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Sample records for nonlinear boundary conditions

  1. Population models with nonlinear boundary conditions

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    Jerome Goddard

    2010-09-01

    Full Text Available We study a two point boundary-value problem describing the steady states of a Logistic growth population model with diffusion and constant yield harvesting. In particular, we focus on a model when a certain nonlinear boundary condition is satisfied.

  2. Nonlinear Elliptic Boundary Value Problems at Resonance with Nonlinear Wentzell Boundary Conditions

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    Ciprian G. Gal

    2017-01-01

    Full Text Available Given a bounded domain Ω⊂RN with a Lipschitz boundary ∂Ω and p,q∈(1,+∞, we consider the quasilinear elliptic equation -Δpu+α1u=f in Ω complemented with the generalized Wentzell-Robin type boundary conditions of the form bx∇up-2∂nu-ρbxΔq,Γu+α2u=g on ∂Ω. In the first part of the article, we give necessary and sufficient conditions in terms of the given functions f, g and the nonlinearities α1, α2, for the solvability of the above nonlinear elliptic boundary value problems with the nonlinear boundary conditions. In other words, we establish a sort of “nonlinear Fredholm alternative” for our problem which extends the corresponding Landesman and Lazer result for elliptic problems with linear homogeneous boundary conditions. In the second part, we give some additional results on existence and uniqueness and we study the regularity of the weak solutions for these classes of nonlinear problems. More precisely, we show some global a priori estimates for these weak solutions in an L∞-setting.

  3. Nonlinear Vibration Analysis of Moving Strip with Inertial Boundary Condition

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    Chong-yi Gao

    2015-01-01

    Full Text Available According to the movement mechanism of strip and rollers in tandem mill, the strip between two stands was simplified to axially moving Euler beam and the rollers were simplified to the inertial component on the fixed axis rotation, namely, inertial boundary. Nonlinear vibration mechanical model of Euler beam with inertial boundary conditions was established. The transverse and longitudinal motion equations were derived based on Hamilton’s principle. Kantorovich averaging method was employed to discretize the motion equations and the inertial boundary equations, and the solutions were obtained using the modified iteration method. Depending on numerical calculation, the amplitude-frequency responses of Euler beam were determined. The axial velocity, tension, and rotational inertia have strong influences on the vibration characteristics. The results would provide an important theoretical reference to control and analyze the vertical vibration of moving strip in continuous rolling process.

  4. Existence results for nonlinear boundary-value problems with integral boundary conditions

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    Mouffak Benchohra

    2005-01-01

    Full Text Available In this paper, we investigate the existence of solutions for a second order nonlinear boundary-value problem with integral boundary conditions. By using suitable fixed point theorems, we study the cases when the right hand side has convex and nonconvex values.

  5. Method of the quasilinearization for nonlinear impulsive differential equations with linear boundary conditions

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    Paul Eloe

    2002-01-01

    Full Text Available The method of quasilinearization for nonlinear impulsive differential equations with linear boundary conditions is studied. The boundary conditions include periodic boundary conditions. It is proved the convergence is quadratic.

  6. On the nonlinear Schrodinger equation with nonzero boundary conditions

    Science.gov (United States)

    Fagerstrom, Emily

    integral, provided the initial condition satisfies further conditions. Modulational instability (focusing NLS with symmetric nonzero boundary conditions at infinity.) The focusing NLS equation is considered with potentials that are "box-like" piecewise constant functions. Several results are obtained. In particular, it is shown that there are conditions on the parameters of the potential for which there are no discrete eigenvalues. Thus there is a class of potentials for which the corresponding solutions of the NLS equation have no solitons. Hence, solitons cannot be the medium for the modulational instability. This contradicts a recent conjecture by Zakharov. On the other hand, it is shown for a different class of potentials the scattering problem always has a discrete eigenvalue along the imaginary axis. Thus, there exist arbitrarily small perturbations of the constant potential for which solitons exist, so no area theorem is possible. The existence, number and location of discrete eigenvalues in other situations are studied numerically. Finally, the small-deviation limit of the IST is computed and compared with the direct linearization of the NLS equation around a constant background. From this it is shown that there is an interval of the continuous spectrum on which the eigenvalue is imaginary and the scattering parameter is imaginary. The Jost eigenfunctions corresponding to this interval are the nonlinear analogue of the unstable Fourier modes. Defocusing NLS equation with asymmetric boundary conditions at infinity. The defocusing NLS equation with asymmetric boundary conditions is considered. To do so, first the case of symmetric boundary conditions is revisited. While the IST for this case has been formulated in the literature, it is usually done through the use of a uniformization variable. This was done because the eigenvalues of the scattering problem have branching; the uniformization variable allows one to move from a 2-sheeted Riemann surface to the complex

  7. Positive solutions of nonlinear fractional boundary value problems with Dirichlet boundary conditions

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    Qingkai Kong

    2012-02-01

    Full Text Available In this paper, we study the existence and multiplicity of positive solutions of a class of nonlinear fractional boundary value problems with  Dirichlet boundary conditions. By applying the fixed point theory on cones we establish a series of criteria for the existence of one, two, any arbitrary finite number, and an infinite number of positive solutions. A criterion for the nonexistence of positive solutions is also derived. Several examples are given for demonstration.

  8. 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.

  9. Nonlinear Vibrations of Multiwalled Carbon Nanotubes under Various Boundary Conditions

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    Hossein Aminikhah

    2011-01-01

    Full Text Available The present work deals with applying the homotopy perturbation method to the problem of the nonlinear oscillations of multiwalled carbon nanotubes embedded in an elastic medium under various boundary conditions. A multiple-beam model is utilized in which the governing equations of each layer are coupled with those of its adjacent ones via the van der Waals interlayer forces. The amplitude-frequency curves for large-amplitude vibrations of single-walled, double-walled, and triple-walled carbon nanotubes are obtained. The influences of some commonly used boundary conditions, changes in material constant of the surrounding elastic medium, and variations of the nanotubes geometrical parameters on the vibration characteristics of multiwalled carbon nanotubes are discussed. The comparison of the generated results with those from the open literature illustrates that the solutions obtained are of very high accuracy and clarifies the capability and the simplicity of the present method. It is worthwhile to say that the results generated are new and can be served as a benchmark for future works.

  10. Nonlinear solution for radiation boundary condition of heat transfer process in human eye.

    Science.gov (United States)

    Dehghani, A; Moradi, A; Dehghani, M; Ahani, A

    2011-01-01

    In this paper we propose a new method based on finite element method for solving radiation boundary condition of heat equation inside the human eye and other applications. Using this method, we can solve heat equation inside human eye without need to model radiation boundary condition to a robin boundary condition. Using finite element method we can obtain a nonlinear equation, and finally we use nonlinear algorithm to solve it. The human eye is modeled as a composition of several homogeneous regions. The Ritz method in the finite element method is used for solving heat differential equation. Applying the boundary conditions, the heat radiation condition and the robin condition on the cornea surface of the eye and on the outer part of sclera are used, respectively. Simulation results of solving nonlinear boundary condition show the accuracy of the proposed method.

  11. Loss of boundary conditions for fully nonlinear parabolic equations with superquadratic gradient terms

    Science.gov (United States)

    Quaas, Alexander; Rodríguez, Andrei

    2018-02-01

    We study whether the solutions of a fully nonlinear, uniformly parabolic equation with superquadratic growth in the gradient satisfy initial and homogeneous boundary conditions in the classical sense, a problem we refer to as the classical Dirichlet problem. Our main results are: the nonexistence of global-in-time solutions of this problem, depending on a specific largeness condition on the initial data, and the existence of local-in-time solutions for initial data C1 up to the boundary. Global existence is know when boundary conditions are understood in the viscosity sense, what is known as the generalized Dirichlet problem. Therefore, our result implies loss of boundary conditions in finite time. Specifically, a solution satisfying homogeneous boundary conditions in the viscosity sense eventually becomes strictly positive at some point of the boundary.

  12. Attractor of Beam Equation with Structural Damping under Nonlinear Boundary Conditions

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    Danxia Wang

    2015-01-01

    Full Text Available Simultaneously, considering the viscous effect of material, damping of medium, and rotational inertia, we study a kind of more general Kirchhoff-type extensible beam equation utt-uxxtt+uxxxx-σ(∫0l‍(ux2dxuxx-ϕ(∫0l‍(ux2dxuxxt=q(x, in  [0,L]×R+ with the structural damping and the rotational inertia term. Little attention is paid to the longtime behavior of the beam equation under nonlinear boundary conditions. In this paper, under nonlinear boundary conditions, we prove not only the existence and uniqueness of global solutions by prior estimates combined with some inequality skills, but also the existence of a global attractor by the existence of an absorbing set and asymptotic compactness of corresponding solution semigroup. In addition, the same results also can be proved under the other nonlinear boundary conditions.

  13. Existence results for boundary-value problems with nonlinear fractional differential inclusions and integral conditions

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    Samira Hamani

    2010-01-01

    Full Text Available In this article, the authors establish sufficient conditions for the existence of solutions for a class of boundary value problem for fractional differential inclusions involving the Caputo fractional derivative and nonlinear integral conditions. Both cases of convex and nonconvex valued right hand sides are considered. The topological structure of the set of solutions also examined.

  14. 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)

  15. Weak solutions for nonlinear fractional differential equations with integral boundary conditions in Banach spaces

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    Mouffak Benchohra

    2012-01-01

    Full Text Available The aim of this paper is to investigate a class of boundary value problems for fractional differential equations involving nonlinear integral conditions. The main tool used in our considerations is the technique associated with measures of weak noncompactness.

  16. Partially solved differential systems with two-point non-linear boundary conditions

    Czech Academy of Sciences Publication Activity Database

    Rontó, András; Rontó, M.; Varga, I.

    2017-01-01

    Roč. 18, č. 2 (2017), s. 1001-1014 ISSN 1787-2405 Institutional support: RVO:67985840 Keywords : implicit differential systems * non-linear two-point boundary conditions * parametrization technique Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 0.388, year: 2016 http://mat76.mat.uni-miskolc.hu/mnotes/article/2491

  17. Blow-up analysis for a system of heat equations coupled through a nonlinear boundary condition

    DEFF Research Database (Denmark)

    Pedersen, M.; Lin, Zhigui

    2001-01-01

    Consider the system of heat equations uit - Δui = 0 (i = 1 , . . . , k, uk+i := u1) in Ω x (0, T) coupled through nonlinear boundary conditions ∂ui/∂η = up1i+1 on ∂Ω x [0, T). The upper and lower bounds of the blow-up rate is derived. © 2000 Elsevier Science Ltd. All rights reserved.......Consider the system of heat equations uit - Δui = 0 (i = 1 , . . . , k, uk+i := u1) in Ω x (0, T) coupled through nonlinear boundary conditions ∂ui/∂η = up1i+1 on ∂Ω x [0, T). The upper and lower bounds of the blow-up rate is derived. © 2000 Elsevier Science Ltd. All rights reserved....

  18. Blow-up analysis for a system of heat equations coupled through a nonlinear boundary condition

    DEFF Research Database (Denmark)

    Pedersen, M.; Lin, Zhigui

    2001-01-01

    Consider the system of heat equations uit - Δui = 0 (i = 1 , . . . , k, uk+i := u1) in Ω x (0, T) coupled through nonlinear boundary conditions ∂ui/∂η = up1i+1 on ∂Ω x [0, T). The upper and lower bounds of the blow-up rate is derived. © 2000 Elsevier Science Ltd. All rights reserved....

  19. Breather type solutions of the vector nonlinear Schroedinger equation with quasi-constant boundary conditions

    International Nuclear Information System (INIS)

    Makhan'kov, V.G.; Slavov, S.I.

    1989-01-01

    Vector nonlinear Schroedinger equations (VS3) is investigated under quasi-constant boundary conditions. New two-soliton solutions are obtained with such non-trivial dynamics that they may be called the breather solutions. A version of the basic Novikov-Dubrovin-Krichever algebro-geometrical approach is applied to obtain breather like solutions existing for all types of internal symmetry is specified are formulated in terms of the soliton velocity expressed via the parameters of the problem. 4 refs

  20. POSITIVE SOLUTIONS OF A NONLINEAR THREE-POINT EIGENVALUE PROBLEM WITH INTEGRAL BOUNDARY CONDITIONS

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    FAOUZI HADDOUCHI

    2015-11-01

    Full Text Available In this paper, we study the existence of positive solutions of a three-point integral boundary value problem (BVP for the following second-order differential equation u''(t + \\lambda a(tf(u(t = 0; 0 0 is a parameter, 0 <\\eta < 1, 0 <\\alpha < 1/{\\eta}. . By using the properties of the Green's function and Krasnoselskii's fixed point theorem on cones, the eigenvalue intervals of the nonlinear boundary value problem are considered, some sufficient conditions for the existence of at least one positive solutions are established.

  1. On the compatibility equations of nonlinear and linear elasticity in the presence of boundary conditions

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    Angoshtari, Arzhang; Yavari, Arash

    2015-12-01

    We use Hodge-type orthogonal decompositions for studying the compatibility equations of the displacement gradient and the linear strain with prescribed boundary displacements. We show that the displacement gradient is compatible if and only if for any equilibrated virtual first Piola-Kirchhoff stress tensor field, the virtual work done by the displacement gradient is equal to the virtual work done by the prescribed boundary displacements. This condition is very similar to the classical compatibility equations for the linear strain. Since these compatibility equations for linear and nonlinear strains involve infinite-dimensional spaces and consequently are not easy to use in practice, we derive alternative compatibility equations, which are written in terms of some finite-dimensional spaces and are more useful in practice. Using these new compatibility equations, we present some non-trivial examples that show that compatible strains may become incompatible in the presence of prescribed boundary displacements.

  2. On nonlinear inverse problems of heat transfer with radiation boundary conditions : application to dehydratation of gypsum plasterboards exposed to fire.

    OpenAIRE

    Belmiloudi , Aziz; Mahé , Fabrice

    2014-01-01

    International audience; The paper investigates boundary optimal controls and parameter estimates to the well-posedness nonlinear model of dehydration of thermic problems. We summarize the general formulations for the boundary control for initial-boundary value problem for nonlinear partial differential equations modeling the heat transfer and derive necessary optimality conditions, including the adjoint equation, for the optimal set of parameters minimizing objective functions J. Numerical si...

  3. Inverse scattering transform for the focusing nonlinear Schrödinger equation with nonzero boundary conditions

    Energy Technology Data Exchange (ETDEWEB)

    Biondini, Gino [Department of Mathematics, State University of New York at Buffalo, Buffalo, New York 14260 (United States); Kovačič, Gregor [Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, New York 12180 (United States)

    2014-03-15

    The inverse scattering transform for the focusing nonlinear Schrödinger equation with non-zero boundary conditions at infinity is presented, including the determination of the analyticity of the scattering eigenfunctions, the introduction of the appropriate Riemann surface and uniformization variable, the symmetries, discrete spectrum, asymptotics, trace formulae and the so-called theta condition, and the formulation of the inverse problem in terms of a Riemann-Hilbert problem. In addition, the general behavior of the soliton solutions is discussed, as well as the reductions to all special cases previously discussed in the literature.

  4. A boundary condition to the Khokhlov-Zabolotskaya equation for modeling strongly focused nonlinear ultrasound fields

    Energy Technology Data Exchange (ETDEWEB)

    Rosnitskiy, P., E-mail: pavrosni@yandex.ru; Yuldashev, P., E-mail: petr@acs366.phys.msu.ru; Khokhlova, V., E-mail: vera@acs366.phys.msu.ru [Physics Faculty, Moscow State University, Leninskie Gory, 119991 Moscow (Russian Federation)

    2015-10-28

    An equivalent source model was proposed as a boundary condition to the nonlinear parabolic Khokhlov-Zabolotskaya (KZ) equation to simulate high intensity focused ultrasound (HIFU) fields generated by medical ultrasound transducers with the shape of a spherical shell. The boundary condition was set in the initial plane; the aperture, the focal distance, and the initial pressure of the source were chosen based on the best match of the axial pressure amplitude and phase distributions in the Rayleigh integral analytic solution for a spherical transducer and the linear parabolic approximation solution for the equivalent source. Analytic expressions for the equivalent source parameters were derived. It was shown that the proposed approach allowed us to transfer the boundary condition from the spherical surface to the plane and to achieve a very good match between the linear field solutions of the parabolic and full diffraction models even for highly focused sources with F-number less than unity. The proposed method can be further used to expand the capabilities of the KZ nonlinear parabolic equation for efficient modeling of HIFU fields generated by strongly focused sources.

  5. Modified Taylor series method for solving nonlinear differential equations with mixed boundary conditions defined on finite intervals.

    Science.gov (United States)

    Vazquez-Leal, Hector; Benhammouda, Brahim; Filobello-Nino, Uriel Antonio; Sarmiento-Reyes, Arturo; Jimenez-Fernandez, Victor Manuel; Marin-Hernandez, Antonio; Herrera-May, Agustin Leobardo; Diaz-Sanchez, Alejandro; Huerta-Chua, Jesus

    2014-01-01

    In this article, we propose the application of a modified Taylor series method (MTSM) for the approximation of nonlinear problems described on finite intervals. The issue of Taylor series method with mixed boundary conditions is circumvented using shooting constants and extra derivatives of the problem. In order to show the benefits of this proposal, three different kinds of problems are solved: three-point boundary valued problem (BVP) of third-order with a hyperbolic sine nonlinearity, two-point BVP for a second-order nonlinear differential equation with an exponential nonlinearity, and a two-point BVP for a third-order nonlinear differential equation with a radical nonlinearity. The result shows that the MTSM method is capable to generate easily computable and highly accurate approximations for nonlinear equations. 34L30.

  6. Nonlinear Seismic Behavior of Different Boundary Conditions of Transmission Line Systems under Earthquake Loading

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    Li Tian

    2016-01-01

    Full Text Available Nonlinear seismic behaviors of different boundary conditions of transmission line system under earthquake loading are investigated in this paper. The transmission lines are modeled by cable element accounting for the nonlinearity of the cable. For the suspension type, three towers and two span lines with spring model (Model 1 and three towers and four span lines’ model (Model 2 are established, respectively. For the tension type, three towers and two span lines’ model (Model 3 and three towers and four span lines’ model (Model 4 are created, respectively. The frequencies of the transmission towers and transmission lines of the suspension type and tension type are calculated, respectively. The responses of the suspension type and tension type are investigated using nonlinear time history analysis method, respectively. The results show that the responses of the transmission tower and transmission line of the two models of the suspension type are slightly different. However, the responses of transmission tower and transmission line of the two models of the tension type are significantly different. Therefore, in order to obtain accurate results, a reasonable model should be considered. The results could provide a reference for the seismic analysis of the transmission tower-line system.

  7. Existence Results for a Coupled System of Nonlinear Fractional Hybrid Differential Equations with Homogeneous Boundary Conditions

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    Josefa Caballero

    2014-01-01

    Full Text Available We study an existence result for the following coupled system of nonlinear fractional hybrid differential equations with homogeneous boundary conditions D0+α[x(t/f(t,x(t,y(t]=g(t,x(t,y(t,D0+αy(t/f(t,y(t,x(t=g(t,y(t,x(t,  0

  8. Inverse scattering transform for the nonlocal nonlinear Schrödinger equation with nonzero boundary conditions

    Science.gov (United States)

    Ablowitz, Mark J.; Luo, Xu-Dan; Musslimani, Ziad H.

    2018-01-01

    In 2013, a new nonlocal symmetry reduction of the well-known AKNS (an integrable system of partial differential equations, introduced by and named after Mark J. Ablowitz, David J. Kaup, and Alan C. Newell et al. (1974)) scattering problem was found. It was shown to give rise to a new nonlocal PT symmetric and integrable Hamiltonian nonlinear Schrödinger (NLS) equation. Subsequently, the inverse scattering transform was constructed for the case of rapidly decaying initial data and a family of spatially localized, time periodic one-soliton solutions was found. In this paper, the inverse scattering transform for the nonlocal NLS equation with nonzero boundary conditions at infinity is presented in four different cases when the data at infinity have constant amplitudes. The direct and inverse scattering problems are analyzed. Specifically, the direct problem is formulated, the analytic properties of the eigenfunctions and scattering data and their symmetries are obtained. The inverse scattering problem, which arises from a novel nonlocal system, is developed via a left-right Riemann-Hilbert problem in terms of a suitable uniformization variable and the time dependence of the scattering data is obtained. This leads to a method to linearize/solve the Cauchy problem. Pure soliton solutions are discussed, and explicit 1-soliton solution and two 2-soliton solutions are provided for three of the four different cases corresponding to two different signs of nonlinearity and two different values of the phase difference between plus and minus infinity. In another case, there are no solitons.

  9. Existence and Analytic Approximation of Solutions of Duffing Type Nonlinear Integro-Differential Equation with Integral Boundary Conditions

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    Alsaedi Ahmed

    2009-01-01

    Full Text Available A generalized quasilinearization technique is developed to obtain a sequence of approximate solutions converging monotonically and quadratically to a unique solution of a boundary value problem involving Duffing type nonlinear integro-differential equation with integral boundary conditions. The convergence of order for the sequence of iterates is also established. It is found that the work presented in this paper not only produces new results but also yields several old results in certain limits.

  10. A Study of Nonlinear Fractional Differential Equations of Arbitrary Order with Riemann-Liouville Type Multistrip Boundary Conditions

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    Bashir Ahmad

    2013-01-01

    Full Text Available We develop the existence theory for nonlinear fractional differential equations of arbitrary order with Riemann-Liouville type boundary conditions involving nonintersecting finite many strips of arbitrary length. Our results are based on some standard tools of fixed point theory. For the illustration of the results, some examples are also discussed.

  11. Existence and Uniqueness Results for Nonlinear Implicit Fractional Differential Equations with Boundary Conditions

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    Mouffak Benchohra

    2014-05-01

    Full Text Available In this paper, we establish the existence and uniqueness of solution for a class of boundary value problems for implicit fractional differential equations with Caputo fractional derivative. The arguments are based upon the Banach contraction principle, Schauder's fixed point theorem and the nonlinear alterna- tive of Leray-Schauder type. As applications, two examples are included to show the applicability of our results.

  12. On Nonlinear Inverse Problems of Heat Transfer with Radiation Boundary Conditions: Application to Dehydration of Gypsum Plasterboards Exposed to Fire

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    A. Belmiloudi

    2014-01-01

    Full Text Available The paper investigates boundary optimal controls and parameter estimates to the well-posedness nonlinear model of dehydration of thermic problems. We summarize the general formulations for the boundary control for initial-boundary value problem for nonlinear partial differential equations modeling the heat transfer and derive necessary optimality conditions, including the adjoint equation, for the optimal set of parameters minimizing objective functions J. Numerical simulations illustrate several numerical optimization methods, examples, and realistic cases, in which several interesting phenomena are observed. A large amount of computational effort is required to solve the coupled state equation and the adjoint equation (which is backwards in time, and the algebraic gradient equation (which implements the coupling between the adjoint and control variables. The state and adjoint equations are solved using the finite element method.

  13. Boltzmann’s Six-Moment One-Dimensional Nonlinear System Equations with the Maxwell-Auzhan Boundary Conditions

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    A. Sakabekov

    2016-01-01

    Full Text Available We prove existence and uniqueness of the solution of the problem with initial and Maxwell-Auzhan boundary conditions for nonstationary nonlinear one-dimensional Boltzmann’s six-moment system equations in space of functions continuous in time and summable in square by a spatial variable. In order to obtain a priori estimation of the initial and boundary value problem for nonstationary nonlinear one-dimensional Boltzmann’s six-moment system equations we get the integral equality and then use the spherical representation of vector. Then we obtain the initial value problem for Riccati equation. We have managed to obtain a particular solution of this equation in an explicit form.

  14. Effects of viscous dissipation on MHD tangent hyperbolic fluid over a nonlinear stretching sheet with convective boundary conditions

    Science.gov (United States)

    Hussain, Arif; Malik, M. Y.; Salahuddin, T.; Rubab, A.; Khan, Mair

    Present analysis is concentrating on the thermo-physical aspects of MHD tangent hyperbolic fluid flow over a non-linear stretching sheet with viscous dissipation and convective boundary conditions. Mathematical modelling yields non-linear partial differential equations. The governing equations are transformed into corresponding coupled ordinary differential equations via using local similarity variables. The accomplished boundary layer ordinary differential equations are solved with the aid of both homotopy analysis method and shooting method. The effects of flow govern parameters are visualized on velocity and temperature in both qualitative and quantitative manners. The computations of wall friction factor and local Nusselt number are performed to analyze the behavior in the vicinity of stretching sheet. The contrast between analytically and numerically computed values of wall friction factor and local Nusselt number is presented. It is worth mentioning that the both results are in excellent agreement, this favorable comparison led to confidence on computed results.

  15. Existence of solutions for a coupled system with ∅-Laplacian operators and nonlinear coupled boundary conditions

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    Goli Konan Charles Etienne

    2017-12-01

    Full Text Available We study the existence of solutions of the system submitted to nonlinear coupled boundary conditions on [0, T] where ∅1, ∅2: (-a, a → ℝ, with 0 < a < +∞, are two increasing homeomorphisms such that ∅1(0 = ∅2(0 = 0, and fi : [0, T] × ℝ4 → ℝ, i ∈{1, 2} are two L1-Carathéodory functions. Using some new conditions and Schauder fixed point Theorem, we obtain solvability result.

  16. Inverse scattering transform for the vector nonlinear Schroedinger equation with nonvanishing boundary conditions

    International Nuclear Information System (INIS)

    Prinari, Barbara; Ablowitz, Mark J.; Biondini, Gino

    2006-01-01

    The inverse scattering transform for the vector defocusing nonlinear Schroedinger (NLS) equation with nonvanishing boundary values at infinity is constructed. The direct scattering problem is formulated on a two-sheeted covering of the complex plane. Two out of the six Jost eigenfunctions, however, do not admit an analytic extension on either sheet of the Riemann surface. Therefore, a suitable modification of both the direct and the inverse problem formulations is necessary. On the direct side, this is accomplished by constructing two additional analytic eigenfunctions which are expressed in terms of the adjoint eigenfunctions. The discrete spectrum, bound states and symmetries of the direct problem are then discussed. In the most general situation, a discrete eigenvalue corresponds to a quartet of zeros (poles) of certain scattering data. The inverse scattering problem is formulated in terms of a generalized Riemann-Hilbert (RH) problem in the upper/lower half planes of a suitable uniformization variable. Special soliton solutions are constructed from the poles in the RH problem, and include dark-dark soliton solutions, which have dark solitonic behavior in both components, as well as dark-bright soliton solutions, which have one dark and one bright component. The linear limit is obtained from the RH problem and is shown to correspond to the Fourier transform solution obtained from the linearized vector NLS system

  17. Boundary Controllability of Nonlinear Fractional Integrodifferential Systems

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    Ahmed HamdyM

    2010-01-01

    Full Text Available Sufficient conditions for boundary controllability of nonlinear fractional integrodifferential systems in Banach space are established. The results are obtained by using fixed point theorems. We also give an application for integropartial differential equations of fractional order.

