) are specialized sentinels responsible for coordinating adaptive immunity. This function is dependent upon coupled sensitivity to environmental signs of inflammation and infection to cellular maturation-the programmed alteration of DC phenotype and function to enhance immune cell activation. Although DCs are thus well equipped to respond to pathogens, maturation triggers are not unique to infection. Given that immune cells are exquisitely sensitive to the biological functions of DCs, we now appreciate that multiple layers of suppression are required to restrict the environmental sensitivity, cellular maturation, and even life span of DCs to prevent aberrant immune activation during the steady state. At the same time, steady-state DCs are not quiescent but rather perform key functions that support homeostasis of numerous cell types. Here we review these functions and molecular mechanisms of suppression that control steady-state DC maturation. Corruption of these steady-state operatives has diverse immunological consequences and pinpoints DCs as potent drivers of autoimmune and inflammatory disease.

  14. Implicit solvers for large-scale nonlinear problems

    International Nuclear Information System (INIS)

    Keyes, David E; Reynolds, Daniel R; Woodward, Carol S

    2006-01-01

    Computational scientists are grappling with increasingly complex, multi-rate applications that couple such physical phenomena as fluid dynamics, electromagnetics, radiation transport, chemical and nuclear reactions, and wave and material propagation in inhomogeneous media. Parallel computers with large storage capacities are paving the way for high-resolution simulations of coupled problems; however, hardware improvements alone will not prove enough to enable simulations based on brute-force algorithmic approaches. To accurately capture nonlinear couplings between dynamically relevant phenomena, often while stepping over rapid adjustments to quasi-equilibria, simulation scientists are increasingly turning to implicit formulations that require a discrete nonlinear system to be solved for each time step or steady state solution. Recent advances in iterative methods have made fully implicit formulations a viable option for solution of these large-scale problems. In this paper, we overview one of the most effective iterative methods, Newton-Krylov, for nonlinear systems and point to software packages with its implementation. We illustrate the method with an example from magnetically confined plasma fusion and briefly survey other areas in which implicit methods have bestowed important advantages, such as allowing high-order temporal integration and providing a pathway to sensitivity analyses and optimization. Lastly, we overview algorithm extensions under development motivated by current SciDAC applications

  15. Dark Entangled Steady States of Interacting Rydberg Atoms

    DEFF Research Database (Denmark)

    Dasari, Durga; Mølmer, Klaus

    2013-01-01

    their short-lived excited states lead to rapid, dissipative formation of an entangled steady state. We show that for a wide range of physical parameters, this entangled state is formed on a time scale given by the strengths of coherent Raman and Rabi fields applied to the atoms, while it is only weakly...

  16. Explicit Solutions for Generalized (2+1)-Dimensional Nonlinear Zakharov-Kuznetsov Equation

    International Nuclear Information System (INIS)

    Sun Yuhuai; Ma Zhimin; Li Yan

    2010-01-01

    The exact solutions of the generalized (2+1)-dimensional nonlinear Zakharov-Kuznetsov (Z-K) equation are explored by the method of the improved generalized auxiliary differential equation. Many explicit analytic solutions of the Z-K equation are obtained. The methods used to solve the Z-K equation can be employed in further work to establish new solutions for other nonlinear partial differential equations. (general)

  17. Analytic solutions of nonlinear Cournot duopoly game

    Directory of Open Access Journals (Sweden)

    Akio Matsumoto

    2005-01-01

    Full Text Available We construct a Cournot duopoly model with production externality in which reaction functions are unimodal. We consider the case of a Cournot model which has a stable equilibrium point. Then we show the existence of analytic solutions of the model. Moreover, we seek general solutions of the model in the form of nonlinear second-order difference equation.

  18. Steady-State Crack Growth in Rate-Sensitive Single Crystals

    DEFF Research Database (Denmark)

    Juul, Kristian Jørgensen; Nielsen, Kim Lau; Niordson, Christian Frithiof

    2016-01-01

    The characteristics of the active plastic zone surrounding a crack growingin a single crystal (FCC, BCC, and HCP) at constant velocity is investigated for ModeI loading under plane strain assumptions. The framework builds upon a steady-state relation bringing the desired solution out in a frame...... translating with the crack tip. In the study, the shielding of the crack tip that follows from plastic slip is investigated by adopting the SSV-model. High resolution plots of the plastic zones are obtained and a detailed study confirms the existence of analytically determined velocity discontinuities from...... the literature. The plastic zone is found to be smallest for the FCC structure andlargest for the HCP structure, which is also reected in the shielding ratio, where FCC crystals show the smallest shielding and HCP the largest shielding....

  19. A design of steady state fusion burner

    International Nuclear Information System (INIS)

    Hasegawa, Akira; Hatori, Tadatsugu; Itoh, Kimitaka; Ikuta, Takashi; Kodama, Yuji.

    1975-01-01

    We present a brief design of a steady state fusion burner in which a continuous burning of nuclear fuel may be achieved with output power of a gigawatt. The laser fusion is proposed to ignite the fuel. (auth.)

  20. The non-differentiable solution for local fractional Laplace equation in steady heat-conduction problem

    Directory of Open Access Journals (Sweden)

    Chen Jie-Dong

    2016-01-01

    Full Text Available In this paper, we investigate the local fractional Laplace equation in the steady heat-conduction problem. The solutions involving the non-differentiable graph are obtained by using the characteristic equation method (CEM via local fractional derivative. The obtained results are given to present the accuracy of the technology to solve the steady heat-conduction in fractal media.

  1. The nonlinear Schrödinger equation singular solutions and optical collapse

    CERN Document Server

    Fibich, Gadi

    2015-01-01

    This book is an interdisciplinary introduction to optical collapse of laser beams, which is modelled by singular (blow-up) solutions of the nonlinear Schrödinger equation. With great care and detail, it develops the subject including the mathematical and physical background and the history of the subject. It combines rigorous analysis, asymptotic analysis, informal arguments, numerical simulations, physical modelling, and physical experiments. It repeatedly emphasizes the relations between these approaches, and the intuition behind the results. The Nonlinear Schrödinger Equation will be useful to graduate students and researchers in applied mathematics who are interested in singular solutions of partial differential equations, nonlinear optics and nonlinear waves, and to graduate students and researchers in physics and engineering who are interested in nonlinear optics and Bose-Einstein condensates. It can be used for courses on partial differential equations, nonlinear waves, and nonlinear optics. Gadi Fib...

  2. Operational Solution to the Nonlinear Klein-Gordon Equation

    Science.gov (United States)

    Bengochea, G.; Verde-Star, L.; Ortigueira, M.

    2018-05-01

    We obtain solutions of the nonlinear Klein-Gordon equation using a novel operational method combined with the Adomian polynomial expansion of nonlinear functions. Our operational method does not use any integral transforms nor integration processes. We illustrate the application of our method by solving several examples and present numerical results that show the accuracy of the truncated series approximations to the solutions. Supported by Grant SEP-CONACYT 220603, the first author was supported by SEP-PRODEP through the project UAM-PTC-630, the third author was supported by Portuguese National Funds through the FCT Foundation for Science and Technology under the project PEst-UID/EEA/00066/2013

  3. Analytic continuation of solutions of some nonlinear convolution partial differential equations

    Directory of Open Access Journals (Sweden)

    Hidetoshi Tahara

    2015-01-01

    Full Text Available The paper considers a problem of analytic continuation of solutions of some nonlinear convolution partial differential equations which naturally appear in the summability theory of formal solutions of nonlinear partial differential equations. Under a suitable assumption it is proved that any local holomorphic solution has an analytic extension to a certain sector and its extension has exponential growth when the variable goes to infinity in the sector.

  4. Analysis of the nonlinear dynamics of a 2-axle freight wagon in curves

    DEFF Research Database (Denmark)

    Di Gialleonardo, Egidio; Bruni, Stefano; True, Hans

    2014-01-01

    This paper deals with the study of the nonlinear dynamic behaviour of 2-axle freight wagons in curves, considering the case of one single wagon (neglecting inter-car coupling forces) and of multiple wagons interacting through the buffers and the couplers. A multi-body model of a single wagon...... and of a three-car assembly is introduced, paying particular attention to the nonlinear and nonsmooth modelling of the suspensions and of the inter-car coupling elements. Using this model, a numerical analysis of the steady-state solution reached after the negotiation of curve transition is presented......, it is shown that the coupling forces exchanged by the wagons significantly affect their dynamics in a curve, reducing the amplitude of vibration....

  5. Exact solutions of some nonlinear partial differential equations using ...

    Indian Academy of Sciences (India)

    The functional variable method is a powerful solution method for obtaining exact solutions of some nonlinear partial differential equations. In this paper, the functional variable method is used to establish exact solutions of the generalized forms of Klein–Gordon equation, the (2 + 1)-dimensional Camassa–Holm ...

  6. Exact solutions for nonlinear variants of Kadomtsev–Petviashvili (n ...

    Indian Academy of Sciences (India)

    Studying compactons, solitons, solitary patterns and periodic solutions is important in nonlinear phenomena. In this paper we study nonlinear variants of the Kadomtsev–Petviashvili (KP) and the Korteweg–de Vries (KdV) equations with positive and negative exponents. The functional variable method is used to establish ...

  7. Quasi-steady state natural convection in a tilted porous layer

    Energy Technology Data Exchange (ETDEWEB)

    Robillard, L.; Vasseur, P. (Ecole Polytechnique, Montreal, PQ (Canada))

    1992-12-01

    Natural convection in an inclined porous layer heated or cooled on one side, when its other walls are insulated, has several important engineering applications. These include solar power collection, regenerative heat exchangers, and high performance insulation for buildings and cold storage. Although the problem is basically an unsteady state one, it is known that if the heating (or cooling) process is maintained for a sufficiently long time, a quasi-steady state is approached. Quasi-steady state laminar natural convection in an inclined porous layer is studied analytically and numerically. On the basis of the Darcy-Oberbeck-Boussinesq equations, the problem is solved analytically in the limit of a thin porous layer heated on one side by a heat flux while the other boundaries are maintained adiabatic. For quasi-steady state, the flow and temperature fields overall heat transfer rates are obtained in terms of the controlling parameters and the onset of convection in a bottom heated horizantal system is predicted. It is also demonstrated for the case of a bottom-heated layer that for sufficiently small inclinations, multiple unicellular quasi-steady states exist, some of which are unstable. A numerical study of the same phenomenon, obtained by solving the complete set of governing equations, is conducted. Good agreement is found between the analytical predictions and the numerical simulation. 22 refs., 6 figs.

  8. On Steady-State Tropical Cyclones

    Science.gov (United States)

    2014-01-01

    Press: London. Marks FD, Black PG, Montgomery MT, Burpee RW. 2008. Structure of the eye and eyewall of Hurricane Hugo (1989). Mon. Weather Rev. 136: 1237... hurricanes ; tropical cyclones; typhoons; steady-state Received 18 April 2013; Revised 25 November 2013; Accepted 29 December 2013; Published online in Wiley...the concept of the ‘mature stage’ of a hurricane vortex. The definition of the ‘mature stage’ is commonly based on the time period in which the maximum

  9. STEADY-STATE RELATIVISTIC STELLAR DYNAMICS AROUND A MASSIVE BLACK HOLE

    Energy Technology Data Exchange (ETDEWEB)

    Bar-Or, Ben; Alexander, Tal [Department of Particle Physics and Astrophysics, Weizmann Institute of Science, P.O. Box 26, Rehovot 76100 (Israel)

    2016-04-01

    A massive black hole (MBH) consumes stars whose orbits evolve into the small phase-space volume of unstable orbits, the “loss cone,” which take them into the MBH, or close enough to interact strongly with it. The resulting phenomena, e.g., tidal heating and disruption, binary capture and hyper-velocity star ejection, gravitational wave (GW) emission by inspiraling compact remnants, or hydrodynamical interactions with an accretion disk, can produce observable signatures and thereby reveal the MBH, affect its mass and spin evolution, test strong gravity, and probe stars and gas near the MBH. These continuous stellar loss and resupply processes shape the central stellar distribution. We investigate relativistic stellar dynamics near the loss cone of a non-spinning MBH in steady state, analytically and by Monte Carlo simulations of the diffusion of the orbital parameters. These take into account Newtonian mass precession due to enclosed stellar mass, in-plane precession due to general relativity, dissipation by GW, uncorrelated two-body relaxation, correlated resonant relaxation (RR), and adiabatic invariance due to secular precession, using a rigorously derived description of correlated post-Newtonian dynamics in the diffusion limit. We argue that general maximal entropy considerations strongly constrain the orbital diffusion in steady state, irrespective of the relaxation mechanism. We identify the exact phase-space separatrix between plunges and inspirals, and predict their steady-state rates. We derive the dependence of the rates on the mass of the MBH, show that the contribution of RR in steady state is small, and discuss special cases where unquenched RR in restricted volumes of phase-space may affect the steady state substantially.

  10. Discrete coupled derivative nonlinear Schroedinger equations and their quasi-periodic solutions

    International Nuclear Information System (INIS)

    Geng Xianguo; Su Ting

    2007-01-01

    A hierarchy of nonlinear differential-difference equations associated with a discrete isospectral problem is proposed, in which a typical differential-difference equation is a discrete coupled derivative nonlinear Schroedinger equation. With the help of the nonlinearization of the Lax pairs, the hierarchy of nonlinear differential-difference equations is decomposed into a new integrable symplectic map and a class of finite-dimensional integrable Hamiltonian systems. Based on the theory of algebraic curve, the Abel-Jacobi coordinates are introduced to straighten out the corresponding flows, from which quasi-periodic solutions for these differential-difference equations are obtained resorting to the Riemann-theta functions. Moreover, a (2+1)-dimensional discrete coupled derivative nonlinear Schroedinger equation is proposed and its quasi-periodic solutions are derived

  11. Linear and nonlinear instability theory of a noble gas MHD generator

    International Nuclear Information System (INIS)

    Mesland, A.J.

    1982-01-01

    This thesis deals with the stability of the working medium of a seeded noble gas magnetohydrodynamic generator. The aim of the study is to determine the instability mechanism which is most likely to occur in experimental MHD generators and to describe its behaviour with linear and nonlinear theories. In chapter I a general introduction is given. The pertinent macroscopic basic equations are derived in chapter II, viz. the continuity, the momentum and the energy equation for the electrons and the heavy gas particles, consisting of the seed particles and the noble gas atoms. Chapter III deals with the linear plane wave analysis of small disturbances of a homogeneous steady state. The steady state is discussed in chapter IV. The values for the steady state parameters used for the calculations both for the linear analysis as for the nonlinear analysis are made plausible with the experimental values. Based on the results of the linear plane wave theory a nonlinear plane wave model of the electrothermal instability is introduced in chapter V. (Auth.)

  12. 40 CFR Appendix II to Part 1039 - Steady-State Duty Cycles

    Science.gov (United States)

    2010-07-01

    ... 40 Protection of Environment 32 2010-07-01 2010-07-01 false Steady-State Duty Cycles II Appendix... Appendix II to Part 1039—Steady-State Duty Cycles (a) The following duty cycles apply for constant-speed engines: (1) The following duty cycle applies for discrete-mode testing: D2 mode number Engine speed...

  13. Exact solutions to two higher order nonlinear Schroedinger equations

    International Nuclear Information System (INIS)

    Xu Liping; Zhang Jinliang

    2007-01-01

    Using the homogeneous balance principle and F-expansion method, the exact solutions to two higher order nonlinear Schroedinger equations which describe the propagation of femtosecond pulses in nonlinear fibres are obtained with the aid of a set of subsidiary higher order ordinary differential equations (sub-equations for short)

  14. Nonlinear dynamics of an elliptic vortex embedded in an oscillatory shear flow.

    Science.gov (United States)

    Ryzhov, Eugene A

    2017-11-01

    The nonlinear dynamics of an elliptic vortex subjected to a time-periodic linear external shear flow is studied numerically. Making use of the ideas from the theory of nonlinear resonance overlaps, the study focuses on the appearance of chaotic regimes in the ellipse dynamics. When the superimposed flow is stationary, two general types of the steady-state phase portrait are considered: one that features a homoclinic separatrix delineating bounded and unbounded phase trajectories and one without a separatrix (all the phase trajectories are bounded in a periodic domain). When the external flow is time-periodic, the ensuing nonlinear dynamics differs significantly in both cases. For the case with a separatrix and two distinct types of phase trajectories: bounded and unbounded, the effect of the most influential nonlinear resonance with the winding number of 1:1 is analyzed in detail. Namely, the process of occupying the central stability region associated with the steady-state elliptic critical point by the stability region associated with the nonlinear resonance of 1:1 as the perturbation frequency gradually varies is investigated. A stark increase in the persistence of the central regular dynamics region against perturbation when the resonance of 1:1 associated stability region occupies the region associated with the steady-state elliptic critical point is observed. An analogous persistence of the regular motion occurs for higher perturbation frequencies when the corresponding stability islands reach the central stability region associated with the steady-state elliptic point. An analysis for the case with the resonance of 1:2 is presented. For the second case with only bounded phase trajectories and, therefore, no separatrix, the appearance of much bigger stability islands associated with nonlinear resonances compared with the case with a separatrix is reported.