  18. Nonlinear radiative heat transfer in magnetohydrodynamic (MHD stagnation point flow of nanofluid past a stretching sheet with convective boundary condition

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    Wubshet Ibrahim

    2015-12-01

    Full Text Available Two-dimensional boundary layer flow of nanofluid fluid past a stretching sheet is examined. The paper reveals the effect of non-linear radiative heat transfer on magnetohydrodynamic (MHD stagnation point flow past a stretching sheet with convective heating. Condition of zero normal flux of nanoparticles at the wall for the stretched flow is considered. The nanoparticle fractions on the boundary are considered to be passively controlled. The solution for the velocity, temperature and nanoparticle concentration depends on parameters viz. Prandtl number Pr, velocity ratio parameter A, magnetic parameter M, Lewis number Le, Brownian motion Nb, and the thermophoresis parameter Nt. Moreover, the problem is governed by temperature ratio parameter (Nr=TfT∞ and radiation parameter Rd. Similarity transformation is used to reduce the governing non-linear boundary-value problems into coupled higher order non-linear ordinary differential equation. These equations were numerically solved using the function bvp4c from the matlab software for different values of governing parameters. Numerical results are obtained for velocity, temperature and concentration, as well as the skin friction coefficient and local Nusselt number. The results indicate that the skin friction coefficient Cf increases as the values of magnetic parameter M increase and decreases as the values of velocity ratio parameter A increase. The local Nusselt number −θ′(0 decreases as the values of thermophoresis parameter Nt and radiation parameter Nr increase and it increases as the values of both Biot number Bi and Prandtl number Pr increase. Furthermore, radiation has a positive effect on temperature and concentration profiles.

  19. Nonlinear Kirchhoff-Carrier wave equation in a unit membrane with mixed homogeneous boundary conditions

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    Nguyen Thanh Long

    2005-12-01

    Full Text Available In this paper we consider the nonlinear wave equation problem $$displaylines{ u_{tt}-Big(|u|_0^2,|u_{r}|_0^2ig(u_{rr}+frac{1}{r}u_{r} =f(r,t,u,u_{r},quad 0less than r less than 1,; 0 less than t less than T, ig|lim_{ro 0^+}sqrt{r}u_{r}(r,tig| less than infty, u_{r}(1,t+hu(1,t=0, u(r,0=widetilde{u}_0(r, u_{t}(r,0=widetilde{u}_1(r. }$$ To this problem, we associate a linear recursive scheme for which the existence of a local and unique weak solution is proved, in weighted Sobolev using standard compactness arguments. In the latter part, we give sufficient conditions for quadratic convergence to the solution of the original problem, for an autonomous right-hand side independent on $u_{r}$ and a coefficient function $B$ of the form $B=B(|u|_0^2=b_0+|u|_0^2$ with $b_0$ greater than 0.

  20. A semi analytical method for electro-thermo-mechanical nonlinear vibration analysis of nanobeam resting on the Winkler-Pasternak foundations with general elastic boundary conditions

    Science.gov (United States)

    Zarepour, Misagh; Amirhosein Hosseini, Seyed

    2016-08-01

    This study presents an examination of nonlinear free vibration of a nanobeam under electro-thermo-mechanical loading with elastic medium and various boundary conditions, especially the elastic boundary condition. The nanobeam is modeled as an Euler-Bernoulli beam. The von Kármán strain-displacement relationship together with Hamilton’s principle and Eringen’s theory are employed to derive equations of motion. The nonlinear free vibration frequency is obtained for simply supported (S-S) and elastic supported (E-E) boundary conditions. E-E boundary condition is a general and actual form of boundary conditions and it is chosen because of more realistic behavior. By applying the differential transform method (DTM), the nanobeam’s natural frequencies can be easily obtained for the two different boundary conditions mentioned above. Performing a precise study led to investigation of the influences of nonlocal parameter, temperature change, spring constants (either for elastic medium or boundary condition) and imposed electric potential on the nonlinear free vibration characteristics of nanobeam. The results for S-S and E-E nanobeams are compared with each other. In order to validate the results, some comparisons are presented between DTM results and open literature to show the accuracy of this new approach. It has been discovered that DTM solves the equations with minimum calculation cost.

  1. Exponential convergence for nonlinear diffusion problems with positive lateral boundary conditions

    International Nuclear Information System (INIS)

    Holland, C.J.; Berryman, J.G.

    1985-01-01

    It is established that the solution u of u/sub t/ = Δ(u/sup m/)>0, with positive initial data, positive lateral boundary data, and positive exponent m, converges exponentially to the solution v of the corresponding stationary equation Δ(v/sup m/) = 0. The analysis also provides the form of the leading contribution to the difference

  2. Nonlinear Free Vibration Analysis of Axisymmetric Polar Orthotropic Circular Membranes under the Fixed Boundary Condition

    Directory of Open Access Journals (Sweden)

    Zhoulian Zheng

    2014-01-01

    Full Text Available This paper presents the nonlinear free vibration analysis of axisymmetric polar orthotropic circular membrane, based on the large deflection theory of membrane and the principle of virtual displacement. We have derived the governing equations of nonlinear free vibration of circular membrane and solved them by the Galerkin method and the Bessel function to obtain the generally exact formula of nonlinear vibration frequency of circular membrane with outer edges fixed. The formula could be degraded into the solution from small deflection vibration; thus, its correctness has been verified. Finally, the paper gives the computational examples and comparative analysis with the other solution. The frequency is enlarged with the increase of the initial displacement, and the larger the initial displacement is, the larger the effect on the frequency is, and vice versa. When the initial displacement approaches zero, the result is consistent with that obtained on the basis of the small deflection theory. Results obtained from this paper provide the accurate theory for the measurement of the pretension of polar orthotropic composite materials by frequency method and some theoretical basis for the research of the dynamic response of membrane structure.

  3. On the solvability of initial boundary value problems for nonlinear ...

    African Journals Online (AJOL)

    In this paper, we study the initial boundary value problems for a non-linear time dependent Schrödinger equation with Dirichlet and Neumann boundary conditions, respectively. We prove the existence and uniqueness of solutions of the initial boundary value problems by using Galerkin's method. Keywords: Initial boundary ...

  4. Nonlinear second-order multivalued boundary value problems

    Indian Academy of Sciences (India)

    In this paper we study nonlinear second-order differential inclusions involving the ordinary vector -Laplacian, a multivalued maximal monotone operator and nonlinear multivalued boundary conditions. Our framework is general and unifying and incorporates gradient systems, evolutionary variational inequalities and the ...

  5. Second-Order Boundary Value Problem with Integral Boundary Conditions

    Directory of Open Access Journals (Sweden)

    Nieto JuanJ

    2011-01-01

    Full Text Available The nonlinear alternative of the Leray Schauder type and the Banach contraction principle are used to investigate the existence of solutions for second-order differential equations with integral boundary conditions. The compactness of solutions set is also investigated.

  6. The scaled boundary FEM for nonlinear problems

    Science.gov (United States)

    Lin, Zhiliang; Liao, Shijun

    2011-01-01

    The traditional scaled boundary finite-element method (SBFEM) is a rather efficient semi-analytical technique widely applied in engineering, which is however valid mostly for linear differential equations. In this paper, the traditional SBFEM is combined with the homotopy analysis method (HAM), an analytic technique for strongly nonlinear problems: a nonlinear equation is first transformed into a series of linear equations by means of the HAM, and then solved by the traditional SBFEM. In this way, the traditional SBFEM is extended to nonlinear differential equations. A nonlinear heat transfer problem is used as an example to show the validity and computational efficiency of this new SBFEM.

  7. Existence theory for nonlinear functional boundary value problems

    Directory of Open Access Journals (Sweden)

    Bapurao Dhage

    2004-01-01

    Full Text Available In this paper the existence of a solution of a general nonlinear functional two point boundary value problem is proved under mixed generalized Lipschitz and Carath\\'eodory conditions. An existence theorem for extremal solutions is also proved under certain monotonicity and weaker continuity conditions. Examples are provided to illustrate the theory developed in this paper.

  8. Electromagnetic pulses at the boundary of a nonlinear plasma

    International Nuclear Information System (INIS)

    Satorius, E.H.

    1975-01-01

    An investigation was made of the behavior of strong electromagnetic pulses at the boundary of a nonlinear, cold, collisionless, and uniform plasma. The nonlinearity considered here is due to the nonlinear terms in the fluid equation which is used to describe the plasma. Two cases are studied. First, the case where there is a voltage pulse applied across the plane boundary of a semi-infinite, nonlinear plasma. Two different voltage pulses are considered, i.e., a delta function pulse and a suddenly turned-on sinusoidal pulse. The resulting electromagnetic fields propagating in the nonlinear plasma are found in this case. In the second case, the reflection of incident E-polarized and H-polarized, electromagnetic pulses at various angles of incidence from a nonlinear, semi-infinite plasma are considered. Again, two forms of incident pulses are considered: a delta function pulse and a suddenly turned-on sinusoidal pulse. In case two, the reflected electromagnetic fields are found. In both cases, the method used for finding the fields is to first solve the fluid equation (which describes the plasma) for the nonlinear conduction current in terms of the electric field using a perturbation method (since the nonlinear effects are assumed to be small). Next, this current is substituted into Maxwell's equations, and finally the electromagnetic fields which satisfy the boundary conditions are found. (U.S.)

  9. Topological invariants in nonlinear boundary value problems

    International Nuclear Information System (INIS)

    Vinagre, Sandra; Severino, Ricardo; Ramos, J. Sousa

    2005-01-01

    We consider a class of boundary value problems for partial differential equations, whose solutions are, basically, characterized by the iteration of a nonlinear function. We apply methods of symbolic dynamics of discrete bimodal maps in the interval in order to give a topological characterization of its solutions

  10. Nonlinear streak computation using boundary region equations

    Energy Technology Data Exchange (ETDEWEB)

    Martin, J A; Martel, C, E-mail: juanangel.martin@upm.es, E-mail: carlos.martel@upm.es [Depto. de Fundamentos Matematicos, E.T.S.I Aeronauticos, Universidad Politecnica de Madrid, Plaza Cardenal Cisneros 3, 28040 Madrid (Spain)

    2012-08-01

    The boundary region equations (BREs) are applied for the simulation of the nonlinear evolution of a spanwise periodic array of streaks in a flat plate boundary layer. The well-known BRE formulation is obtained from the complete Navier-Stokes equations in the high Reynolds number limit, and provides the correct asymptotic description of three-dimensional boundary layer streaks. In this paper, a fast and robust streamwise marching scheme is introduced to perform their numerical integration. Typical streak computations present in the literature correspond to linear streaks or to small-amplitude nonlinear streaks computed using direct numerical simulation (DNS) or the nonlinear parabolized stability equations (PSEs). We use the BREs to numerically compute high-amplitude streaks, a method which requires much lower computational effort than DNS and does not have the consistency and convergence problems of the PSE. It is found that the flow configuration changes substantially as the amplitude of the streaks grows and the nonlinear effects come into play. The transversal motion (in the wall normal-streamwise plane) becomes more important and strongly distorts the streamwise velocity profiles, which end up being quite different from those of the linear case. We analyze in detail the resulting flow patterns for the nonlinearly saturated streaks and compare them with available experimental results. (paper)

  11. Inverse scattering transform and soliton solutions for square matrix nonlinear Schrödinger equations with non-zero boundary conditions

    Science.gov (United States)

    Prinari, Barbara; Demontis, Francesco; Li, Sitai; Horikis, Theodoros P.

    2018-04-01

    The inverse scattering transform (IST) with non-zero boundary conditions at infinity is developed for an m × m matrix nonlinear Schrödinger-type equation which, in the case m = 2, has been proposed as a model to describe hyperfine spin F = 1 spinor Bose-Einstein condensates with either repulsive interatomic interactions and anti-ferromagnetic spin-exchange interactions (self-defocusing case), or attractive interatomic interactions and ferromagnetic spin-exchange interactions (self-focusing case). The IST for this system was first presented by Ieda et al. (2007) , using a different approach. In our formulation, both the direct and the inverse problems are posed in terms of a suitable uniformization variable which allows to develop the IST on the standard complex plane, instead of a two-sheeted Riemann surface or the cut plane with discontinuities along the cuts. Analyticity of the scattering eigenfunctions and scattering data, symmetries, properties of the discrete spectrum, and asymptotics are derived. The inverse problem is posed as a Riemann-Hilbert problem for the eigenfunctions, and the reconstruction formula of the potential in terms of eigenfunctions and scattering data is provided. In addition, the general behavior of the soliton solutions is analyzed in detail in the 2 × 2 self-focusing case, including some special solutions not previously discussed in the literature.

  12. On Impulsive Boundary Value Problems of Fractional Differential Equations with Irregular Boundary Conditions

    Directory of Open Access Journals (Sweden)

    Guotao Wang

    2012-01-01

    Full Text Available We study nonlinear impulsive differential equations of fractional order with irregular boundary conditions. Some existence and uniqueness results are obtained by applying standard fixed-point theorems. For illustration of the results, some examples are discussed.

  13. Hausdorff Measure Estimates and Lipschitz Regularity in Inhomogeneous Nonlinear Free Boundary Problems

    Science.gov (United States)

    Moreira, Diego; Wang, Lihe

    2014-08-01

    In this paper, we prove a Hausdorff measure estimate for the free boundaries of subsolutions of fully nonlinear and quasilinear equations of the type and where and μ is a signed Radon measure with some appropriate growth condition. Gradient estimates for nonnegative harmonic functions with bounded normal derivatives along the boundary obtained by Caffarelli and Salsa (Geometric Approach to Free Boundary Problems, 2005) are extended to the context of inhomogeneous problems involving fully nonlinear and p-Laplace equations. As an application, Lipschitz regularity is obtained for one phase solutions of inhomogeneous nonlinear free boundary problems.

  14. Combined effects of slip and convective boundary condition on MHD 3D stretched flow of nanofluid through porous media inspired by non-linear thermal radiation

    Science.gov (United States)

    Nayak, M. K.; Shaw, Sachin; Pandey, V. S.; Chamkha, Ali J.

    2018-02-01

    In the present study, the main concern is to investigate the magnetohydrodynamic nanofluid flow subject to porous matrix and convective heating past a permeable linear stretching sheet. In addition, the influence of velocity slip, viscous dissipation, Joule heating and non-linear thermal radiation are considered. A new micro-convection model known as the Patel model is implemented for considerable enhancement of the thermal conductivity and hence, the heat transfer capability of nanofluids. Moreover, a convective heat transfer model is introduced where the bottom surface of the sheet gets heated due to a convection mechanism from a hot fluid of particular temperature. The numerical results of the transformed governing differential equations have been obtained by using fourth-order Runge-Kutta method along with shooting approach and secant method is used for better approximation. In the present analysis, base fluids such as water and Ethylene glycol and Copper, Silver and Aluminum oxide nanoparticles are considered. Results of the present investigation show that inclusion of porous matrix contributes to slow down the fluid velocity and diminution of wall shear stress (axial as well as transverse). Drag force due to magnetic field strength, velocity slip and imposed fluid suction impede the fluid motion and upsurge the heat transfer rate from the surface. In addition, rise in viscous dissipation widens the thermal boundary layer.

  15. Boundary control of long waves in nonlinear dispersive systems

    DEFF Research Database (Denmark)

    Hasan, Agus; Foss, Bjarne; Aamo, Ole Morten

    2011-01-01

    orders of the nonlinearity, the equation may have unstable solitary wave solutions. Although it is a one dimensional problem, achieving a global result for this equation is not trivial due to the nonlinearity and the mixed partial derivative. In this paper, two sets of nonlinear boundary control laws......Unidirectional propagation of long waves in nonlinear dispersive systems may be modeled by the Benjamin-Bona-Mahony-Burgers equation, a third order partial differential equation incorporating linear dissipative and dispersive terms, as well as a term covering nonlinear wave phenomena. For higher...... that achieve global exponential stability and semi-global exponential stability are derived for both linear and nonlinear cases....

  16. Initial boundary value problems for some damped nonlinear conservation laws

    Directory of Open Access Journals (Sweden)

    Manoj Yadav

    2015-11-01

    Full Text Available In this paper, we study the non-negative solutions of initial boundary value problems for some damped nonlinear conservation laws on the half line modelled by first order nonlinear hyperbolic PDEs. We consider the class of initial profile which are non-negative, bounded and compactly supported. Using the method of characteristics and Rankine-Hugoniot jump condition, an entropy solution is constructed subject to a top-hat initial profile. Then the large time behaviour of the constructed entropy solution is obtained. Finally, taking recourse to some comparison principles and the method of super and sub solutions the large time behaviour of entropy solutions subject to the general class of bounded and compactly supported initial profiles are established as the large time behaviour of the entropy solution subject to top-hat initial profiles.

  17. Quantum cavities with alternating boundary conditions

    Science.gov (United States)

    Facchi, Paolo; Garnero, Giancarlo; Ligabò, Marilena

    2018-03-01

    We consider the quantum dynamics of a free nonrelativistic particle moving in a cavity and we analyze the effect of a rapid switching between two different boundary conditions. We show that this procedure induces, in the limit of infinitely frequent switchings, a new effective dynamics in the cavity related to a novel boundary condition. We obtain a dynamical composition law for boundary conditions which gives the emerging boundary condition in terms of the two initial ones.

  18. On the wave equation with semilinear porous acoustic boundary conditions

    KAUST Repository

    Graber, Philip Jameson

    2012-05-01

    The goal of this work is to study a model of the wave equation with semilinear porous acoustic boundary conditions with nonlinear boundary/interior sources and a nonlinear boundary/interior damping. First, applying the nonlinear semigroup theory, we show the existence and uniqueness of local in time solutions. The main difficulty in proving the local existence result is that the Neumann boundary conditions experience loss of regularity due to boundary sources. Using an approximation method involving truncated sources and adapting the ideas in Lasiecka and Tataru (1993) [28], we show that the existence of solutions can still be obtained. Second, we prove that under some restrictions on the source terms, then the local solution can be extended to be global in time. In addition, it has been shown that the decay rates of the solution are given implicitly as solutions to a first order ODE and depends on the behavior of the damping terms. In several situations, the obtained ODE can be easily solved and the decay rates can be given explicitly. Third, we show that under some restrictions on the initial data and if the interior source dominates the interior damping term and if the boundary source dominates the boundary damping, then the solution ceases to exists and blows up in finite time. Moreover, in either the absence of the interior source or the boundary source, then we prove that the solution is unbounded and grows as an exponential function. © 2012 Elsevier Inc.

  19. Stabilization of infinite dimensional port-Hamiltonian systems by nonlinear dynamic boundary control

    NARCIS (Netherlands)

    Ramirez, Hector; Zwart, Hans; Le Gorrec, Yann

    2017-01-01

    The conditions for existence of solutions and stability, asymptotic and exponential, of a large class of boundary controlled systems on a 1D spatial domain subject to nonlinear dynamic boundary actuation are given. The consideration of such class of control systems is motivated by the use of

  20. Asymptotic Analysis of a Nonlinear Problem on Domain Boundaries in Convection Patterns by Homotopy Renormalization Method

    Science.gov (United States)

    Xin, Hua

    2017-09-01

    In this article, using the homotopy renormalization method, the asymptotic analysis to a nonlinear problem on domain boundaries in convection patterns are given. In particular, by taking a variable coefficient homotopy equation, the global asymptotic solutions satisfying boundary conditions are obtained. These results are better than the existing analytic approximation solutions.

  1. Robust Monotone Iterates for Nonlinear Singularly Perturbed Boundary Value Problems

    Directory of Open Access Journals (Sweden)

    Boglaev Igor

    2009-01-01

    Full Text Available This paper is concerned with solving nonlinear singularly perturbed boundary value problems. Robust monotone iterates for solving nonlinear difference scheme are constructed. Uniform convergence of the monotone methods is investigated, and convergence rates are estimated. Numerical experiments complement the theoretical results.

  2. Nonlinear interaction of the surface waves at a plasma boundary

    International Nuclear Information System (INIS)

    Dolgopolov, V.V.; El-Naggar, I.A.; Hussein, A.M.; Khalil, Sh.M.

    1976-01-01

    Amplitudes of electromagnetic waves with combination frequencies, radiating from the plasma boundary due to nonlinear interaction of the surface waves, have been found. Previous papers on this subject did not take into account that the tangential components of the electric field of waves with combination frequencies were discontinuous at the plasma boundary. (Auth.)

  3. Integrability and boundary conditions of supersymmetric systems

    International Nuclear Information System (INIS)

    Yue Ruihong; Liang Hong

    1996-01-01

    By studying the solutions of the reflection equations, we find out a series of integrable supersymmetric systems with different boundary conditions. The Hamiltonian contains four free parameters which describe the contribution of the boundary terms

  4. Boundary Conditions of Methamphetamine Craving

    Science.gov (United States)

    Lopez, Richard B.; Onyemekwu, Chukwudi; Hart, Carl L.; Ochsner, Kevin N.; Kober, Hedy

    2015-01-01

    Methamphetamine use has increased significantly and become a global health concern. Craving is known to predict methamphetamine use and relapse following abstinence. Some have suggested that cravings are automatic, generalized, and uncontrollable, but experimental work addressing these claims is lacking. In two exploratory studies we tested the boundary conditions of methamphetamine craving by asking: (1) is craving specific to users’ preferred route of administration? and (2) can craving be regulated by cognitive strategies? Two groups of methamphetamine users were recruited. In Study 1, participants were grouped by their preferred route of administration (intranasal vs. smoking), and rated their craving in response to photographs and movies depicting methamphetamine use (via the intranasal vs. smoking route). In Study 2, methamphetamine smokers implemented cognitive regulation strategies while viewing photographs depicting methamphetamine smoking. Strategies involved either focusing on the positive aspects of smoking methamphetamine or the negative consequences of doing so – the latter strategy based on treatment protocols for addiction. In Study 1, we found a significant interaction between group and route of administration, such that participants who preferred to smoke methamphetamine reported significantly stronger craving for smoking stimuli, whereas those who preferred the intranasal route reported stronger craving for intranasal stimuli. In Study 2, participants reported significantly lower craving when focusing on the negative consequences associated with methamphetamine use. Taken together, these findings suggest that strength of craving for methamphetamine is moderated by users’ route of administration and can be reduced by cognitive strategies. This has important theoretical, methodological, and clinical implications. PMID:26302338

  5. On radiative-magnetoconvective heat and mass transfer of a nanofluid past a non-linear stretching surface with Ohmic heating and convective surface boundary condition

    Directory of Open Access Journals (Sweden)

    Shweta Mishra

    2016-12-01

    Full Text Available In this paper magnetoconvective heat and mass transfer characteristics of a two-dimensional steady flow of a nanofluid over a non-linear stretching sheet in the presence of thermal radiation, Ohmic heating and viscous dissipation have been investigated numerically. The model used for the nanofluid incorporates the effects of the Brownian motion and the presence of nanoparticles in the base fluid. The governing equations are transformed into a system of nonlinear ordinary differential equations by using similarity transformation. The numerical solutions are obtained by using fifth order Runge–Kutta–Fehlberg method with shooting technique. The non-dimensional parameters on velocity, temperature and concentration profiles and also on local Nusselt number and Sherwood number are discussed. The results indicate that the local skin friction coefficient decreases as the value of the magnetic parameter increases whereas the Nusselt number and Sherwood number increase as the values of the Brownian motion parameter and magnetic parameter increase.

  6. Thermo-mechanical nonlinear vibration analysis of fluid-conveying structures subjected to different boundary conditions using Galerkin-Newton-Harmonic balancing method

    Directory of Open Access Journals (Sweden)

    Gbeminiyi Sobamowo

    2017-04-01

    Full Text Available The development of mathematical models for describing the dynamic behaviours of fluid conveying pipes, micro-pipes and nanotubes under the influence of some thermo-mechanical parameters results into nonlinear equations that are very difficult to solve analytically. In cases where the exact analytical solutions are presented either in implicit or explicit forms, high skills and rigorous mathematical analyses were employed. It is noted that such solutions do not provide general exact solutions. Inevitably, comparatively simple, flexible yet accurate and practicable solutions are required for the analyses of these structures. Therefore, in this study, approximate analytical solutions are provided to the nonlinear equations arising in flow-induced vibration of pipes, micro-pipes and nanotubes using Galerkin-Newton-Harmonic Method (GNHM. The developed approximate analytical solutions are shown to be valid for both small and large amplitude oscillations. The accuracies and explicitness of these solutions were examined in limiting cases to establish the suitability of the method.

  7. Boundary conditions of methamphetamine craving.

    Science.gov (United States)

    Lopez, Richard B; Onyemekwu, Chukwudi; Hart, Carl L; Ochsner, Kevin N; Kober, Hedy

    2015-12-01

    Methamphetamine use has increased significantly and become a global health concern. Craving is known to predict methamphetamine use and relapse following abstinence. Some have suggested that cravings are automatic, generalized, and uncontrollable, but experimental work addressing these claims is lacking. In 2 exploratory studies, we tested the boundary conditions of methamphetamine craving by asking: (a) is craving specific to users' preferred route of administration?, and (b) can craving be regulated by cognitive strategies? Two groups of methamphetamine users were recruited. In Study 1, participants were grouped by their preferred route of administration (intranasal vs. smoking), and rated their craving in response to photographs and movies depicting methamphetamine use (via the intranasal vs. smoking route). In Study 2, methamphetamine smokers implemented cognitive regulation strategies while viewing photographs depicting methamphetamine smoking. Strategies involved either focusing on the positive aspects of smoking methamphetamine or the negative consequences of doing so-the latter strategy based on treatment protocols for addiction. In Study 1, we found a significant interaction between group and route of administration, such that participants who preferred to smoke methamphetamine reported significantly stronger craving for smoking stimuli, whereas those who preferred the intranasal route reported stronger craving for intranasal stimuli. In Study 2, participants reported significantly lower craving when focusing on the negative consequences associated with methamphetamine use. Taken together, these findings suggest that strength of craving for methamphetamine is moderated by users' route of administration and can be reduced by cognitive strategies. This has important theoretical, methodological, and clinical implications. (PsycINFO Database Record (c) 2015 APA, all rights reserved).

  8. Boundary control of nonlinear coupled heat systems using backstepping

    KAUST Repository

    Bendevis, Paul

    2016-10-20

    A state feedback boundary controller is designed for a 2D coupled PDE system modelling heat transfer in a membrane distillation system for water desalination. Fluid is separated into two compartments with nonlinear coupling at a membrane boundary. The controller sets the temperature on one boundary in order to track a temperature difference across the membrane boundary. The control objective is achieved by an extension of backstepping methods to these coupled equations. Stability of the target system via Lyapunov like methods, and the invertibility of the integral transformation are used to show the stability of the tracking error.

  9. Absorption boundary conditions for geomertical acoustics

    DEFF Research Database (Denmark)

    Jeong, Cheol-Ho

    2012-01-01

    Defining accurate acoustical boundary conditions is of crucial importance for room acoustic simulations. In predicting sound fields using phased geometrical acoustics methods, the absorption coefficients or surface impedances of the boundary surfaces can be used, but no guideline has been developed...... on which boundary condition produces the best results. In this study, various boundary conditions in terms of normal and random incidence absorption coefficients, and normal incidence surface impedances are used in a phased beam tracing model, and simulated results are validated with boundary element...... solutions. Two rectangular rooms with uniform and non-uniform absorption distributions are tested. It is concluded that the impedance and random incidence absorption boundary conditions produce reasonable results with some exceptions at low frequencies for acoustically soft materials....

  10. A Note on Fractional Differential Equations with Fractional Separated Boundary Conditions

    Directory of Open Access Journals (Sweden)

    Bashir Ahmad

    2012-01-01

    Full Text Available We consider a new class of boundary value problems of nonlinear fractional differential equations with fractional separated boundary conditions. A connection between classical separated and fractional separated boundary conditions is developed. Some new existence and uniqueness results are obtained for this class of problems by using standard fixed point theorems. Some illustrative examples are also discussed.

  11. Boundary conditions in random sequential adsorption

    Science.gov (United States)

    Cieśla, Michał; Ziff, Robert M.

    2018-04-01

    The influence of different boundary conditions on the density of random packings of disks is studied. Packings are generated using the random sequential adsorption algorithm with three different types of boundary conditions: periodic, open, and wall. It is found that the finite size effects are smallest for periodic boundary conditions, as expected. On the other hand, in the case of open and wall boundaries it is possible to introduce an effective packing size and a constant correction term to significantly improve the packing densities.

  12. Implementation of Boundary Condition to THALES Code

    International Nuclear Information System (INIS)

    Jang, Beomjun; Chun, Chong Kuk; Park, Ho Young; Woo, Hae-Seuk

    2016-01-01

    The boundary condition of momentum equation of THALES code utilizes the exit pressure boundary to solve the elliptic partial difference momentum equations. This method is the same as the most of the subchannel analysis codes. Other codes such as VIPRE utilize the uniform pressure distribution as outlet boundary condition. In this case, uniform inlet flow rate is assumed. In order to test the core flow field regarding the boundary conditions, analysis was performed for two core conditions. One condition is nominal plant operating condition. In this paper, generic THALES power distribution is used. For nominal operation case, there are no different results depending on the type of outlet pressure boundary condition. But low-power and high-peaking case, density difference for lateral direction becomes large due to high peaking power of core. Since density change causes pressure change, In this case, uniform outlet pressure distribution can't be assumed anymore. Design outlet pressure distribution is measured at nominal core condition. Therefore, design outlet pressure distribution also can't be used due to the difference in core power and flow rate. As a result, it is reasonable that neumann boundary condition is applied in low-power and high peaking core condition including various accident condition

  13. Lyapunov Based Estimation of Flight Stability Boundary under Icing Conditions

    Directory of Open Access Journals (Sweden)

    Binbin Pei

    2017-01-01

    Full Text Available Current fight boundary of the envelope protection in icing conditions is usually defined by the critical values of state parameters; however, such method does not take the interrelationship of each parameter and the effect of the external disturbance into consideration. This paper proposes constructing the stability boundary of the aircraft in icing conditions through analyzing the region of attraction (ROA around the equilibrium point. Nonlinear icing effect model is proposed according to existing wind tunnel test results. On this basis, the iced polynomial short period model can be deduced further to obtain the stability boundary under icing conditions using ROA analysis. Simulation results for a series of icing severity demonstrate that, regardless of the icing severity, the boundary of the calculated ROA can be treated as an estimation of the stability boundary around an equilibrium point. The proposed methodology is believed to be a promising way for ROA analysis and stability boundary construction of the aircraft in icing conditions, and it will provide theoretical support for multiple boundary protection of icing tolerant flight.

  14. On nonlinear boundary value problems with deviating arguments and discontinuous right hand side

    Directory of Open Access Journals (Sweden)

    B. C. Dhage

    1993-01-01

    Full Text Available In this paper we shall study the existence of the extremal solutions of a nonlinear boundary value problem of a second order differential equation with general Dirichlet/Neumann form boundary conditions. The right hand side of the differential equation is assumed to contain a deviating argument, and it is allowed to possess discontinuities in all the variables. The proof is based on a generalized iteration method.

  15. Solution of moving boundary problems with implicit boundary condition

    International Nuclear Information System (INIS)

    Moyano, E.A.

    1990-01-01

    An algorithm that solves numerically a model for studying one dimensional moving boundary problems, with implicit boundary condition, is described. Landau's transformation is used, in order to work with a fixed number of nodes at each instant. Then, it is necessary to deal with a parabolic partial differential equation, whose diffusive and convective terms have variable coefficients. The partial differential equation is implicitly discretized, using Laasonen's scheme, always stable, instead of employing Crank-Nicholson sheme, as it has been done by Ferris and Hill. Fixed time and space steps (Δt, Δξ) are used, and the iteration is made with variable positions of the interface, i.e. varying δs until a boundary condition is satisfied. The model has the same features of the oxygen diffusion in absorbing tissue. It would be capable of estimating time variant radiation treatments of cancerous tumors. (Author) [es

  16. Boundary behavior of blow-up solutions to some weighted non-linear differential equations

    Directory of Open Access Journals (Sweden)

    Ahmed Mohammed

    2002-09-01

    Full Text Available We investigate, under appropriate conditions on the weight $g$ and the non-linearity $f$, the boundary behavior of solutions to $$(r^{alpha}(u'^{p-1}'=r^alpha g(rf(u, $$ $0

  17. Modelling classroom conditions with different boundary conditions

    DEFF Research Database (Denmark)

    Marbjerg, Gerd Høy; Jeong, Cheol-Ho; Brunskog, Jonas

    2014-01-01

    both specular and diffuse reflections with complex-valued acoustical descriptions of the surfaces. In this paper the PARISM model is used to simulate a rectangular room with most of the absorption located in the ceiling. This room configuration is typical for classroom conditions. The simulations...... measures which are important for evaluation of the acoustics in classrooms....

  18. Reconstruction of boundary conditions from internal conditions using viability theory

    KAUST Repository

    Hofleitner, Aude

    2012-06-01

    This article presents a method for reconstructing downstream boundary conditions to a HamiltonJacobi partial differential equation for which initial and upstream boundary conditions are prescribed as piecewise affine functions and an internal condition is prescribed as an affine function. Based on viability theory, we reconstruct the downstream boundary condition such that the solution of the Hamilton-Jacobi equation with the prescribed initial and upstream conditions and reconstructed downstream boundary condition satisfies the internal value condition. This work has important applications for estimation in flow networks with unknown capacity reductions. It is applied to urban traffic, to reconstruct signal timings and temporary capacity reductions at intersections, using Lagrangian sensing such as GPS devices onboard vehicles.

  19. The Ablowitz-Ladik system with linearizable boundary conditions

    Science.gov (United States)

    Biondini, Gino; Bui, Anh

    2015-09-01

    The boundary value problem (BVP) for the Ablowitz-Ladik (AL) system on the natural numbers with linearizable boundary conditions is studied. In particular: (i) a discrete analogue is derived of the Bäcklund transformation that was used to solved similar BVPs for the nonlinear Schrödinger equation; (ii) an explicit proof is given that the Bäcklund-transformed solution of AL remains within the class of solutions that can be studied by the inverse scattering transform; (iii) an explicit linearizing transformation for the Bäcklund transformation is provided; (iv) explicit relations are obtained among the norming constants associated with symmetric eigenvalues; (v) conditions for the existence of self-symmetric eigenvalues are obtained. The results are illustrated by several exact soliton solutions, which describe the soliton reflection at the boundary with or without the presence of self-symmetric eigenvalues. This article is dedicated to Mark Ablowitz on the occasion of his seventieth birthday.

  20. Boundary conditions for the gravitational field

    International Nuclear Information System (INIS)

    Winicour, Jeffrey

    2012-01-01

    A review of the treatment of boundaries in general relativity is presented with the emphasis on application to the formulations of Einstein's equations used in numerical relativity. At present, it is known how to treat boundaries in the harmonic formulation of Einstein's equations and a tetrad formulation of the Einstein-Bianchi system. However, a universal approach valid for other formulations is not in hand. In particular, there is no satisfactory boundary theory for the 3+1 formulations which have been highly successful in binary black hole simulation. I discuss the underlying problems that make the initial-boundary-value problem much more complicated than the Cauchy problem. I review the progress that has been made and the important open questions that remain. Science is a differential equation. Religion is a boundary condition. (Alan Turing, quoted in J D Barrow, 'Theories of Everything') (topical review)

  1. Tracking control of a flexible beam by nonlinear boundary feedback

    Directory of Open Access Journals (Sweden)

    Bao-Zhu Guo

    1995-01-01

    Full Text Available This paper is concerned with tracking control of a dynamic model consisting of a flexible beam rotated by a motor in a horizontal plane at the one end and a tip body rigidly attached at the free end. The well-posedness of the closed loop systems considering the dissipative nonlinear boundary feedback is discussed and the asymptotic stability about difference energy of the hybrid system is also investigated.

  2. Upper and lower solutions method for differential inclusions with integral boundary conditions

    Directory of Open Access Journals (Sweden)

    Abdelghani Ouahab

    2006-03-01

    Full Text Available A nonlinear alternative of the Leray-Schauder type for multivalued maps combined with upper and lower solutions is used to investigate the existence of solutions for second-order differential inclusions with integral boundary conditions.

  3. Casimir pistons with general boundary conditions

    Directory of Open Access Journals (Sweden)

    Guglielmo Fucci

    2015-02-01

    Full Text Available In this work we analyze the Casimir energy and force for a scalar field endowed with general self-adjoint boundary conditions propagating in a higher dimensional piston configuration. The piston is constructed as a direct product I×N, with I=[0,L]⊂R and N a smooth, compact Riemannian manifold with or without boundary. The study of the Casimir energy and force for this configuration is performed by employing the spectral zeta function regularization technique. The obtained analytic results depend explicitly on the spectral zeta function associated with the manifold N and the parameters describing the general boundary conditions imposed. These results are then specialized to the case in which the manifold N is a d-dimensional sphere.

  4. Nonlinear Dynamics of Vortices in Different Types of Grain Boundaries

    Energy Technology Data Exchange (ETDEWEB)

    Sheikhzada, Ahmad [Old Dominion Univ., Norfolk, VA (United States)

    2017-05-01

    As a major component of linear particle accelerators, superconducting radio-frequency (SRF) resonator cavities are required to operate with lowest energy dissipation and highest accelerating gradient. SRF cavities are made of polycrystalline materials in which grain boundaries can limit maximum RF currents and produce additional power dissipation sources due to local penetration of Josephson vortices. The essential physics of vortex penetration and mechanisms of dissipation of vortices driven by strong RF currents along networks of grain boundaries and their contribution to the residual surface resistance have not been well understood. To evaluate how GBs can limit the performance of SRF materials, particularly Nb and Nb3Sn, we performed extensive numerical simulations of nonlinear dynamics of Josephson vortices in grain boundaries under strong dc and RF fields. The RF power due to penetration of vortices both in weakly-coupled and strongly-coupled grain boundaries was calculated as functions of the RF field and frequency. The result of this calculation manifested a quadratic dependence of power to field amplitude at strong RF currents, an illustration of resistive behavior of grain boundaries. Our calculations also showed that the surface resistance is a complicated function of field controlled by penetration and annihilation of vortices and antivortices in strong RF fields which ultimately saturates to normal resistivity of grain boundary. We found that Cherenkov radiation of rapidly moving vortices in grain boundaries can produce a new instability causing generation of expanding vortex-antivortex pair which ultimately drives the entire GB in a resistive state. This effect is more pronounced in polycrystalline thin film and multilayer coating structures in which it can cause significant increase in power dissipation and results in hysteresis effects in I-V characteristics, particularly at low temperatures.

  5. Entropy Stable Wall Boundary Conditions for the Three-Dimensional Compressible Navier-Stokes Equations

    Science.gov (United States)

    Parsani, Matteo; Carpenter, Mark H.; Nielsen, Eric J.

    2015-01-01

    Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the three-dimensional compressible Navier-Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although discontinuous spectral collocation operators on unstructured grids are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite difference, finite volume, discontinuous Galerkin, and flux reconstruction/correction procedure via reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary conditions.

  6. Entropy Stable Wall Boundary Conditions for the Compressible Navier-Stokes Equations

    Science.gov (United States)

    Parsani, Matteo; Carpenter, Mark H.; Nielsen, Eric J.

    2014-01-01

    Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the compressible Navier-Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although discontinuous spectral collocation operators are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite volume, finite difference, discontinuous Galerkin, and flux reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary conditions.

  7. Unconditionally stable perfectly matched layer boundary conditions

    NARCIS (Netherlands)

    De Raedt, H.; Michielsen, K.

    2007-01-01

    A brief review is given of a systematic, product-formula based approach to construct unconditionally stable algorithms for solving the time-dependent Maxwell equations. The fundamental difficulties that arise when we want to incorporate uniaxial perfectly matched layer boundary conditions into this

  8. An h-principle with boundary condition

    DEFF Research Database (Denmark)

    Dotto, Emanuele

    2010-01-01

    We prove an h-principle with boundary condition for a certain class of topological spaces valued sheaves. The techniques used in the proof come from the study of the homotopy type of the cobordism categories, and they are of simplicial and categorical nature. Applying the main result of this paper...

  9. Automated Boundary Conditions for Wind Tunnel Simulations

    Science.gov (United States)

    Carlson, Jan-Renee

    2018-01-01

    Computational fluid dynamic (CFD) simulations of models tested in wind tunnels require a high level of fidelity and accuracy particularly for the purposes of CFD validation efforts. Considerable effort is required to ensure the proper characterization of both the physical geometry of the wind tunnel and recreating the correct flow conditions inside the wind tunnel. The typical trial-and-error effort used for determining the boundary condition values for a particular tunnel configuration are time and computer resource intensive. This paper describes a method for calculating and updating the back pressure boundary condition in wind tunnel simulations by using a proportional-integral-derivative controller. The controller methodology and equations are discussed, and simulations using the controller to set a tunnel Mach number in the NASA Langley 14- by 22-Foot Subsonic Tunnel are demonstrated.

  10. Thermal Simulations, Open Boundary Conditions and Switches

    Science.gov (United States)

    Burnier, Yannis; Florio, Adrien; Kaczmarek, Olaf; Mazur, Lukas

    2018-03-01

    SU(N) gauge theories on compact spaces have a non-trivial vacuum structure characterized by a countable set of topological sectors and their topological charge. In lattice simulations, every topological sector needs to be explored a number of times which reflects its weight in the path integral. Current lattice simulations are impeded by the so-called freezing of the topological charge problem. As the continuum is approached, energy barriers between topological sectors become well defined and the simulations get trapped in a given sector. A possible way out was introduced by Lüscher and Schaefer using open boundary condition in the time extent. However, this solution cannot be used for thermal simulations, where the time direction is required to be periodic. In this proceedings, we present results obtained using open boundary conditions in space, at non-zero temperature. With these conditions, the topological charge is not quantized and the topological barriers are lifted. A downside of this method are the strong finite-size effects introduced by the boundary conditions. We also present some exploratory results which show how these conditions could be used on an algorithmic level to reshuffle the system and generate periodic configurations with non-zero topological charge.

  11. On nonlinear statistical thermodynamics of boundary plasma with postactions

    International Nuclear Information System (INIS)

    Temko, S.W.; Temko, K.W.; Kuz'min, S.K.

    1992-01-01

    The authors use the statistical thermodynamics of small systems proposed before their publications for boundary weakly ionized plasma with postaction. Boundary properties of the plasma is taken into account by two ways: (1) suppose that only small number of very quick particles are able to leave the cloud having done entrance into outer medium work; (2) take into account the interaction between particles and inner surface of the cloud. Interactions in the boundary plasma are described by corresponding potential functions. The potential functions are mathematical models of real interactions in boundary plasma. Choosing of potential functions, their numerical parameters, geometrical form and dimensions of the cloud is made by using the methods of optimal experiment planning, maximum likelihood and computer experiment. Free energy of the cloud is a likelihood function. State of boundary plasma with admixtures is described by vector-density of particles distribution. Term ''distribution'' is used here in Sobolev-Schwartc sense. The authors obtain the vector-density of particles distribution in cloud which gives the condition minimum of free energy for every time moment under quasistatistical equilibrium. The system of conditions for free energy conditional minimizing for every time moment includes integral equilibrium equations, ''non-hard normalization'' and additional conditions taken as a result of analyzing physical and physical-chemical nature of boundary plasma. To obtain conditional minimum of free energy it is necessary to solve the system of conditions. First of all they solve equilibrium problem by the authors method. They obtain vector-density of particles distribution in the cloud. Then using method of random walk with postaction between sets of random walk process they build distribution function of random vector-density

  12. Boundary value problem for the nonlinear analogues of the Boussinesq equation: Numerical solution and its stability

    Directory of Open Access Journals (Sweden)

    Sherif Amirov

    2017-08-01

    Full Text Available The recent work on the solvability of the boundary value problem for the nonlinear analogue of the Boussinesq equation has been further extended to focus on the characteristics of the solution. Since this type of equation does not have a known analytical solution for arbitrary boundary conditions, the problem has been solved numerically. The stability of the solution and the effect of the input function on the stability have been investigated from the physics point of view. For the special case of a discontinuous function at the right hand side of the equation, the solution has been analyzed around the discontinuity points.

  13. Boundary conditions in conformal and integrable theories

    CERN Document Server

    Petkova, V B

    2000-01-01

    The study of boundary conditions in rational conformal field theories is not only physically important. It also reveals a lot on the structure of the theory ``in the bulk''. The same graphs classify both the torus and the cylinder partition functions and provide data on their hidden ``quantum symmetry''. The Ocneanu triangular cells -- the 3j-symbols of these symmetries, admit various interpretations and make a link between different problems.

  14. Molecular Dynamics with Helical Periodic Boundary Conditions

    Czech Academy of Sciences Publication Activity Database

    Kessler, Jiří; Bouř, Petr

    2014-01-01

    Roč. 35, č. 21 (2014), s. 1552-1559 ISSN 0192-8651 R&D Projects: GA ČR GAP208/11/0105; GA MŠk(CZ) LH11033 Grant - others:GA AV ČR(CZ) M200551205; GA MŠk(CZ) LM2010005 Institutional support: RVO:61388963 Keywords : periodic boundary conditions * helical symmetry * molecular dynamics * protein structure * amyloid fibrils Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 3.589, year: 2014

  15. Numerical experiment with upstream boundary conditions

    Science.gov (United States)

    Huml, Jaroslav; Kozel, Karel

    2012-04-01

    The work deals with a numerical solution of subsonic and transonic flows described by the system of Euler equations in 2D and 3D flows in a channel. Authors used Lax-Wendroff and the multistage Runge-Kutta scheme to numerically solve the flows in a 2D G AMM channel and an extended 3D channel. Authors compare the results achieved by two different upstream boundary conditions in 2D and also in 3D transonic channel flows.

  16. Existence and asymptotic behavior of the wave equation with dynamic boundary conditions

    KAUST Repository

    Graber, Philip Jameson

    2012-03-07

    The goal of this work is to study a model of the strongly damped wave equation with dynamic boundary conditions and nonlinear boundary/interior sources and nonlinear boundary/interior damping. First, applying the nonlinear semigroup theory, we show the existence and uniqueness of local in time solutions. In addition, we show that in the strongly damped case solutions gain additional regularity for positive times t>0. Second, we show that under some restrictions on the initial data and if the interior source dominates the interior damping term and if the boundary source dominates the boundary damping, then the solution grows as an exponential function. Moreover, in the absence of the strong damping term, we prove that the solution ceases to exists and blows up in finite time. © 2012 Springer Science+Business Media, LLC.

  17. Quantum quench with hard wall boundary conditions

    Science.gov (United States)

    Goldstein, Garry; Andrei, Natan

    2015-03-01

    In this work we present analysis of a quench for the Lieb Liniger gas contained in a large box with hard wall boundary conditions. We study the time average of local correlation functions. We show that both the quench action logic and the GGE are applicable. We show that the time average of the system corresponds to an eigenstate of the Lieb Liniger Hamiltonian. We show that this eigenstate is related to an eigenstate of a Lieb Liniger Hamiltonian with periodic boundary conditions on an interval of twice the length and with twice as many particles (a doubled system). We further show that local operators with support far away from the boundaries of the hard wall Lieb Liniger gas have the same expectation values as corresponding operators for the doubled system. We present an example of a quench where the Lieb Liniger gas is initially confined in several traps and then released into a bigger container, an approximate description of the Newton cradle experiment. This research was supported by NSF Grant DMR 1006684 and Rutgers CMT fellowship.

  18. Bosonization relations as bag boundary conditions

    International Nuclear Information System (INIS)

    Nadkarni, S.; Nielsen, H.B.; Zahed, I.

    1984-10-01

    The more sophisticated bag models of hadrons become, the less precisely they seem to determine the bag radius. Idealizing this situation leads to the concept of exact bag models - ''Cheshire Cat'' models, CCM'S - where the physics is completely insensitive to changes in the bag radius. CCM's are constructed explitly in 1+1-dimensions, where exact bosonization relations are known. In the formalism of bag models, these relations appear as boundary conditions which ensure that the shifting of the bag wall has no physical effect. Other notable features of 1+1-dimensional CCM's are: (i) Fermion number, though classically confined, can escape the bag via a vector current anomaly at the surface. (ii) Essentially the same boundary action works for a variety of models and its symmetries determine those of the external boson fields. Remarkably enough, this 1+1-dimensional boundary action has precisely the same form as the one used in 3+1-dimensional chiral bag models, lending support to the belief that the latter are indeed approximateCCM's. These 1+1-dimensional results are expected to provide useful guidelines in the attempt to, at least approximately, besonize 3+1-dimensional QCD. (orig.)

  19. Canonical group quantization and boundary conditions

    International Nuclear Information System (INIS)

    Jung, Florian

    2012-01-01

    In the present thesis, we study quantization of classical systems with non-trivial phase spaces using the group-theoretical quantization technique proposed by Isham. Our main goal is a better understanding of global and topological aspects of quantum theory. In practice, the group-theoretical approach enables direct quantization of systems subject to constraints and boundary conditions in a natural and physically transparent manner -- cases for which the canonical quantization method of Dirac fails. First, we provide a clarification of the quantization formalism. In contrast to prior treatments, we introduce a sharp distinction between the two group structures that are involved and explain their physical meaning. The benefit is a consistent and conceptually much clearer construction of the Canonical Group. In particular, we shed light upon the 'pathological' case for which the Canonical Group must be defined via a central Lie algebra extension and emphasise the role of the central extension in general. In addition, we study direct quantization of a particle restricted to a half-line with 'hard wall' boundary condition. Despite the apparent simplicity of this example, we show that a naive quantization attempt based on the cotangent bundle over the half-line as classical phase space leads to an incomplete quantum theory; the reflection which is a characteristic aspect of the 'hard wall' is not reproduced. Instead, we propose a different phase space that realises the necessary boundary condition as a topological feature and demonstrate that quantization yields a suitable quantum theory for the half-line model. The insights gained in the present special case improve our understanding of the relation between classical and quantum theory and illustrate how contact interactions may be incorporated.

  20. Canonical group quantization and boundary conditions

    Energy Technology Data Exchange (ETDEWEB)

    Jung, Florian

    2012-07-16

    In the present thesis, we study quantization of classical systems with non-trivial phase spaces using the group-theoretical quantization technique proposed by Isham. Our main goal is a better understanding of global and topological aspects of quantum theory. In practice, the group-theoretical approach enables direct quantization of systems subject to constraints and boundary conditions in a natural and physically transparent manner -- cases for which the canonical quantization method of Dirac fails. First, we provide a clarification of the quantization formalism. In contrast to prior treatments, we introduce a sharp distinction between the two group structures that are involved and explain their physical meaning. The benefit is a consistent and conceptually much clearer construction of the Canonical Group. In particular, we shed light upon the 'pathological' case for which the Canonical Group must be defined via a central Lie algebra extension and emphasise the role of the central extension in general. In addition, we study direct quantization of a particle restricted to a half-line with 'hard wall' boundary condition. Despite the apparent simplicity of this example, we show that a naive quantization attempt based on the cotangent bundle over the half-line as classical phase space leads to an incomplete quantum theory; the reflection which is a characteristic aspect of the 'hard wall' is not reproduced. Instead, we propose a different phase space that realises the necessary boundary condition as a topological feature and demonstrate that quantization yields a suitable quantum theory for the half-line model. The insights gained in the present special case improve our understanding of the relation between classical and quantum theory and illustrate how contact interactions may be incorporated.

  1. Numerical experiment with upstream boundary conditions

    Directory of Open Access Journals (Sweden)

    Huml Jaroslav

    2012-04-01

    Full Text Available The work deals with a numerical solution of subsonic and transonic flows described by the system of Euler equations in 2D and 3D flows in a channel. Authors used Lax-Wendroff and the multistage Runge-Kutta scheme to numerically solve the flows in a 2D G AMM channel and an extended 3D channel. Authors compare the results achieved by two different upstream boundary conditions in 2D and also in 3D transonic channel flows.

  2. Non-linear processes in the Earth atmosphere boundary layer

    Science.gov (United States)

    Grunskaya, Lubov; Valery, Isakevich; Dmitry, Rubay

    2013-04-01

    The work is connected with studying electromagnetic fields in the resonator Earth-Ionosphere. There is studied the interconnection of tide processes of geophysical and astrophysical origin with the Earth electromagnetic fields. On account of non-linear property of the resonator Earth-Ionosphere the tides (moon and astrophysical tides) in the electromagnetic Earth fields are kinds of polyharmonic nature. It is impossible to detect such non-linear processes with the help of the classical spectral analysis. Therefore to extract tide processes in the electromagnetic fields, the method of covariance matrix eigen vectors is used. Experimental investigations of electromagnetic fields in the atmosphere boundary layer are done at the distance spaced stations, situated on Vladimir State University test ground, at Main Geophysical Observatory (St. Petersburg), on Kamchatka pen., on Lake Baikal. In 2012 there was continued to operate the multichannel synchronic monitoring system of electrical and geomagnetic fields at the spaced apart stations: VSU physical experimental proving ground; the station of the Institute of Solar and Terrestrial Physics of Russian Academy of Science (RAS) at Lake Baikal; the station of the Institute of volcanology and seismology of RAS in Paratunka; the station in Obninsk on the base of the scientific and production society "Typhoon". Such investigations turned out to be possible after developing the method of scanning experimental signal of electromagnetic field into non- correlated components. There was used a method of the analysis of the eigen vectors ofthe time series covariance matrix for exposing influence of the moon tides on Ez. The method allows to distribute an experimental signal into non-correlated periodicities. The present method is effective just in the situation when energetical deposit because of possible influence of moon tides upon the electromagnetic fields is little. There have been developed and realized in program components

  3. Behavior of the reversed field pinch with nonideal boundary conditions

    International Nuclear Information System (INIS)

    Ho, Yung-Lung.

    1988-11-01

    The linear and nonlinear magnetohydrodynamic stability of current-driven modes are studied for a reversed field pinch with nonideal boundary conditions. The plasma is bounded by a thin resistive shell surrounded by a vacuum region out to a radius at which a perfectly conducting wall is situated. The distant wall and the thin shell problems are studied by removing either the resistive shell or the conducting wall. Linearly, growth rates of tearing modes and kink modes are calculated by analytical solutions based on the modified Bessel function model for the equilibrium. The effects of variation of the shell resistivity and wall proximity on the growth rates are investigated. The modes that may be important in different parameter regimes and with different boundary conditions are identified. The nonlinear behaviors are studied with a three-dimensional magnetohydrodynamics code. The fluctuations generally rise with increasing distance between the conducting wall and the plasma. The enhanced fluctuation induced v x b electric field primarily oppose toroidal current; hence, loop voltage must increase to sustain the constant. Quasilinear interaction between modes typically associated with the dynamo action is identified as the most probable nonlinear destabilization mechanism. The helicity and energy balance properties of the simulation results are discussed. The interruption of current density along field lines intersecting the resistive shell is shown to lead to surface helicity leakage. This effect is intimately tied to stability, as fluctuation induced v x b electric field is necessary to transport the helicity to the surface. In this manner, all aspects of helicity balance, i.e., injection, transport, and dissipation, are considered self-consistently. The importance of the helicity and energy dissipation by the mean components of the magnetic field and current density is discussed. 88 refs., 41 figs., 3 tabs

  4. Existence and Stability of the Solution of a Nonlinear Boundary Value Problem

    Directory of Open Access Journals (Sweden)

    Agneta M. Balint

    2012-01-01

    Full Text Available The purpose is to find conditions assuring the existence of solutions for a nonlinear, boundary value problem in case of the axis-symmetric Young-Laplace differential equation. The equation describes the capillary surface between two static fluids. Necessary or sufficient conditions are found for the existence of a solution. The static stability of the obtained solution is also analyzed and stability or instability results are revealed. For the NdYAG microfiber growth, by the pulling-down method, numerical illustrations are given.

  5. Initial boundary value problems of nonlinear wave equations in an exterior domain

    International Nuclear Information System (INIS)

    Chen Yunmei.