  15. Analysis of steady state creep of southeastern New Mexico bedded salt

    International Nuclear Information System (INIS)

    Herrmann, W.; Wawersik, W.R.; Lauson, H.S.

    1980-03-01

    Steady state creep rates have been obtained from a large suite of existing experimental creep data relating to bedded rock salt from the Salado formation of S.E. New Mexico. Experimental conditions covered an intermediate temperature range from 22 0 C to 200 0 C, and shear stresses from 1000 psi (7 MPa) to 6000 psi (31 MPa). An expression, based on a single diffusion controlled dislocation climb mechanism, has been found to fit the observed dependence of steady state creep rate on shear stress and temperature, yielding an activation energy of 12 kcal/mole (50 kJ/mole) and a stress exponent of 4.9. Multiple regression analysis revealed a dependence on stratigraphy, but no statistically significant dependence on pressure of specimen size. No consistent dilatancy or compaction associated with steady state creep was found, although some individual specimens dilated or compacted during creep. The steady state creep data were found to agree very well with creep data for both bedded and dome salt from a variety of other locations

  16. Quasi-periodic solutions of nonlinear beam equations with quintic quasi-periodic nonlinearities

    Directory of Open Access Journals (Sweden)

    Qiuju Tuo

    2015-01-01

    Full Text Available In this article, we consider the one-dimensional nonlinear beam equations with quasi-periodic quintic nonlinearities $$ u_{tt}+u_{xxxx}+(B+ \\varepsilon\\phi(tu^5=0 $$ under periodic boundary conditions, where B is a positive constant, $\\varepsilon$ is a small positive parameter, $\\phi(t$ is a real analytic quasi-periodic function in t with frequency vector $\\omega=(\\omega_1,\\omega_2,\\dots,\\omega_m$. It is proved that the above equation admits many quasi-periodic solutions by KAM theory and partial Birkhoff normal form.

  17. Chlorine decay under steady and unsteady-state hydraulic conditions

    DEFF Research Database (Denmark)

    Stoianov, Ivan; Aisopou, Angeliki

    2014-01-01

    This paper describes a simulation framework for the scale-adaptive hydraulic and chlorine decay modelling under steady and unsteady-state flows. Bulk flow and pipe wall reaction coefficients are replaced with steady and unsteady-state reaction coefficients. An unsteady decay coefficient is defined...... which depends upon the absolute value of shear stress and the rate of change of shear stress for quasi-unsteady and unsteady-state flows. A preliminary experimental and analytical investigation was carried out in a water transmission main. The results were used to model monochloramine decay...... and these demonstrate that the dynamic hydraulic conditions have a significant impact on water quality deterioration and the rapid loss of disinfectant residual. © 2013 The Authors....

  18. Steady-state heat transfer in an inverted U-tube steam generator

    International Nuclear Information System (INIS)

    Boucher, T.J.

    1986-01-01

    Experimental results are presented involving U-tube steam generator tube bundle local heat transfer and fluid conditions during steady-state, full-power operations performed at high temperatures and pressures with conditions typical of a pressurized water reactor (15.0 MPa primary pressure, 600 K hot-leg fluid temperatures, 6.2 MPa secondary pressure). The MOD-2C facility represents the state-of-the-art in measurement of tube local heat transfer data and average tube bundle secondary fluid density at several elevations, which allows an estimate of the axial heat transfer and void distributions during steady-state and transient operations. The method of heat transfer data reduction is presented and the heat flux, secondary convective heat transfer coefficient, and void fraction distributions are quantified for steady-state, full-power operations

  19. Nonlinear features of the energy beam-driven instability

    International Nuclear Information System (INIS)

    Lesur, M.; Idomura, Y.; Garbet, X.

    2009-01-01

    Full text: A concern with ignited fusion plasmas is that, as a result of the instabilities they trigger, the high-energy particles eject themselves before they could give their energy to the core to sustain the reaction. Similarities between this class of instabilities and the so-called Berk-Breizman problem motivate us to study a single-mode instability driven by an energetic particle beam. For this purpose, a one dimensional Vlasov simulation is extended to include a Krook collision operator and external damping processes. The code is benchmarked with previous work. The fully nonlinear behavior is recovered in the whole parameter space characterized by an effective relaxation rate ν a and an external damping rate γ d . Steady state, periodic and chaotic behaviors are observed in nonlinear solutions. In the regime above marginal stability where both ν a and γ d are smaller than the linear drive γ L , we observe a good agreement of steady saturation levels between the simulation and theory. Near marginal stability, the role of the normalized relaxation rate ν a /(γ L -γ d ), which is a key parameter to predict the behavior of the solution, is investigated for an initial distribution with relatively small γ L , which correspond to the situation considered in the theory. In the low relaxation rate regime, frequency sweeping events are observed, and the time-evolution of such event is investigated. (author)

  20. 40 CFR Appendix II to Part 1042 - Steady-State Duty Cycles

    Science.gov (United States)

    2010-07-01

    ... 40 Protection of Environment 32 2010-07-01 2010-07-01 false Steady-State Duty Cycles II Appendix..., App. II Appendix II to Part 1042—Steady-State Duty Cycles (a) The following duty cycles apply as specified in § 1042.505(b)(1): (1) The following duty cycle applies for discrete-mode testing: E3 mode No...

  1. On some nonlinear problems arising in the physics of ionized gases

    International Nuclear Information System (INIS)

    Hilhorst-Goldman, D.

    1981-01-01

    The author reports results obtained by rigorous analysis of a nonlinear differential equation for the electron density nsub(e) in a specific type of electrical discharge. The problem is essentially two-dimensional. She discusses in particular the escape of electrons to infinity above a critical temperature and the boundary layer exhibited by nsub(e) near zero temperature. A singular boundary value problem arising in a pre-breakdown gas discharge is discussed. A Coulomb gas is considered in a special experimental situation: the pre-breakdown gas discharge between two electrodes. The equation for the negative charge density can be formulated as a nonlinear parabolic equation degenerate at the origin. The existence and uniqueness of the solution are proved as well as the asymptotic stability of its unique steady state. Some results are also given about the rate of convergence. The variational characterisation of the limit solution of a singular perturbation problem and variational analysis of a perturbed free boundary problem are considered. (Auth./C.F.)

  2. Convection and reaction in a diffusive boundary layer in a porous medium: nonlinear dynamics.

    Science.gov (United States)

    Andres, Jeanne Therese H; Cardoso, Silvana S S

    2012-09-01

    We study numerically the nonlinear interactions between chemical reaction and convective fingering in a diffusive boundary layer in a porous medium. The reaction enhances stability by consuming a solute that is unstably distributed in a gravitational field. We show that chemical reaction profoundly changes the dynamics of the system, by introducing a steady state, shortening the evolution time, and altering the spatial patterns of velocity and concentration of solute. In the presence of weak reaction, finger growth and merger occur effectively, driving strong convective currents in a thick layer of solute. However, as the reaction becomes stronger, finger growth is inhibited, tip-splitting is enhanced and the layer of solute becomes much thinner. Convection enhances the mass flux of solute consumed by reaction in the boundary layer but has a diminishing effect as reaction strength increases. This nonlinear behavior has striking differences to the density fingering of traveling reaction fronts, for which stronger chemical kinetics result in more effective finger merger owing to an increase in the speed of the front. In a boundary layer, a strong stabilizing effect of reaction can maintain a long-term state of convection in isolated fingers of wavelength comparable to that at onset of instability.

  3. Jacobian elliptic function expansion solutions of nonlinear stochastic equations

    International Nuclear Information System (INIS)

    Wei Caimin; Xia Zunquan; Tian Naishuo

    2005-01-01

    Jacobian elliptic function expansion method is extended and applied to construct the exact solutions of the nonlinear Wick-type stochastic partial differential equations (SPDEs) and some new exact solutions are obtained via this method and Hermite transformation

  4. Buoyancy-driven chaotic regimes during solute dispersion in pore networks

    International Nuclear Information System (INIS)

    Tsakiroglou, C.D.; Theodoropoulou, M.A.; Karoutsos, V.

    2005-01-01

    In an attempt to investigate gravity effects on solute dispersion at the scale of a pore network, single source-solute transport visualization experiments are performed on glass-etched pore networks of varying morphology and degree of pore-scale heterogeneities. The (lighter) low solute concentration aqueous solution flows steadily through the porous medium and the (heavier) high solute concentration solution is injected at a very low and constant flow rate through an inner port. The transient evolution of the solute concentration distribution over various regions of the pore network is determined at different scales by capturing and video-recording snapshots of the dispersion on PC, measuring automatically the spatial variation of the color intensity of the solution, and transforming the color intensities to solute concentrations. Without the action of gravity, the steady-state dispersion regime changes with Peclet (Pe) number, and the longitudinal and transverse dispersivities are estimated by fitting the experimental datasets to approximate analytic solutions of the advection-dispersion equation. Under the action of gravity, multiple of steady-state solute dispersion regimes is developed at each Pe value, and lobe-shaped instabilities of the solute concentration are observed across the pore network, as the downward flow of the denser (higher solute concentration) fluid is counterbalanced by the upward flow of the less dense (lower solute concentration) fluid. The steady-state dispersion regimes may be periodic, quasi-periodic or chaotic depending on the system parameters. The nature of the transient fluctuations of the average solute concentration is analyzed by identifying the periodicity of the fluctuations, determining the autocorrelation function and the statistical moments of the time series, and inspecting the FFT (fast Fourier transform) power spectra. It is found that the mixing zone tends to be stabilized at higher values of the Peclet (Pe) number

  5. Exact bright and dark spatial soliton solutions in saturable nonlinear media

    International Nuclear Information System (INIS)

    Calvo, Gabriel F.; Belmonte-Beitia, Juan; Perez-Garcia, Victor M.

    2009-01-01

    We present exact analytical bright and dark (black and grey) solitary wave solutions of a nonlinear Schroedinger-type equation describing the propagation of spatial beams in media exhibiting a saturable nonlinearity (such as centrosymmetric photorefractive materials). A qualitative study of the stationary equation is carried out together with a discussion of the stability of the solutions.

  6. Compacton-like solutions for modified KdV and nonlinear ...

    Indian Academy of Sciences (India)

    ]; it was shown by linear stability analysis as well as by Lyapunov stability criterion that, these solutions are stable for arbitrary values of nonlinear parameters. Recently, in [8], envelope compacton and solitary pattern solutions of a generalized ...

  7. Emergence of advance waves in a steady-state universe

    Energy Technology Data Exchange (ETDEWEB)

    Hobart, R.H.

    1979-10-01

    In standard Wheeler-Feynman electrodynamics advanced waves from any source are absolutely canceled by the advanced waves from the absorber responding to that source. The present work shows this cancellation fails over cosmic distances in a steady-state universe. A test of the view proposed earlier, in a paper which assumed failure of cancellation ad hoc, that zero-point fluctuations of the electromagnetic field are such emergent advanced waves, is posed. The view entails anomalous slowing of spontaneous transition rates at longer emission wavelengths; available data go against this, furnishing additional argument against the suspect assumption that the universe is steady-state.

  8. Emergence of advance waves in a steady-state universe

    International Nuclear Information System (INIS)

    Hobart, R.H.

    1979-01-01

    In standard Wheeler-Feynman electrodynamics advanced waves from any source are absolutely canceled by the advanced waves from the absorber responding to that source. The present work shows this cancellation fails over cosmic distances in a steady-state universe. A test of the view proposed earlier, in a paper which assumed failure of cancellation ad hoc, that zero-point fluctuations of the electromagnetic field are such emergent advanced waves, is posed. The view entails anomalous slowing of spontaneous transition rates at longer emission wavelengths; available data go against this, furnishing additional argument against the suspect assumption that the universe is steady-state

  9. Decay Properties of Axially Symmetric D-Solutions to the Steady Navier-Stokes Equations

    Science.gov (United States)

    Weng, Shangkun

    2018-03-01

    We investigate the decay properties of smooth axially symmetric D-solutions to the steady Navier-Stokes equations. The achievements of this paper are two folds. One is improved decay rates of u_{θ } and \

  10. Two simple ansaetze for obtaining exact solutions of high dispersive nonlinear Schroedinger equations

    International Nuclear Information System (INIS)

    Palacios, Sergio L.

    2004-01-01

    We propose two simple ansaetze that allow us to obtain different analytical solutions of the high dispersive cubic and cubic-quintic nonlinear Schroedinger equations. Among these solutions we can find solitary wave and periodic wave solutions representing the propagation of different waveforms in nonlinear media

  11. Mechanism for multiplicity of steady states with distinct cell concentration in continuous culture of mammalian cells.

    Science.gov (United States)

    Yongky, Andrew; Lee, Jongchan; Le, Tung; Mulukutla, Bhanu Chandra; Daoutidis, Prodromos; Hu, Wei-Shou

    2015-07-01

    Continuous culture for the production of biopharmaceutical proteins offers the possibility of steady state operations and thus more consistent product quality and increased productivity. Under some conditions, multiplicity of steady states has been observed in continuous cultures of mammalian cells, wherein with the same dilution rate and feed nutrient composition, steady states with very different cell and product concentrations may be reached. At those different steady states, cells may exhibit a high glycolysis flux with high lactate production and low cell concentration, or a low glycolysis flux with low lactate and high cell concentration. These different steady states, with different cell concentration, also have different productivity. Developing a mechanistic understanding of the occurrence of steady state multiplicity and devising a strategy to steer the culture toward the desired steady state is critical. We establish a multi-scale kinetic model that integrates a mechanistic intracellular metabolic model and cell growth model in a continuous bioreactor. We show that steady state multiplicity exists in a range of dilution rate in continuous culture as a result of the bistable behavior in glycolysis. The insights from the model were used to devise strategies to guide the culture to the desired steady state in the multiple steady state region. The model provides a guideline principle in the design of continuous culture processes of mammalian cells. © 2015 Wiley Periodicals, Inc.

  12. ALMOST PERIODIC SOLUTIONS TO SOME NONLINEAR DELAY DIFFERENTIAL EQUATION

    Institute of Scientific and Technical Information of China (English)

    2009-01-01

    The existence of an almost periodic solutions to a nonlinear delay diffierential equation is considered in this paper. A set of sufficient conditions for the existence and uniqueness of almost periodic solutions to some delay diffierential equations is obtained.

  13. A comprehensive analytical solution of the nonlinear pendulum

    International Nuclear Information System (INIS)

    Ochs, Karlheinz

    2011-01-01

    In this paper, an analytical solution for the differential equation of the simple but nonlinear pendulum is derived. This solution is valid for any time and is not limited to any special initial instance or initial values. Moreover, this solution holds if the pendulum swings over or not. The method of approach is based on Jacobi elliptic functions and starts with the solution of a pendulum that swings over. Due to a meticulous sign correction term, this solution is also valid if the pendulum does not swing over.

  14. Approximate Series Solutions for Nonlinear Free Vibration of Suspended Cables

    Directory of Open Access Journals (Sweden)

    Yaobing Zhao

    2014-01-01

    Full Text Available This paper presents approximate series solutions for nonlinear free vibration of suspended cables via the Lindstedt-Poincare method and homotopy analysis method, respectively. Firstly, taking into account the geometric nonlinearity of the suspended cable as well as the quasi-static assumption, a mathematical model is presented. Secondly, two analytical methods are introduced to obtain the approximate series solutions in the case of nonlinear free vibration. Moreover, small and large sag-to-span ratios and initial conditions are chosen to study the nonlinear dynamic responses by these two analytical methods. The numerical results indicate that frequency amplitude relationships obtained with different analytical approaches exhibit some quantitative and qualitative differences in the cases of motions, mode shapes, and particular sag-to-span ratios. Finally, a detailed comparison of the differences in the displacement fields and cable axial total tensions is made.

  15. Regarding on the exact solutions for the nonlinear fractional differential equations

    Directory of Open Access Journals (Sweden)

    Kaplan Melike

    2016-01-01

    Full Text Available In this work, we have considered the modified simple equation (MSE method for obtaining exact solutions of nonlinear fractional-order differential equations. The space-time fractional equal width (EW and the modified equal width (mEW equation are considered for illustrating the effectiveness of the algorithm. It has been observed that all exact solutions obtained in this paper verify the nonlinear ordinary differential equations which was obtained from nonlinear fractional-order differential equations under the terms of wave transformation relationship. The obtained results are shown graphically.

  16. Traveling wavefront solutions to nonlinear reaction-diffusion-convection equations

    Science.gov (United States)

    Indekeu, Joseph O.; Smets, Ruben

    2017-08-01

    Physically motivated modified Fisher equations are studied in which nonlinear convection and nonlinear diffusion is allowed for besides the usual growth and spread of a population. It is pointed out that in a large variety of cases separable functions in the form of exponentially decaying sharp wavefronts solve the differential equation exactly provided a co-moving point source or sink is active at the wavefront. The velocity dispersion and front steepness may differ from those of some previously studied exact smooth traveling wave solutions. For an extension of the reaction-diffusion-convection equation, featuring a memory effect in the form of a maturity delay for growth and spread, also smooth exact wavefront solutions are obtained. The stability of the solutions is verified analytically and numerically.

  17. Traveling wavefront solutions to nonlinear reaction-diffusion-convection equations

    International Nuclear Information System (INIS)

    Indekeu, Joseph O; Smets, Ruben

    2017-01-01

    Physically motivated modified Fisher equations are studied in which nonlinear convection and nonlinear diffusion is allowed for besides the usual growth and spread of a population. It is pointed out that in a large variety of cases separable functions in the form of exponentially decaying sharp wavefronts solve the differential equation exactly provided a co-moving point source or sink is active at the wavefront. The velocity dispersion and front steepness may differ from those of some previously studied exact smooth traveling wave solutions. For an extension of the reaction-diffusion-convection equation, featuring a memory effect in the form of a maturity delay for growth and spread, also smooth exact wavefront solutions are obtained. The stability of the solutions is verified analytically and numerically. (paper)

  18. Toward Analytic Solution of Nonlinear Differential Difference Equations via Extended Sensitivity Approach

    International Nuclear Information System (INIS)

    Darmani, G.; Setayeshi, S.; Ramezanpour, H.

    2012-01-01

    In this paper an efficient computational method based on extending the sensitivity approach (SA) is proposed to find an analytic exact solution of nonlinear differential difference equations. In this manner we avoid solving the nonlinear problem directly. By extension of sensitivity approach for differential difference equations (DDEs), the nonlinear original problem is transformed into infinite linear differential difference equations, which should be solved in a recursive manner. Then the exact solution is determined in the form of infinite terms series and by intercepting series an approximate solution is obtained. Numerical examples are employed to show the effectiveness of the proposed approach. (general)

  19. SOLUTION OF HARMONIC OSCILLATOR OF NONLINEAR MASTER SCHRÖDINGER

    Directory of Open Access Journals (Sweden)

    T B Prayitno

    2012-02-01

    Full Text Available We have computed the solution of a nonrelativistic particle motion in a harmonic oscillator potential of the nonlinear master Schrödinger equation. The equation itself is based on two classical conservation laws, the Hamilton-Jacobi and the continuity equations. Those two equations give each contribution for the definition of quantum particle. We also prove that the solution can’t be normalized.   Keywords : harmonic oscillator, nonlinear Schrödinger.

  20. Nonlinear two-fluid hydromagnetic waves in the solar wind: Rotational discontinuity, soliton, and finite-extent Alfven wave train solutions

    International Nuclear Information System (INIS)

    Lyu, L.H.; Kan, J.R.

    1989-01-01

    Nonlinear one-dimensional constant-profile hydromagnetic wave solutions are obtained in finite-temperature two-fluid collisionless plasmas under adiabatic equation of state. The nonlinear wave solutions can be classified according to the wavelength. The long-wavelength solutions are circularly polarized incompressible oblique Alfven wave trains with wavelength greater than hudreds of ion inertial length. The oblique wave train solutions can explain the high degree of alignment between the local average magnetic field and the wave normal direction observed in the solar wind. The short-wavelength solutions include rarefaction fast solitons, compression slow solitons, Alfven solitons and rotational discontinuities, with wavelength of several tens of ion inertial length, provided that the upstream flow speed is less than the fast-mode speed

  1. Stabilization of solutions to higher-order nonlinear Schrodinger equation with localized damping

    Directory of Open Access Journals (Sweden)

    Eleni Bisognin

    2007-01-01

    Full Text Available We study the stabilization of solutions to higher-order nonlinear Schrodinger equations in a bounded interval under the effect of a localized damping mechanism. We use multiplier techniques to obtain exponential decay in time of the solutions of the linear and nonlinear equations.

  2. Viscosity solutions of fully nonlinear functional parabolic PDE

    Directory of Open Access Journals (Sweden)

    Liu Wei-an

    2005-01-01

    Full Text Available By the technique of coupled solutions, the notion of viscosity solutions is extended to fully nonlinear retarded parabolic equations. Such equations involve many models arising from optimal control theory, economy and finance, biology, and so forth. The comparison principle is shown. Then the existence and uniqueness are established by the fixed point theory.

  3. Lie Symmetries and Solitons in Nonlinear Systems with Spatially Inhomogeneous Nonlinearities

    International Nuclear Information System (INIS)

    Belmonte-Beitia, Juan; Perez-Garcia, Victor M.; Vekslerchik, Vadym; Torres, Pedro J.

    2007-01-01

    Using Lie group theory and canonical transformations, we construct explicit solutions of nonlinear Schroedinger equations with spatially inhomogeneous nonlinearities. We present the general theory, use it to show that localized nonlinearities can support bound states with an arbitrary number solitons, and discuss other applications of interest to the field of nonlinear matter waves

  4. Steady-state Operational Characteristics of Ghana Research ...

    African Journals Online (AJOL)

    Steady state operational characteristics of the 30 kW tank-in-pool type reactor named Ghana Research Reactor-1 were investigated after a successful on-site zero power critical experiments. The steadystate operational character-istics determined were the thermal neutron fluxes, maximum period of operation at nominal ...

  5. The presentation of explicit analytical solutions of a class of nonlinear evolution equations

    International Nuclear Information System (INIS)

    Feng Jinshun; Guo Mingpu; Yuan Deyou

    2009-01-01

    In this paper, we introduce a function set Ω m . There is a conjecture that an arbitrary explicit travelling-wave analytical solution of a real constant coefficient nonlinear evolution equation is necessarily a linear (or nonlinear) combination of the product of some elements in Ω m . A widespread applicable approach for solving a class of nonlinear evolution equations is established. The new analytical solutions to two kinds of nonlinear evolution equations are described with the aid of the guess.

  6. Effect of steady deflections on the aeroelastic stability of a turbine blade

    DEFF Research Database (Denmark)

    Kallesøe, Bjarne Skovmose

    2011-01-01

    This paper deals with effects of geometric non-linearities on the aeroelastic stability of a steady-state defl ected blade. Today, wind turbine blades are long and slender structures that can have a considerable steady-state defl ection which affects the dynamic behaviour of the blade. The fl...... apwise blade defl ection causes the edgewise blade motion to couple to torsional blade motion and thereby to the aerodynamics through the angle of attack. The analysis shows that in the worst case for this particular blade, the edgewise damping can be decreased by half. Copyright © 2010 John Wiley & Sons......, Ltd....

  7. Evidence for forcing-dependent steady states in a turbulent swirling flow.

    Science.gov (United States)

    Saint-Michel, B; Dubrulle, B; Marié, L; Ravelet, F; Daviaud, F

    2013-12-06

    We study the influence on steady turbulent states of the forcing in a von Karman flow, at constant impeller speed, or at constant torque. We find that the different forcing conditions change the nature of the stability of the steady states and reveal dynamical regimes that bear similarities to low-dimensional systems. We suggest that this forcing dependence may be applicable to other turbulent systems.

  8. Constructive interference in steady-state/FIESTA-C clinical applications in neuroimaging

    International Nuclear Information System (INIS)

    Kulkami, Makarand

    2011-01-01

    Full text: High spatial resolution is one of the major problems in neuroimaging, par ticularly in cranial and spinal nerve imaging. Constructive interference in steady-state/fast imaging employing steady-state acquisition with phase cycling is a robust sequence in imaging the cranial and spinal nerve patholo gies. This pictorial review is a concise article about the applications of this sequence in neuroimaging with clinical examples.

  9. Solitary wave solutions to nonlinear evolution equations in ...

    Indian Academy of Sciences (India)

    1Computer Engineering Technique Department, Al-Rafidain University College, Baghdad, ... applied to extract solutions are tan–cot method and functional variable approaches. ... Consider the nonlinear partial differential equation in the form.

  10. Current drive efficiency requirements for an attractive steady-state reactor

    Energy Technology Data Exchange (ETDEWEB)

    Tonon, G

    1994-12-31

    The expected values of the figure of merit and the electrical efficiency of various non-inductive current drive methods are considered. The main experimental results achieved today with neutral beams and radiofrequency systems are summarized. Taking into account the simplified energy flow diagram of a steady state reactor, the figure of merit and the electrical efficiency values which are necessary in order to envisage an attractive steady-state reactor are determined. These values are compared to the theoretical predictions. (author). 16 refs., 11 figs., 2 tabs.

  11. Current drive efficiency requirements for an attractive steady-state reactor

    International Nuclear Information System (INIS)

    Tonon, G.

    1994-01-01

    The expected values of the figure of merit and the electrical efficiency of various non-inductive current drive methods are considered. The main experimental results achieved today with neutral beams and radiofrequency systems are summarized. Taking into account the simplified energy flow diagram of a steady state reactor, the figure of merit and the electrical efficiency values which are necessary in order to envisage an attractive steady-state reactor are determined. These values are compared to the theoretical predictions. (author). 16 refs., 11 figs., 2 tabs

  12. A steady state analysis indicates that negative feedback regulation of PTP1B by Akt elicits bistability in insulin-stimulated GLUT4 translocation

    Directory of Open Access Journals (Sweden)

    Giri Lopamudra

    2004-08-01

    Full Text Available Abstract Background The phenomenon of switch-like response to graded input signal is the theme involved in various signaling pathways in living systems. Positive feedback loops or double negative feedback loops embedded with nonlinearity exhibit these switch-like bistable responses. Such feedback regulations exist in insulin signaling pathway as well. Methods In the current manuscript, a steady state analysis of the metabolic insulin-signaling pathway is presented. The threshold concentration of insulin required for glucose transporter GLUT4 translocation was studied with variation in system parameters and component concentrations. The dose response curves of GLUT4 translocation at various concentration of insulin obtained by steady state analysis were quantified in-terms of half saturation constant. Results We show that, insulin-stimulated GLUT4 translocation can operate as a bistable switch, which ensures that GLUT4 settles between two discrete, but mutually exclusive stable steady states. The threshold concentration of insulin required for GLUT4 translocation changes with variation in system parameters and component concentrations, thus providing insights into possible pathological conditions. Conclusion A steady state analysis indicates that negative feedback regulation of phosphatase PTP1B by Akt elicits bistability in insulin-stimulated GLUT4 translocation. The threshold concentration of insulin required for GLUT4 translocation and the corresponding bistable response at different system parameters and component concentrations was compared with reported experimental observations on specific defects in regulation of the system.

  13. A new auxiliary equation and exact travelling wave solutions of nonlinear equations

    International Nuclear Information System (INIS)

    Sirendaoreji

    2006-01-01

    A new auxiliary ordinary differential equation and its solutions are used for constructing exact travelling wave solutions of nonlinear partial differential equations in a unified way. The main idea of this method is to take full advantage of the auxiliary equation which has more new exact solutions. More new exact travelling wave solutions are obtained for the quadratic nonlinear Klein-Gordon equation, the combined KdV and mKdV equation, the sine-Gordon equation and the Whitham-Broer-Kaup equations

  14. Generalized nonlinear Proca equation and its free-particle solutions

    Energy Technology Data Exchange (ETDEWEB)

    Nobre, F.D. [Centro Brasileiro de Pesquisas Fisicas and National Institute of Science and Technology for Complex Systems, Rio de Janeiro, RJ (Brazil); Plastino, A.R. [Universidad Nacional Buenos Aires-Noreoeste, CeBio y Secretaria de Investigacion, Junin (Argentina)

    2016-06-15

    We introduce a nonlinear extension of Proca's field theory for massive vector (spin 1) bosons. The associated relativistic nonlinear wave equation is related to recently advanced nonlinear extensions of the Schroedinger, Dirac, and Klein-Gordon equations inspired on the non-extensive generalized thermostatistics. This is a theoretical framework that has been applied in recent years to several problems in nuclear and particle physics, gravitational physics, and quantum field theory. The nonlinear Proca equation investigated here has a power-law nonlinearity characterized by a real parameter q (formally corresponding to the Tsallis entropic parameter) in such a way that the standard linear Proca wave equation is recovered in the limit q → 1. We derive the nonlinear Proca equation from a Lagrangian, which, besides the usual vectorial field Ψ{sup μ}(vector x,t), involves an additional field Φ{sup μ}(vector x,t). We obtain exact time-dependent soliton-like solutions for these fields having the form of a q-plane wave, and we show that both field equations lead to the relativistic energy-momentum relation E{sup 2} = p{sup 2}c{sup 2} + m{sup 2}c{sup 4} for all values of q. This suggests that the present nonlinear theory constitutes a new field theoretical representation of particle dynamics. In the limit of massless particles the present q-generalized Proca theory reduces to Maxwell electromagnetism, and the q-plane waves yield localized, transverse solutions of Maxwell equations. Physical consequences and possible applications are discussed. (orig.)

  15. General solution of string inspired nonlinear equations

    International Nuclear Information System (INIS)

    Bandos, I.A.; Ivanov, E.; Kapustnikov, A.A.; Ulanov, S.A.

    1998-07-01

    We present the general solution of the system of coupled nonlinear equations describing dynamics of D-dimensional bosonic string in the geometric (or embedding) approach. The solution is parametrized in terms of two sets of the left- and right-moving Lorentz harmonic variables providing a special coset space realization of the product of two (D-2) dimensional spheres S D-2 = SO(1,D-1)/SO(1,1)xSO(D-2) contained in K D-2 . (author)

  16. An analytical method for solving exact solutions of the nonlinear Bogoyavlenskii equation and the nonlinear diffusive predator–prey system

    Directory of Open Access Journals (Sweden)

    Md. Nur Alam

    2016-06-01

    Full Text Available In this article, we apply the exp(-Φ(ξ-expansion method to construct many families of exact solutions of nonlinear evolution equations (NLEEs via the nonlinear diffusive predator–prey system and the Bogoyavlenskii equations. These equations can be transformed to nonlinear ordinary differential equations. As a result, some new exact solutions are obtained through the hyperbolic function, the trigonometric function, the exponential functions and the rational forms. If the parameters take specific values, then the solitary waves are derived from the traveling waves. Also, we draw 2D and 3D graphics of exact solutions for the special diffusive predator–prey system and the Bogoyavlenskii equations by the help of programming language Maple.

  17. Analytical approximate solutions for a general class of nonlinear delay differential equations.

    Science.gov (United States)

    Căruntu, Bogdan; Bota, Constantin

    2014-01-01

    We use the polynomial least squares method (PLSM), which allows us to compute analytical approximate polynomial solutions for a very general class of strongly nonlinear delay differential equations. The method is tested by computing approximate solutions for several applications including the pantograph equations and a nonlinear time-delay model from biology. The accuracy of the method is illustrated by a comparison with approximate solutions previously computed using other methods.

  18. A solution approach for non-linear analysis of concrete members

    International Nuclear Information System (INIS)

    Hadi, N. M.; Das, S.

    1999-01-01

    Non-linear solution of reinforced concrete structural members, at and beyond its maximum strength poses complex numerical problems. This is due to the fact that concrete exhibits strain softening behaviour once it reaches its maximum strength. This paper introduces an improved non-linear solution capable to overcome the numerical problems efficiently. The paper also presents a new concept of modeling discrete cracks in concrete members by using gap elements. Gap elements are placed in between two adjacent concrete elements in tensile zone. The magnitude of elongation of gap elements, which represents the width of the crack in concrete, increases edith the increase of tensile stress in those elements. As a result, transfer of local from one concrete element to adjacent elements reduces. Results of non-linear finite element analysis of three concrete beams using this new solution strategy are compared with those obtained by other researchers, and a good agreement is achieved. (authors). 13 refs. 9 figs.,

  19. Burn cycle requirements comparison of pulsed and steady-state tokamak reactors

    International Nuclear Information System (INIS)

    Brooks, J.N.; Ehst, D.A.