    1987-06-01

    In this paper, we investigate the existence and uniqueness of the global solutions to the initial boundary value problems of nonlinear wave equations in an exterior domain. When the space dimension n >= 3, the unique global solution of the above problem is obtained for small initial data, even if the nonlinear term is fully nonlinear and contains the unknown function itself. (author). 10 refs

  6. On Perturbative Cubic Nonlinear Schrodinger Equations under Complex Nonhomogeneities and Complex Initial Conditions

    Directory of Open Access Journals (Sweden)

    Magdy A. El-Tawil

    2009-01-01

    Full Text Available A perturbing nonlinear Schrodinger equation is studied under general complex nonhomogeneities and complex initial conditions for zero boundary conditions. The perturbation method together with the eigenfunction expansion and variational parameters methods are used to introduce an approximate solution for the perturbative nonlinear case for which a power series solution is proved to exist. Using Mathematica, the symbolic solution algorithm is tested through computing the possible approximations under truncation procedures. The method of solution is illustrated through case studies and figures.

  7. On Hydroelastic Body-Boundary Condition of Floating Structures

    DEFF Research Database (Denmark)

    Xia, Jinzhu

    1996-01-01

    A general linear body boundary condition of hydroelastic analysis of arbitrary shaped floating structures generalizes the classic kinematic rigid-body (Timman-Newman) boundary condition for seakeeping problems. The new boundary condition is consistent with the existing theories under certain...

  8. Fractional partial differential equations with boundary conditions

    Science.gov (United States)

    Baeumer, Boris; Kovács, Mihály; Sankaranarayanan, Harish

    2018-01-01

    We identify the stochastic processes associated with one-sided fractional partial differential equations on a bounded domain with various boundary conditions. This is essential for modelling using spatial fractional derivatives. We show well-posedness of the associated Cauchy problems in C0 (Ω) and L1 (Ω). In order to do so we develop a new method of embedding finite state Markov processes into Feller processes on bounded domains and then show convergence of the respective Feller processes. This also gives a numerical approximation of the solution. The proof of well-posedness closes a gap in many numerical algorithm articles approximating solutions to fractional differential equations that use the Lax-Richtmyer Equivalence Theorem to prove convergence without checking well-posedness.

  9. Unsteady Squeezing Flow of Carbon Nanotubes with Convective Boundary Conditions.

    Directory of Open Access Journals (Sweden)

    Tasawar Hayat

    Full Text Available Unsteady flow of nanofluids squeezed between two parallel plates is discussed in the presence of viscous dissipation. Heat transfer phenomenon is disclosed via convective boundary conditions. Carbon nanotubes (single-wall and multi-wall are used as nanoparticles which are homogeneously distributed in the base fluid (water. A system of non-linear differential equations for the flow is obtained by utilizing similarity transformations through the conservation laws. Influence of various emerging parameters on the velocity and temperature profiles are sketched graphically and discussed comprehensively. Analyses of skin fraction coefficient and Nusselt number are also elaborated numerically. It is found out that velocity is smaller for squeezing parameter in the case of multi-wall carbon nanotubes when compared with single-wall carbon nanotubes.

  10. On the boundary conditions in cylindrical cell approximation

    International Nuclear Information System (INIS)

    Altiparmakov, D.V.

    1980-01-01

    A solution of the integral transport equation for an arbitrary boundary condition is obtained by solving the integral transport equation for homogeneous (vacuum) boundary condition and using the neutron balance condition. An effective boundary condition satisfying the zero gradient of the neutron flux on the cell boundary is assumed. The numerical solution is obtained by using a pointwise approximation based on a polynomial flux approximation. Disadvantage factor calculations of the Thie lattice cells are carried out. Comparisons are performed with the results obtained for the actual cells by two-dimensional methods as well as their cylindrical approximations applying various boundary conditions. It is obvious from the results shown here that the proposed boundary condition has advantages in respect to others. The errors introduced by the proposed boundary condition are of the lower order in respect to the inaccuracy of the existing transport methods. Thus, the applications of the two-dimensional methods for regular lattice calculations is unnecessary. (author)

  11. Boundary and initial conditions in protostar calculations

    International Nuclear Information System (INIS)

    Disney, M.J.

    1976-01-01

    On first fragmentation protostars probably form part of a larger protocluster cloud already in a state of dynamic collapse. In that case it is argued that the protostar boundary is initially collapsing at supersonic speed relative to the core. This prevents information from the boundary reaching the core and calls into question models like Larson's, which start homogeneously but become centrally condensed due to the propagation of a rarefaction wave from the boundary. (author)

  12. Long-time behaviour of absorbing boundary conditions

    Science.gov (United States)

    Engquist, B.; Halpern, L.

    1990-01-01

    A new class of computational far-field boundary conditions for hyperbolic partial differential equations was recently introduced by the authors. These boundary conditions combine properties of absorbing conditions for transient solutions and properties of far-field conditions for steady states. This paper analyses the properties of the wave equation coupled with these new boundary conditions: well-posedness, dissipativity and convergence in time.

  13. Surface free energy for systems with integrable boundary conditions

    International Nuclear Information System (INIS)

    Goehmann, Frank; Bortz, Michael; Frahm, Holger

    2005-01-01

    The surface free energy is the difference between the free energies for a system with open boundary conditions and the same system with periodic boundary conditions. We use the quantum transfer matrix formalism to express the surface free energy in the thermodynamic limit of systems with integrable boundary conditions as a matrix element of certain projection operators. Specializing to the XXZ spin-1/2 chain we introduce a novel 'finite temperature boundary operator' which characterizes the thermodynamical properties of surfaces related to integrable boundary conditions

  14. Existence of Positive Solutions to a Boundary Value Problem for a Delayed Nonlinear Fractional Differential System

    Directory of Open Access Journals (Sweden)

    Chen Yuming

    2011-01-01

    Full Text Available Though boundary value problems for fractional differential equations have been extensively studied, most of the studies focus on scalar equations and the fractional order between 1 and 2. On the other hand, delay is natural in practical systems. However, not much has been done for fractional differential equations with delays. Therefore, in this paper, we consider a boundary value problem of a general delayed nonlinear fractional system. With the help of some fixed point theorems and the properties of the Green function, we establish several sets of sufficient conditions on the existence of positive solutions. The obtained results extend and include some existing ones and are illustrated with some examples for their feasibility.

  15. Analytic approximations to nonlinear boundary value problems modeling beam-type nano-electromechanical systems

    Energy Technology Data Exchange (ETDEWEB)

    Zou, Li [Dalian Univ. of Technology, Dalian City (China). State Key Lab. of Structural Analysis for Industrial Equipment; Liang, Songxin; Li, Yawei [Dalian Univ. of Technology, Dalian City (China). School of Mathematical Sciences; Jeffrey, David J. [Univ. of Western Ontario, London (Canada). Dept. of Applied Mathematics

    2017-06-01

    Nonlinear boundary value problems arise frequently in physical and mechanical sciences. An effective analytic approach with two parameters is first proposed for solving nonlinear boundary value problems. It is demonstrated that solutions given by the two-parameter method are more accurate than solutions given by the Adomian decomposition method (ADM). It is further demonstrated that solutions given by the ADM can also be recovered from the solutions given by the two-parameter method. The effectiveness of this method is demonstrated by solving some nonlinear boundary value problems modeling beam-type nano-electromechanical systems.

  16. An Efficient Numerical Approach for Solving Nonlinear Coupled Hyperbolic Partial Differential Equations with Nonlocal Conditions

    Directory of Open Access Journals (Sweden)

    A. H. Bhrawy

    2014-01-01

    Full Text Available One of the most important advantages of collocation method is the possibility of dealing with nonlinear partial differential equations (PDEs as well as PDEs with variable coefficients. A numerical solution based on a Jacobi collocation method is extended to solve nonlinear coupled hyperbolic PDEs with variable coefficients subject to initial-boundary nonlocal conservation conditions. This approach, based on Jacobi polynomials and Gauss-Lobatto quadrature integration, reduces solving the nonlinear coupled hyperbolic PDEs with variable coefficients to a system of nonlinear ordinary differential equation which is far easier to solve. In fact, we deal with initial-boundary coupled hyperbolic PDEs with variable coefficients as well as initial-nonlocal conditions. Using triangular, soliton, and exponential-triangular solutions as exact solutions, the obtained results show that the proposed numerical algorithm is efficient and very accurate.

  17. Unsteady MHD Mixed Convection Slip Flow of Casson Fluid over Nonlinearly Stretching Sheet Embedded in a Porous Medium with Chemical Reaction, Thermal Radiation, Heat Generation/Absorption and Convective Boundary Conditions.

    Directory of Open Access Journals (Sweden)

    Imran Ullah

    Full Text Available Numerical results are presented for the effect of first order chemical reaction and thermal radiation on mixed convection flow of Casson fluid in the presence of magnetic field. The flow is generated due to unsteady nonlinearly stretching sheet placed inside a porous medium. Convective conditions on wall temperature and wall concentration are also employed in the investigation. The governing partial differential equations are converted to ordinary differential equations using suitable transformations and then solved numerically via Keller-box method. It is noticed that fluid velocity rises with increase in radiation parameter in the case of assisting flow and is opposite in the case of opposing fluid while radiation parameter has no effect on fluid velocity in the forced convection. It is also seen that fluid velocity and concentration enhances in the case of generative chemical reaction whereas both profiles reduces in the case of destructive chemical reaction. Further, increase in local unsteadiness parameter reduces fluid velocity, temperature and concentration. Over all the effects of physical parameters on fluid velocity, temperature and concentration distribution as well as on the wall shear stress, heat and mass transfer rates are discussed in detail.

  18. Unsteady MHD Mixed Convection Slip Flow of Casson Fluid over Nonlinearly Stretching Sheet Embedded in a Porous Medium with Chemical Reaction, Thermal Radiation, Heat Generation/Absorption and Convective Boundary Conditions.

    Science.gov (United States)

    Ullah, Imran; Bhattacharyya, Krishnendu; Shafie, Sharidan; Khan, Ilyas

    2016-01-01

    Numerical results are presented for the effect of first order chemical reaction and thermal radiation on mixed convection flow of Casson fluid in the presence of magnetic field. The flow is generated due to unsteady nonlinearly stretching sheet placed inside a porous medium. Convective conditions on wall temperature and wall concentration are also employed in the investigation. The governing partial differential equations are converted to ordinary differential equations using suitable transformations and then solved numerically via Keller-box method. It is noticed that fluid velocity rises with increase in radiation parameter in the case of assisting flow and is opposite in the case of opposing fluid while radiation parameter has no effect on fluid velocity in the forced convection. It is also seen that fluid velocity and concentration enhances in the case of generative chemical reaction whereas both profiles reduces in the case of destructive chemical reaction. Further, increase in local unsteadiness parameter reduces fluid velocity, temperature and concentration. Over all the effects of physical parameters on fluid velocity, temperature and concentration distribution as well as on the wall shear stress, heat and mass transfer rates are discussed in detail.

  19. The Stochastic Ising Model with the Mixed Boundary Conditions

    Directory of Open Access Journals (Sweden)

    Wang Jun

    2009-01-01

    Full Text Available Abstract We estimate the spectral gap of the two-dimensional stochastic Ising model for four classes of mixed boundary conditions. On a finite square, in the absence of an external field, two-sided estimates on the spectral gap for the first class of (weak positive boundary conditions are given. Further, at inverse temperatures , we will show lower bounds of the spectral gap of the Ising model for the other three classes mixed boundary conditions.

  20. Boundary Conditions, Data Assimilation, and Predictability in Coastal Ocean Models

    National Research Council Canada - National Science Library

    Samelson, Roger M; Allen, John S; Egbert, Gary D; Kindle, John C; Snyder, Chris

    2007-01-01

    ...: The specific objectives of this research are to determine the impact on coastal ocean circulation models of open ocean boundary conditions from Global Ocean Data Assimilation Experiment (GODAE...

  1. Stabilizing local boundary conditions for two-dimensional shallow water equations

    KAUST Repository

    Dia, Ben Mansour

    2018-03-27

    In this article, we present a sub-critical two-dimensional shallow water flow regulation. From the energy estimate of a set of one-dimensional boundary stabilization problems, we obtain a set of polynomial equations with respect to the boundary values as a requirement for the energy decrease. Using the Riemann invariant analysis, we build stabilizing local boundary conditions that guarantee the stability of the hydrodynamical state around a given steady state. Numerical results for the controller applied to the nonlinear problem demonstrate the performance of the method.

  2. Quantum “violation” of Dirichlet boundary condition

    Directory of Open Access Journals (Sweden)

    I.Y. Park

    2017-02-01

    Full Text Available Dirichlet boundary conditions have been widely used in general relativity. They seem at odds with the holographic property of gravity simply because a boundary configuration can be varying and dynamic instead of dying out as required by the conditions. In this work we report what should be a tension between the Dirichlet boundary conditions and quantum gravitational effects, and show that a quantum-corrected black hole solution of the 1PI action no longer obeys, in the naive manner one may expect, the Dirichlet boundary conditions imposed at the classical level. We attribute the ‘violation’ of the Dirichlet boundary conditions to a certain mechanism of the information storage on the boundary.

  3. Numerical study for nanofluid flow due to a nonlinear curved stretching surface with convective heat and mass conditions

    Directory of Open Access Journals (Sweden)

    Tasawar Hayat

    Full Text Available This article presents the simultaneous effects of convective heat and mass conditions in boundary-layer flow of nanoliquid due to a nonlinear curved stretching surface. A nonlinear curved stretching surface is used to generate the flow. Thermophoretic diffusion and random motion features are also incorporated. Convective heat and mass conditions are imposed at boundary. Suitable variables are utilized to convert the nonlinear partial differential system into nonlinear ordinary differential system. The obtained nonlinear systems are solved numerically through shooting technique. Plots are displayed in order to explore the role of physical flow variables on the solutions. The skin-friction coefficient and local Nusselt and Sherwood numbers are computed and examined. Our findings indicate that the local Nusselt and Sherwood numbers are reduced for larger values of thermophoresis parameter. Keywords: Nonlinear curved stretching surface, Nanoparticles, Convective heat and mass conditions, Numerical solution

  4. On time boundary of functional metal properties maintainance under extreme conditions

    Directory of Open Access Journals (Sweden)

    Zhabyka L.V.

    2012-08-01

    Full Text Available There are established the boundaries of conserving functional properties of metals at dynamic failure under extreme conditions (longevity range t ∼10−6÷10−10s. The methods of non-linear physics made it possible to determine universal attributes of non-equilibrium systems evolution conditioned by collective effects and phenomena of self-organization in the appearing dissipative structures. In the paper there is presented a universal failure surface that allows simulation of metals behavior under laboratory conditions and forecast of time boundary of functional properties conservation.

  5. Gowdy waves as a test-bed for constraint-preserving boundary conditions

    Energy Technology Data Exchange (ETDEWEB)

    Bona, Carles; Bona-Casas, Carles, E-mail: cbona@uib.e [Departament de Fisica, Universitat de les Illes Balears, Palma de Mallorca, Spain Institute for Applied Computation with Community Code (IAC3) (Spain)

    2010-05-01

    Gowdy waves, one of the standard 'apples with apples' tests, is proposed as a test-bed for constraint-preserving boundary conditions in the non-linear regime. As an illustration, energy-constraint preservation is separately tested in the Z4 framework. Both algebraic conditions, derived from energy estimates, and derivative conditions, deduced from the constraint-propagation system, are considered. The numerical errors at the boundary are of the same order than those at the interior points.

  6. Application of the comparison principle to analysis of nonlinear systems. [using Lipschitz condition and differential equations

    Science.gov (United States)

    Gunderson, R. W.

    1975-01-01

    A comparison principle based on a Kamke theorem and Lipschitz conditions is presented along with its possible applications and modifications. It is shown that the comparison lemma can be used in the study of such areas as classical stability theory, higher order trajectory derivatives, Liapunov functions, boundary value problems, approximate dynamic systems, linear and nonlinear systems, and bifurcation analysis.

  7. Nonlinear reversed field pinch dynamics with nonideal boundaries

    International Nuclear Information System (INIS)

    Ho, Y.L.; Prager, S.C.

    1991-03-01

    The nonlinear behavior of the reversed field pinch bounded by a resistive shell or a distant conducting wall is investigated with a three-dimensional magnetohydrodynamic code. Nonlinear interaction between modes enhances fluctuation levels as the conducting wall is removed. The enhanced fluctuation induced v x b electric field, which produces the dynamo effect, suppresses toroidal current and enhances surface helicity dissipation. Thus, loop voltage must increase to sustain the current and maintain helicity balance. 46 refs., 21 figs., 2 tabs

  8. The femur as a musculo-skeletal construct: a free boundary condition modelling approach.

    Science.gov (United States)

    Phillips, A T M

    2009-07-01

    Previous finite element studies of the femur have made simplifications to varying extents with regard to the boundary conditions used during analysis. Fixed boundary conditions are generally applied to the distal femur when examining the proximal behaviour at the hip joint, while the same can be said for the proximal femur when examining the distal behaviour at the knee joint. While fixed boundary condition analyses have been validated against in vitro experiments it remains a matter of debate as to whether the numerical and experimental models are indicative of the in vivo situation. This study presents a finite element model in which the femur is treated as a complete musculo-skeletal construct, spanning between the hip and knee joints. Linear and non-linear implementations of a free boundary condition modelling approach are applied to the bone through the explicit inclusion of muscles and ligaments spanning both the hip joint and the knee joint. A non-linear force regulated, muscle strain based activation strategy was found to result in lower observed principal strains in the cortex of the femur, compared to a linear activation strategy. The non-linear implementation of the model in particular, was found to produce hip and knee joint reaction forces consistent with in vivo data from instrumented implants.

  9. New Modified Adomian Decomposition Recursion Schemes for Solving Certain Types of Nonlinear Fractional Two-Point Boundary Value Problems

    Directory of Open Access Journals (Sweden)

    Sekson Sirisubtawee

    2017-01-01

    Full Text Available We apply new modified recursion schemes obtained by the Adomian decomposition method (ADM to analytically solve specific types of two-point boundary value problems for nonlinear fractional order ordinary and partial differential equations. The new modified recursion schemes, which sometimes utilize the technique of Duan’s convergence parameter, are derived using the Duan-Rach modified ADM. The Duan-Rach modified ADM employs all of the given boundary conditions to compute the remaining unknown constants of integration, which are then embedded in the integral solution form before constructing recursion schemes for the solution components. New modified recursion schemes obtained by the method are generated in order to analytically solve nonlinear fractional order boundary value problems with a variety of two-point boundary conditions such as Robin and separated boundary conditions. Some numerical examples of such problems are demonstrated graphically. In addition, the maximal errors (MEn or the error remainder functions (ERn(x of each problem are calculated.

  10. Nonlinear boundary value problems in quantum field theory

    International Nuclear Information System (INIS)

    Schrader, R.

    1989-01-01

    We discuss the general structure of a quantum field theory which is free in the interior of a bounded set B of R n . It is shown how to recover the field theory in the interior of B from a certain quantum field theory on the boundary. With an application to string theory in mind, we discuss the example where B equals an interval and the boundary value problem is given in terms of a euclidean functional integral with a P(var phi) interaction restricted to the boundary. copyright 1989 Academic Press, Inc

  11. On domain wall boundary conditions for the XXZ spin Hamiltonian

    DEFF Research Database (Denmark)

    Orlando, Domenico; Reffert, Susanne; Reshetikhin, Nicolai

    In this note, we derive the spectrum of the infinite quantum XXZ spin chain with domain wall boundary conditions. The eigenstates are constructed as limits of Bethe states for the finite XXZ spin chain with quantum sl(2) invariant boundary conditions....

  12. Scattering through a straight quantum waveguide with combined boundary conditions

    Czech Academy of Sciences Publication Activity Database

    Briet, Ph.; Dittrich, Jaroslav; Soccorsi, E.

    2014-01-01

    Roč. 55, č. 11 (2014), s. 112104 ISSN 0022-2488 R&D Projects: GA ČR(CZ) GA14-06818S Institutional support: RVO:61389005 Keywords : quantum waveguide * scattering * Dirichlet boundary condition * Neumann boundary condition Subject RIV: BE - Theoretical Physics Impact factor: 1.243, year: 2014

  13. Effective velocity boundary condition at a mixed slip surface

    NARCIS (Netherlands)

    Sbragaglia, M.; Prosperetti, Andrea

    2007-01-01

    This paper studies the nature of the effective velocity boundary condition for liquid flow over a plane boundary on which small free-slip islands are randomly distributed. It is found that an effective Navier partial-slip condition for the velocity emerges from a statistical analysis valid for

  14. Curved planar quantum wires with Dirichlet and Neumann boundary conditions

    Czech Academy of Sciences Publication Activity Database

    Dittrich, Jaroslav; Kříž, J.

    2002-01-01

    Roč. 35, - (2002), s. 269-275 ISSN 0305-4470 R&D Projects: GA AV ČR IAA1048101; GA AV ČR KSK1010104 Keywords : quantum wires * laplace operation * Dirichlet boundary conditions * Neumann boundary conditions Subject RIV: BE - Theoretical Physics Impact factor: 1.406, year: 2002

  15. Divergence-Free Wavelets on the Hypercube : General Boundary Conditions

    NARCIS (Netherlands)

    Stevenson, R.

    2016-01-01

    On the n-dimensional hypercube, for given k∈N, wavelet Riesz bases are constructed for the subspace of divergence-free vector fields of the Sobolev space Hk((0,1)n)n with general homogeneous Dirichlet boundary conditions, including slip or no-slip boundary conditions. Both primal and suitable dual

  16. Periodic Boundary Conditions in the ALEGRA Finite Element Code

    International Nuclear Information System (INIS)

    Aidun, John B.; Robinson, Allen C.; Weatherby, Joe R.

    1999-01-01

    This document describes the implementation of periodic boundary conditions in the ALEGRA finite element code. ALEGRA is an arbitrary Lagrangian-Eulerian multi-physics code with both explicit and implicit numerical algorithms. The periodic boundary implementation requires a consistent set of boundary input sets which are used to describe virtual periodic regions. The implementation is noninvasive to the majority of the ALEGRA coding and is based on the distributed memory parallel framework in ALEGRA. The technique involves extending the ghost element concept for interprocessor boundary communications in ALEGRA to additionally support on- and off-processor periodic boundary communications. The user interface, algorithmic details and sample computations are given

  17. Entropy Stability and the No-Slip Wall Boundary Condition

    KAUST Repository

    Svärd, Magnus

    2018-01-18

    We present an entropy stable numerical scheme subject to no-slip wall boundary conditions. To enforce entropy stability only the no-penetration boundary condition and a temperature condition are needed at a wall, and this leads to an L bound on the conservative variables. In this article, we take the next step and design a finite difference scheme that also bounds the velocity gradients. This necessitates the use of the full no-slip conditions.

  18. MHD boundary layer flow of a power-law nanofluid with new mass flux condition

    Directory of Open Access Journals (Sweden)

    Masood Khan

    2016-02-01

    Full Text Available An analysis is carried out to study the magnetohydrodynamic MHD boundary layer flow of power-law nanofluid over a non-linear stretching sheet. In the presence of a transverse magnetic field, the flow is generated due to non-linear stretching sheet. By using similarity transformations, the governing boundary layer equations are reduced into a system of ordinary differential equations. A recently proposed boundary condition requiring zero nanoparticle mass flux is employed in the flow analysis of power-law fluid. The reduced coupled differential equations are then solved numerically by the shooting method. The variations of dimensionless temperature and nanoparticle concentration with various parameters are graphed and discussed in detail. Numerical values of physical quantities such as the skin-friction coefficient and the reduced local Nusselt number are computed in tabular form.

  19. Monopole Giant Resonances and TDHF boundary conditions

    International Nuclear Information System (INIS)

    Stevenson, P.D.; Almehed, D.; Reinhard, P.-G.; Maruhn, J.A.

    2007-01-01

    Using time-dependent Hartree-Fock, we induce isoscalar and isovector monopole vibrations and follow the subsequent vibrations of both the same and opposite isospin nature in the N Z nucleus 132 Sn. By suitable scaling of the proton and neutron parts of the excitation operators, the coupling between the modes is studied, and the approximate normal modes found. Chaotic dynamics are then analysed in the isoscalar giant monopole resonance by using reflecting boundaries in a large space to build up a large number of 0 + states whose spacings are then analysed. A Wigner-like distribution is found

  20. Stabilization of Hypersonic Boundary Layers by Linear and Nonlinear Optimal Perturbations

    Science.gov (United States)

    Paredes, Pedro; Choudhari, Meelan M.; Li, Fei

    2017-01-01

    The effect of stationary, finite-amplitude, linear and nonlinear optimal perturbations on the modal disturbance growth in a Mach 6 axisymmetric flow over a 7 deg. half-angle cone with 0:126 mm nose radius and 0:305 m length is investigated. The freestream parameters (M = 6, Re(exp 1) = 18 x 10(exp. 6) /m) are selected to match the flow conditions of a previous experiment in the VKI H3 hypersonic tunnel. Plane-marching parabolized stability equations are used in conjunction with a partial-differential equation based planar eigenvalue analysis to characterize the boundary layer instability in the presence of azimuthally periodic streaks. The streaks are observed to stabilize nominally planar Mack mode instabilities, although oblique Mack mode and first-mode disturbances are destabilized. Experimentally measured transition onset in the absence of any streaks correlates with an amplification factor of N = 6 for the planar Mack modes. For high enough streak amplitudes, the transition threshold of N = 6 is not reached by the Mack mode instabilities within the length of the cone; however, subharmonic first-mode instabilities, which are destabilized by the presence of the streaks, do reach N = 6 near the end of the cone. The highest stabilization is observed at streak amplitudes of approximately 20 percent of the freestream velocity. Because the use of initial disturbance profiles based on linear optimal growth theory may yield suboptimal control in the context of nonlinear streaks, the computational predictions are extended to nonlinear optimal growth theory. Results show that by using nonlinearly optimal perturbation leads to slightly enhanced stabilization of plane Mack mode disturbances as well as reduced destabilization of subharmonic first-mode disturbances.

  1. Silent inflow condition for turbulent boundary layers

    Science.gov (United States)

    Gloerfelt, X.; Robinet, J.-C.

    2017-12-01

    The generation of a turbulent inflow is a tricky problem. In the framework of aeroacoustics, another important constraint is that the numerical strategy used to reach a turbulent state induces a spurious noise which is lower than the acoustic field of interest. For the study of noise radiated directly by a turbulent boundary layer on a flat plate, this constraint is severe since wall turbulence is a very inefficient source. That is why a method based on a transition by modal interaction using a base flow with an inflection point is proposed to cope with that. The base flow must be a solution of the equations so we use a profile behind a backward-facing step representative of experimental trip bands. A triad of resonant waves is selected by a local stability analysis of the linearized compressible equations and is added with a weak amplitude in the inlet plane. The compressible stability calculation allows the specification of the thermodynamic quantities at the inlet, which turns out to be fundamental to ensure a quiet inflow. A smooth transition is achieved with the rapid formation of Λ -shape vortices in a staggered organization as in subharmonic transition. The dominance of oblique waves promotes a rapid breakdown by the liftup mechanism of low-speed streaks. The quality of the fully turbulent state is assessed and the direct noise radiation from a turbulent boundary layer at Mach 0.5 is obtained with a very low level of spurious noise.

  2. Minimization of heat slab nodes with higher order boundary conditions

    International Nuclear Information System (INIS)

    Solbrig, C.W.