    1983-12-01

    Burn cycle parameters and energy transfer system requirements were analyzed for an 8-m commercial tokamak reactor using four types of cycles: conventional, hybrid, internal transformer, and steady state. Not surprisingly, steady state is the best burn mode if it can be achieved. The hybrid cycle is a promising alternative to the conventional. In contrast, the internal transformer cycle does not appear attractive for the size tokamak in question

  20. Approximate Solutions of Nonlinear Partial Differential Equations by Modified q-Homotopy Analysis Method

    Directory of Open Access Journals (Sweden)

    Shaheed N. Huseen

    2013-01-01

    Full Text Available A modified q-homotopy analysis method (mq-HAM was proposed for solving nth-order nonlinear differential equations. This method improves the convergence of the series solution in the nHAM which was proposed in (see Hassan and El-Tawil 2011, 2012. The proposed method provides an approximate solution by rewriting the nth-order nonlinear differential equation in the form of n first-order differential equations. The solution of these n differential equations is obtained as a power series solution. This scheme is tested on two nonlinear exactly solvable differential equations. The results demonstrate the reliability and efficiency of the algorithm developed.

  1. Analytic solutions of a class of nonlinearly dynamic systems

    International Nuclear Information System (INIS)

    Wang, M-C; Zhao, X-S; Liu, X

    2008-01-01

    In this paper, the homotopy perturbation method (HPM) is applied to solve a coupled system of two nonlinear differential with first-order similar model of Lotka-Volterra and a Bratus equation with a source term. The analytic approximate solutions are derived. Furthermore, the analytic approximate solutions obtained by the HPM with the exact solutions reveals that the present method works efficiently

  2. Brief communication: A nonlinear self-similar solution to barotropic flow over varying topography

    Science.gov (United States)

    Ibanez, Ruy; Kuehl, Joseph; Shrestha, Kalyan; Anderson, William

    2018-03-01

    Beginning from the shallow water equations (SWEs), a nonlinear self-similar analytic solution is derived for barotropic flow over varying topography. We study conditions relevant to the ocean slope where the flow is dominated by Earth's rotation and topography. The solution is found to extend the topographic β-plume solution of Kuehl (2014) in two ways. (1) The solution is valid for intensifying jets. (2) The influence of nonlinear advection is included. The SWEs are scaled to the case of a topographically controlled jet, and then solved by introducing a similarity variable, η = cxnxyny. The nonlinear solution, valid for topographies h = h0 - αxy3, takes the form of the Lambert W-function for pseudo velocity. The linear solution, valid for topographies h = h0 - αxy-γ, takes the form of the error function for transport. Kuehl's results considered the case -1 ≤ γ < 1 which admits expanding jets, while the new result considers the case γ < -1 which admits intensifying jets and a nonlinear case with γ = -3.

  3. Global optimum spacecraft orbit control subject to bounded thrust in presence of nonlinear and random disturbances in a low earth orbit

    Directory of Open Access Journals (Sweden)

    Tamer Mekky Ahmed Habib

    2012-06-01

    Full Text Available The primary objective of this work is to develop an effective spacecraft orbit control algorithm suitable for spacecraft orbital maneuver and/or rendezvous. The actual governing equation of a spacecraft orbiting the earth is merely nonlinear. Disturbance forces resulting from aerodynamic drag, oblateness of the earth till the fourth order (i.e. J4, and random disturbances are modeled for the initial and target orbits. These disturbances increase the complexity of nonlinear governing equations. Global optimum solutions of the control algorithm parameters are determined throughout real coded genetic algorithms such that the steady state difference between the actual and desired trajectories is minimized. The resulting solutions are constrained to avoid spacecraft collision with the surface of the earth taking into account limited thrust budget.

  4. 40 CFR 1033.515 - Discrete-mode steady-state emission tests of locomotives and locomotive engines.

    Science.gov (United States)

    2010-07-01

    ... 40 Protection of Environment 32 2010-07-01 2010-07-01 false Discrete-mode steady-state emission... Procedures § 1033.515 Discrete-mode steady-state emission tests of locomotives and locomotive engines. This... a warm-up followed by a sequence of nominally steady-state discrete test modes, as described in...

  5. New analytical solutions for nonlinear physical models of the ...

    Indian Academy of Sciences (India)

    In mathematical physics, we studied two complex systems, the Maccari system and the coupled Higgs field equation. We construct sufficient exact solutions for nonlinear evolution equations. To study travelling wave solutions, we used a fractional complex transform to convert the particular partial differential equation of ...

  6. Travelling wave solutions to nonlinear physical models by means

    Indian Academy of Sciences (India)

    This paper presents the first integral method to carry out the integration of nonlinear partial differential equations in terms of travelling wave solutions. For illustration, three important equations of mathematical physics are analytically investigated. Through the established first integrals, exact solutions are successfully ...

  7. Exact Solutions of Five Complex Nonlinear Schrödinger Equations by Semi-Inverse Variational Principle

    International Nuclear Information System (INIS)

    Najafi Mohammad; Arbabi Somayeh

    2014-01-01

    In this paper, we establish exact solutions for five complex nonlinear Schrödinger equations. The semi-inverse variational principle (SVP) is used to construct exact soliton solutions of five complex nonlinear Schrödinger equations. Many new families of exact soliton solutions of five complex nonlinear Schrödinger equations are successfully obtained. (general)

  8. Localized and periodic exact solutions to the nonlinear Schroedinger equation with spatially modulated parameters: Linear and nonlinear lattices

    International Nuclear Information System (INIS)

    Belmonte-Beitia, Juan; Konotop, Vladimir V.; Perez-Garcia, Victor M.; Vekslerchik, Vadym E.

    2009-01-01

    Using similarity transformations we construct explicit solutions of the nonlinear Schroedinger equation with linear and nonlinear periodic potentials. We present explicit forms of spatially localized and periodic solutions, and study their properties. We put our results in the framework of the exploited perturbation techniques and discuss their implications on the properties of associated linear periodic potentials and on the possibilities of stabilization of gap solitons using polychromatic lattices.

  9. Existence of solutions to second-order nonlinear coupled systems with nonlinear coupled boundary conditions

    Directory of Open Access Journals (Sweden)

    Imran Talib

    2015-12-01

    Full Text Available In this article, study the existence of solutions for the second-order nonlinear coupled system of ordinary differential equations $$\\displaylines{ u''(t=f(t,v(t,\\quad t\\in [0,1],\\cr v''(t=g(t,u(t,\\quad t\\in [0,1], }$$ with nonlinear coupled boundary conditions $$\\displaylines{ \\phi(u(0,v(0,u(1,v(1,u'(0,v'(0=(0,0, \\cr \\psi(u(0,v(0,u(1,v(1,u'(1,v'(1=(0,0, }$$ where $f,g:[0,1]\\times \\mathbb{R}\\to \\mathbb{R}$ and $\\phi,\\psi:\\mathbb{R}^6\\to \\mathbb{R}^2$ are continuous functions. Our main tools are coupled lower and upper solutions, Arzela-Ascoli theorem, and Schauder's fixed point theorem.

  10. Nonlinear Schrödinger equations with single power nonlinearity and harmonic potential

    Science.gov (United States)

    Cipolatti, R.; de Macedo Lira, Y.; Trallero-Giner, C.

    2018-03-01

    We consider a generalized nonlinear Schrödinger equation (GNLS) with a single power nonlinearity of the form λ ≤ft\\vert \\varphi \\right\\vert p , with p  >  0 and λ\\in{R} , in the presence of a harmonic confinement. We report the conditions that p and λ must fulfill for the existence and uniqueness of ground states of the GNLS. We discuss the Cauchy problem and summarize which conditions are required for the nonlinear term λ ≤ft\\vert \\varphi \\right\\vert p to render the ground state solutions orbitally stable. Based on a new variational method we provide exact formulæ for the minimum energy for each index p and the changing range of values of the nonlinear parameter λ. Also, we report an approximate close analytical expression for the ground state energy, performing a comparative analysis of the present variational calculations with those obtained by a generalized Thomas-Fermi approach, and soliton solutions for the respective ranges of p and λ where these solutions can be implemented to describe the minimum energy.

  11. TRUMP, Steady-State and Transient 1-D, 2-D and 3-D Potential Flow, Temperature Distribution

    International Nuclear Information System (INIS)

    Elrod, D.C.; Turner, W.D.

    1981-01-01

    1 - Description of problem or function: TRUMP solves a general non- linear parabolic partial differential equation describing flow in various kinds of potential fields, such as fields of temperature, pressure, or electricity and magnetism; simultaneously, it will solve two additional equations representing, in thermal problems, heat production by decomposition of two reactants having rate constants with a general Arrhenius temperature dependence. Steady- state and transient flow in one, two, or three dimensions are considered in geometrical configurations having simple or complex shapes and structures. Problem parameters may vary with spatial position, time, or primary dependent variables--temperature, pressure, or field strength. Initial conditions may vary with spatial position, and among the criteria that may be specified for ending a problem are upper and lower limits on the size of the primary dependent variable, upper limits on the problem time or on the number of time-steps or on the computer time, and attainment of steady state. 2 - Method of solution: Solutions may be obtained by use of explicit- or implicit-difference equations, or by an optimized combination of both. 3 - Restrictions on the complexity of the problem: The program currently provides for maxima of: 40 materials, 5 reactants, 105 surface conditions, 20 boundary nodes, 16 entries per tabulated function (table-length)

  12. Multigrid techniques for nonlinear eigenvalue probems: Solutions of a nonlinear Schroedinger eigenvalue problem in 2D and 3D

    Science.gov (United States)

    Costiner, Sorin; Taasan, Shlomo

    1994-01-01

    This paper presents multigrid (MG) techniques for nonlinear eigenvalue problems (EP) and emphasizes an MG algorithm for a nonlinear Schrodinger EP. The algorithm overcomes the mentioned difficulties combining the following techniques: an MG projection coupled with backrotations for separation of solutions and treatment of difficulties related to clusters of close and equal eigenvalues; MG subspace continuation techniques for treatment of the nonlinearity; an MG simultaneous treatment of the eigenvectors at the same time with the nonlinearity and with the global constraints. The simultaneous MG techniques reduce the large number of self consistent iterations to only a few or one MG simultaneous iteration and keep the solutions in a right neighborhood where the algorithm converges fast.

  13. Influence of longitudinal position on the evolution of steady-state signal in cardiac cine balanced steady-state free precession imaging.

    Science.gov (United States)

    Spear, Tyler J; Stromp, Tori A; Leung, Steve W; Vandsburger, Moriel H

    2017-11-01

    Emerging quantitative cardiac magnetic resonance imaging (CMRI) techniques use cine balanced steady-state free precession (bSSFP) to measure myocardial signal intensity and probe underlying physiological parameters. This correlation assumes that steady-state is maintained uniformly throughout the heart in space and time. To determine the effects of longitudinal cardiac motion and initial slice position on signal deviation in cine bSSFP imaging by comparing two-dimensional (2D) and three-dimensional (3D) acquisitions. Nine healthy volunteers completed cardiac MRI on a 1.5-T scanner. Short axis images were taken at six slice locations using both 2D and 3D cine bSSFP. 3D acquisitions spanned two slices above and below selected slice locations. Changes in myocardial signal intensity were measured across the cardiac cycle and compared to longitudinal shortening. For 2D cine bSSFP, 46% ± 9% of all frames and 84% ± 13% of end-diastolic frames remained within 10% of initial signal intensity. For 3D cine bSSFP the proportions increased to 87% ± 8% and 97% ± 5%. There was no correlation between longitudinal shortening and peak changes in myocardial signal. The initial slice position significantly impacted peak changes in signal intensity for 2D sequences ( P  cine bSSFP that is only restored at the center of a 3D excitation volume. During diastole, a transient steady-state is established similar to that achieved with 3D cine bSSFP regardless of slice location.

  14. Non-linear dynamics and alternating 'flip' solutions in ferrofluidic Taylor-Couette flow

    Science.gov (United States)

    Altmeyer, Sebastian

    2018-04-01

    This study treats with the influence of a symmetry-breaking transversal magnetic field on the nonlinear dynamics of ferrofluidic Taylor-Couette flow - flow confined between two concentric independently rotating cylinders. We detected alternating 'flip' solutions which are flow states featuring typical characteristics of slow-fast-dynamics in dynamical systems. The flip corresponds to a temporal change in the axial wavenumber and we find them to appear either as pure 2-fold axisymmetric (due to the symmetry-breaking nature of the applied transversal magnetic field) or involving non-axisymmetric, helical modes in its interim solution. The latter ones show features of typical ribbon solutions. In any case the flip solutions have a preferential first axial wavenumber which corresponds to the more stable state (slow dynamics) and second axial wavenumber, corresponding to the short appearing more unstable state (fast dynamics). However, in both cases the flip time grows exponential with increasing the magnetic field strength before the flip solutions, living on 2-tori invariant manifolds, cease to exist, with lifetime going to infinity. Further we show that ferrofluidic flow turbulence differ from the classical, ordinary (usually at high Reynolds number) turbulence. The applied magnetic field hinders the free motion of ferrofluid partials and therefore smoothen typical turbulent quantities and features so that speaking of mildly chaotic dynamics seems to be a more appropriate expression for the observed motion.

  15. Exact solutions of the Navier-Stokes equations generalized for flow in porous media

    Science.gov (United States)

    Daly, Edoardo; Basser, Hossein; Rudman, Murray

    2018-05-01

    Flow of Newtonian fluids in porous media is often modelled using a generalized version of the full non-linear Navier-Stokes equations that include additional terms describing the resistance to flow due to the porous matrix. Because this formulation is becoming increasingly popular in numerical models, exact solutions are required as a benchmark of numerical codes. The contribution of this study is to provide a number of non-trivial exact solutions of the generalized form of the Navier-Stokes equations for parallel flow in porous media. Steady-state solutions are derived in the case of flows in a medium with constant permeability along the main direction of flow and a constant cross-stream velocity in the case of both linear and non-linear drag. Solutions are also presented for cases in which the permeability changes in the direction normal to the main flow. An unsteady solution for a flow with velocity driven by a time-periodic pressure gradient is also derived. These solutions form a basis for validating computational models across a wide range of Reynolds and Darcy numbers.

  16. Simulation of steady-state natural convection using CFD

    Energy Technology Data Exchange (ETDEWEB)

    Zitzmann, T.; Pfrommer, P. [Univ. of Applied Sciences, Coberg (Germany); Cook, M.; Rees, S.; Marjanovic, L. [De Montfort Univ., Leicester (United Kingdom). Inst. of Energy and Sustainable Development

    2005-07-01

    Building materials play an important role in the creation of comfortable indoor environments and can reduce dependence on high energy use mechanical systems. Correct predictions between building structure and heat transfer are needed in order to achieve optimal conditions. Heat transfer is dependent on the velocity and temperature distribution in a room, particularly in the wall boundary layer. This paper discussed the modeling of air flow and heat transfer over a heated vertical plate in a differentially-heated cavity using Computational Fluid Dynamics (CFD). Guidelines on the use of CFD with unstructured meshes to model buoyancy-driven flow in a cavity were presented. Benchmark CFD results were compared with published analytical data. The finite volume method was employed using an unstructured mesh containing tetrahedral and prism elements, so that local numerical diffusion was reduced and therefore suitable for complex flows. The code was based on a couple solver for solving the differential equations using the fully implicit discretization method. Hydrodynamic equations were treated as one single system. A false time stepping method was used to reduce the number of iterations required for convergence, which also guided the solutions to a steady-state solution. It was concluded that the methodology achieves accurate predictions, and is suitable for the modeling of heat transfer optimizations. 13 refs., 7 figs.

  17. Closed form solutions of two time fractional nonlinear wave equations

    Science.gov (United States)

    Akbar, M. Ali; Ali, Norhashidah Hj. Mohd.; Roy, Ripan

    2018-06-01

    In this article, we investigate the exact traveling wave solutions of two nonlinear time fractional wave equations. The fractional derivatives are described in the sense of conformable fractional derivatives. In addition, the traveling wave solutions are accomplished in the form of hyperbolic, trigonometric, and rational functions involving free parameters. To investigate such types of solutions, we implement the new generalized (G‧ / G) -expansion method. The extracted solutions are reliable, useful and suitable to comprehend the optimal control problems, chaotic vibrations, global and local bifurcations and resonances, furthermore, fission and fusion phenomena occur in solitons, the relativistic energy-momentum relation, scalar electrodynamics, quantum relativistic one-particle theory, electromagnetic interactions etc. The results reveal that the method is very fruitful and convenient for exploring nonlinear differential equations of fractional order treated in theoretical physics.

  18. Progress and prospect of true steady state operation with RF

    Directory of Open Access Journals (Sweden)

    Jacquinot Jean

    2017-01-01

    Full Text Available Operation of fusion confinement experiments in full steady state is a major challenge for the development towards fusion energy. Critical to achieving this goal is the availability of actively cooled plasma facing components and auxiliary systems withstanding the very harsh plasma environment. Equally challenging are physics issues related to achieving plasma conditions and current drive efficiency required by reactor plasmas. RF heating and current drive systems have been key instruments for obtaining the progress made until today towards steady state. They hold all the records of long pulse plasma operation both in tokamaks and in stellarators. Nevertheless much progress remains to be made in particular for integrating all the requirements necessary for maintaining in steady state the density and plasma pressure conditions of a reactor. This is an important stated aim of ITER and of devices equipped with superconducting magnets. After considering the present state of the art, this review will address the key issues which remain to be solved both in physics and technology for reaching this goal. They constitute very active subjects of research which will require much dedicated experimentation in the new generation of superconducting devices which are now in operation or becoming close to it.

  19. Gravity currents in rotating channels. Part 1. Steady-state theory

    Science.gov (United States)

    Hacker, J. N.; Linden, P. F.

    2002-04-01

    A theory is developed for the speed and structure of steady-state non-dissipative gravity currents in rotating channels. The theory is an extension of that of Benjamin (1968) for non-rotating gravity currents, and in a similar way makes use of the steady-state and perfect-fluid (incompressible, inviscid and immiscible) approximations, and supposes the existence of a hydrostatic ‘control point’ in the current some distance away from the nose. The model allows for fully non-hydrostatic and ageostrophic motion in a control volume V ahead of the control point, with the solution being determined by the requirements, consistent with the perfect-fluid approximation, of energy and momentum conservation in V, as expressed by Bernoulli's theorem and a generalized flow-force balance. The governing parameter in the problem, which expresses the strength of the background rotation, is the ratio W = B/R, where B is the channel width and R = (g[prime prime or minute]H)1/2/f is the internal Rossby radius of deformation based on the total depth of the ambient fluid H. Analytic solutions are determined for the particular case of zero front-relative flow within the gravity current. For each value of W there is a unique non-dissipative two-layer solution, and a non-dissipative one-layer solution which is specified by the value of the wall-depth h0. In the two-layer case, the non-dimensional propagation speed c = cf(g[prime prime or minute]H)[minus sign]1/2 increases smoothly from the non-rotating value of 0.5 as W increases, asymptoting to unity for W [rightward arrow] [infty infinity]. The gravity current separates from the left-hand wall of the channel at W = 0.67 and thereafter has decreasing width. The depth of the current at the right-hand wall, h0, increases, reaching the full depth at W = 1.90, after which point the interface outcrops on both the upper and lower boundaries, with the distance over which the interface slopes being 0.881R. In the one-layer case, the wall

  20. Steady-state spheromak

    International Nuclear Information System (INIS)

    Jarboe, T.R.

    1982-01-01

    A major effort is being made in the national program to make the operation of axisymmetric, toroidal confinement systems steady state by the application of expensive rf current drive. Described here is a method by which such a confinement system, the spheromak, can be refluxed indefinitely through the application of dc power. As a step towards dc sustainment we have operated the present CTX source in the slow source mode with a longer power application time (approx. 0.1 ms) and successfully generated long-lived spheromaks. If the erosion of the electrodes can be controlled as well as it is with MPD arcs then dc operation should be very clean. If only a small fraction (approx. 10% for an experiment) of the poloidal flux of the spheromak connects to the source then the dc sustainment can be very efficient. The amount of connecting flux that is necessary for sustainment needs to be determined experimentally

  1. Any order approximate analytical solution of the nonlinear Volterra's integral equation for accelerator dynamic systems

    International Nuclear Information System (INIS)

    Liu Chunliang; Xie Xi; Chen Yinbao

    1991-01-01

    The universal nonlinear dynamic system equation is equivalent to its nonlinear Volterra's integral equation, and any order approximate analytical solution of the nonlinear Volterra's integral equation is obtained by exact analytical method, thus giving another derivation procedure as well as another computation algorithm for the solution of the universal nonlinear dynamic system equation

  2. The Steady State Calculation for SMART with MIDAS/SMR

    International Nuclear Information System (INIS)

    Park, Jong Hwa; Kim, Dong Ha; Chung, Young Jong; Park, Sun Hee; Cho, Seong Won

    2010-01-01

    KAERI is developing a new concept of reactor that all the main components such as the steam generator, the coolant pumps and the pressurizer are located inside the reactor vessel. Before the severe accident sequences are estimated, it is prerequisite that MIDAS code predicts the steady state conditions properly. But MIDAS code does not include the heat transfer model for the helical tube. Therefore, the heat transfer models for the helical tube from TASS/SMR-S were implemented into MIDAS code. To estimate the validity of the implemented heat transfer correlations for the helical tube and the input data, the steady state was recalculated with MIDAS/SMR based on design level 2 and compared with the design values

  3. On the optimization of a steady-state bootstrap-reactor

    International Nuclear Information System (INIS)

    Polevoy, A.R.; Martynov, A.A.; Medvedev, S.Yu.

    1993-01-01

    A commercial fusion tokamak-reactor may be economically acceptable only for low recirculating power fraction r 0 ≡ P CD /P α BS ≡I BS /I > 0.9 to sustain the steady-state operation mode for high plasma densities > 1.5 10 20 m -3 , fulfilled the divertor conditions. This paper presents the approximate expressions for the optimal set of reactor parameters for r BS /I∼1, based on the self-consistent plasma simulations by 1.5D ASTRA code. The linear MHD stability analysis for ideal n=1 kink and ballooning modes has been carried out to determine the conditions of stabilization for bootstrap steady state tokamak reactor BSSTR configurations. (author) 10 refs., 1 tab

  4. Steady-state creep of discontinuous fibre composites

    International Nuclear Information System (INIS)

    Boecker Pedersen, O.

    1975-07-01

    A review is given of the relevant literature on creep of composites, including a presentation of existing models for the steady-state creep of composites containing aligned discontinuous fibres where creep of the matrix and fibres is assumed to follow a power law. A model is suggested for predicting the composite creep law from a matrix creep law given in a general form, in the case where the fibres do not creep. The composite creep law predicted by this model is compared with those predicted by previous models, when these are extended to comprise a general matrix creep law. Experimentally, pure copper and composites consisting of aligned discontinuous tungsten fibres in a copper matrix were creep tested at a temperature of 500 deg C. The results indicate a relatively low stress sensitivity of the steady-state creep-rate for pure copper and relatively high stress sensitivity for the composites. This may be explained by the creep models based upon a general matrix creep law. A quantitative prediction shows promising agreement with the present experimental results. (author)

  5. Steady state statistical correlations predict bistability in reaction motifs.

    Science.gov (United States)

    Chakravarty, Suchana; Barik, Debashis

    2017-03-28

    Various cellular decision making processes are regulated by bistable switches that take graded input signals and convert them to binary all-or-none responses. Traditionally, a bistable switch generated by a positive feedback loop is characterized either by a hysteretic signal response curve with two distinct signaling thresholds or by characterizing the bimodality of the response distribution in the bistable region. To identify the intrinsic bistability of a feedback regulated network, here we propose that bistability can be determined by correlating higher order moments and cumulants (≥2) of the joint steady state distributions of two components connected in a positive feedback loop. We performed stochastic simulations of four feedback regulated models with intrinsic bistability and we show that for a bistable switch with variation of the signal dose, the steady state variance vs. covariance adopts a signatory cusp-shaped curve. Further, we find that the (n + 1)th order cross-cumulant vs. nth order cross-cumulant adopts a closed loop structure for at least n = 3. We also propose that our method is capable of identifying systems without intrinsic bistability even though the system may show bimodality in the marginal response distribution. The proposed method can be used to analyze single cell protein data measured at steady state from experiments such as flow cytometry.

  6. Understanding void fraction in steady state and dynamic environments

    International Nuclear Information System (INIS)

    Chexal, B.; Maulbetsch, J.; Harrison, J.; Petersen, C.; Jensen, P.; Horowitz, J.

    1997-01-01

    Understanding void fraction behavior in steady-state and dynamic environments is important to accurately predict the thermal-hydraulic behavior of two-phase or two-component systems. The Chexal-Lellouche (C-L) void fraction mode described herein covers the full range of pressures, flows, void fractions, and fluid types (steam-water, air-water, and refrigerants). A drift flux model formulation is used which covers the complete range of concurrent and countercurrent flows. The (1996) model revises the earlier C-L void fraction correlation, improves the capability of the model in countercurrent flow based on the incorporation of additional data, and improves the characteristics of the correlation that are important in transient programs. The model has been qualified with data from a number of steady state two-phase and two-component tests, and has been incorporated into the transient analysis code RELAP5 and RETRAN-3D and evaluated with a variety of transient and steady state tests. A 'plug-in' module for the void fraction correlation has been developed and implemented in RELAP5 and RETRAN-3D. The module is available as source code for inclusion into other thermal-hydraulic programs and can be used in any program that utilizes the same interface variables

  7. Stationary solutions and self-trapping in discrete quadratic nonlinear systems

    DEFF Research Database (Denmark)

    Bang, Ole; Christiansen, Peter Leth; Clausen, Carl A. Balslev

    1998-01-01

    We consider the simplest equations describing coupled quadratic nonlinear (chi((2))) systems, which each consists of a fundamental mode resonantly interacting with its second harmonic. Such discrete equations apply, e.g., to optics, where they can describe arrays of chi((2)) waveguides...... the nonintegrable dimer reduce to the discrete nonlinear Schrodinger (DNLS) equation with two degrees of freedom, which is integrable. We show how the stationary solutions to the two systems correspond to each other and how the self-trapped DNLS solutions gradually develop chaotic dynamics in the chi((2)) system...

  8. Extracting Steady State Components from Synchrophasor Data Using Kalman Filters

    Directory of Open Access Journals (Sweden)

    Farhan Mahmood

    2016-04-01

    Full Text Available Data from phasor measurement units (PMUs may be exploited to provide steady state information to the applications which require it. As PMU measurements may contain errors and missing data, the paper presents the application of a Kalman Filter technique for real-time data processing. PMU data captures the power system’s response at different time-scales, which are generated by different types of power system events; the presented Kalman Filter methods have been applied to extract the steady state components of PMU measurements that can be fed to steady state applications. Two KF-based methods have been proposed, i.e., a windowing-based KF method and “the modified KF”. Both methods are capable of reducing noise, compensating for missing data and filtering outliers from input PMU signals. A comparison of proposed methods has been carried out using the PMU data generated from a hardware-in-the-loop (HIL experimental setup. In addition, a performance analysis of the proposed methods is performed using an evaluation metric.

  9. Non-intrusive reduced order modeling of nonlinear problems using neural networks

    Science.gov (United States)

    Hesthaven, J. S.; Ubbiali, S.

    2018-06-01

    We develop a non-intrusive reduced basis (RB) method for parametrized steady-state partial differential equations (PDEs). The method extracts a reduced basis from a collection of high-fidelity solutions via a proper orthogonal decomposition (POD) and employs artificial neural networks (ANNs), particularly multi-layer perceptrons (MLPs), to accurately approximate the coefficients of the reduced model. The search for the optimal number of neurons and the minimum amount of training samples to avoid overfitting is carried out in the offline phase through an automatic routine, relying upon a joint use of the Latin hypercube sampling (LHS) and the Levenberg-Marquardt (LM) training algorithm. This guarantees a complete offline-online decoupling, leading to an efficient RB method - referred to as POD-NN - suitable also for general nonlinear problems with a non-affine parametric dependence. Numerical studies are presented for the nonlinear Poisson equation and for driven cavity viscous flows, modeled through the steady incompressible Navier-Stokes equations. Both physical and geometrical parametrizations are considered. Several results confirm the accuracy of the POD-NN method and show the substantial speed-up enabled at the online stage as compared to a traditional RB strategy.

  10. Some problems on non-linear semigroups and the blow-up of integral solutions

    International Nuclear Information System (INIS)

    Pavel, N.H.

    1983-07-01

    After some introductory remarks, this highly mathematical document considers a unifying approach in the theory of non-linear semigroups. Then a brief survey is given on blow-up of mild solutions from the semilinear case. Finally, the global behavior of solutions to non-linear evolution equations is addressed; it is found that classical results on the behavior of the maximal solution u as t up-arrow tsub(max) hold also for integral solutions

  11. Numerical solution of non-linear diffusion problems

    International Nuclear Information System (INIS)

    Carmen, A. del; Ferreri, J.C.

    1998-01-01

    This paper presents a method for the numerical solution of non-linear diffusion problems using finite-differences in moving grids. Due to the presence of steep fronts in the solution domain and to the presence of advective terms originating in the grid movement, an implicit TVD scheme, first order in time and second order in space has been developed. Some algebraic details of the derivation are given. Results are shown for the pure advection of a scalar as a test case and an example dealing with the slow spreading of viscous fluids over plane surfaces. The agreement between numerical and analytical solutions is excellent. (author). 8 refs., 3 figs

  12. Variation Iteration Method for The Approximate Solution of Nonlinear ...

    African Journals Online (AJOL)

    In this study, we considered the numerical solution of the nonlinear Burgers equation using the Variational Iteration Method (VIM). The method seeks to examine the convergence of solutions of the Burgers equation at the expense of the parameters x and t of which the amount of errors depends. Numerical experimentation ...

  13. Analysis of physical properties controlling steady-state infiltration rates on tropical savannah soils

    International Nuclear Information System (INIS)

    Mbagwu, J.S.C.

    1993-10-01

    A knowledge of physical properties influencing the steady-state infiltration rates (ic) of soils is needed for the hydrologic modelling of the infiltration process. In this study evidence is provided to show that effective porosity (Pe) (i.e. the proportion of macro pore spaces with equivalent radius of > 15 μm) and dry bulk density are the most important soil physical properties controlling the steady-state infiltration rates on a tropical savannah with varying land use histories. At a macro porosity value of ≤ 5.0% the steady-state infiltration rate is zero. Total porosity and the proportion of water-retaining pores explained only a small fraction of the variation in this property. Steady-state infiltration rates can also be estimated from either the saturated hydraulic conductivity (Ks) by the equation, i c = 31.1 + 1.06 (Ks), (R 2 = 0.8104, p ≤ 0.001) or the soil water transmissivity (A) by the equation, i c = 30.0 + 29.9(A), (R 2 = 0.8228, ρ ≤ 0.001). The Philip two-parameter model under predicted steady-state infiltration rates generally. Considering the ease of determination and reliability it is suggested that effective porosity be used to estimate the steady-state infiltration rates of these other soils with similar characteristics. The model is, i c 388.7(Pe) - 10.8(R 2 = 0.7265, p ≤ 0.001) where i c is in (cm/hr) and Pe in (cm 3 /cm 3 ). (author). 20 refs, 3 figs, 4 tabs

  14. An implicit meshless scheme for the solution of transient non-linear Poisson-type equations

    KAUST Repository

    Bourantas, Georgios

    2013-07-01

    A meshfree point collocation method is used for the numerical simulation of both transient and steady state non-linear Poisson-type partial differential equations. Particular emphasis is placed on the application of the linearization method with special attention to the lagging of coefficients method and the Newton linearization method. The localized form of the Moving Least Squares (MLS) approximation is employed for the construction of the shape functions, in conjunction with the general framework of the point collocation method. Computations are performed for regular nodal distributions, stressing the positivity conditions that make the resulting system stable and convergent. The accuracy and the stability of the proposed scheme are demonstrated through representative and well-established benchmark problems. © 2013 Elsevier Ltd.

  15. An implicit meshless scheme for the solution of transient non-linear Poisson-type equations

    KAUST Repository

    Bourantas, Georgios; Burganos, Vasilis N.

    2013-01-01

    A meshfree point collocation method is used for the numerical simulation of both transient and steady state non-linear Poisson-type partial differential equations. Particular emphasis is placed on the application of the linearization method with special attention to the lagging of coefficients method and the Newton linearization method. The localized form of the Moving Least Squares (MLS) approximation is employed for the construction of the shape functions, in conjunction with the general framework of the point collocation method. Computations are performed for regular nodal distributions, stressing the positivity conditions that make the resulting system stable and convergent. The accuracy and the stability of the proposed scheme are demonstrated through representative and well-established benchmark problems. © 2013 Elsevier Ltd.