    1992-01-01

    The accuracy of a numerical solution can be limited by the numerical approximation to the boundary conditions rather than the accuracy of the equations which describe the interior. The study presented in this paper compares the results from two different numerical formulations of the convective boundary condition on the face of a heat transfer slab. The standard representation of the boundary condition in a test problem yielded an unacceptable error even when the heat transfer slab was partitioned into over 300 nodes. A higher order boundary condition representation was obtained by using a second order approximation for the first derivative at the boundary and combining it with the general equation used for inner nodes. This latter formulation produced reasonable results when as few as ten nodes were used

  3. Regularity of the solutions to a nonlinear boundary problem with indefinite weight

    Directory of Open Access Journals (Sweden)

    Aomar Anane

    2011-01-01

    Full Text Available In this paper we study the regularity of the solutions to the problemDelta_p u = |u|^{p−2}u in the bounded smooth domainOmega ⊂ R^N,with|∇u|^{p−2} partial_{nu} u = lambda V (x|u|^{p−2}u + h as a nonlinear boundary condition, where partial Omega is C^{2,beta}, with beta ∈]0, 1[, and V is a weight in L^s(partial Omega and h ∈ L^s(partial Omega for some s ≥ 1. We prove that all solutions are in L^{infty}(Omega cap L^{infty}(Omega, and using the D.Debenedetto’s theorem of regularity in [1] we conclude that those solutions are in C^{1,alpha} overline{Omega} for some alpha ∈ ]0, 1[.

  4. Boundary conditions of normal and anomalous diffusion from thermal equilibrium.

    Science.gov (United States)

    Korabel, Nickolay; Barkai, Eli

    2011-05-01

    Infiltration of diffusing particles from one material to another, where the diffusion mechanism is either normal or anomalous, is a widely observed phenomenon. Starting with an underlying continuous-time random-walk model, we derive the boundary conditions for the diffusion equations describing this problem. We discuss a simple method showing how the boundary conditions can be determined from equilibrium experiments. When the diffusion processes are close to thermal equilibrium, the boundary conditions are determined by a thermal Boltzmann factor, which in turn controls the solution of the problem.

  5. Crucial effect of boundary conditions on the buckling of shells

    International Nuclear Information System (INIS)

    Combescure, A.

    1989-01-01

    We want to show here that the boundary conditions can have a drastic effect on the prediction of buckling loads and that this influence can even be more drastic that the initial imperfection in some cases. This is a very important feature because the design rules in case of buckling take into account the effect of initial imperfections but do not consider the effect of unknown boundary conditions. We shall first give two examples showing this drastic effect and then develop a methodology to prevent the designer against over estimation of buckling loads due to a non conservative choice of boundary conditions

  6. Cubic Hermite Collocation Method for Solving Boundary Value Problems with Dirichlet, Neumann, and Robin Conditions

    Directory of Open Access Journals (Sweden)

    Ishfaq Ahmad Ganaie

    2014-01-01

    Full Text Available Cubic Hermite collocation method is proposed to solve two point linear and nonlinear boundary value problems subject to Dirichlet, Neumann, and Robin conditions. Using several examples, it is shown that the scheme achieves the order of convergence as four, which is superior to various well known methods like finite difference method, finite volume method, orthogonal collocation method, and polynomial and nonpolynomial splines and B-spline method. Numerical results for both linear and nonlinear cases are presented to demonstrate the effectiveness of the scheme.

  7. A new approach to implement absorbing boundary condition in biomolecular electrostatics.

    Science.gov (United States)

    Goni, Md Osman

    2013-01-01

    This paper discusses a novel approach to employ the absorbing boundary condition in conjunction with the finite-element method (FEM) in biomolecular electrostatics. The introduction of Bayliss-Turkel absorbing boundary operators in electromagnetic scattering problem has been incorporated by few researchers. However, in the area of biomolecular electrostatics, this boundary condition has not been investigated yet. The objective of this paper is twofold. First, to solve nonlinear Poisson-Boltzmann equation using Newton's method and second, to find an efficient and acceptable solution with minimum number of unknowns. In this work, a Galerkin finite-element formulation is used along with a Bayliss-Turkel absorbing boundary operator that explicitly accounts for the open field problem by mapping the Sommerfeld radiation condition from the far field to near field. While the Bayliss-Turkel condition works well when the artificial boundary is far from the scatterer, an acceptable tolerance of error can be achieved with the second order operator. Numerical results on test case with simple sphere show that the treatment is able to reach the same level of accuracy achieved by the analytical method while using a lower grid density. Bayliss-Turkel absorbing boundary condition (BTABC) combined with the FEM converges to the exact solution of scattering problems to within discretization error.

  8. MHD axisymmetric flow of power-law fluid over an unsteady stretching sheet with convective boundary conditions

    Directory of Open Access Journals (Sweden)

    Jawad Ahmed

    Full Text Available This paper examines the boundary layer flow and heat transfer characteristic in power law fluid model over unsteady radially stretching sheet under the influence of convective boundary conditions. A uniform magnetic field is applied transversely to the direction of the flow. The governing time dependent nonlinear boundary layer equations are reduced into nonlinear ordinary differential equations with the help of similarity transformations. The transformed coupled ordinary differential equations are then solved analytically by homotopy analysis method (HAM and numerically by shooting procedure. Effects of various governing parameters like, power law index n, magnetic parameter M, unsteadiness A, suction/injection S, Biot number γ and generalized Prandtl number Pr on velocity, temperature, local skin friction and the local Nusselt number are studied and discussed. It is found from the analysis that the magnetic parameter diminishes the velocity profile and the corresponding thermal boundary layer thickness. Keywords: Axisymmetric flow, Power law fluid, Unsteady stretching, Convective boundary conditions

  9. On the Stability of Three-Dimensional Boundary Layers. Part 1; Linear and Nonlinear Stability

    Science.gov (United States)

    Janke, Erik; Balakumar, Ponnampalam

    1999-01-01

    The primary stability of incompressible three-dimensional boundary layers is investigated using the Parabolized Stability Equations (PSE). We compute the evolution of stationary and traveling disturbances in the linear and nonlinear region prior to transition. As model problems, we choose Swept Hiemenz Flow and the DLR Transition Experiment. The primary stability results for Swept Hiemenz Flow agree very well with computations by Malik et al. For the DLR Experiment, the mean flow profiles are obtained by solving the boundary layer equations for the measured pressure distribution. Both linear and nonlinear results show very good agreement with the experiment.

  10. The topology of non-linear global carbon dynamics: from tipping points to planetary boundaries

    International Nuclear Information System (INIS)

    Anderies, J M; Carpenter, S R; Steffen, Will; Rockström, Johan

    2013-01-01

    We present a minimal model of land use and carbon cycle dynamics and use it to explore the relationship between non-linear dynamics and planetary boundaries. Only the most basic interactions between land cover and terrestrial, atmospheric, and marine carbon stocks are considered in the model. Our goal is not to predict global carbon dynamics as it occurs in the actual Earth System. Rather, we construct a conceptually reasonable heuristic model of a feedback system between different carbon stocks that captures the qualitative features of the actual Earth System and use it to explore the topology of the boundaries of what can be called a ‘safe operating space’ for humans. The model analysis illustrates the existence of dynamic, non-linear tipping points in carbon cycle dynamics and the potential complexity of planetary boundaries. Finally, we use the model to illustrate some challenges associated with navigating planetary boundaries. (letter)

  11. A New Spectral Local Linearization Method for Nonlinear Boundary Layer Flow Problems

    Directory of Open Access Journals (Sweden)

    S. S. Motsa

    2013-01-01

    Full Text Available We propose a simple and efficient method for solving highly nonlinear systems of boundary layer flow problems with exponentially decaying profiles. The algorithm of the proposed method is based on an innovative idea of linearizing and decoupling the governing systems of equations and reducing them into a sequence of subsystems of differential equations which are solved using spectral collocation methods. The applicability of the proposed method, hereinafter referred to as the spectral local linearization method (SLLM, is tested on some well-known boundary layer flow equations. The numerical results presented in this investigation indicate that the proposed method, despite being easy to develop and numerically implement, is very robust in that it converges rapidly to yield accurate results and is more efficient in solving very large systems of nonlinear boundary value problems of the similarity variable boundary layer type. The accuracy and numerical stability of the SLLM can further be improved by using successive overrelaxation techniques.

  12. Boundary condition effect on response modification factor of X-braced steel frames

    Directory of Open Access Journals (Sweden)

    Walid A. Attia

    2018-04-01

    Full Text Available Design of the structures to resist seismic force depends on the theory of dissipation in elastic energy that already exists in response modification factor “R-factor”. The main problem in codes gives a constant value for R-factor, since change in boundary conditions of building change in behavior of braced steel frame structures and that effects on R-factor. This study is an attempt to assess overstrength, ductility and response modification factor of X-braced steel frame under change in boundary conditions, as change in the direction of strong axis of column and connection support type of column besides variation in storey and bays numbers to be 21 frames and each frame has 8 different boundary conditions as sum of 168 cases for analysis. These frames were analyzed by using nonlinear static “pushover” analysis. As results of this study change in support type and direction of strong axis of column give large change in value of R-factor; the minimum value was 4.37 and maximum value 10.97. Minimum value is close to code value that’s mean the code is more conservative in suggesting of R-factor and gives a large factor of safety. Change in the location of bracing gives change in value of R-factor for all boundary conditions. Change in direction of strong axis of columns and support type didn’t give change in value of fundamental period, all boundary conditions. Keywords: Response modification factor, Ductility reduction factor, Overstrength factor, Boundary conditions, Brace frame, Nonlinear static analysis “Pushover”

  13. Facilitating conditions for boundary-spanning behavior in governance networks

    OpenAIRE

    Meerkerk, Ingmar; Edelenbos, Jurian

    2017-01-01

    textabstractThis article examines the impact of two facilitating conditions for boundary-spanning behaviour in urban governance networks. While research on boundary spanning is growing, there is little attention for antecedents. Combining governance network literature on project management and organizational literature on facilitative and servant leadership, we examine two potential conditions: a facilitative project management style and executive support. We conducted survey research among p...

  14. Nonlinear Cointegration Approach for Condition Monitoring of Wind Turbines

    Directory of Open Access Journals (Sweden)

    Konrad Zolna

    2015-01-01

    Full Text Available Monitoring of trends and removal of undesired trends from operational/process parameters in wind turbines is important for their condition monitoring. This paper presents the homoscedastic nonlinear cointegration for the solution to this problem. The cointegration approach used leads to stable variances in cointegration residuals. The adapted Breusch-Pagan test procedure is developed to test for the presence of heteroscedasticity in cointegration residuals obtained from the nonlinear cointegration analysis. Examples using three different time series data sets—that is, one with a nonlinear quadratic deterministic trend, another with a nonlinear exponential deterministic trend, and experimental data from a wind turbine drivetrain—are used to illustrate the method and demonstrate possible practical applications. The results show that the proposed approach can be used for effective removal of nonlinear trends form various types of data, allowing for possible condition monitoring applications.

  15. A Galleria Boundary Element Method for two-dimensional nonlinear magnetostatics

    Science.gov (United States)

    Brovont, Aaron D.

    The Boundary Element Method (BEM) is a numerical technique for solving partial differential equations that is used broadly among the engineering disciplines. The main advantage of this method is that one needs only to mesh the boundary of a solution domain. A key drawback is the myriad of integrals that must be evaluated to populate the full system matrix. To this day these integrals have been evaluated using numerical quadrature. In this research, a Galerkin formulation of the BEM is derived and implemented to solve two-dimensional magnetostatic problems with a focus on accurate, rapid computation. To this end, exact, closed-form solutions have been derived for all the integrals comprising the system matrix as well as those required to compute fields in post-processing; the need for numerical integration has been eliminated. It is shown that calculation of the system matrix elements using analytical solutions is 15-20 times faster than with numerical integration of similar accuracy. Furthermore, through the example analysis of a c-core inductor, it is demonstrated that the present BEM formulation is a competitive alternative to the Finite Element Method (FEM) for linear magnetostatic analysis. Finally, the BEM formulation is extended to analyze nonlinear magnetostatic problems via the Dual Reciprocity Method (DRBEM). It is shown that a coarse, meshless analysis using the DRBEM is able to achieve RMS error of 3-6% compared to a commercial FEM package in lightly saturated conditions.

  16. Boundary Control Problem for Heat Convection Equations with Slip Boundary Condition

    Directory of Open Access Journals (Sweden)

    Exequiel Mallea-Zepeda

    2018-01-01

    Full Text Available We analyze an optimal boundary control problem for heat convection equations in a three-dimensional domain, with mixed boundary conditions. We prove the existence of optimal solutions, by considering boundary controls for the velocity vector and the temperature. The analyzed optimal control problem includes the minimization of a Lebesgue norm between the velocity and some desired field, as well as the temperature and some desired temperature. By using the Lagrange multipliers theorem we derive an optimality system. We also give a second-order sufficient condition.

  17. New stability conditions for nonlinear time varying delay systems

    Science.gov (United States)

    Elmadssia, S.; Saadaoui, K.; Benrejeb, M.

    2016-07-01

    In this paper, new practical stability conditions for a class of nonlinear time varying delay systems are proposed. The study is based on the use of a specific state space description, known as the Benrejeb characteristic arrow form matrix, and aggregation techniques to obtain delay-dependent stability conditions. Application of this method to delayed Lurie-Postnikov nonlinear systems is given. Illustrative examples are presented to show the effectiveness of the proposed approach.

  18. Open boundary condition, Wilson flow and the scalar glueball mass

    International Nuclear Information System (INIS)

    Chowdhury, Abhishek; Harindranath, A.; Maiti, Jyotirmoy

    2014-01-01

    A major problem with periodic boundary condition on the gauge fields used in current lattice gauge theory simulations is the trapping of topological charge in a particular sector as the continuum limit is approached. To overcome this problem open boundary condition in the temporal direction has been proposed recently. One may ask whether open boundary condition can reproduce the observables calculated with periodic boundary condition. In this work we find that the extracted lowest glueball mass using open and periodic boundary conditions at the same lattice volume and lattice spacing agree for the range of lattice scales explored in the range 3 GeV≤(1/a)≤5 GeV. The problem of trapping is overcome to a large extent with open boundary and we are able to extract the glueball mass at even larger lattice scale ≈ 5.7 GeV. To smoothen the gauge fields we have used recently proposed Wilson flow which, compared to HYP smearing, exhibits better systematics in the extraction of glueball mass. The extracted glueball mass shows remarkable insensitivity to the lattice spacings in the range explored in this work, 3 GeV≤(1/a)≤5.7 GeV.

  19. Three-Field Modelling of Nonlinear Nonsmooth Boundary Value Problems and Stability of Differential Mixed Variational Inequalities

    Directory of Open Access Journals (Sweden)

    J. Gwinner

    2013-01-01

    Full Text Available The purpose of this paper is twofold. Firstly we consider nonlinear nonsmooth elliptic boundary value problems, and also related parabolic initial boundary value problems that model in a simplified way steady-state unilateral contact with Tresca friction in solid mechanics, respectively, stem from nonlinear transient heat conduction with unilateral boundary conditions. Here a recent duality approach, that augments the classical Babuška-Brezzi saddle point formulation for mixed variational problems to twofold saddle point formulations, is extended to the nonsmooth problems under consideration. This approach leads to variational inequalities of mixed form for three coupled fields as unknowns and to related differential mixed variational inequalities in the time-dependent case. Secondly we are concerned with the stability of the solution set of a general class of differential mixed variational inequalities. Here we present a novel upper set convergence result with respect to perturbations in the data, including perturbations of the associated nonlinear maps, the nonsmooth convex functionals, and the convex constraint set. We employ epiconvergence for the convergence of the functionals and Mosco convergence for set convergence. We impose weak convergence assumptions on the perturbed maps using the monotonicity method of Browder and Minty.

  20. Influence of convective conditions on three dimensional mixed convective hydromagnetic boundary layer flow of Casson nanofluid

    Energy Technology Data Exchange (ETDEWEB)

    Rauf, A., E-mail: raufamar@ciitsahiwal.edu.pk [Department of Mathematics, Comsats Institute of Information Technology, Sahiwal 57000 (Pakistan); Siddiq, M.K. [Centre for Advanced Studies in Pure and Applied Mathematics, Department of Mathematics, Bahauddin Zakariya University, Multan 63000 (Pakistan); Abbasi, F.M. [Department of Mathematics, Comsats Institute of Information Technology, Islamabad 44000 (Pakistan); Meraj, M.A. [Department of Mathematics, Comsats Institute of Information Technology, Sahiwal 57000 (Pakistan); Ashraf, M. [Centre for Advanced Studies in Pure and Applied Mathematics, Department of Mathematics, Bahauddin Zakariya University, Multan 63000 (Pakistan); Shehzad, S.A. [Department of Mathematics, Comsats Institute of Information Technology, Sahiwal 57000 (Pakistan)

    2016-10-15

    The present work deals with the steady laminar three-dimensional mixed convective magnetohydrodynamic (MHD) boundary layer flow of Casson nanofluid over a bidirectional stretching surface. A uniform magnetic field is applied normal to the flow direction. Similarity variables are implemented to convert the non-linear partial differential equations into ordinary ones. Convective boundary conditions are utilized at surface of the sheet. A numerical technique of Runge–Kutta–Fehlberg (RFK45) is used to obtain the results of velocity, temperature and concentration fields. The physical dimensionless parameters are discussed through tables and graphs. - Highlights: • Mixed convective boundary layer flow of Casson nanofluid is taken into account. • Impact of magnetic field is examined. • Convective heat and mass conditions are imposed. • Numerical solutions are presented and discussed.

  1. Unique solvability of a non-linear non-local boundary-value problem for systems of non-linear functional differential equations

    Czech Academy of Sciences Publication Activity Database

    Dilna, N.; Rontó, András

    2010-01-01

    Roč. 60, č. 3 (2010), s. 327-338 ISSN 0139-9918 R&D Projects: GA ČR(CZ) GA201/06/0254 Institutional research plan: CEZ:AV0Z10190503 Keywords : non-linear boundary value-problem * functional differential equation * non-local condition * unique solvability * differential inequality Subject RIV: BA - General Mathematics Impact factor: 0.316, year: 2010 http://link.springer.com/article/10.2478%2Fs12175-010-0015-9

  2. Existence of three solutions for impulsive nonlinear fractional boundary value problems

    Directory of Open Access Journals (Sweden)

    Shapour Heidarkhani

    2017-01-01

    Full Text Available In this work we present new criteria on the existence of three solutions for a class of impulsive nonlinear fractional boundary-value problems depending on two parameters. We use variational methods for smooth functionals defined on reflexive Banach spaces in order to achieve our results.

  3. The focal boundary value problem for strongly singular higher-order nonlinear functional-differential equations

    Czech Academy of Sciences Publication Activity Database

    Mukhigulashvili, Sulkhan; Půža, B.

    2015-01-01

    Roč. 2015, January (2015), s. 17 ISSN 1687-2770 Institutional support: RVO:67985840 Keywords : higher order nonlinear functional-differential equations * two-point right-focal boundary value problem * strong singularity Subject RIV: BA - General Mathematics Impact factor: 0.642, year: 2015 http://link.springer.com/article/10.1186%2Fs13661-014-0277-1

  4. Infinitely Many Solutions for a Boundary Value Problem with Discontinuous Nonlinearities

    Directory of Open Access Journals (Sweden)

    2009-03-01

    Full Text Available The existence of infinitely many solutions for a Sturm-Liouville boundary value problem, under an appropriate oscillating behavior of the possibly discontinuous nonlinear term, is obtained. Several special cases and consequences are pointed out and some examples are presented. The technical approach is mainly based on a result of infinitely many critical points for locally Lipschitz functions.

  5. The unified method: II. NLS on the half-line with t-periodic boundary conditions

    International Nuclear Information System (INIS)

    Lenells, J; Fokas, A S

    2012-01-01

    Boundary value problems for integrable nonlinear evolution PDEs formulated on the half-line can be analyzed by the unified method introduced by one of the authors and used extensively in the literature. The implementation of this general method to this particular class of problems yields the solution in terms of the unique solution of a matrix Riemann–Hilbert problem formulated in the complex k-plane (the Fourier plane), which has a jump matrix with explicit (x, t)-dependence involving four scalar functions of k, called spectral functions. Two of these functions depend on the initial data, whereas the other two depend on all boundary values. The most difficult step of the new method is the characterization of the latter two spectral functions in terms of the given initial and boundary data, i.e. the elimination of the unknown boundary values. For certain boundary conditions, called linearizable, this can be achieved by simply using algebraic manipulations. Here, we first present an effective characterization of the spectral functions in terms of the given initial and boundary data for the general case of non-linearizable boundary conditions. This characterization is based on the analysis of the so-called global relation and on the introduction of the so-called Gelfand–Levitan–Marchenko representations of the eigenfunctions defining the spectral functions. We then concentrate on the physically significant case of t-periodic Dirichlet boundary data. After presenting certain heuristic arguments which suggest that the Neumann boundary values become periodic as t → ∞, we show that for the case of the NLS with a sine-wave as Dirichlet data, the asymptotics of the Neumann boundary values can be computed explicitly at least up to third order in a perturbative expansion and indeed at least up to this order are asymptotically periodic. (paper)

  6. Asymptotic boundary conditions for dissipative waves: General theory

    Science.gov (United States)

    Hagstrom, Thomas

    1990-01-01

    An outstanding issue in the computational analysis of time dependent problems is the imposition of appropriate radiation boundary conditions at artificial boundaries. Accurate conditions are developed which are based on the asymptotic analysis of wave propagation over long ranges. Employing the method of steepest descents, dominant wave groups are identified and simple approximations to the dispersion relation are considered in order to derive local boundary operators. The existence of a small number of dominant wave groups may be expected for systems with dissipation. Estimates of the error as a function of domain size are derived under general hypotheses, leading to convergence results. Some practical aspects of the numerical construction of the asymptotic boundary operators are also discussed.

  7. Asymptotic boundary conditions for dissipative waves - General theory

    Science.gov (United States)

    Hagstrom, Thomas

    1991-01-01

    An outstanding issue in computational analysis of time dependent problems is the imposition of appropriate radiation boundary conditions at artificial boundaries. Accurate conditions are developed which are based on the asymptotic analysis of wave propagation over long ranges. Employing the method of steepest descents, dominant wave groups are identified and simple approximations to the dispersion relation are considered in order to derive local boundary operators. The existence of a small number of dominant wave groups may be expected for systems with dissipation. Estimates of the error as a function of domain size are derived under general hypotheses, leading to convergence results. Some practical aspects of the numerical construction of the asymptotic boundary operators are also discussed.

  8. Asymptotics for inhomogeneous Dirichlet initial-boundary value problem for the nonlinear Schrödinger equation

    Energy Technology Data Exchange (ETDEWEB)

    Kaikina, Elena I., E-mail: ekaikina@matmor.unam.mx [Centro de Ciencias Matemáticas, UNAM Campus Morelia, AP 61-3 (Xangari), Morelia CP 58089, Michoacán (Mexico)

    2013-11-15

    We consider the inhomogeneous Dirichlet initial-boundary value problem for the nonlinear Schrödinger equation, formulated on a half-line. We study traditionally important problems of the theory of nonlinear partial differential equations, such as global in time existence of solutions to the initial-boundary value problem and the asymptotic behavior of solutions for large time.

  9. Asymptotics for inhomogeneous Dirichlet initial-boundary value problem for the nonlinear Schrödinger equation

    International Nuclear Information System (INIS)

    Kaikina, Elena I.

    2013-01-01

    We consider the inhomogeneous Dirichlet initial-boundary value problem for the nonlinear Schrödinger equation, formulated on a half-line. We study traditionally important problems of the theory of nonlinear partial differential equations, such as global in time existence of solutions to the initial-boundary value problem and the asymptotic behavior of solutions for large time

  10. Hydromagnetic conditions near the core-mantle boundary

    Science.gov (United States)

    Backus, George E.

    1995-01-01

    The main results of the grant were (1) finishing the manuscript of a proof of completeness of the Poincare modes in an incompressible nonviscous fluid corotating with a rigid ellipsoidal boundary, (2) partial completion of a manuscript describing a definition of helicity that resolved questions in the literature about calculating the helicities of vector fields with complicated topologies, and (3) the beginning of a reexamination of the inverse problem of inferring properties of the geomagnetic field B just outside the core-mantle boundary (CMB) from measurements of elements of B at and above the earth's surface. This last work has led to a simple general formalism for linear and nonlinear inverse problems that appears to include all the inversion schemes so far considered for the uniqueness problem in geomagnetic inversion. The technique suggests some new methods for error estimation that form part of this report.

  11. Quasisteady primitive equations with associated upper boundary conditions

    International Nuclear Information System (INIS)

    Gordon, P.

    1979-01-01

    This paper presents another approach to the problem of modeling large scale atmospheric flow. The major thrust of the method is to search for quasi-steady-state phenomena. This leads to sets of diagnostic and predictive equations that differ from those presently in use. Another important feature of the analysis is the introduction of a slowly floating upper boundary. In addition to simplifying the question of boundary conditions at the upper boundary, the floating top requires a highly significant change in the set of diagnostic variables. Two possible upper boundary conditions are derived in conjunction with the floating top. The first assumes continuous flow at the upper boundary, while the second assumes a compression-wave type discontinuity. Two specific criteria are formulated for checking the validity of the quasi-steady-state model. One is a scale assumption, between the physical scale and the time scale. The other is the requirement that the solution of the diagnostic equations be the steady-state limit of the original time-dependent equations. Various examples are given in order to attempt to clarify the techniques and philosophy of this approach. In addition, a specific test case is solved numerically with three models: The fixed top quasi-steady-state model, the floating top quasi-steady-state model, and a hydrostatic model. At the same time various upper boundary conditions are tested and compared. The results of the investigation indicate several significant advantages in favor of the floating top quasi-steady-state model

  12. Transport synthetic acceleration with opposing reflecting boundary conditions

    International Nuclear Information System (INIS)

    Zika, M.R.; Adams, M.L.

    2000-01-01

    The transport synthetic acceleration (TSA) scheme is extended to problems with opposing reflecting boundary conditions. This synthetic method employs a simplified transport operator as its low-order approximation. A procedure is developed that allows the use of the conjugate gradient (CG) method to solve the resulting low-order system of equations. Several well-known transport iteration algorithms are cast in a linear algebraic form to show their equivalence to standard iterative techniques. Source iteration in the presence of opposing reflecting boundary conditions is shown to be equivalent to a (poorly) preconditioned stationary Richardson iteration, with the preconditioner defined by the method of iterating on the incident fluxes on the reflecting boundaries. The TSA method (and any synthetic method) amounts to a further preconditioning of the Richardson iteration. The presence of opposing reflecting boundary conditions requires special consideration when developing a procedure to realize the CG method for the proposed system of equations. The CG iteration may be applied only to symmetric positive definite matrices; this condition requires the algebraic elimination of the boundary angular corrections from the low-order equations. As a consequence of this elimination, evaluating the action of the resulting matrix on an arbitrary vector involves two transport sweeps and a transmission iteration. Results of applying the acceleration scheme to a simple test problem are presented

  13. Transport Synthetic Acceleration with Opposing Reflecting Boundary Conditions

    International Nuclear Information System (INIS)

    Zika, Michael R.; Adams, Marvin L.

    2000-01-01

    The transport synthetic acceleration (TSA) scheme is extended to problems with opposing reflecting boundary conditions. This synthetic method employs a simplified transport operator as its low-order approximation. A procedure is developed that allows the use of the conjugate gradient (CG) method to solve the resulting low-order system of equations.Several well-known transport iteration algorithms are cast in a linear algebraic form to show their equivalence to standard iterative techniques. Source iteration in the presence of opposing reflecting boundary conditions is shown to be equivalent to a (poorly) preconditioned stationary Richardson iteration, with the preconditioner defined by the method of iterating on the incident fluxes on the reflecting boundaries. The TSA method (and any synthetic method) amounts to a further preconditioning of the Richardson iteration.The presence of opposing reflecting boundary conditions requires special consideration when developing a procedure to realize the CG method for the proposed system of equations. The CG iteration may be applied only to symmetric positive definite matrices; this condition requires the algebraic elimination of the boundary angular corrections from the low-order equations. As a consequence of this elimination, evaluating the action of the resulting matrix on an arbitrary vector involves two transport sweeps and a transmission iteration. Results of applying the acceleration scheme to a simple test problem are presented

  14. Critical effects of downstream boundary conditions on vortex breakdown

    Science.gov (United States)

    Kandil, Osama; Kandil, Hamdy A.; Liu, C. H.