  16. Full transmission modes and steady states in defect gratings,

    NARCIS (Netherlands)

    van Groesen, Embrecht W.C.; Sopaheluwakan, A.; Andonowati, A.; de Ridder, R.M; Altena, G; Geuzebroek, D.H.; Dekker, R

    2003-01-01

    For a symmetric grating structure with a defect, we show that a fully transmitted defect mode in the band gap can be obtained as a superposition of two steady states: an amplified and an attenuated defect state. Without scanning the whole band gap by transmission calculations, this simplifies the

  17. Bioaccumulation factors and the steady state assumption for cesium isotopes in aquatic foodwebs near nuclear facilities.

    Science.gov (United States)

    Rowan, D J

    2013-07-01

    Steady state approaches, such as transfer coefficients or bioaccumulation factors, are commonly used to model the bioaccumulation of (137)Cs in aquatic foodwebs from routine operations and releases from nuclear generating stations and other nuclear facilities. Routine releases from nuclear generating stations and facilities, however, often consist of pulses as liquid waste is stored, analyzed to ensure regulatory compliance and then released. The effect of repeated pulse releases on the steady state assumption inherent in the bioaccumulation factor approach has not been evaluated. In this study, I examine the steady state assumption for aquatic biota by analyzing data for two cesium isotopes in the same biota, one isotope in steady state (stable (133)Cs) from geologic sources and the other released in pulses ((137)Cs) from reactor operations. I also compare (137)Cs bioaccumulation factors for similar upstream populations from the same system exposed solely to weapon test (137)Cs, and assumed to be in steady state. The steady state assumption appears to be valid for small organisms at lower trophic levels (zooplankton, rainbow smelt and 0+ yellow perch) but not for older and larger fish at higher trophic levels (walleye). Attempts to account for previous exposure and retention through a biokinetics approach had a similar effect on steady state, upstream and non-steady state, downstream populations of walleye, but were ineffective in explaining the more or less constant deviation between fish with steady state exposures and non-steady state exposures of about 2-fold for all age classes of walleye. These results suggest that for large, piscivorous fish, repeated exposure to short duration, pulse releases leads to much higher (137)Cs BAFs than expected from (133)Cs BAFs for the same fish or (137)Cs BAFs for similar populations in the same system not impacted by reactor releases. These results suggest that the steady state approach should be used with caution in any

  18. Continuous dependence estimates for viscosity solutions of fully nonlinear degenerate elliptic equations

    Directory of Open Access Journals (Sweden)

    Espen R. Jakobsen

    2002-05-01

    Full Text Available Using the maximum principle for semicontinuous functions [3,4], we prove a general ``continuous dependence on the nonlinearities'' estimate for bounded Holder continuous viscosity solutions of fully nonlinear degenerate elliptic equations. Furthermore, we provide existence, uniqueness, and Holder continuity results for bounded viscosity solutions of such equations. Our results are general enough to encompass Hamilton-Jacobi-Bellman-Isaacs's equations of zero-sum, two-player stochastic differential games. An immediate consequence of the results obtained herein is a rate of convergence for the vanishing viscosity method for fully nonlinear degenerate elliptic equations.

  19. Even and odd combinations of nonlinear coherent states

    International Nuclear Information System (INIS)

    De los Santos-Sanchez, O; Recamier, J

    2011-01-01

    In this work we present some statistical properties of even and odd combinations of nonlinear coherent states associated with two nonlinear potentials; one supporting a finite number of bound states and the other supporting an infinite number of bound states, within the framework of an f-deformed algebra. We calculate their normalized variance and the temporal evolution of their dispersion relations using nonlinear coherent states defined as (a) eigensates of the deformed annihilation operator and (b) those states created by the application of a deformed displacement operator upon the ground state of the oscillator.

  20. Vacuum system problems of EBT: a steady-state fusion experiment

    International Nuclear Information System (INIS)

    Livesey, R.L.

    1981-01-01

    Many of the vacuum problems faced by EBT will soon be shared by other plasma devices as high-power microwave systems and long pulse lengths become more common. The solutions used on EBT (such as the raised lip with elastomer seal) are not unique; however, experience has shown that microwave-compatible designs must be carefully thought out. All details of the vacuum must be carefully thought out. All details of the vacuum must be carefully screened in advance to insure that microwaves do not leak into pumps or diagnostics where they can cause major damage. Sputter coating, which even now is noticeably present in most pulsed plasma systems, becomes much worse as systems approach steady state. And finally, radiation degradation of components which is presently a minor problem will become significant on high-power microwave-fed devices, such as EBT-P

  1. Time Reversibility, Correlation Decay and the Steady State Fluctuation Relation for Dissipation

    Directory of Open Access Journals (Sweden)

    Denis J. Evans

    2013-04-01

    Full Text Available Steady state fluctuation relations for nonequilibrium systems are under intense investigation because of their important practical implications in nanotechnology and biology. However the precise conditions under which they hold need clarification. Using the dissipation function, which is related to the entropy production of linear irreversible thermodynamics, we show time reversibility, ergodic consistency and a recently introduced form of correlation decay, called T-mixing, are sufficient conditions for steady state fluctuation relations to hold. Our results are not restricted to a particular model and show that the steady state fluctuation relation for the dissipation function holds near or far from equilibrium subject to these conditions. The dissipation function thus plays a comparable role in nonequilibrium systems to thermodynamic potentials in equilibrium systems.

  2. Existence of Solutions of Nonlinear Integrodifferential Equations of ...

    Indian Academy of Sciences (India)

    Abstract. In this paper we prove the existence of mild and strong solutions of a nonlinear integrodifferential equation of Sobolev type with nonlocal condition. The results are obtained by using semigroup theory and the Schauder fixed point theorem.

  3. Exact travelling wave solutions for some important nonlinear ...

    Indian Academy of Sciences (India)

    The study of nonlinear partial differential equations is an active area of research in applied mathematics, theoretical physics and engineering fields. In particular ... In [16–18], the author applied this method to construct the exact solutions of.

  4. Exact solutions for an oscillator with anti-symmetric quadratic nonlinearity

    Science.gov (United States)

    Beléndez, A.; Martínez, F. J.; Beléndez, T.; Pascual, C.; Alvarez, M. L.; Gimeno, E.; Arribas, E.

    2018-04-01

    Closed-form exact solutions for an oscillator with anti-symmetric quadratic nonlinearity are derived from the first integral of the nonlinear differential equation governing the behaviour of this oscillator. The mathematical model is an ordinary second order differential equation in which the sign of the quadratic nonlinear term changes. Two parameters characterize this oscillator: the coefficient of the linear term and the coefficient of the quadratic term. Not only the common case in which both coefficients are positive but also all possible combinations of positive and negative signs of these coefficients which provide periodic motions are considered, giving rise to four different cases. Three different periods and solutions are obtained, since the same result is valid in two of these cases. An interesting feature is that oscillatory motions whose equilibrium points are not at x = 0 are also considered. The periods are given in terms of an incomplete or complete elliptic integral of the first kind, and the exact solutions are expressed as functions including Jacobi elliptic cosine or sine functions.

  5. New exact travelling wave solutions for the generalized nonlinear Schroedinger equation with a source

    International Nuclear Information System (INIS)

    Abdou, M.A.

    2008-01-01

    The generalized F-expansion method with a computerized symbolic computation is used for constructing a new exact travelling wave solutions for the generalized nonlinear Schrodinger equation with a source. As a result, many exact travelling wave solutions are obtained which include new periodic wave solution, trigonometric function solutions and rational solutions. The method is straightforward and concise, and it can also be applied to other nonlinear evolution equations in physics

  6. Closed form solutions of two time fractional nonlinear wave equations

    Directory of Open Access Journals (Sweden)

    M. Ali Akbar

    2018-06-01

    Full Text Available In this article, we investigate the exact traveling wave solutions of two nonlinear time fractional wave equations. The fractional derivatives are described in the sense of conformable fractional derivatives. In addition, the traveling wave solutions are accomplished in the form of hyperbolic, trigonometric, and rational functions involving free parameters. To investigate such types of solutions, we implement the new generalized (G′/G-expansion method. The extracted solutions are reliable, useful and suitable to comprehend the optimal control problems, chaotic vibrations, global and local bifurcations and resonances, furthermore, fission and fusion phenomena occur in solitons, the relativistic energy-momentum relation, scalar electrodynamics, quantum relativistic one-particle theory, electromagnetic interactions etc. The results reveal that the method is very fruitful and convenient for exploring nonlinear differential equations of fractional order treated in theoretical physics. Keywords: Traveling wave solution, Soliton, Generalized (G′/G-expansion method, Time fractional Duffing equation, Time fractional Riccati equation

  7. Exact criteria for uniqueness and multiplicity of an nth order chemical reaction via catastrophe theory approach. [Determines boundaries between unique and multiple steady state conditions

    Energy Technology Data Exchange (ETDEWEB)

    Chang, H C; Calo, J M

    1979-01-01

    A simple, generalized technique for the exact determination of the boundaries between regions of unique and of multiple solutions to certain nonlinear equations was developed by applying catastrophe theory to the mapping of implicit and explicit functions. Its application to an nth order reaction in continuous stirred tank reactor (CSTR) yields exact, explicit expressions for the boundaries between regions of single and multiple steady states, expressed in terms of the dimensionless heat transfer coefficient and activation energy. An exact implicit expression for the boundaries between regions of uniqueness and multiplicity was also derived for an nth order reaction in a catalyst particle with an intraparticle concentration gradient and uniform temperature and is fully demonstrated for the first-order reaction. In addition, explicit criteria were developed by assuming the limits on d ln g/d ln q, where g is the effectiveness factor and q the Thiele modulus, proposed by van den Bosch and Luss.

  8. Efficient decoding with steady-state Kalman filter in neural interface systems.

    Science.gov (United States)

    Malik, Wasim Q; Truccolo, Wilson; Brown, Emery N; Hochberg, Leigh R

    2011-02-01

    The Kalman filter is commonly used in neural interface systems to decode neural activity and estimate the desired movement kinematics. We analyze a low-complexity Kalman filter implementation in which the filter gain is approximated by its steady-state form, computed offline before real-time decoding commences. We evaluate its performance using human motor cortical spike train data obtained from an intracortical recording array as part of an ongoing pilot clinical trial. We demonstrate that the standard Kalman filter gain converges to within 95% of the steady-state filter gain in 1.5±0.5 s (mean ±s.d.). The difference in the intended movement velocity decoded by the two filters vanishes within 5 s, with a correlation coefficient of 0.99 between the two decoded velocities over the session length. We also find that the steady-state Kalman filter reduces the computational load (algorithm execution time) for decoding the firing rates of 25±3 single units by a factor of 7.0±0.9. We expect that the gain in computational efficiency will be much higher in systems with larger neural ensembles. The steady-state filter can thus provide substantial runtime efficiency at little cost in terms of estimation accuracy. This far more efficient neural decoding approach will facilitate the practical implementation of future large-dimensional, multisignal neural interface systems.

  9. The quasi-steady state of the valley wind system

    Directory of Open Access Journals (Sweden)

    Juerg eSchmidli

    2015-12-01

    Full Text Available The quasi-steady-state limit of the diurnal valley wind system is investigated overidealized three-dimensional topography. Although this limit is rarely attained inreality due to ever-changing forcings, the investigation of this limit canprovide valuable insight, in particular on the mass and heat fluxes associatedwith the along-valley wind. We derive a scaling relation for the quasi-steady-state along-valleymass flux as a function of valley geometry, valley size, atmospheric stratification,and surface sensible heat flux forcing. The scaling relation is tested by comparisonwith the mass flux diagnosed from numerical simulations of the valleywind system. Good agreement is found. The results also provide insight into the relationbetween surface friction and the strength of the along-valley pressure gradient.

  10. Soliton solution for nonlinear partial differential equations by cosine-function method

    International Nuclear Information System (INIS)

    Ali, A.H.A.; Soliman, A.A.; Raslan, K.R.

    2007-01-01

    In this Letter, we established a traveling wave solution by using Cosine-function algorithm for nonlinear partial differential equations. The method is used to obtain the exact solutions for five different types of nonlinear partial differential equations such as, general equal width wave equation (GEWE), general regularized long wave equation (GRLW), general Korteweg-de Vries equation (GKdV), general improved Korteweg-de Vries equation (GIKdV), and Coupled equal width wave equations (CEWE), which are the important soliton equations

  11. Exact solitary and periodic wave solutions for a generalized nonlinear Schroedinger equation

    International Nuclear Information System (INIS)

    Sun Chengfeng; Gao Hongjun

    2009-01-01

    The generalized nonlinear Schroedinger equation (GNLS) iu t + u xx + β | u | 2 u + γ | u | 4 u + iα (| u | 2 u) x + iτ(| u | 2 ) x u = 0 is studied. Using the bifurcation of travelling waves of this equation, some exact solitary wave solutions were obtained in [Wang W, Sun J,Chen G, Bifurcation, Exact solutions and nonsmooth behavior of solitary waves in the generalized nonlinear Schroedinger equation. Int J Bifucat Chaos 2005:3295-305.]. In this paper, more explicit exact solitary wave solutions and some new smooth periodic wave solutions are obtained.

  12. Bright and dark soliton solutions for some nonlinear fractional differential equations

    International Nuclear Information System (INIS)

    Guner, Ozkan; Bekir, Ahmet

    2016-01-01

    In this work, we propose a new approach, namely ansatz method, for solving fractional differential equations based on a fractional complex transform and apply it to the nonlinear partial space–time fractional modified Benjamin–Bona–Mahoney (mBBM) equation, the time fractional mKdV equation and the nonlinear fractional Zoomeron equation which gives rise to some new exact solutions. The physical parameters in the soliton solutions: amplitude, inverse width, free parameters and velocity are obtained as functions of the dependent model coefficients. This method is suitable and more powerful for solving other kinds of nonlinear fractional PDEs arising in mathematical physics. Since the fractional derivatives are described in the modified Riemann–Liouville sense. (paper)

  13. A Review of Fusion and Tokamak Research Towards Steady-State Operation: A JAEA Contribution

    Directory of Open Access Journals (Sweden)

    Mitsuru Kikuchi

    2010-11-01

    Full Text Available Providing a historical overview of 50 years of fusion research, a review of the fundamentals and concepts of fusion and research efforts towards the implementation of a steady state tokamak reactor is presented. In 1990, a steady-state tokamak reactor (SSTR best utilizing the bootstrap current was developed. Since then, significant efforts have been made in major tokamaks, including JT-60U, exploring advanced regimes relevant to the steady state operation of tokamaks. In this paper, the fundamentals of fusion and plasma confinement, and the concepts and research on current drive and MHD stability of advanced tokamaks towards realization of a steady-state tokamak reactor are reviewed, with an emphasis on the contributions of the JAEA. Finally, a view of fusion energy utilization in the 21st century is introduced.

  14. Finite element modelling of creep process - steady state stresses and strains

    Directory of Open Access Journals (Sweden)

    Sedmak Aleksandar S.

    2014-01-01

    Full Text Available Finite element modelling of steady state creep process has been described. Using an analogy of visco-plastic problem with a described procedure, the finite element method has been used to calculate steady state stresses and strains in 2D problems. An example of application of such a procedure have been presented, using real life problem - cylindrical pipe with longitudinal crack at high temperature, under internal pressure, and estimating its residual life, based on the C*integral evaluation.

  15. Derivation and solution of a time-dependent, nonlinear, Schrodinger-like equation for the superconductivity order parameter

    International Nuclear Information System (INIS)

    Esrick, M.A.

    1981-01-01

    A time-dependent, nonlinear, Schrodinger-like equation for the superconductivity order parameter is derived from the Gor'kov equations. Three types of traveling wave solutions of the equation are discussed. The phases and amplitudes of these solutions propagate at different speeds. The first type of solution has an amplitude that propagates as a soliton and it is suggested that this solution might correspond to the recently observed propagating collective modes of the order parameter. The amplitude of the second type of solution propagates as a periodic disturbance in space and time. It is suggested that this type of solution might explain the recently observed multiple values of the superconductor energy gap as well as the spatially inhomogenous superconducting state. The third type of solution, which is of a more general character, might provide some insight into non-periodic, inhomogeneous states occuring in superconductors. It is also proposed that quasiparticle injection and microwave irradiation might generate soliton-like disturbances in superconductors

  16. Exact solutions of certain nonlinear chemotaxis diffusion reaction ...

    Indian Academy of Sciences (India)

    constructed coupled differential equations. The results obtained ... Nonlinear diffusion reaction equation; chemotaxis; auxiliary equation method; solitary wave solutions. ..... fact limits the scope of applications of the derived results. ... Research Fellowship and AP acknowledges DU and DST for PURSE grant for financial.

  17. Efficient multigrid computation of steady hypersonic flows

    NARCIS (Netherlands)

    Koren, B.; Hemker, P.W.; Murthy, T.K.S.