    1992-01-01

    The unsteady, compressible, full Navier-Stokes (NS) equations are used to study the critical effects of the downstream boundary conditions on the supersonic vortex breakdown. The present study is applied to two supersonic vortex breakdown cases. In the first case, quasi-axisymmetric supersonic swirling flow is considered in a configured circular duct, and in the second case, quasi-axisymmetric supersonic swirling jet, that is issued from a nozzle into a supersonic jet of lower Mach number, is considered. For the configured duct flow, four different types of downstream boundary conditions are used, and for the swirling jet flow from the nozzle, two types of downstream boundary conditions are used. The solutions are time accurate which are obtained using an implicit, upwind, flux-difference splitting, finite-volume scheme.

  15. Superradiance in the BTZ black hole with Robin boundary conditions

    Science.gov (United States)

    Dappiaggi, Claudio; Ferreira, Hugo R. C.; Herdeiro, Carlos A. R.

    2018-03-01

    We show the existence of superradiant modes of massive scalar fields propagating in BTZ black holes when certain Robin boundary conditions, which never include the commonly considered Dirichlet boundary conditions, are imposed at spatial infinity. These superradiant modes are defined as those solutions whose energy flux across the horizon is towards the exterior region. Differently from rotating, asymptotically flat black holes, we obtain that not all modes which grow up exponentially in time are superradiant; for some of these, the growth is sourced by a bulk instability of AdS3, triggered by the scalar field with Robin boundary conditions, rather than by energy extraction from the BTZ black hole. Thus, this setup provides an example wherein Bosonic modes with low frequency are pumping energy into, rather than extracting energy from, a rotating black hole.

  16. Vibration Analysis of Annular Sector Plates under Different Boundary Conditions

    Directory of Open Access Journals (Sweden)

    Dongyan Shi

    2014-01-01

    Full Text Available An analytical framework is developed for the vibration analysis of annular sector plates with general elastic restraints along each edge of plates. Regardless of boundary conditions, the displacement solution is invariably expressed as a new form of trigonometric expansion with accelerated convergence. The expansion coefficients are treated as the generalized coordinates and determined using the Rayleigh-Ritz technique. This work allows a capability of modeling annular sector plates under a variety of boundary conditions and changing the boundary conditions as easily as modifying the material properties or dimensions of the plates. Of equal importance, the proposed approach is universally applicable to annular sector plates of any inclusion angles up to 2π. The reliability and accuracy of the current method are adequately validated through numerical examples.

  17. Function Substitution in Partial Differential Equations: Nonhomogeneous Boundary Conditions

    Directory of Open Access Journals (Sweden)

    T. V. Oblakova

    2017-01-01

    Full Text Available The paper considers a mixed initial-boundary value problem for a parabolic equation with nonhomogeneous boundary conditions. The classical approach to search for analytical solution of such problems in the first phase involves variable substitution, leading to a problem with homogeneous boundary conditions. Reference materials [1] give, as a rule, the simplest types of variable substitutions where new and old unknown functions differ by a term, linear in the spatial variable. The form of this additive term depends on the type of the boundary conditions, but is in no way related to the equation under consideration. Moreover, in the case of the second boundary-value problem, it is necessary to use a quadratic additive, since a linear substitution for this type of conditions may be unavailable. The courseware [2] - [4], usually, ends only with the first boundary-value problem generally formulated.The paper considers a substitution that takes into account, in principle, the form of a linear differential operator. Namely, as an additive term, it is proposed to use the parametrically time-dependent solution of the boundary value problem for an ordinary differential equation obtained from the original partial differential equation by the method of separation of the Fourier variables.The existence of the proposed substitution for boundary conditions of any type is proved by the example of a non-stationary heat-transfer equation with the heat exchange available with the surrounding medium. In this case, the additive term is a linear combination of hyperbolic functions. It is shown that, in addition to the "insensitivity" to the type of boundary conditions, the advantages of a new substitution in comparison with the traditional linear (or quadratic one include a much simpler structure of the solution obtained. Just the described approach allows us to obtain a solution with a clearly distinguished stationary component, in case a stationarity occurs, for

  18. Effect of boundary conditions on magnetocapacitance effect in a ring-type magnetoelectric structure

    Science.gov (United States)

    Zhang, Juanjuan

    2017-12-01

    By considering the nonlinear magneto-elastic coupling relationships of magnetostrictive materials, an analytical model is proposed. The resonance frequencies can be accurately predicted by this theoretical model, and they are in good agreement with experimental data. Subsequently, the magnetocapacitance effect in a ring-type magnetoelectric (ME) structure with different boundary conditions is investigated, and it is found that various mechanical boundaries, the frequency, the magnetic field, the geometric size, and the interface bonding significantly affect the capacitance of the ME structure. Further, additional resonance frequencies can be predicted by considering appropriate imperfect interface bonding. Finally, the influence of an external force on the capacitance is studied. The result shows that an external force on the boundary changes the capacitance, but has only a weak influence on the resonance frequency.

  19. Simulations of QCD and QED with C* boundary conditions

    OpenAIRE

    Hansen, Martin; Lucini, Biagio; Patella, Agostino; Tantalo, Nazario

    2017-01-01

    We present exploratory results from dynamical simulations of QCD in isolation, as well as QCD coupled to QED, with C* boundary conditions. In finite volume, the use of C* boundary conditions allows for a gauge invariant and local formulation of QED without zero modes. In particular we show that the simulations reproduce known results and that masses of charged mesons can be extracted in a completely gauge invariant way. For the simulations we use a modified version of the HiRep code. The prim...

  20. Optimal control problems for impulsive systems with integral boundary conditions

    Directory of Open Access Journals (Sweden)

    Allaberen Ashyralyev

    2013-03-01

    Full Text Available In this article, the optimal control problem is considered when the state of the system is described by the impulsive differential equations with integral boundary conditions. Applying the Banach contraction principle the existence and uniqueness of the solution is proved for the corresponding boundary problem by the fixed admissible control. The first and second variation of the functional is calculated. Various necessary conditions of optimality of the first and second order are obtained by the help of the variation of the controls.

  1. On higher-order boundary conditions at elastic-plastic boundaries in strain-gradient plasticity

    DEFF Research Database (Denmark)

    Niordson, Christian Frithiof

    2008-01-01

    are suppressed by using a very high artificial hardening modulus. Through numerical studies of pure bending under plane strain conditions, it is shown that this method predicts the build-up of higher order stresses in the pseudo-elastic regime. This has the effect of delaying the onset of incipient yield......A computational method for dealing with higher order boundary conditions on moving elastic-plastic boundaries in strain gradient plasticity is proposed. The basic idea is to skip the notion of a purely elastic regime, and instead introduce a pseudo-elastic regime, where plastic deformations...

  2. Stress and mixed boundary conditions for two-dimensional ...

    Indian Academy of Sciences (India)

    For plate bending and stretching problems in two-dimensional (2D) dodecagonal quasi-crystal (QC) media, the reciprocal theorem and the general solution for QCs are applied in a novel way to obtain the appropriate stress and mixed boundary conditions accurate to all order. The method developed by Gregory and Wan is ...

  3. The Hardy inequality with boundary or intermediate conditions

    Czech Academy of Sciences Publication Activity Database

    Kufner, Alois

    2017-01-01

    Roč. 8, č. 2 (2017), s. 105-109 ISSN 2077-9879 Institutional support: RVO:67985840 Keywords : Hardy's inequality * boundary conditions Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics http://www.mathnet.ru/ php /archive.phtml?wshow=paper&jrnid=emj&paperid=259&option_lang=eng

  4. The No-Slip Boundary Condition in Fluid Mechanics

    Indian Academy of Sciences (India)

    Home; Journals; Resonance – Journal of Science Education; Volume 9; Issue 5. The No-Slip Boundary Condition in Fluid Mechanics - Solution of the Sticky Problem. Sandeep Prabhakara M D Deshpande. General Article Volume 9 Issue 5 May 2004 pp 61-71 ...

  5. On a stochastic Burgers equation with Dirichlet boundary conditions

    Directory of Open Access Journals (Sweden)

    Ekaterina T. Kolkovska

    2003-01-01

    Full Text Available We consider the one-dimensional Burgers equation perturbed by a white noise term with Dirichlet boundary conditions and a non-Lipschitz coefficient. We obtain existence of a weak solution proving tightness for a sequence of polygonal approximations for the equation and solving a martingale problem for the weak limit.

  6. The No-Slip Boundary Condition in Fluid Mechanics

    Indian Academy of Sciences (India)

    http://www.ias.ac.in/article/fulltext/reso/009/04/0050-0060. Keywords. No-slip boundary condition; Navier-Stokes equations; Poiseuille flow; flow resistance. Author Affiliations. Sandeep Prabhakara1 M D Deshpande2. Indian Institute of Technology, Kharagpur 721 302, India. CTFD Division National Aerospace Laboratories ...

  7. Boundary conditions for open quantum systems driven far from equilibrium

    Science.gov (United States)

    Frensley, William R.

    1990-07-01

    This is a study of simple kinetic models of open systems, in the sense of systems that can exchange conserved particles with their environment. The system is assumed to be one dimensional and situated between two particle reservoirs. Such a system is readily driven far from equilibrium if the chemical potentials of the reservoirs differ appreciably. The openness of the system modifies the spatial boundary conditions on the single-particle Liouville-von Neumann equation, leading to a non-Hermitian Liouville operator. If the open-system boundary conditions are time reversible, exponentially growing (unphysical) solutions are introduced into the time dependence of the density matrix. This problem is avoided by applying time-irreversible boundary conditions to the Wigner distribution function. These boundary conditions model the external environment as ideal particle reservoirs with properties analogous to those of a blackbody. This time-irreversible model may be numerically evaluated in a discrete approximation and has been applied to the study of a resonant-tunneling semiconductor diode. The physical and mathematical properties of the irreversible kinetic model, in both its discrete and its continuum formulations, are examined in detail. The model demonstrates the distinction in kinetic theory between commutator superoperators, which may become non-Hermitian to describe irreversible behavior, and anticommutator superoperators, which remain Hermitian and are used to evaluate physical observables.

  8. Existence of solutions for fractional differential inclusions with boundary conditions

    Directory of Open Access Journals (Sweden)

    Dandan Yang

    2010-07-01

    Full Text Available This article concerns the existence of solutions for fractional-order differential inclusions with boundary-value conditions. The main tools are based on fixed point theorems due to Bohnerblust-Karlin and Leray-Schauder together with a continuous selection theorem for upper semi-continuous multi-valued maps.

  9. Nonlinear Lyapunov-based boundary control of distributed heat transfer mechanisms in membrane distillation plant

    KAUST Repository

    Eleiwi, Fadi

    2015-07-01

    This paper presents a nonlinear Lyapunov-based boundary control for the temperature difference of a membrane distillation boundary layers. The heat transfer mechanisms inside the process are modeled with a 2D advection-diffusion equation. The model is semi-descretized in space, and a nonlinear state-space representation is provided. The control is designed to force the temperature difference along the membrane sides to track a desired reference asymptotically, and hence a desired flux would be generated. Certain constraints are put on the control law inputs to be within an economic range of energy supplies. The effect of the controller gain is discussed. Simulations with real process parameters for the model, and the controller are provided. © 2015 American Automatic Control Council.

  10. Euclidean pseudoduality and boundary conditions in sigma models

    Energy Technology Data Exchange (ETDEWEB)

    Sar Latin-Small-Letter-Dotless-I saman, Mustafa, E-mail: msarisaman@ku.edu.tr [Department of Mathematics, Koc University, 34450 Sar Latin-Small-Letter-Dotless-I yer, Istanbul (Turkey)

    2013-03-01

    We discuss pseudoduality transformations in two-dimensional conformally invariant classical sigma models, and extend our analysis to a given boundaries of world-sheet, which gives rise to an appropriate framework for the discussion of the pseudoduality between D-branes. We perform analysis using the Euclidean spacetime and show that structures on the target space can be transformed into pseudodual manifold identically. This map requires that torsions and curvatures related to individual spaces are the same when connections are Riemannian. Boundary pseudoduality imposes locality condition.

  11. The boundary conditions for point transformed electromagnetic invisibility cloaks

    International Nuclear Information System (INIS)

    Weder, Ricardo

    2008-01-01

    In this paper we study point transformed electromagnetic invisibility cloaks in transformation media that are obtained by transformation from general anisotropic media. We assume that there are several point transformed electromagnetic cloaks located in different points in space. Our results apply in particular to the first-order invisibility cloaks introduced by Pendry et al and to the high-order invisibility cloaks introduced by Hendi et al and by Cai et al. We identify the appropriate cloaking boundary conditions that the solutions of Maxwell equations have to satisfy at the outside, ∂K + , and at the inside, ∂K - , of the boundary of the cloaked object K in the case where the permittivity and the permeability are bounded below and above in K. Namely, that the tangential components of the electric and the magnetic fields have to vanish at ∂K + -which is always true-and that the normal components of the curl of the electric and the magnetic fields have to vanish at ∂K - . These results are proven requiring that energy be conserved. In the case of one spherical cloak with a spherically stratified K and a radial current at ∂K we verify by an explicit calculation that our cloaking boundary conditions are satisfied and that cloaking of active devices holds, even if the current is at the boundary of the cloaked object. As we prove our results for media that are obtained by transformation from general anisotropic media, our results apply to the cloaking of objects with passive and active devices contained in general anisotropic media, in particular to objects with passive and active devices contained inside general crystals. Our results suggest a method to enhance cloaking in the approximate transformation media that are used in practice. Namely, to coat the boundary of the cloaked object (the inner boundary of the cloak) with a material that imposes the boundary conditions above. As these boundary conditions have to be satisfied for exact transformation

  12. Most general AdS{sub 3} boundary conditions

    Energy Technology Data Exchange (ETDEWEB)

    Grumiller, Daniel; Riegler, Max [Institute for Theoretical Physics, TU Wien,Wiedner Hauptstr. 8-10/136, A-1040 Vienna (Austria)

    2016-10-06

    We consider the most general asymptotically anti-de Sitter boundary conditions in three-dimensional Einstein gravity with negative cosmological constant. The metric contains in total twelve independent functions, six of which are interpreted as chemical potentials (or non-normalizable fluctuations) and the other half as canonical boundary charges (or normalizable fluctuations). Their presence modifies the usual Fefferman-Graham expansion. The asymptotic symmetry algebra consists of two sl(2){sub k} current algebras, the levels of which are given by k=ℓ/(4G{sub N}), where ℓ is the AdS radius and G{sub N} the three-dimensional Newton constant.

  13. The boundary conditions for point transformed electromagnetic invisibility cloaks

    Energy Technology Data Exchange (ETDEWEB)

    Weder, Ricardo [Departamento de Metodos Matematicos y Numericos, Instituto de Investigaciones en Matematicas Aplicadas y en Sistemas, Universidad Nacional Autonoma de Mexico, Apartado Postal 20-726, Mexico DF 01000 (Mexico)], E-mail: weder@servidor.unam.mx

    2008-10-17

    In this paper we study point transformed electromagnetic invisibility cloaks in transformation media that are obtained by transformation from general anisotropic media. We assume that there are several point transformed electromagnetic cloaks located in different points in space. Our results apply in particular to the first-order invisibility cloaks introduced by Pendry et al and to the high-order invisibility cloaks introduced by Hendi et al and by Cai et al. We identify the appropriate cloaking boundary conditions that the solutions of Maxwell equations have to satisfy at the outside, {partial_derivative}K{sub +}, and at the inside, {partial_derivative}K{sub -}, of the boundary of the cloaked object K in the case where the permittivity and the permeability are bounded below and above in K. Namely, that the tangential components of the electric and the magnetic fields have to vanish at {partial_derivative}K{sub +}-which is always true-and that the normal components of the curl of the electric and the magnetic fields have to vanish at {partial_derivative}K{sub -}. These results are proven requiring that energy be conserved. In the case of one spherical cloak with a spherically stratified K and a radial current at {partial_derivative}K we verify by an explicit calculation that our cloaking boundary conditions are satisfied and that cloaking of active devices holds, even if the current is at the boundary of the cloaked object. As we prove our results for media that are obtained by transformation from general anisotropic media, our results apply to the cloaking of objects with passive and active devices contained in general anisotropic media, in particular to objects with passive and active devices contained inside general crystals. Our results suggest a method to enhance cloaking in the approximate transformation media that are used in practice. Namely, to coat the boundary of the cloaked object (the inner boundary of the cloak) with a material that imposes the

  14. A Parameter Estimation Method for Nonlinear Systems Based on Improved Boundary Chicken Swarm Optimization

    Directory of Open Access Journals (Sweden)

    Shaolong Chen

    2016-01-01

    Full Text Available Parameter estimation is an important problem in nonlinear system modeling and control. Through constructing an appropriate fitness function, parameter estimation of system could be converted to a multidimensional parameter optimization problem. As a novel swarm intelligence algorithm, chicken swarm optimization (CSO has attracted much attention owing to its good global convergence and robustness. In this paper, a method based on improved boundary chicken swarm optimization (IBCSO is proposed for parameter estimation of nonlinear systems, demonstrated and tested by Lorenz system and a coupling motor system. Furthermore, we have analyzed the influence of time series on the estimation accuracy. Computer simulation results show it is feasible and with desirable performance for parameter estimation of nonlinear systems.

  15. Lattice Boltzmann simulations of pressure-driven flows in microchannels using Navier–Maxwell slip boundary conditions

    KAUST Repository

    Reis, Tim

    2012-01-01

    We present lattice Boltzmann simulations of rarefied flows driven by pressure drops along two-dimensional microchannels. Rarefied effects lead to non-zero cross-channel velocities, nonlinear variations in the pressure along the channel. Both effects are absent in flows driven by uniform body forces. We obtain second-order accuracy for the two components of velocity the pressure relative to asymptotic solutions of the compressible Navier-Stokes equations with slip boundary conditions. Since the common lattice Boltzmann formulations cannot capture Knudsen boundary layers, we replace the usual discrete analogs of the specular diffuse reflection conditions from continuous kinetic theory with a moment-based implementation of the first-order Navier-Maxwell slip boundary conditions that relate the tangential velocity to the strain rate at the boundary. We use these conditions to solve for the unknown distribution functions that propagate into the domain across the boundary. We achieve second-order accuracy by reformulating these conditions for the second set of distribution functions that arise in the derivation of the lattice Boltzmann method by an integration along characteristics. Our moment formalism is also valuable for analysing the existing boundary conditions. It reveals the origin of numerical slip in the bounce-back other common boundary conditions that impose conditions on the higher moments, not on the local tangential velocity itself. © 2012 American Institute of Physics.

  16. On the Derivation of Boundary Conditions for Continuum Dislocation Dynamics

    Directory of Open Access Journals (Sweden)

    Thomas Hochrainer

    2017-07-01

    Full Text Available Continuum dislocation dynamics (CDD is a single crystal strain gradient plasticity theory based exclusively on the evolution of the dislocation state. Recently, we derived a constitutive theory for the average dislocation velocity in CDD in a phase field-type description for an infinite domain. In the current work, so-called rational thermodynamics is employed to obtain thermodynamically consistent boundary conditions for the dislocation density variables of CDD. We find that rational thermodynamics reproduces the bulk constitutive equations as obtained from irreversible thermodynamics. The boundary conditions we find display strong parallels to the microscopic traction conditions derived by Gurtin and Needleman (M.E. Gurtin and A. Needleman, J. Mech. Phys. Solids 53 (2005 1–31 for strain gradient theories based on the Kröner–Nye tensor.

  17. Threshold condition for nonlinear tearing modes in tokamaks

    International Nuclear Information System (INIS)

    Zabiego, M.F.; Callen, J.D.

    1996-04-01

    Low-mode-number tearing mode nonlinear evolution is analyzed emphasizing the need for a threshold condition, to account for observations in tokamaks. The discussion is illustrated by two models recently introduced in the literature. Introducing a threshold condition in the tearing mode stability analysis is found to reveal some bifurcation points and thus domains of intrinsic stability in the island dynamics operational space. (author)

  18. Matrix albedo for discrete ordinates infinite-medium boundary condition

    International Nuclear Information System (INIS)

    Mathews, K.; Dishaw, J.

    2007-01-01

    Discrete ordinates problems with an infinite exterior medium (reflector) can be more efficiently computed by eliminating grid cells in the exterior medium and applying a matrix albedo boundary condition. The albedo matrix is a discretized bidirectional reflection distribution function (BRDF) that accounts for the angular quadrature set, spatial quadrature method, and spatial grid that would have been used to model a portion of the exterior medium. The method is exact in slab geometry, and could be used as an approximation in multiple dimensions or curvilinear coordinates. We present an adequate method for computing albedo matrices and demonstrate their use in verifying a discrete ordinates code in slab geometry by comparison with Ganapol's infinite medium semi-analytic TIEL benchmark. With sufficient resolution in the spatial and angular grids and iteration tolerance to yield solutions converged to 6 digits, the conventional (scalar) albedo boundary condition yielded 2-digit accuracy at the boundary, but the matrix albedo solution reproduced the benchmark scalar flux at the boundary to all 6 digits. (authors)

  19. Existence theory for sequential fractional differential equations with anti-periodic type boundary conditions

    Directory of Open Access Journals (Sweden)

    Aqlan Mohammed H.

    2016-01-01

    Full Text Available We develop the existence theory for sequential fractional differential equations involving Liouville-Caputo fractional derivative equipped with anti-periodic type (non-separated and nonlocal integral boundary conditions. Several existence criteria depending on the nonlinearity involved in the problems are presented by means of a variety of tools of the fixed point theory. The applicability of the results is shown with the aid of examples. Our results are not only new in the given configuration but also yield some new special cases for specific choices of parameters involved in the problems.

  20. Numerical Study of Outlet Boundary Conditions for Unsteady Turbulent Internal Flows Using the NCC

    Science.gov (United States)

    Liu, Nan-Suey; Shih, Tsan-Hsing

    2009-01-01

    This paper presents the results of studies on the outlet boundary conditions for turbulent internal flow simulations. Several outlet boundary conditions have been investigated by applying the National Combustion Code (NCC) to the configuration of a LM6000 single injector flame tube. First of all, very large eddy simulations (VLES) have been performed using the partially resolved numerical simulation (PRNS) approach, in which both the nonlinear and linear dynamic subscale models were employed. Secondly, unsteady Reynolds averaged Navier- Stokes (URANS) simulations have also been performed for the same configuration to investigate the effects of different outlet boundary conditions in the context of URANS. Thirdly, the possible role of the initial condition is inspected by using three different initial flow fields for both the PRNS/VLES simulation and the URANS simulation. The same grid is used for all the simulations and the number of mesh element is about 0.5 million. The main purpose of this study is to examine the long-time behavior of the solution as determined by the imposed outlet boundary conditions. For a particular simulation to be considered as successful under the given initial and boundary conditions, the solution must be sustainable in a physically meaningful manner over a sufficiently long period of time. The commonly used outlet boundary condition for steady Reynolds averaged Navier-Stokes (RANS) simulation is a fixed pressure at the outlet with all the other dependent variables being extrapolated from the interior. The results of the present study suggest that this is also workable for the URANS simulation of the LM6000 injector flame tube. However, it does not work for the PRNS/VLES simulation due to the unphysical reflections of the pressure disturbances at the outlet boundary. This undesirable situation can be practically alleviated by applying a simple unsteady convection equation for the pressure disturbances at the outlet boundary. The

  1. Revisiting Johnson and Jackson boundary conditions for granular flows

    Energy Technology Data Exchange (ETDEWEB)

    Li, Tingwen; Benyahia, Sofiane

    2012-07-01

    In this article, we revisit Johnson and Jackson boundary conditions for granular flows. The oblique collision between a particle and a flat wall is analyzed by adopting the classic rigid-body theory and a more realistic semianalytical model. Based on the kinetic granular theory, the input parameter for the partial-slip boundary conditions, specularity coefficient, which is not measurable in experiments, is then interpreted as a function of the particle-wall restitution coefficient, the frictional coefficient, and the normalized slip velocity at the wall. An analytical expression for the specularity coefficient is suggested for a flat, frictional surface with a low frictional coefficient. The procedure for determining the specularity coefficient for a more general problem is outlined, and a working approximation is provided.

  2. Matrix factorisations for rational boundary conditions by defect fusion

    International Nuclear Information System (INIS)

    Behr, Nicolas; Fredenhagen, Stefan

    2015-01-01

    A large class of two-dimensional N=(2,2) superconformal field theories can be understood as IR fixed-points of Landau-Ginzburg models. In particular, there are rational conformal field theories that also have a Landau-Ginzburg description. To understand better the relation between the structures in the rational conformal field theory and in the Landau-Ginzburg theory, we investigate how rational B-type boundary conditions are realised as matrix factorisations in the SU(3)/U(2) Grassmannian Kazama-Suzuki model. As a tool to generate the matrix factorisations we make use of a particular interface between the Kazama-Suzuki model and products of minimal models, whose fusion can be realised as a simple functor on ring modules. This allows us to formulate a proposal for all matrix factorisations corresponding to rational boundary conditions in the SU(3)/U(2) model.

  3. The existence of positive solutions for nonlinear boundary system with $p$-Laplacian operator based on sign-changing nonlinearities

    Directory of Open Access Journals (Sweden)

    Fuyi Xu

    2010-12-01

    (\\phi_{p_1}(u''+a_1(tf(u,v=0, 01, i=1,2$. We obtain some sufficient conditions for the existence of two positive solutions or infinitely many positive solutions by using a fixed-point theorem in cones. Especially, the nonlinear terms $f,g $ are allowed to change sign. The conclusions essentially extend and improve the known results.

  4. Positivity for equations involving polyharmonic operators with Dirichlet boundary conditions

    NARCIS (Netherlands)

    Grunau, H.-Ch.; Sweers, G.

    1996-01-01

    Cranston, Fabes and Zhao ([26], [5]) established the uniform bound sup x; y 2 x 6= y R G1;n (x; z)G1;n (z; y) dz G1;n (x; y) M < 1; (1) where G1;n (x; y) is the Green function for the Laplacian - with Dirichlet boundary conditions on a Lipschitz domain - Rn with n 3 (see [27] for n = 2).

  5. Boundary conditions for simulating large SAW devices using ANSYS.

    Science.gov (United States)

    Peng, Dasong; Yu, Fengqi; Hu, Jian; Li, Peng

    2010-08-01

    In this report, we propose improved substrate left and right boundary conditions for simulating SAW devices using ANSYS. Compared with the previous methods, the proposed method can greatly reduce computation time. Furthermore, the longer the distance from the first reflector to the last one, the more computation time can be reduced. To verify the proposed method, a design example is presented with device center frequency 971.14 MHz.

  6. Bound states in waveguides with complex Robin boundary conditions

    Czech Academy of Sciences Publication Activity Database

    Novák, Radek

    2016-01-01

    Roč. 96, 3-4 (2016), s. 251-281 ISSN 0921-7134 R&D Projects: GA ČR(CZ) GA14-06818S Institutional support: RVO:61389005 Keywords : non-self-adjointness * waveguide * Robin boundary conditions * spectral analysis * essential spectrum * weak coupling * Birman-Schwinger principle * reality of the spectrum Subject RIV: BE - Theoretical Physics Impact factor: 0.933, year: 2016

  7. Eigenvalue inequalities for the Laplacian with mixed boundary conditions

    Czech Academy of Sciences Publication Activity Database

    Lotoreichik, Vladimir; Rohleder, J.

    2017-01-01

    Roč. 263, č. 1 (2017), s. 491-508 ISSN 0022-0396 R&D Projects: GA ČR(CZ) GA14-06818S Institutional support: RVO:61389005 Keywords : Laplace operator * mixed boundary conditions * eigenvalue inequality * polyhedral domain * Lipschitz domain Subject RIV: BE - Theoretical Physics OBOR OECD: Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect) Impact factor: 1.988, year: 2016

  8. Slarti: A boundary condition editor for a coupled climate model

    Science.gov (United States)

    Mickelson, S. A.; Jacob, R. L.; Pierrehumbert, R.

    2006-12-01

    One of the largest barriers to making climate models more flexible is the difficulty in creating new boundary conditions, especially for "deep time" paleoclimate cases where continents are in different positions. Climate models consist of several mutually-interacting component models and the boundary conditions must be consistent between them. We have developed a program called Slarti which uses a Graphical User Interface and a set of consistency rules to aid researchers in creating new, consistent, boundary condition files for the Fast Ocean Atmosphere Model (FOAM). Users can start from existing mask, topography, or bathymetry data or can build a "world" entirely from scratch (e.g. a single island continent). Once a case has been started, users can modify mask, vegetation, bathymetry, topography, and river flow fields by drawing new data through a "paint" interface. Users activate a synchronization button which goes through the fields to eliminate inconsistencies. When the changes are complete and save is selected, Slarti creates all the necessary files for an initial run of FOAM. The data is edited at the highest resolution (the ocean-land surface in FOAM) and then interpolated to the atmosphere resolution. Slarti was implemented in Java to maintain portability across platforms. We also relied heavily on Java Swing components to create the interface. This allowed us to create an object-oriented interface that could be used on many different systems. Since Slarti allows users to visualize their changes, they are able to see areas that may cause problems when the model is ran. Some examples would be lakes from the river flow field and narrow trenches within the bathymetry. Through different checks and options available through its interface, Slarti makes the process of creating new boundary conditions for FOAM easier and faster while reducing the chance for user errors.

  9. Validation of Boundary Conditions for CFD Simulations on Ventilated Rooms

    DEFF Research Database (Denmark)

    Topp, Claus; Jensen, Rasmus Lund; Pedersen, D.N.

    2001-01-01

    The application of Computational Fluid Dynamics (CFD) for ventilation research and design of ventilation systems has increased during the recent years. This paper provides an investigation of direct description of boundary conditions for a complex inlet diffuser and a heated surface. A series of ...... diffuser showed good agreement with the experimentally obtained results although differences were observed in the flow far from the inlet. None of the investigated models of the heated surface did provide satisfactory results....

  10. New boundary conditions for oil reservoirs with fracture

    Science.gov (United States)

    Andriyanova, Elena; Astafev, Vladimir

    2017-06-01

    Based on the fact that most of oil fields are on the late stage of field development, it becomes necessary to produce hard-to-extract oil, which can be obtained only by use of enhance oil recovery methods. For example many low permeable or shale formations can be developed only with application of massive hydraulic fracturing technique. In addition, modern geophysical researches show that mostly oil bearing formations are complicated with tectonic faults of different shape and permeability. These discontinuities exert essential influence on the field development process and on the well performance. For the modeling of fluid flow in the reservoir with some area of different permeability, we should determine the boundary conditions. In this article for the first time the boundary conditions for the problem of fluid filtration in the reservoir with some discontinuity are considered. This discontinuity represents thin but long area, which can be hydraulic fracturing of tectonic fault. The obtained boundary condition equations allow us to take into account pressure difference above and below the section and different values of permeability.

  11. Electromagnetic transitions between states satisfying free-boundary conditions

    International Nuclear Information System (INIS)

    Nikolopoulos, L. A. A.

    2006-01-01

    We address the problem of calculating electromagnetic transition matrix elements between states of a particle in spherically symmetrical potentials with no assumed boundary conditions at finite distance (free-boundary-condition method). For this, the Schroedinger equation is solved in a finite box of radius R and bound and continuum states, appropriately normalized, are numerically represented, through a variational finite-basis-set (B-spline) approach. The equivalence between the three transition operator forms (length, velocity, acceleration), within this approach, is discussed, and bound-continuum and continuum-continuum matrix elements are calculated in all three gauges. Results for the strong electromagnetic radiation of hydrogen are presented through the calculation of two-photon ionization cross sections and photoelectron angular distributions. It is demonstrated that the present approach is well suited for the calculation of multiphoton transitions when ionization in the continuum is allowed (above-threshold ionization). With the free-boundary-condition method complete control over the density of scattering states is feasible and, as the result of that, the degeneracy in the continuum between partial waves is preserved

  12. Hydromagnetic natural convection flow between vertical parallel plates with time-periodic boundary conditions

    International Nuclear Information System (INIS)

    Adesanya, S.O.; Oluwadare, E.O.; Falade, J.A.; Makinde, O.D.

    2015-01-01

    In this paper, the free convective flow of magnetohydrodynamic fluid through a channel with time periodic boundary condition is investigated by taking the effects of Joule dissipation into consideration. Based on simplifying assumptions, the coupled governing equations are reduced to a set of nonlinear boundary valued problem. Approximate solutions are obtained by using semi-analytical Adomian decomposition method. The effect of pertinent parameters on the fluid velocity, temperature distribution, Nusselt number and skin friction are presented graphically and discussed. The result of the computation shows that an increase in the magnetic field intensity has significant influence on the fluid flow. - Highlights: • The influence of magnetic field on the free convective fluid flow is considered. • The coupled equations are solved by using Adomian decomposition method. • The Adomian series solution agreed with previously obtained result. • Magnetic field decreases the velocity maximum but enhances temperature field

  13. Adaptive nonlinear polynomial neural networks for control of boundary layer/structural interaction

    Science.gov (United States)

    Parker, B. Eugene, Jr.; Cellucci, Richard L.; Abbott, Dean W.; Barron, Roger L.; Jordan, Paul R., III; Poor, H. Vincent

    1993-01-01

    The acoustic pressures developed in a boundary layer can interact with an aircraft panel to induce significant vibration in the panel. Such vibration is undesirable due to the aerodynamic drag and structure-borne cabin noises that result. The overall objective of this work is to develop effective and practical feedback control strategies for actively reducing this flow-induced structural vibration. This report describes the results of initial evaluations using polynomial, neural network-based, feedback control to reduce flow induced vibration in aircraft panels due to turbulent boundary layer/structural interaction. Computer simulations are used to develop and analyze feedback control strategies to reduce vibration in a beam as a first step. The key differences between this work and that going on elsewhere are as follows: that turbulent and transitional boundary layers represent broadband excitation and thus present a more complex stochastic control scenario than that of narrow band (e.g., laminar boundary layer) excitation; and secondly, that the proposed controller structures are adaptive nonlinear infinite impulse response (IIR) polynomial neural network, as opposed to the traditional adaptive linear finite impulse response (FIR) filters used in most studies to date. The controllers implemented in this study achieved vibration attenuation of 27 to 60 dB depending on the type of boundary layer established by laminar, turbulent, and intermittent laminar-to-turbulent transitional flows. Application of multi-input, multi-output, adaptive, nonlinear feedback control of vibration in aircraft panels based on polynomial neural networks appears to be feasible today. Plans are outlined for Phase 2 of this study, which will include extending the theoretical investigation conducted in Phase 2 and verifying the results in a series of laboratory experiments involving both bum and plate models.

  14. Supersymmetric Boundary Conditions in mathcal{N}=4 Super Yang-Mills Theory

    Science.gov (United States)

    Gaiotto, Davide; Witten, Edward

    2009-06-01

    We study boundary conditions in {N}=4 super Yang-Mills theory that preserve one-half the supersymmetry. The obvious Dirichlet boundary conditions can be modified to allow some of the scalar fields to have a "pole" at the boundary. The obvious Neumann boundary conditions can be modified by coupling to additional fields supported at the boundary. The obvious boundary conditions associated with orientifolds can also be generalized. In preparation for a separate study of how electric-magnetic duality acts on these boundary conditions, we explore moduli spaces of solutions of Nahm's equations that appear in the presence of a boundary. Though our main interest is in boundary conditions that are Lorentz-invariant (to the extent possible in the presence of a boundary), we also explore non-Lorentz-invariant but half-BPS deformations of Neumann boundary conditions. We make preliminary comments on the action of electric-magnetic duality, deferring a more serious study to a later paper.

  15. High Energy Boundary Conditions for a Cartesian Mesh Euler Solver

    Science.gov (United States)

    Pandya, Shishir A.; Murman, Scott M.; Aftosmis, Michael J.

    2004-01-01

    Inlets and exhaust nozzles are often omitted or fared over in aerodynamic simulations of aircraft due to the complexities involving in the modeling of engine details such as complex geometry and flow physics. However, the assumption is often improper as inlet or plume flows have a substantial effect on vehicle aerodynamics. A tool for specifying inlet and exhaust plume conditions through the use of high-energy boundary conditions in an established inviscid flow solver is presented. The effects of the plume on the flow fields near the inlet and plume are discussed.

  16. Nonlinear Dynamics of the Nearshore Boundary Layer of a Large Lake (Lake Geneva)

    Science.gov (United States)

    Cimatoribus, Andrea A.; Lemmin, U.; Bouffard, D.; Barry, D. A.

    2018-02-01

    We examine nearshore and pelagic current variability in Lake Geneva, a large and deep lake in western Europe, using observations from several measurement locations and a three-dimensional numerical model for the period 2014-2016. Linear internal seiche modes excited by wind forcing clearly appear as peaks in the energy spectra for measurements in offshore locations. In contrast, spectra from the nearshore data, where currents interact with the lake bed, reveal a negligible contribution of internal seiches to the total kinetic energy. A similar contrast is seen in the spectra obtained from the numerical model at the same locations. Comparing the contribution of the different terms in the vertically averaged momentum equation from the modeling results shows that the nonlinear advective term dominates in the nearshore boundary layer. Its contribution decays with distance from shore. The width of this nearshore boundary layer, which may extend for several kilometers, seems to be mainly determined by local topography. Both field measurements and modeling results indicate that nonlinear dynamics are of primary importance in the nearshore boundary layer.

  17. Boundary layer flow and heat transfer to Carreau fluid over a nonlinear stretching sheet

    Directory of Open Access Journals (Sweden)

    Masood Khan

    2015-10-01

    Full Text Available This article studies the Carreau viscosity model (which is a generalized Newtonian model and then use it to obtain a formulation for the boundary layer equations of the Carreau fluid. The boundary layer flow and heat transfer to a Carreau model over a nonlinear stretching surface is discussed. The Carreau model, adequate for many non-Newtonian fluids, is used to characterize the behavior of the fluids having shear thinning properties and fluids with shear thickening properties for numerical values of the power law exponent n. The modeled boundary layer conservation equations are converted to non-linear coupled ordinary differential equations by a suitable transformation. Numerical solution of the resulting equations are obtained by using the Runge-Kutta Fehlberg method along with shooting technique. This analysis reveals many important physical aspects of flow and heat transfer. Computations are performed for different values of the stretching parameter (m, the Weissenberg number (We and the Prandtl number (Pr. The obtained results show that for shear thinning fluid the fluid velocity is depressed by the Weissenberg number while opposite behavior for the shear thickening fluid is observed. A comparison with previously published data in limiting cases is performed and they are in excellent agreement.

  18. Repulsive Casimir force from fractional Neumann boundary conditions

    International Nuclear Information System (INIS)

    Lim, S.C.; Teo, L.P.

    2009-01-01

    This Letter studies the finite temperature Casimir force acting on a rectangular piston associated with a massless fractional Klein-Gordon field at finite temperature. Dirichlet boundary conditions are imposed on the walls of a d-dimensional rectangular cavity, and a fractional Neumann condition is imposed on the piston that moves freely inside the cavity. The fractional Neumann condition gives an interpolation between the Dirichlet and Neumann conditions, where the Casimir force is known to be always attractive and always repulsive respectively. For the fractional Neumann boundary condition, the attractive or repulsive nature of the Casimir force is governed by the fractional order which takes values from zero (Dirichlet) to one (Neumann). When the fractional order is larger than 1/2, the Casimir force is always repulsive. For some fractional orders that are less than but close to 1/2, it is shown that the Casimir force can be either attractive or repulsive depending on the aspect ratio of the cavity and the temperature.

  19. Boundary conditions for Kerr-AdS perturbations

    Science.gov (United States)

    Dias, Óscar J. C.; Santos, Jorge E.

    2013-10-01

    The Teukolsky master equation and its associated spin-weighted spheroidal harmonic decomposition simplify considerably the study of linear gravitational perturbations of the Kerr(-AdS) black hole. However, the formulation of the problem is not complete before we assign the physically relevant boundary conditions. We find a set of two Robin boundary conditions (BCs) that must be imposed on the Teukolsky master variables to get perturbations that are asymptotically global AdS, i.e. that asymptotes to the Einstein Static Universe. In the context of the AdS/CFT correspondence, these BCs allow a non-zero expectation value for the CFT stress-energy tensor while keeping fixed the boundary metric. When the rotation vanishes, we also find the gauge invariant differential map between the Teukolsky and the Kodama-Ishisbashi (Regge-Wheeler-Zerilli) formalisms. One of our Robin BCs maps to the scalar sector and the other to the vector sector of the Kodama-Ishisbashi decomposition. The Robin BCs on the Teukolsky variables will allow for a quantitative study of instability timescales and quasinormal mode spectrum of the Kerr-AdS black hole. As a warm-up for this programme, we use the Teukolsky formalism to recover the quasinormal mode spectrum of global AdS-Schwarzschild, complementing previous analysis in the literature.

  20. Allowed wavevectors under the application of incommensurate periodic boundary conditions

    International Nuclear Information System (INIS)

    Boykin, Timothy B; Kharche, Neerav; Klimeck, Gerhard

    2006-01-01

    While the energy bands of solids are often thought of as continuous functions of the wavevector, k, they are in fact discrete functions, due to the periodic boundary conditions applied over a finite number of primitive cells. The traditional approach enforces periodicity over a volume containing N i primitive unit cells along the direction of the primitive lattice vector a i . While this method yields a simple formula for the allowed k, it can be problematic computer programs for lattices such as face-centred cubic (FCC) where the boundary faces of the primitive cell are not orthogonal. The fact that k is discrete is of critical importance for supercell calculations since they include only a finite number of unit cells, which determines the number of wavevectors, and have a given geometry, which determines their spacing. Rectangular supercells, with the faces orthogonal to the Cartesian axes, are computationally simplest but are not commensurate with the FCC unit cell, so that the traditional approach for determining the allowed k-values is no longer useful. Here, we present a simple method for finding the allowed k-values when periodic boundary conditions are applied over a rectangular supercell, answering the question in both its practical and pedagogical aspects

  1. Electrostatics of solvated systems in periodic boundary conditions

    Science.gov (United States)

    Andreussi, Oliviero; Marzari, Nicola

    2014-12-01

    Continuum solvation methods can provide an accurate and inexpensive embedding of quantum simulations in liquid or complex dielectric environments. Notwithstanding a long history and manifold applications to isolated systems in open boundary conditions, their extension to materials simulations, typically entailing periodic boundary conditions, is very recent, and special care is needed to address correctly the electrostatic terms. We discuss here how periodic boundary corrections developed for systems in vacuum should be modified to take into account solvent effects, using as a general framework the self-consistent continuum solvation model developed within plane-wave density-functional theory [O. Andreussi et al., J. Chem. Phys. 136, 064102 (2012), 10.1063/1.3676407]. A comprehensive discussion of real- and reciprocal-space corrective approaches is presented, together with an assessment of their ability to remove electrostatic interactions between periodic replicas. Numerical results for zero- and two-dimensional charged systems highlight the effectiveness of the different suggestions, and underline the importance of a proper treatment of electrostatic interactions in first-principles studies of charged systems in solution.

  2. Boundary control of fluid flow through porous media

    DEFF Research Database (Denmark)

    Hasan, Agus; Foss, Bjarne; Sagatun, Svein Ivar

    2010-01-01

    The flow of fluids through porous media can be described by the Boussinesq’s equation with mixed boundary conditions; a Neumann’s boundary condition and a nonlinear boundary condition. The nonlinear boundary condition provides a means to control the fluid flow through porous media. In this paper...

  3. A damping boundary condition for atomistic-continuum coupling

    International Nuclear Information System (INIS)

    Zhang Jie; Tieu, Kiet; Michal, Guillaume; Zhu Hongtao; Zhang Liang; Su Lihong; Deng Guanyu; Wang Hui

    2017-01-01

    The minimization of spurious wave reflection is a challenge in multiscale coupling due to the difference of spatial resolution between atomistic and continuum regions. In this study, a new damping condition is presented for eliminating spurious wave reflection at the interface between atomistic and continuum regions. This damping method starts by a coarse–fine decomposition of the atomic velocity based on the bridging scale method. The fine scale velocity of the atoms in the damping region is reduced by applying nonlinear damping coefficients. The effectiveness of this damping method is verified by one- and two- dimensional simulations. (paper)

  4. Modeling granular materials as compressible nonlinear fluids: Heat transfer boundary value problems

    Directory of Open Access Journals (Sweden)

    Mehrdad Massoudi

    2006-01-01

    Full Text Available We discuss three boundary value problems in the flow and heat transfer analysis in flowing granular materials: (i the flow down an inclined plane with radiation effects at the free surface; (ii the natural convection flow between two heated vertical walls; (iii the shearing motion between two horizontal flat plates with heat conduction. It is assumed that the material behaves like a continuum, similar to a compressible nonlinear fluid where the effects of density gradients are incorporated in the stress tensor. For a fully developed flow the equations are simplified to a system of three nonlinear ordinary differential equations. The equations are made dimensionless and a parametric study is performed where the effects of various dimensionless numbers representing the effects of heat conduction, viscous dissipation, radiation, and so forth are presented.

  5. Linear and nonlinear dynamic analysis by boundary element method. Ph.D. Thesis, 1986 Final Report

    Science.gov (United States)

    Ahmad, Shahid

    1991-01-01

    An advanced implementation of the direct boundary element method (BEM) applicable to free-vibration, periodic (steady-state) vibration and linear and nonlinear transient dynamic problems involving two and three-dimensional isotropic solids of arbitrary shape is presented. Interior, exterior, and half-space problems can all be solved by the present formulation. For the free-vibration analysis, a new real variable BEM formulation is presented which solves the free-vibration problem in the form of algebraic equations (formed from the static kernels) and needs only surface discretization. In the area of time-domain transient analysis, the BEM is well suited because it gives an implicit formulation. Although the integral formulations are elegant, because of the complexity of the formulation it has never been implemented in exact form. In the present work, linear and nonlinear time domain transient analysis for three-dimensional solids has been implemented in a general and complete manner. The formulation and implementation of the nonlinear, transient, dynamic analysis presented here is the first ever in the field of boundary element analysis. Almost all the existing formulation of BEM in dynamics use the constant variation of the variables in space and time which is very unrealistic for engineering problems and, in some cases, it leads to unacceptably inaccurate results. In the present work, linear and quadratic isoparametric boundary elements are used for discretization of geometry and functional variations in space. In addition, higher order variations in time are used. These methods of analysis are applicable to piecewise-homogeneous materials, such that not only problems of the layered media and the soil-structure interaction can be analyzed but also a large problem can be solved by the usual sub-structuring technique. The analyses have been incorporated in a versatile, general-purpose computer program. Some numerical problems are solved and, through comparisons

  6. Variational Iteration Method for Nonlinear Singular Two-Point Boundary Value Problems Arising in Human Physiology

    Directory of Open Access Journals (Sweden)

    Marwan Abukhaled

    2013-01-01

    Full Text Available The variational iteration method is applied to solve a class of nonlinear singular boundary value problems that arise in physiology. The process of the method, which produces solutions in terms of convergent series, is explained. The Lagrange multipliers needed to construct the correctional functional are found in terms of the exponential integral and Whittaker functions. The method easily overcomes the obstacle of singularities. Examples will be presented to test the method and compare it to other existing methods in order to confirm fast convergence and significant accuracy.

  7. Inlet and outlet boundary conditions for the discrete velocity direction model

    Science.gov (United States)

    Zhang, Zhenyu; Zhao, Wei; Zhao, Qingjun; Lu, Guojing; Xu, Jianzhong

    2018-02-01

    The discrete velocity direction model is an approximate method to the Boltzmann equation, which is an optional kinetic method to microgas flow and heat transfer. In this paper, the treatment of the inlet and outlet boundary conditions for the model is proposed. In the computation strategy, the microscopic molecular speed distribution functions at inlet and outlet are indirectly determined by the macroscopic gas pressure, mass flux and temperature, which are all measurable parameters in microgas flow and heat transfer. The discrete velocity direction model with the pressure correction boundary conditions was applied into the plane Poiseuille flow in microscales and the calculations cover all flow regimes. The numerical results agree well with the data of the NS equation near the continuum regime and the date of linearized Boltzmann equation and the DSMC method in the transition regime and free molecular flow. The Knudsen paradox and the nonlinear pressure distributions have been accurately captured by the discrete velocity direction model with the present boundary conditions.

  8. Mathematical and numerical study of nonlinear boundary problems related to plasma physics

    International Nuclear Information System (INIS)

    Sermange, M.

    1982-06-01

    After the study of some equations based on the Hodgkin-Huxley model, the work presented here is concerned with nonlinear boundary problems in MHD. They are gathered in two subjects: equilibrium equations and stability equations. The axisymmetric MHD equilibrium equations with free boundary have been studied by different authors, particularly the existence, regularity, unicity and non-unicity. Here, bifurcation, convergence of calculation methods existence of solutions in a discontinuous frame are studied. MHD stability can be determined by the principle of Bernstein et al; the mathematical work concerned here bears on the equivalence, in the case of two-dimensional or axisymmetric stability, between this model and a scalar eigenvalue problem which is introduced. At last, modules for computing MHD equilibrium for the simulation of plasma confinement in a tokamak are described [fr

  9. Investigating effects of boundary conditions on the evaluation of R-factor of un-braced steel frames

    Directory of Open Access Journals (Sweden)

    Masood M.M. Irheem

    2017-08-01

    Full Text Available Design of Structures to resist seismic load depends on the theory of dissipation in elastic of energy that already exists in response modification factor “R-factor”. The main problem in codes gives a constant value for R-factor, since change in boundary conditions of building change in behavior of steel frame structures and that effect on R-factor. This study is an attempt to assess overstrength, ductility and response modification factor of un-braced steel frames under change in boundary conditions as change in the direction of strong axis of column and support type beside to variation in story and bay number to be 9 frame and each frame has 8 different boundary conditions as sum of 72 case for analysis. These frames were analyzed by using nonlinear static “pushover” analysis using SAP2000 program. As a result of this study R-factor does not has a constant value, when change in boundary conditions R-factor directly changes, minimum value of 8 boundary conditions is close to the code value that is mean the code is more conservative and give a large factor of safety. Ductility reduction factor increases with increasing number of story for all boundary conditions, but overstrength has different rule. Response modification factor, overstrength factor and ductility reduction factor decrease when fundamentals period increasing for the studied frames.

  10. Threshold condition for nonlinear tearing modes in tokamaks

    International Nuclear Information System (INIS)

    Zabiego, M.F.; Callen, J.D.

    1996-03-01

    Low-mode-number tearing, mode nonlinear evolution is analyzed emphasizing the need for a threshold condition, to account for observations in tokamaks. The discussion is illustrated by two models recently introduced in the literature. The models can be compared with the available data and/or serve as a basis for planning some experiments in order to either test theory (by means of beta-limit scaling laws, as proposed in this paper) or attempt to control undesirable tearing modes. Introducing a threshold condition in the tearing mode stability analysis is found to reveal some bifurcation points and thus domains of intrinsic stability in the island dynamics operational space

  11. Time-dependent density functional theory with twist-averaged boundary conditions

    Science.gov (United States)

    Schuetrumpf, B.; Nazarewicz, W.; Reinhard, P.-G.

    2016-05-01

    Background: Time-dependent density functional theory is widely used to describe excitations of many-fermion systems. In its many applications, three-dimensional (3D) coordinate-space representation is used, and infinite-domain calculations are limited to a finite volume represented by a spatial box. For finite quantum systems (atoms, molecules, nuclei, hadrons), the commonly used periodic or reflecting boundary conditions introduce spurious quantization of the continuum states and artificial reflections from boundary; hence, an incorrect treatment of evaporated particles. Purpose: The finite-volume artifacts for finite systems can be practically cured by invoking an absorbing potential in a certain boundary region sufficiently far from the described system. However, such absorption cannot be applied in the calculations of infinite matter (crystal electrons, quantum fluids, neutron star crust), which suffer from unphysical effects stemming from a finite computational box used. Here, twist-averaged boundary conditions (TABC) have been used successfully to diminish the finite-volume effects. In this work, we extend TABC to time-dependent modes. Method: We use the 3D time-dependent density functional framework with the Skyrme energy density functional. The practical calculations are carried out for small- and large-amplitude electric dipole and quadrupole oscillations of 16O. We apply and compare three kinds of boundary conditions: periodic, absorbing, and twist-averaged. Results: Calculations employing absorbing boundary conditions (ABC) and TABC are superior to those based on periodic boundary conditions. For low-energy excitations, TABC and ABC variants yield very similar results. With only four twist phases per spatial direction in TABC, one obtains an excellent reduction of spurious fluctuations. In the nonlinear regime, one has to deal with evaporated particles. In TABC, the floating nucleon gas remains in the box; the amount of nucleons in the gas is found to be

  12. Bayesian Inference for Linear Parabolic PDEs with Noisy Boundary Conditions

    KAUST Repository

    Ruggeri, Fabrizio

    2016-01-06

    In this work we develop a hierarchical Bayesian setting to infer unknown parameters in initial-boundary value problems (IBVPs) for one-dimensional linear parabolic partial differential equations. Noisy boundary data and known initial condition are assumed. We derive the likelihood function associated with the forward problem, given some measurements of the solution field subject to Gaussian noise. Such function is then analytically marginalized using the linearity of the equation. Gaussian priors have been assumed for the time-dependent Dirichlet boundary values. Our approach is applied to synthetic data for the one-dimensional heat equation model, where the thermal diffusivity is the unknown parameter. We show how to infer the thermal diffusivity parameter when its prior distribution is lognormal or modeled by means of a space-dependent stationary lognormal random field. We use the Laplace method to provide approximated Gaussian posterior distributions for the thermal diffusivity. Expected information gains and predictive posterior densities for observable quantities are numerically estimated for different experimental setups.

  13. Bayesian Inference for Linear Parabolic PDEs with Noisy Boundary Conditions

    KAUST Repository

    Ruggeri, Fabrizio

    2015-01-07

    In this work we develop a hierarchical Bayesian setting to infer unknown parameters in initial-boundary value problems (IBVPs) for one-dimensional linear parabolic partial differential equations. Noisy boundary data and known initial condition are assumed. We derive the likelihood function associated with the forward problem, given some measurements of the solution field subject to Gaussian noise. Such function is then analytically marginalized using the linearity of the equation. Gaussian priors have been assumed for the time-dependent Dirichlet boundary values. Our approach is applied to synthetic data for the one-dimensional heat equation model, where the thermal diffusivity is the unknown parameter. We show how to infer the thermal diffusivity parameter when its prior distribution is lognormal or modeled by means of a space-dependent stationary lognormal random field. We use the Laplace method to provide approximated Gaussian posterior distributions for the thermal diffusivity. Expected information gains and predictive posterior densities for observable quantities are numerically estimated for different experimental setups.