    1991-01-01

    In steady hypersonic flow computations, Newton iteration as a local relaxation procedure and nonlinear multigrid iteration as an acceleration procedure may both easily fail. In the present chapter, same remedies are presented for overcoming these problems. The equations considered are the steady,

  18. 40 CFR 86.1363-2007 - Steady-state testing with a discrete-mode cycle.

    Science.gov (United States)

    2010-07-01

    ... 40 Protection of Environment 19 2010-07-01 2010-07-01 false Steady-state testing with a discrete-mode cycle. 86.1363-2007 Section 86.1363-2007 Protection of Environment ENVIRONMENTAL PROTECTION AGENCY... Exhaust Test Procedures § 86.1363-2007 Steady-state testing with a discrete-mode cycle. This section...

  19. Perturbation method for periodic solutions of nonlinear jerk equations

    International Nuclear Information System (INIS)

    Hu, H.

    2008-01-01

    A Lindstedt-Poincare type perturbation method with bookkeeping parameters is presented for determining accurate analytical approximate periodic solutions of some third-order (jerk) differential equations with cubic nonlinearities. In the process of the solution, higher-order approximate angular frequencies are obtained by Newton's method. A typical example is given to illustrate the effectiveness and simplicity of the proposed method

  20. Herd-Level Modeling and Steady-State Livestock Productivity ...

    African Journals Online (AJOL)

    ... an outline of the scope for applications and addresses the prospects for refinement and model extensions. The algorithms for use in development of steady state derivations include transition of matrices in a Markov Chain approach, continuous differential equations and actuarial approach built on life and fecundity tables.

  1. Principle of Entropy Maximization for Nonequilibrium Steady States

    DEFF Research Database (Denmark)

    Shapiro, Alexander; Stenby, Erling Halfdan

    2002-01-01

    The goal of this contribution is to find out to what extent the principle of entropy maximization, which serves as a basis for the equilibrium thermodynamics, may be generalized onto non-equilibrium steady states. We prove a theorem that, in the system of thermodynamic coordinates, where entropy...

  2. Enhanced Multistage Homotopy Perturbation Method: Approximate Solutions of Nonlinear Dynamic Systems

    Directory of Open Access Journals (Sweden)

    Daniel Olvera

    2014-01-01

    Full Text Available We introduce a new approach called the enhanced multistage homotopy perturbation method (EMHPM that is based on the homotopy perturbation method (HPM and the usage of time subintervals to find the approximate solution of differential equations with strong nonlinearities. We also study the convergence of our proposed EMHPM approach based on the value of the control parameter h by following the homotopy analysis method (HAM. At the end of the paper, we compare the derived EMHPM approximate solutions of some nonlinear physical systems with their corresponding numerical integration solutions obtained by using the classical fourth order Runge-Kutta method via the amplitude-time response curves.

  3. Steady-state operation of spheromaks by inductive techniques

    International Nuclear Information System (INIS)

    Janos, A.

    1984-04-01

    A method to maintain a steady-state spheromak configuration inductively using the S-1 Spheromak device is described. The S-1 Spheromak formation apparatus can be utilized to inject magnetic helicity continuously (C.W., not pulsed or D.C.) into the spheromak configuration after equilibrium is achieved in the linked mode of operation. Oscillation of both poloidal- and toroidal-field currents in the flux core (psi-phi Pumping), with proper phasing, injects a net time-averaged helicity into the plasma. Steady-state maintenance relies on flux conversion, which has been earlier identified. Relevant experimental data from the operation of S-1 are described. Helicity flow has been measured and the proposed injection scheme simulated. In a reasonable time practical voltages and frequencies can inject an amount of helicity comparable to that in the initial plasma. Plasma currents can be maintained or increased. This pumping technique is similar to F-THETA Pumping of a Reversed-Field-Pinch but is applied to this inverse-pinch formation

  4. Statistical steady states in turbulent droplet condensation

    Science.gov (United States)

    Bec, Jeremie; Krstulovic, Giorgio; Siewert, Christoph

    2017-11-01

    We investigate the general problem of turbulent condensation. Using direct numerical simulations we show that the fluctuations of the supersaturation field offer different conditions for the growth of droplets which evolve in time due to turbulent transport and mixing. This leads to propose a Lagrangian stochastic model consisting of a set of integro-differential equations for the joint evolution of the squared radius and the supersaturation along droplet trajectories. The model has two parameters fixed by the total amount of water and the thermodynamic properties, as well as the Lagrangian integral timescale of the turbulent supersaturation. The model reproduces very well the droplet size distributions obtained from direct numerical simulations and their time evolution. A noticeable result is that, after a stage where the squared radius simply diffuses, the system converges exponentially fast to a statistical steady state independent of the initial conditions. The main mechanism involved in this convergence is a loss of memory induced by a significant number of droplets undergoing a complete evaporation before growing again. The statistical steady state is characterised by an exponential tail in the droplet mass distribution.

  5. Jumps and bi-stability in the phase-gain characteristics of a nonlinear parametric amplifier

    DEFF Research Database (Denmark)

    Neumeyer, Stefan; van de Looij, Ruud; Thomsen, Jon Juel

    2014-01-01

    This work experimentally investigates the impact of nonlinearity on macromechanical parametric amplification. For a strong cubic stiffness nonlinearity we observe jumps in gain (ratio of steady-state vibration amplitude of the externally and parametrically excited system, to vibration amplitude o...

  6. A Numerical Scheme for Ordinary Differential Equations Having Time Varying and Nonlinear Coefficients Based on the State Transition Matrix

    Science.gov (United States)

    Bartels, Robert E.

    2002-01-01

    A variable order method of integrating initial value ordinary differential equations that is based on the state transition matrix has been developed. The method has been evaluated for linear time variant and nonlinear systems of equations. While it is more complex than most other methods, it produces exact solutions at arbitrary time step size when the time variation of the system can be modeled exactly by a polynomial. Solutions to several nonlinear problems exhibiting chaotic behavior have been computed. Accuracy of the method has been demonstrated by comparison with an exact solution and with solutions obtained by established methods.

  7. Simple and complex chimera states in a nonlinearly coupled oscillatory medium

    Science.gov (United States)

    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.

  8. Experimental verificatio of load resistance switching for global stabilization of high-energy response of a nonlinear wideband electromagnetic vibration energy harvester

    International Nuclear Information System (INIS)

    Sato, T; Masuda, A; Sanada, T

    2015-01-01

    This paper presents an experimental verification of a self-excitation control of a resonance- type vibration energy harvester with a Duffing-type nonlinearity which is designed to perform effectively in a wide frequency range. For the conventional linear vibration energy harvester, the performance of the power generation at the resonance frequency and the bandwidth of the resonance peak are trade-off. The resonance frequency band can be expanded by introducing a Duffing-type nonlinear oscillator in order to enable the harvester to generate larger electric power in a wider frequency range. However, since such nonlinear oscillator can have multiple stable steady-state solutions in the resonance band, it is difficult for the nonlinear harvester to maintain the high performance of the power generation constantly. The principle of self-excitation and entrainment has been utilized to provide the global stability to the highest-energy solution by destabilizing other unexpected lower-energy solutions by introducing a switching circuit of the load resistance between positive and the negative values depending on the response amplitude of the oscillator. It has been experimentally validated that this control law imparts the self-excitation capability to the oscillator to show an entrainment into the highest-energy solution. (paper)

  9. Rogue waves and rational solutions of a (3+1)-dimensional nonlinear evolution equation

    International Nuclear Information System (INIS)

    Zhaqilao,

    2013-01-01

    A simple symbolic computation approach for finding the rogue waves and rational solutions to the nonlinear evolution equation is proposed. It turns out that many rational solutions with real and complex forms of a (3+1)-dimensional nonlinear evolution equation are obtained. Some features of rogue waves and rational solutions are graphically discussed. -- Highlights: •A simple symbolic computation approach for finding the rational solutions to the NEE is proposed. •Some rogue waves and rational solutions with real and complex forms of a (3+1)-D NEE are obtained. •Some features of rogue waves are graphically discussed

  10. Rogue waves and rational solutions of a (3+1)-dimensional nonlinear evolution equation

    Energy Technology Data Exchange (ETDEWEB)

    Zhaqilao,, E-mail: zhaqilao@imnu.edu.cn

    2013-12-06

    A simple symbolic computation approach for finding the rogue waves and rational solutions to the nonlinear evolution equation is proposed. It turns out that many rational solutions with real and complex forms of a (3+1)-dimensional nonlinear evolution equation are obtained. Some features of rogue waves and rational solutions are graphically discussed. -- Highlights: •A simple symbolic computation approach for finding the rational solutions to the NEE is proposed. •Some rogue waves and rational solutions with real and complex forms of a (3+1)-D NEE are obtained. •Some features of rogue waves are graphically discussed.

  11. How should we understand non-equilibrium many-body steady states?

    Science.gov (United States)

    Maghrebi, Mohammad; Gorshkov, Alexey

    : Many-body systems with both coherent dynamics and dissipation constitute a rich class of models which are nevertheless much less explored than their dissipationless counterparts. The advent of numerous experimental platforms that simulate such dynamics poses an immediate challenge to systematically understand and classify these models. In particular, nontrivial many-body states emerge as steady states under non-equilibrium dynamics. In this talk, I use a field-theoretic approach based on the Keldysh formalism to study nonequilibrium phases and phase transitions in such models. I show that an effective temperature generically emerges as a result of dissipation, and the universal behavior including the dynamics near the steady state is described by a thermodynamic universality class. In the end, I will also discuss possibilities that go beyond the paradigm of an effective thermodynamic behavior.

  12. Classical solutions for the 4-dimensional σ-nonlinear model

    International Nuclear Information System (INIS)

    Tataru-Mihai, P.

    1979-01-01

    By interpreting the σ-nonlinear model as describing the Gauss map associated to a certain immersion, several classes of classical solutions for the 4-dimensional model are derived. As by-products one points out i) an intimate connection between the energy-momentum tensor of the solution and the second differential form of the immersion associated to it and ii) a connection between self- (antiself-)duality of the solution and the minimality of the associated immersion. (author)

  13. Invariant Solutions for a Class of Perturbed Nonlinear Wave Equations

    Directory of Open Access Journals (Sweden)

    Waheed A. Ahmed

    2017-11-01

    Full Text Available Approximate symmetries of a class of perturbed nonlinear wave equations are computed using two newly-developed methods. Invariant solutions associated with the approximate symmetries are constructed for both methods. Symmetries and solutions are compared through discussing the advantages and disadvantages of each method.

  14. General Unified Integral Controller with Zero Steady-State Error for Single-Phase Grid-Connected Inverters

    DEFF Research Database (Denmark)

    Guo, Xiaoqiang; Guerrero, Josep M.

    2016-01-01

    Current regulation is crucial for operating single-phase grid-connected inverters. The challenge of the current controller is how to fast and precisely tracks the current with zero steady-state error. This paper proposes a novel feedback mechanism for the conventional PI controller. It allows...... done indicates that the widely used PR (P+Resonant) control is just a special case of the proposed control solution. The time-domain simulation in Matlab/Simulink and experimental results from a TMS320F2812 DSP based laboratory prototypes are in good agreement, which verify the effectiveness...

  15. A combined dynamic analysis method for geometrically nonlinear vibration isolators with elastic rings

    Science.gov (United States)

    Hu, Zhan; Zheng, Gangtie

    2016-08-01

    A combined analysis method is developed in the present paper for studying the dynamic properties of a type of geometrically nonlinear vibration isolator, which is composed of push-pull configuration rings. This method combines the geometrically nonlinear theory of curved beams and the Harmonic Balance Method to overcome the difficulty in calculating the vibration and vibration transmissibility under large deformations of the ring structure. Using the proposed method, nonlinear dynamic behaviors of this isolator, such as the lock situation due to the coulomb damping and the usual jump resulting from the nonlinear stiffness, can be investigated. Numerical solutions based on the primary harmonic balance are first verified by direct integration results. Then, the whole procedure of this combined analysis method is demonstrated and validated by slowly sinusoidal sweeping experiments with different amplitudes of the base excitation. Both numerical and experimental results indicate that this type of isolator behaves as a hardening spring with increasing amplitude of the base excitation, which makes it suitable for isolating both steady-state vibrations and transient shocks.

  16. Exact solutions for nonlinear evolution equations using Exp-function method

    International Nuclear Information System (INIS)

    Bekir, Ahmet; Boz, Ahmet

    2008-01-01

    In this Letter, the Exp-function method is used to construct solitary and soliton solutions of nonlinear evolution equations. The Klein-Gordon, Burger-Fisher and Sharma-Tasso-Olver equations are chosen to illustrate the effectiveness of the method. The method is straightforward and concise, and its applications are promising. The Exp-function method presents a wider applicability for handling nonlinear wave equations

  17. Hybrid diffusion-P3 equation in N-layered turbid media: steady-state domain.

    Science.gov (United States)

    Shi, Zhenzhi; Zhao, Huijuan; Xu, Kexin

    2011-10-01

    This paper discusses light propagation in N-layered turbid media. The hybrid diffusion-P3 equation is solved for an N-layered finite or infinite turbid medium in the steady-state domain for one point source using the extrapolated boundary condition. The Fourier transform formalism is applied to derive the analytical solutions of the fluence rate in Fourier space. Two inverse Fourier transform methods are developed to calculate the fluence rate in real space. In addition, the solutions of the hybrid diffusion-P3 equation are compared to the solutions of the diffusion equation and the Monte Carlo simulation. For the case of small absorption coefficients, the solutions of the N-layered diffusion equation and hybrid diffusion-P3 equation are almost equivalent and are in agreement with the Monte Carlo simulation. For the case of large absorption coefficients, the model of the hybrid diffusion-P3 equation is more precise than that of the diffusion equation. In conclusion, the model of the hybrid diffusion-P3 equation can replace the diffusion equation for modeling light propagation in the N-layered turbid media for a wide range of absorption coefficients.

  18. A quaternionic map for the steady states of the Heisenberg spin-chain

    Energy Technology Data Exchange (ETDEWEB)

    Mehta, Mitaxi P., E-mail: mitaxi.mehta@ahduni.edu.in [IICT, Ahmedabad University, Opp. IIM, Navrangpura, Ahmedabad (India); Dutta, Souvik; Tiwari, Shubhanshu [BITS-Pilani, K.K. Birla Goa campus, Goa (India)

    2014-01-17

    We show that the steady states of the classical Heisenberg XXX spin-chain in an external magnetic field can be found by iterations of a quaternionic map. A restricted model, e.g., the xy spin-chain is known to have spatially chaotic steady states and the phase space occupied by these chaotic states is known to go through discrete changes as the field strength is varied. The same phenomenon is studied for the xxx spin-chain. It is seen that in this model the phase space volume varies smoothly with the external field.

  19. A quaternionic map for the steady states of the Heisenberg spin-chain

    International Nuclear Information System (INIS)

    Mehta, Mitaxi P.; Dutta, Souvik; Tiwari, Shubhanshu

    2014-01-01

    We show that the steady states of the classical Heisenberg XXX spin-chain in an external magnetic field can be found by iterations of a quaternionic map. A restricted model, e.g., the xy spin-chain is known to have spatially chaotic steady states and the phase space occupied by these chaotic states is known to go through discrete changes as the field strength is varied. The same phenomenon is studied for the xxx spin-chain. It is seen that in this model the phase space volume varies smoothly with the external field.

  20. The primary results for the mixed carbon material used for high flux steady-state tokamak operation in China

    International Nuclear Information System (INIS)

    Guo, Q.G.; Li, J.G.; Zhai, G.T.; Liu, L.; Song, J.R.; Zhang, L.F.; He, Y.X.; Chen, J.L.

    2001-01-01

    Several types of carbon mixed materials have been developed in China to be used for high flux steady-state tokamak operation. Performance evaluation of these materials is necessary to determine their applicability as PFCs for high flux steady state. This paper describes the primary results of carbon mixed materials and the effects of dopants on properties are primarily discussed. Test results reveal that bulk boronized graphite has excellent physical and mechanical properties while their thermal conductivity is no more than 73 W/m K due to the formation of a uniform boron-carbon solid solution. In case of multi-element doped graphite, titanium dopant or a decreased boron content is favorable to enhance thermal conductivity. A kind of doped graphite has been developed with thermal conductivity as high as 278 W/m K by optimizing the compositions. Correlations among compositions, microstructure and properties of such doped graphite are discussed

  1. Inverse operator theory method mathematics-mechanization for the solutions of nonlinear equations and some typical applications in nonlinear physics

    International Nuclear Information System (INIS)

    Fang Jinqing; Yao Weiguang

    1992-12-01

    Inverse operator theory method (IOTM) has developed rapidly in the last few years. It is an effective and useful procedure for quantitative solution of nonlinear or stochastic continuous dynamical systems. Solutions are obtained in series form for deterministic equations, and in the case of stochastic equation it gives statistic measures of the solution process. A very important advantage of the IOTM is to eliminate a number of restrictive and assumption on the nature of stochastic processes. Therefore, it provides more realistic solutions. The IOTM and its mathematics-mechanization (MM) are briefly introduced. They are used successfully to study the chaotic behaviors of the nonlinear dynamical systems for the first time in the world. As typical examples, the Lorentz equation, generalized Duffing equation, two coupled generalized Duffing equations are investigated by the use of the IOTM and the MM. The results are in good agreement with ones by the Runge-Kutta method (RKM). It has higher accuracy and faster convergence. So the IOTM realized by the MM is of potential application valuable in nonlinear science

  2. EXISTENCE AND UNIQUENESS OF SOLUTIONS TO A NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION

    Institute of Scientific and Technical Information of China (English)

    2011-01-01

    The initial value problem of a nonlinear fractional differential equation is discussed in this paper. Using the nonlinear alternative of Leray-Schauder type and the contraction mapping principle,we obtain the existence and uniqueness of solutions to the fractional differential equation,which extend some results of the previous papers.

  3. New exact solutions for two nonlinear equations

    International Nuclear Information System (INIS)

    Wang Quandi; Tang Minying

    2008-01-01

    In this Letter, we investigate two nonlinear equations given by u t -u xxt +3u 2 u x =2u x u xx +uu xxx and u t -u xxt +4u 2 u x =3u x u xx +uu xxx . Through some special phase orbits we obtain four new exact solutions for each equation above. Some previous results are extended

  4. Entire solutions of nonlinear differential-difference equations.

    Science.gov (United States)

    Li, Cuiping; Lü, Feng; Xu, Junfeng

    2016-01-01

    In this paper, we describe the properties of entire solutions of a nonlinear differential-difference equation and a Fermat type equation, and improve several previous theorems greatly. In addition, we also deduce a uniqueness result for an entire function f(z) that shares a set with its shift [Formula: see text], which is a generalization of a result of Liu.

  5. Isotope partitioning for NAD-malic enzyme from Ascaris suum confirms a steady-state random kinetic mechanism

    International Nuclear Information System (INIS)

    Chen, C.Y.; Harris, B.G.; Cook, P.F.

    1988-01-01

    Isotope partitioning studies beginning with E-[ 14 C]NAD, E-[ 14 C] malate, E-[ 14 C] NAD-Mg 2+ , and E-Mg-[ 14 C]malate suggest a steady-state random mechanism for the NAD-malic enzyme. Isotope trapping beginning with E-[ 14 C]NAD and with varying concentrations of Mg 2+ and malate in the chase solution indicates that Mg 2+ is added in rapid equilibrium and must be added prior to malate for productive ternary complex formation. Equal percentage trapping from E-[ 14 C]NAD-Mg and E-Mg-[ 14 C] malate indicates the mechanism is steady-state random with equal off-rates for NAD and malate from E-NAD-Mg-malate. The off-rates for both do not change significantly in the ternary E-Mg-malate and E-NAD-Mg complexes, nor does the off-rate change for NAD from E-NAD. No trapping of malate was obtained from E-[ 14 C] malate, suggesting that this complex is nonproductive. A quantitative analysis of the data allows an estimation of values for a number of the rate constants along the reaction pathway

  6. Weierstrass Elliptic Function Solutions to Nonlinear Evolution Equations

    International Nuclear Information System (INIS)

    Yu Jianping; Sun Yongli

    2008-01-01

    This paper is based on the relations between projection Riccati equations and Weierstrass elliptic equation, combined with the Groebner bases in the symbolic computation. Then the novel method for constructing the Weierstrass elliptic solutions to the nonlinear evolution equations is given by using the above relations

  7. Oscillating particle-like solutions of nonlinear Klein-Gordon equation

    International Nuclear Information System (INIS)

    Bogolubsky, I.L.

    1976-01-01

    A denumerable set of oscillating spherically-symmetric particle-like solutions of the Klein-Gordon equation with cubic nonlinearity is found. Extended particles modelled by them turn out to be slightly radiating and long-lived

  8. Efficient determination of the Markovian time-evolution towards a steady-state of a complex open quantum system

    Science.gov (United States)

    Jonsson, Thorsteinn H.; Manolescu, Andrei; Goan, Hsi-Sheng; Abdullah, Nzar Rauf; Sitek, Anna; Tang, Chi-Shung; Gudmundsson, Vidar

    2017-11-01

    Master equations are commonly used to describe time evolution of open systems. We introduce a general computationally efficient method for calculating a Markovian solution of the Nakajima-Zwanzig generalized master equation. We do so for a time-dependent transport of interacting electrons through a complex nano scale system in a photon cavity. The central system, described by 120 many-body states in a Fock space, is weakly coupled to the external leads. The efficiency of the approach allows us to place the bias window defined by the external leads high into the many-body spectrum of the cavity photon-dressed states of the central system revealing a cascade of intermediate transitions as the system relaxes to a steady state. The very diverse relaxation times present in the open system, reflecting radiative or non-radiative transitions, require information about the time evolution through many orders of magnitude. In our approach, the generalized master equation is mapped from a many-body Fock space of states to a Liouville space of transitions. We show that this results in a linear equation which is solved exactly through an eigenvalue analysis, which supplies information on the steady state and the time evolution of the system.

  9. Steady state ion acceleration by a circularly polarized laser pulse

    International Nuclear Information System (INIS)

    Zhang Xiaomei; Shen Baifei; Cang Yu; Li Xuemei; Jin Zhangying; Wang Fengchao

    2007-01-01

    The steady state ion acceleration at the front of a cold solid target by a circularly polarized flat-top laser pulse is studied with one-dimensional particle-in-cell (PIC) simulation. A model that ions are reflected by a steady laser-driven piston is used by comparing with the electrostatic shock acceleration. A stable profile with a double-flat-top structure in phase space forms after ions enter the undisturbed region of the target with a constant velocity

  10. The modified simplest equation method to look for exact solutions of nonlinear partial differential equations

    OpenAIRE

    Efimova, Olga Yu.

    2010-01-01

    The modification of simplest equation method to look for exact solutions of nonlinear partial differential equations is presented. Using this method we obtain exact solutions of generalized Korteweg-de Vries equation with cubic source and exact solutions of third-order Kudryashov-Sinelshchikov equation describing nonlinear waves in liquids with gas bubbles.

  11. Non-equilibrium transport in the quantum dot: quench dynamics and non-equilibrium steady state

    Science.gov (United States)

    Culver, Adrian; Andrei, Natan

    We present an exact method of calculating the non-equilibrium current driven by a voltage drop across a quantum dot. The system is described by the two lead Anderson model at zero temperature with on-site Coulomb repulsion and non-interacting, linearized leads. We prepare the system in an initial state consisting of a free Fermi sea in each lead with the voltage drop given as the difference between the two Fermi levels. We quench the system by coupling the dot to the leads at t = 0 and following the time evolution of the wavefunction. In the long time limit a new type of Bethe Ansatz wavefunction emerges, which satisfies the Lippmann-Schwinger equation with the two Fermi seas serving as the boundary conditions. This exact, non-perturbative solution describes the non-equilibrium steady state of the system. We describe how to use this solution to compute the infinite time limit of the expectation value of the current operator at a given voltage, which would yield the I-V characteristic of the dot. Research supported by NSF Grant DMR 1410583.

  12. Stochastic response and bifurcation of periodically driven nonlinear oscillators by the generalized cell mapping method

    Science.gov (United States)

    Han, Qun; Xu, Wei; Sun, Jian-Qiao

    2016-09-01

    The stochastic response of nonlinear oscillators under periodic and Gaussian white noise excitations is studied with the generalized cell mapping based on short-time Gaussian approximation (GCM/STGA) method. The solutions of the transition probability density functions over a small fraction of the period are constructed by the STGA scheme in order to construct the GCM over one complete period. Both the transient and steady-state probability density functions (PDFs) of a smooth and discontinuous (SD) oscillator are computed to illustrate the application of the method. The accuracy of the results is verified by direct Monte Carlo simulations. The transient responses show the evolution of the PDFs from being Gaussian to non-Gaussian. The effect of a chaotic saddle on the stochastic response is also studied. The stochastic P-bifurcation in terms of the steady-state PDFs occurs with the decrease of the smoothness parameter, which corresponds to the deterministic pitchfork bifurcation.

  13. A Novel Chronic Opioid Monitoring Tool to Assess Prescription Drug Steady State Levels in Oral Fluid.

    Science.gov (United States)

    Shaparin, Naum; Mehta, Neel; Kunkel, Frank; Stripp, Richard; Borg, Damon; Kolb, Elizabeth

    2017-11-01

    Interpretation limitations of urine drug testing and the invasiveness of blood toxicology have motivated the desire for the development of simpler methods to assess biologically active drug levels on an individualized patient basis. Oral fluid is a matrix well-suited for the challenge because collections are based on simple noninvasive procedures and drug concentrations better correlate to blood drug levels as oral fluid is a filtrate of the blood. Well-established pharmacokinetic models were utilized to generate oral fluid steady state concentration ranges to assess the interpretive value of the alternative matrix to monitor steady state plasma oxycodone levels. Paired oral fluid and plasma samples were collected from patients chronically prescribed oxycodone and quantitatively analyzed by liquid chromatography tandem mass spectrometry. Steady state plasma concentration ranges were calculated for each donor and converted to an equivalent range in oral fluid. Measured plasma and oral fluid oxycodone concentrations were compared with respective matrix-matched steady state ranges, using each plasma steady state classification as the control. A high degree of correlation was observed between matrices when classifying donors according to expected steady state oxycodone concentration. Agreement between plasma and oral fluid steady state classifications was observed in 75.6% of paired samples. This study supports novel application of basic pharmacokinetic knowledge to the pain management industry, simplifying and improving individualized drug monitoring and risk assessment through the use of oral fluid drug testing. Many benefits of established therapeutic drug monitoring in plasma can be realized in oral fluid for patients chronically prescribed oxycodone at steady state. © 2017 American Academy of Pain Medicine. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com

  14. Poiseuille flow of soft glasses in narrow channels: from quiescence to steady state.

    Science.gov (United States)

    Chaudhuri, Pinaki; Horbach, Jürgen

    2014-10-01

    Using numerical simulations, the onset of Poiseuille flow in a confined soft glass is investigated. Starting from the quiescent state, steady flow sets in at a time scale which increases with a decrease in applied forcing. At this onset time scale, a rapid transition occurs via the simultaneous fluidization of regions having different local stresses. In the absence of steady flow at long times, creep is observed even in regions where the local stress is larger than the bulk yielding threshold. Finally, we show that the time scale to attain steady flow depends strongly on the history of the initial state.

  15. Solution strategies for linear and nonlinear instability phenomena for arbitrarily thin shell structures

    International Nuclear Information System (INIS)

    Eckstein, U.; Harte, R.; Kraetzig, W.B.; Wittek, U.

    1983-01-01

    In order to describe nonlinear response and instability behaviour the paper starts with the total potential energy considering the basic kinematic equations of a consistent nonlinear shell theory for large displacements and moderate rotations. The material behaviour is assumed to be hyperelastic and isotropic. The incrementation and discretization of the total potential energy leads to the tangent stiffness relation, which is the central equation of computational algorithms based on combined incremental and iterative techniques. Here a symmetrized form of the RIKS/WEMPNER-algorithm for positive and negative load incrementation represents the basis of the nonlinear solution technique. To detect secondary equilibrium branches at points of neutral equilibrium within nonlinear primary paths a quadratic eigenvalue-problem has to be solved. In order to follow those complicated nonlinear response phenomena the RIKS/WEMPNER incrementation/iteration process is combined with a simultaneous solution of the linearized quadratic eigenvalue-problem. Additionally the essentials of a recently derived family of arbitrarily curved shell elements for linear (LACS) and geometrically nonlinear (NACS) shell problems are presented. The main advantage of these elements is the exact description of all geometric properties as well as the energy-equivalent representation of the applied loads in combination with an efficient algorithm to form the stiffness submatrices. Especially the NACS-elements are designed to improve the accuracy of the solution in the deep postbuckling range including moderate rotations. The derived finite elements and solution strategies are applied to a certain number of typical shell problems to prove the precision of the shell elements and to demonstrate the possibilities of tracing linear and nonlinear bifurcation problems as well as snap-through phenomena with and without secondary bifurcation branches. (orig.)

  16. Steady-state bifurcations of the three-dimensional Kolmogorov problem

    Directory of Open Access Journals (Sweden)

    Zhi-Min Chen

    2000-08-01

    Full Text Available This paper studies the spatially periodic incompressible fluid motion in $mathbb R^3$ excited by the external force $k^2(sin kz, 0,0$ with $kgeq 2$ an integer. This driving force gives rise to the existence of the unidirectional basic steady flow $u_0=(sin kz,0, 0$ for any Reynolds number. It is shown in Theorem 1.1 that there exist a number of critical Reynolds numbers such that $u_0$ bifurcates into either 4 or 8 or 16 different steady states, when the Reynolds number increases across each of such numbers.

  17. Fabrication and Characterization of Ultrathin-ring Electrodes for Pseudo-steady-state Amperometric Detection.

    Science.gov (United States)

    Kitazumi, Yuki; Hamamoto, Katsumi; Noda, Tatsuo; Shirai, Osamu; Kano, Kenji

    2015-01-01

    The fabrication of ultrathin-ring electrodes with a diameter of 2 mm and a thickness of 100 nm is established. The ultrathin-ring electrodes provide a large density of pseudo-steady-state currents, and realize pseudo-steady-state amperometry under quiescent conditions without a Faraday cage. Under the limiting current conditions, the current response at the ultrathin-ring electrode can be well explained by the theory of the microband electrode response. Cyclic voltammograms at the ultrathin-ring electrode show sigmoidal characteristics with some hysteresis. Numerical simulation reveals that the hysteresis can be ascribed to the time-dependence of pseudo-steady-state current. The performance of amperometry with the ultrathin-ring electrode has been verified in its application to redox enzyme kinetic measurements.

  18. Traveling wave solutions for two nonlinear evolution equations with nonlinear terms of any order

    International Nuclear Information System (INIS)

    Feng Qing-Hua; Zhang Yao-Ming; Meng Fan-Wei

    2011-01-01

    In this paper, based on the known first integral method and the Riccati sub-ordinary differential equation (ODE) method, we try to seek the exact solutions of the general Gardner equation and the general Benjamin—Bona—Mahoney equation. As a result, some traveling wave solutions for the two nonlinear equations are established successfully. Also we make a comparison between the two methods. It turns out that the Riccati sub-ODE method is more effective than the first integral method in handling the proposed problems, and more general solutions are constructed by the Riccati sub-ODE method. (general)

  19. Steady-state heat transfer in an inverted U-tube steam generator

    International Nuclear Information System (INIS)

    Boucher, T.J.

    1987-01-01

    Experimental results are presented involving U-tube steam generator tube bundle local heat transfer and fluid conditions during stead-state, full-power operations performed at high temperatures and pressures with conditions typical of a pressurized water reactor (15.0 MPa primary pressure, 600 K steam generator inlet plenum fluid temperatures, 6.2 MPa secondary pressure). The Semiscale (MOD-2C facility represents the state-of-the-art in measurement of tube local heat transfer data and average tube bundle secondary fluid density at several elevations, which allows an estimate of the axial heat transfer and void distributions during steady-state and transient operations. The method of heat transfer data reduction is presented and the heat flux, secondary convective heat transfer coefficient, and void fraction distributions are quantified for steady-state, full-power operations

  20. Soliton solutions of an integrable nonlinear Schrödinger equation with quintic terms.

    Science.gov (United States)

    Chowdury, A; Kedziora, D J; Ankiewicz, A; Akhmediev, N

    2014-09-01

    We present the fifth-order equation of the nonlinear Schrödinger hierarchy. This integrable partial differential equation contains fifth-order dispersion and nonlinear terms related to it. We present the Lax pair and use Darboux transformations to derive exact expressions for the most representative soliton solutions. This set includes two-soliton collisions and the degenerate case of the two-soliton solution, as well as beating structures composed of two or three solitons. Ultimately, the new quintic operator and the terms it adds to the standard nonlinear Schrödinger equation (NLSE) are found to primarily affect the velocity of solutions, with complicated flow-on effects. Furthermore, we present a new structure, composed of coincident equal-amplitude solitons, which cannot exist for the standard NLSE.