  14. Outcome of homogeneous and heterogeneous reactions in Darcy-Forchheimer flow with nonlinear thermal radiation and convective condition

    Science.gov (United States)

    Hayat, T.; Shah, Faisal; Alsaedi, A.; Hussain, Zakir

    The present analysis aims to report the consequences of nonlinear radiation, convective condition and heterogeneous-homogeneous reactions in Darcy-Forchheimer flow over a non-linear stretching sheet with variable thickness. Non-uniform magnetic field and nonuniform heat generation/absorption are accounted. The governing boundary layer partial differential equations are converted into a system of nonlinear ordinary differential equations. The computations are organized and the effects of physical variables such as thickness parameter, power index, Hartman number, inertia and porous parameters, radiation parameter, Biot number, Prandtl number, ratio parameter, heat generation parameter and homogeneous-heterogeneous reaction parameter are investigated. The variations of skin friction coefficient and Nusselt number for different interesting variables are plotted and discussed. It is noticed that Biot number and heat generation variable lead to enhance the temperature distribution. The solutal boundary layer thickness decreases for larger homogeneous variable while reverse trend is seen for heterogeneous reaction.

  15. Evolution of passive movement in advective environments: General boundary condition

    Science.gov (United States)

    Zhou, Peng; Zhao, Xiao-Qiang

    2018-03-01

    In a previous work [16], Lou et al. studied a Lotka-Volterra competition-diffusion-advection system, where two species are supposed to differ only in their advection rates and the environment is assumed to be spatially homogeneous and closed (no-flux boundary condition), and showed that weaker advective movements are more beneficial for species to win the competition. In this paper, we aim to extend this result to a more general situation, where the environmental heterogeneity is taken into account and the boundary condition at the downstream end becomes very flexible including the standard Dirichlet, Neumann and Robin type conditions as special cases. Our main approaches are to exclude the existence of co-existence (positive) steady state and to provide a clear picture on the stability of semi-trivial steady states, where we introduced new ideas and techniques to overcome the emerging difficulties. Based on these two aspects and the theory of abstract competitive systems, we achieve a complete understanding on the global dynamics.

  16. Boundary conditions for soft glassy flows: slippage and surface fluidization.

    Science.gov (United States)

    Mansard, Vincent; Bocquet, Lydéric; Colin, Annie

    2014-09-28

    We explore the question of surface boundary conditions for the flow of a dense emulsion. We make use of microlithographic tools to create surfaces with well controlled roughness patterns and measure using dynamic confocal microscopy both the slip velocity and the shear rate close to the wall, which we relate to the notion of surface fluidization. Both slippage and wall fluidization depend non-monotonously on the roughness. We interpret this behavior within a simple model in terms of the building of a stratified layer and the activation of plastic events by the surface roughness.

  17. Thermal properties of nuclear matter under the periodic boundary condition

    International Nuclear Information System (INIS)

    Otuka, Naohiko; Ohnishi, Akira

    1999-01-01

    We present the thermal properties of nuclear matter under the periodic boundary condition by the use of our hadronic nucleus-nucleus cascade model (HANDEL) which is developed to treat relativistic heavy-ion collisions from BNL-AGS to CERN-SPS. We first show some results of p-p scattering calculation in our new version which is improved in order to treat isospin ratio and multiplicity more accurately. We then display the results of calculation of nuclear matter with baryon density ρ b = 0.77 fm 3 at some energy densities. Time evolution of particle abundance and temperature are shown. (author)

  18. Validation of Boundary Conditions for CFD Simulations on Ventilated Rooms

    DEFF Research Database (Denmark)

    Topp, Claus; Jensen, Rasmus Lund; Pedersen, D.N.

    2001-01-01

    The application of Computational Fluid Dynamics (CFD) for ventilation research and design of ventilation systems has increased during the recent years. This paper provides an investigation of direct description of boundary conditions for a complex inlet diffuser and a heated surface. A series...... of full-scale experiments in a room ventilated by the mixing principle have been performed for validation of the models. The experimental results include measurements of temperature as well as measurements of velocity and turbulence by Laser Doppler Anemometry (LDA). A simple model of the complex inlet...

  19. The Casimir effect for pistons with transmittal boundary conditions

    Science.gov (United States)

    Fucci, Guglielmo

    2017-11-01

    This work focuses on the analysis of the Casimir effect for pistons subject to transmittal boundary conditions. In particular we consider, as piston configuration, a direct product manifold of the type I × N where I is a closed interval of the real line and N is a smooth compact Riemannian manifold. By utilizing the spectral zeta function regularization technique, we compute the Casimir energy of the system and the Casimir force acting on the piston. Explicit results for the force are provided when the manifold N is a d-dimensional sphere.

  20. Magnetospheric conditions near the equatorial footpoints of proton isotropy boundaries

    Directory of Open Access Journals (Sweden)

    V. A. Sergeev

    2015-12-01

    Full Text Available Data from a cluster of three THEMIS (Time History of Events and Macroscale Interactions during Substorms spacecraft during February–March 2009 frequently provide an opportunity to construct local data-adaptive magnetospheric models, which are suitable for the accurate mapping along the magnetic field lines at distances of 6–9 Re in the nightside magnetosphere. This allows us to map the isotropy boundaries (IBs of 30 and 80 keV protons observed by low-altitude NOAA POES (Polar Orbiting Environmental Satellites to the equatorial magnetosphere (to find the projected isotropy boundary, PIB and study the magnetospheric conditions, particularly to evaluate the ratio KIB (Rc/rc; the magnetic field curvature radius to the particle gyroradius in the neutral sheet at that point. Special care is taken to control the factors which influence the accuracy of the adaptive models and mapping. Data indicate that better accuracy of an adaptive model is achieved when the PIB distance from the closest spacecraft is as small as 1–2 Re. For this group of most accurate predictions, the spread of KIB values is still large (from 4 to 32, with the median value KIB ~13 being larger than the critical value Kcr ~ 8 expected at the inner boundary of nonadiabatic angular scattering in the current sheet. It appears that two different mechanisms may contribute to form the isotropy boundary. The group with K ~ [4,12] is most likely formed by current sheet scattering, whereas the group having KIB ~ [12,32] could be formed by the resonant scattering of low-energy protons by the electromagnetic ion-cyclotron (EMIC waves. The energy dependence of the upper K limit and close proximity of the latter event to the plasmapause locations support this conclusion. We also discuss other reasons why the K ~ 8 criterion for isotropization may fail to work, as well as a possible relationship between the two scattering mechanisms.

  1. The effects of external conditions in turbulent boundary layers

    Science.gov (United States)

    Brzek, Brian G.

    The effects of multiple external conditions on turbulent boundary layers were studied in detail. These external conditions include: surface roughness, upstream turbulence intensity, and pressure gradient. Furthermore, the combined effects of these conditions show the complicated nature of many realistic flow conditions. It was found that the effects of surface roughness are difficult to generalize, given the importance of so many parameters. These parameters include: roughness geometry, roughness regime, roughness height to boundary layer thickness, (k/delta), roughness parameter, ( k+), Reynolds number, and roughness function (Delta B+). A further complication, is the difficulty in computing the wall shear stress, tauw/rho. For the sand grain type roughness, the mean velocity and Reynolds stresses were studied in inner and outer variables, as well as, boundary layer parameters, anisotropy tensor, production term, and viscous stress and form drag contributions. To explore the effects of roughness and Reynolds number dependence in the boundary layer, a new experiment was carefully designed to properly capture the x-dependence of the single-point statistics. It was found that roughness destroys the viscous layer near the wall, thus, reducing the contribution of the viscous stress in the wall region. As a result, the contribution in the skin friction due to form drag increases, while the viscous stress decreases. This yields Reynolds number invariance in the skin friction, near-wall roughness parameters, and inner velocity profiles as k + increases into the fully rough regime. However, in the transitionally rough regime, (i.e., 5 component shows the largest influence of roughness, where the high peak near the wall was decreased and became nearly flat for the fully rough regime profiles. In addition, the Reynolds stresses in outer variables show self-similarity for fixed experimental conditions. However, as the roughness parameter, k +, increases, all Reynolds stress

  2. Numerical study of magnetohydrodynamics (MHD boundary layer slip flow of a Maxwell nanofluid over an exponentially stretching surface with convective boundary condition

    Directory of Open Access Journals (Sweden)

    P.BalaAnki Reddy

    2017-12-01

    Full Text Available This paper focuses on a theoretical analysis of a steady two-dimensional magnetohydrodynamic boundary layer flow of a Maxwell fluid over an exponentially stretching surface in the presence of velocity slip and convective boundary condition. This model is used for a nanofluid, which incorporates the effects of Brownian motion and thermophoresis. The resulting non-linear partial differential equations of the governing flow field are converted into a system of coupled non-linear ordinary differential equations by using suitable similarity transformations, and the resultant equations are then solved numerically by using Runge-Kutta fourth order method along with shooting technique. A parametric study is conducted to illustrate the behavior of the velocity, temperature and concentration. The influence of significant parameters on velocity, temperature, concentration, skin friction coefficient and Nusselt number has been studied and numerical results are presented graphically and in tabular form. The reported numerical results are compared with previously published works on various special cases and are found to be an in excellent agreement. It is found that momentum boundary layer thickness decreases with the increase of magnetic parameter. It can also be found that the thermal boundary layer thickness increases with Brownian motion and thermophoresis parameters.

  3. Nonlinear observer-based Lyapunov boundary control of distributed heat transfer mechanisms for membrane distillation plant

    KAUST Repository

    Eleiwi, Fadi

    2016-09-19

    This paper presents a nonlinear observer-based Lyapunov control for a membrane distillation (MD) process. The control considers the inlet temperatures of the feed and the permeate solutions as inputs, transforming it to boundary control process, and seeks to maintain the temperature difference along the membrane boundaries around a sufficient level to promote water production. MD process is modeled with advection diffusion equation model in two dimensions, where the diffusion and convection heat transfer mechanisms are best described. Model analysis, effective order reduction and parameters physical interpretation, are provided. Moreover, a nonlinear observer has been designed to provide the control with estimates of the temperature evolution at each time instant. In addition, physical constraints are imposed on the control to have an acceptable range of feasible inputs, and consequently, better energy consumption. Numerical simulations for the complete process with real membrane parameter values are provided, in addition to detailed explanations for the role of the controller and the observer. (C) 2016 Elsevier Ltd. All rights reserved.

  4. Radiation Boundary Conditions for the Two-Dimensional Wave Equation from a Variational Principle

    NARCIS (Netherlands)

    Broeze, J.; Broeze, Jan; van Daalen, Edwin F.G.; van Daalen, E.F.G.

    1992-01-01

    A variational principle is used to derive a new radiation boundary condition for the two-dimensional wave equation. This boundary condition is obtained from an expression for the local energy flux velocity on the boundary in normal direction. The wellposedness of the wave equation with this boundary

  5. On nonlinear wave-structure interaction using an immersed boundary method in 2D

    DEFF Research Database (Denmark)

    Kontos, Stavros; Bingham, Harry B.; Lindberg, Ole

    2016-01-01

    . The structure geometry is introduced using an Immersed Boundary Method (IBM) and the body boundary condition (BC) is satisfied with a Weighted Least Squares (WLS) approximation [7]. This allows complex geometries to be represented with high accuracy. The stability of the scheme is ensured by adopting...... the Weighted Essentially Non-Oscillatory (WENO) scheme [8] together with a Lax-Friedrichs type flux applied to the free surface conditions in Hamilton-Jacobi form. This work can be viewed as a novel extension of the flexible order finite difference potential flow solver OceanWave3D [2] to include the presence...

  6. Twin Positive Solutions of a Nonlinear m-Point Boundary Value Problem for Third-Order p-Laplacian Dynamic Equations on Time Scales

    Directory of Open Access Journals (Sweden)

    Wei Han

    2008-01-01

    Full Text Available Several existence theorems of twin positive solutions are established for a nonlinear m-point boundary value problem of third-order p-Laplacian dynamic equations on time scales by using a fixed point theorem. We present two theorems and four corollaries which generalize the results of related literature. As an application, an example to demonstrate our results is given. The obtained conditions are different from some known results.

  7. Development of a Discrete Mass Inflow Boundary Condition for MFIX

    Directory of Open Access Journals (Sweden)

    Jordan Musser

    2011-02-01

    Full Text Available MFIX (Multiphase Flow with Interphase eXchanges is an open source software package developed by the National Energy Technology Laboratory (NETL used for modeling the chemical reactions, heat transfer, and hydrodynamics of fluid-solid systems. Currently, the stable publically available release of MFIX does not include a discrete mass inflow boundary condition (DMIBC for its discrete element method (DEM package. Inflow boundary conditions are useful for simulating systems where particles are consumed through chemical reactions and an incoming feed is necessary to sustain the reaction. To implement the DMIBC an inlet staging area is designated outside the computational domain and particles are passed through the wall region associated with the inlet. Forces incurred on entering particles, generated from collisions with particles already in the system, are ignored whereas, particles already in the system respond to contact forces and react accordingly, moving away from the inlet. This approach prevents any unphysical overlap between new and existing particles. It also ensures that particles entering the system will enter the computational domain regardless of opposing forces. Once an incoming particle is fully within the domain, it reacts appropriately to any and all contact force. This approach for a DMIBC has been implemented and is available within the current development version of MFIX.

  8. Nonlinear modeling of magnetorheological energy absorbers under impact conditions

    Science.gov (United States)

    Mao, Min; Hu, Wei; Choi, Young-Tai; Wereley, Norman M.; Browne, Alan L.; Ulicny, John; Johnson, Nancy

    2013-11-01

    Magnetorheological energy absorbers (MREAs) provide adaptive vibration and shock mitigation capabilities to accommodate varying payloads, vibration spectra, and shock pulses, as well as other environmental factors. A key performance metric is the dynamic range, which is defined as the ratio of the force at maximum field to the force in the absence of field. The off-state force is typically assumed to increase linearly with speed, but at the higher shaft speeds occurring in impact events, the off-state damping exhibits nonlinear velocity squared damping effects. To improve understanding of MREA behavior under high-speed impact conditions, this study focuses on nonlinear MREA models that can more accurately predict MREA dynamic behavior for nominal impact speeds of up to 6 m s-1. Three models were examined in this study. First, a nonlinear Bingham-plastic (BP) model incorporating Darcy friction and fluid inertia (Unsteady-BP) was formulated where the force is proportional to the velocity. Second, a Bingham-plastic model incorporating minor loss factors and fluid inertia (Unsteady-BPM) to better account for high-speed behavior was formulated. Third, a hydromechanical (HM) analysis was developed to account for fluid compressibility and inertia as well as minor loss factors. These models were validated using drop test data obtained using the drop tower facility at GM R&D Center for nominal drop speeds of up to 6 m s-1.

  9. Nonlinear modeling of magnetorheological energy absorbers under impact conditions

    International Nuclear Information System (INIS)

    Mao, Min; Hu, Wei; Choi, Young-Tai; Wereley, Norman M; Browne, Alan L; Ulicny, John; Johnson, Nancy

    2013-01-01

    Magnetorheological energy absorbers (MREAs) provide adaptive vibration and shock mitigation capabilities to accommodate varying payloads, vibration spectra, and shock pulses, as well as other environmental factors. A key performance metric is the dynamic range, which is defined as the ratio of the force at maximum field to the force in the absence of field. The off-state force is typically assumed to increase linearly with speed, but at the higher shaft speeds occurring in impact events, the off-state damping exhibits nonlinear velocity squared damping effects. To improve understanding of MREA behavior under high-speed impact conditions, this study focuses on nonlinear MREA models that can more accurately predict MREA dynamic behavior for nominal impact speeds of up to 6 m s −1 . Three models were examined in this study. First, a nonlinear Bingham-plastic (BP) model incorporating Darcy friction and fluid inertia (Unsteady-BP) was formulated where the force is proportional to the velocity. Second, a Bingham-plastic model incorporating minor loss factors and fluid inertia (Unsteady-BPM) to better account for high-speed behavior was formulated. Third, a hydromechanical (HM) analysis was developed to account for fluid compressibility and inertia as well as minor loss factors. These models were validated using drop test data obtained using the drop tower facility at GM R and D Center for nominal drop speeds of up to 6 m s −1 . (paper)

  10. Spectral boundary conditions and solitonic solutions in a classical Sellmeier dielectric

    Energy Technology Data Exchange (ETDEWEB)

    Belgiorno, F. [Politecnico di Milano, Dipartimento di Matematica, Milan (Italy); INdAM-GNFM, Rome (Italy); INFN, Milan (Italy); Cacciatori, S.L. [Universita dell' Insubria, Department of Science and High Technology, Como (Italy); INFN, Milan (Italy); Vigano, A. [Universita degli Studi di Milano, Dipartimento di Fisica, Milan (Italy)

    2017-06-15

    Electromagnetic field interactions in a dielectric medium represent a longstanding field of investigation, both at the classical level and at the quantum one. We propose a 1+1 dimensional toy-model which consists of an half-line filling dielectric medium, with the aim to set up a simplified situation where technicalities related to gauge invariance and, as a consequence, physics of constrained systems are avoided, and still interesting features appear. In particular, we simulate the electromagnetic field and the polarization field by means of two coupled scalar fields φ, ψ, respectively, in a Hopfield-like model. We find that, in order to obtain a physically meaningful behavior for the model, one has to introduce spectral boundary conditions depending on the particle spectrum one is dealing with. This is the first interesting achievement of our analysis. The second relevant achievement is that, by introducing a nonlinear contribution in the polarization field ψ, with the aim of mimicking a third order nonlinearity in a nonlinear dielectric, we obtain solitonic solutions in the Hopfield model framework, whose classical behavior is analyzed too. (orig.)

  11. Space-dependent core/reflector boundary conditions generated by the boundary element method for pressurized water reactors

    International Nuclear Information System (INIS)

    Itagaki, M.; Brebbia, C.A.

    1991-01-01

    This paper reports on the boundary element method used to generate energy-dependent matrix-type boundary conditions along core/reflector interfaces and along baffle-plate surfaces of pressurized water reactors. This method enables one to deal with all types of boundary geometries including convex and concave corners. The method is applicable to neutron diffusion problems with more than two energy groups and also can be used to model a reflector with or without a baffle plate. Excellent eigenvalue and flux shape results can be obtained when the boundary conditions generated by this technique are coupled with core-only finite difference calculations

  12. On non-linear boundary value problems and parametrisation at multiple nodes

    Czech Academy of Sciences Publication Activity Database

    Rontó, András; Rontó, M.; Varha, J.

    2016-01-01

    Roč. 2016, Č. 80 (2016), s. 1-18 ISSN 1417-3875 Institutional support: RVO:67985840 Keywords : non-local boundary conditions * parametrisation * successive approximations * interval division Subject RIV: BA - General Math ematics Impact factor: 0.926, year: 2016 http://www. math .u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=5302

  13. Eigenvalue Problems for Systems of Nonlinear Boundary Value Problems on Time Scales

    Directory of Open Access Journals (Sweden)

    Henderson J

    2007-01-01

    Full Text Available Values of λ are determined for which there exist positive solutions of the system of dynamic equations, , , for , satisfying the boundary conditions, , where is a time scale. A Guo-Krasnosel'skii fixed point-theorem is applied.

  14. Influence of Spanwise Boundary Conditions on Slat Noise Simulations

    Science.gov (United States)

    Lockard, David P.; Choudhari, Meelan M.; Buning, Pieter G.

    2015-01-01

    The slat noise from the 30P/30N high-lift system is being investigated through computational fluid dynamics simulations with the OVERFLOW code in conjunction with a Ffowcs Williams-Hawkings acoustics solver. In the present study, two different spanwise grids are being used to investigate the effect of the spanwise extent and periodicity on the near-field unsteady structures and radiated noise. The baseline grid with periodic boundary conditions has a short span equal to 1/9th of the stowed chord, whereas the other, longer span grid adds stretched grids on both sides of the core, baseline grid to allow inviscid surface boundary conditions at both ends. The results indicate that the near-field mean statistics obtained using the two grids are similar to each other, as are the directivity and spectral shapes of the radiated noise. However, periodicity forces all acoustic waves with less than one wavelength across the span to be two-dimensional, without any variation in the span. The spanwise coherence of the acoustic waves is what is needed to make estimates of the noise that would be radiated from realistic span lengths. Simulations with periodic conditions need spans of at least six slat chords to allow spanwise variation in the low-frequencies associated with the peak of broadband slat noise. Even then, the full influence of the periodicity is unclear, so employing grids with a fine, central region and highly stretched meshes that go to slip walls may be a more efficient means of capturing the spanwise decorrelation of low-frequency acoustic phenomena.

  15. Theory of a curved planar waveguide with Robin boundary conditions.

    Science.gov (United States)

    Olendski, O; Mikhailovska, L

    2010-03-01

    A model of a thin straight strip with a uniformly curved section and with boundary requirements zeroing at the edges a linear superposition of the wave function and its normal derivative (Robin boundary condition) is analyzed theoretically within the framework of the linear Schrödinger equation and is applied to the study of the processes in the bent magnetic multilayers, superconducting films and metallic ferrite-filled waveguides. In particular, subband thresholds of the straight and curved parts of the film are calculated and analyzed as a function of the Robin parameter 1/Lambda , with Lambda being an extrapolation length entering Robin boundary condition. For the arbitrary Robin coefficients which are equal on the opposite interfaces of the strip and for all bend parameters the lowest-mode energy of the continuously curved duct is always smaller than its straight counterpart. Accordingly, the bound state below the fundamental propagation threshold of the straight arms always exists as a result of the bend. In terms of the superconductivity language it means an increased critical temperature of the curved film compared to its straight counterpart. Localized-level dependence on the parameters of the curve is investigated with its energy decreasing with increasing bend angle and decreasing bend radius. Conditions of the bound-state existence for the different Robin parameters on the opposite edges are analyzed too; in particular, it is shown that the bound state below the first transverse threshold of the straight arm always exists if the inner extrapolation length is not larger than the outer one. In the opposite case there is a range of the bend parameters where the curved film cannot trap the wave and form the localized mode; for example, for the fixed bend radius the bound state emerges from the continuum at some nonzero bend angle that depends on the difference of the two lengths Lambda at the opposite interfaces. Various transport properties of the film

  16. Homogenization of the stochastic Navier–Stokes equation with a stochastic slip boundary condition

    KAUST Repository

    Bessaih, Hakima

    2015-11-02

    The two-dimensional Navier–Stokes equation in a perforated domain with a dynamical slip boundary condition is considered. We assume that the dynamic is driven by a stochastic perturbation on the interior of the domain and another stochastic perturbation on the boundaries of the holes. We consider a scaling (ᵋ for the viscosity and 1 for the density) that will lead to a time-dependent limit problem. However, the noncritical scaling (ᵋ, β > 1) is considered in front of the nonlinear term. The homogenized system in the limit is obtained as a Darcy’s law with memory with two permeabilities and an extra term that is due to the stochastic perturbation on the boundary of the holes. The nonhomogeneity on the boundary contains a stochastic part that yields in the limit an additional term in the Darcy’s law. We use the two-scale convergence method after extending the solution with 0 inside the holes to pass to the limit. By Itô stochastic calculus, we get uniform estimates on the solution in appropriate spaces. Due to the stochastic integral, the pressure that appears in the variational formulation does not have enough regularity in time. This fact made us rely only on the variational formulation for the passage to the limit on the solution. We obtain a variational formulation for the limit that is solution of a Stokes system with two pressures. This two-scale limit gives rise to three cell problems, two of them give the permeabilities while the third one gives an extra term in the Darcy’s law due to the stochastic perturbation on the boundary of the holes.

  17. Homogenized boundary conditions and resonance effects in Faraday cages

    Science.gov (United States)

    Hewitt, I. J.

    2016-01-01

    We present a mathematical study of two-dimensional electrostatic and electromagnetic shielding by a cage of conducting wires (the so-called ‘Faraday cage effect’). Taking the limit as the number of wires in the cage tends to infinity, we use the asymptotic method of multiple scales to derive continuum models for the shielding, involving homogenized boundary conditions on an effective cage boundary. We show how the resulting models depend on key cage parameters such as the size and shape of the wires, and, in the electromagnetic case, on the frequency and polarization of the incident field. In the electromagnetic case, there are resonance effects, whereby at frequencies close to the natural frequencies of the equivalent solid shell, the presence of the cage actually amplifies the incident field, rather than shielding it. By appropriately modifying the continuum model, we calculate the modified resonant frequencies, and their associated peak amplitudes. We discuss applications to radiation containment in microwave ovens and acoustic scattering by perforated shells. PMID:27279775

  18. The exact solution to the one-dimensional Poisson–Boltzmann equation with asymmetric boundary conditions

    DEFF Research Database (Denmark)

    Johannessen, Kim

    2014-01-01

    The exact solution to the one-dimensional Poisson–Boltzmann equation with asymmetric boundary conditions can be expressed in terms of the Jacobi elliptic functions. The boundary conditions determine the modulus of the Jacobi elliptic functions. The boundary conditions can not be solved analytically...

  19. Vibration modes of a single plate with general boundary conditions

    Directory of Open Access Journals (Sweden)

    Phamová L.

    2016-06-01

    Full Text Available This paper deals with free flexural vibration modes and natural frequencies of a thin plate with general boundary conditions — a simply supported plate connected to its surroundings with torsional springs. Vibration modes were derived on the basis of the Rajalingham, Bhat and Xistris approach. This approach was originally used for a clamped thin plate, so its adaptation was needed. The plate vibration function was usually expressed as a single partial differential equation. This partial differential equation was transformed into two ordinary differential equations that can be solved in the simpler way. Theoretical background of the computations is briefly described. Vibration modes of the supported plate with torsional springs are presented graphically and numerically for three different values of stiffness of torsional springs.

  20. Atom-partitioned multipole expansions for electrostatic potential boundary conditions

    Energy Technology Data Exchange (ETDEWEB)

    Lee, M., E-mail: michael.s.lee131.civ@mail.mil [Simulation Sciences Branch, U.S. Army Research Laboratory, Aberdeen Proving Ground, MD 21005 (United States); Leiter, K. [Simulation Sciences Branch, U.S. Army Research Laboratory, Aberdeen Proving Ground, MD 21005 (United States); Eisner, C. [Secure Mission Solutions, a Parsons Company (United States); Simulation Sciences Branch, U.S. Army Research Laboratory, Aberdeen Proving Ground, MD 21005 (United States); Knap, J. [Simulation Sciences Branch, U.S. Army Research Laboratory, Aberdeen Proving Ground, MD 21005 (United States)

    2017-01-01

    Applications such as grid-based real-space density functional theory (DFT) use the Poisson equation to compute electrostatics. However, the expected long tail of the electrostatic potential requires either the use of a large and costly outer domain or Dirichlet boundary conditions estimated via multipole expansion. We find that the oft-used single-center spherical multipole expansion is only appropriate for isotropic mesh domains such as spheres and cubes. In this work, we introduce a method suitable for high aspect ratio meshes whereby the charge density is partitioned into atomic domains and multipoles are computed for each domain. While this approach is moderately more expensive than a single-center expansion, it is numerically stable and still a small fraction of the overall cost of a DFT calculation. The net result is that when high aspect ratio systems are being studied, form-fitted meshes can now be used in lieu of cubic meshes to gain computational speedup.

  1. Boundary conditions for free surface inlet and outlet problems

    KAUST Repository

    Taroni, M.

    2012-08-10

    We investigate and compare the boundary conditions that are to be applied to free-surface problems involving inlet and outlets of Newtonian fluid, typically found in coating processes. The flux of fluid is a priori known at an inlet, but unknown at an outlet, where it is governed by the local behaviour near the film-forming meniscus. In the limit of vanishing capillary number Ca it is well known that the flux scales with Ca 2/3, but this classical result is non-uniform as the contact angle approaches π. By examining this limit we find a solution that is uniformly valid for all contact angles. Furthermore, by considering the far-field behaviour of the free surface we show that there exists a critical capillary number above which the problem at an inlet becomes over-determined. The implications of this result for the modelling of coating flows are discussed. © 2012 Cambridge University Press.

  2. Uniqueness theorems for differential pencils with eigenparameter boundary conditions and transmission conditions

    Science.gov (United States)

    Yang, Chuan-Fu

    Inverse spectral problems are considered for differential pencils with boundary conditions depending polynomially on the spectral parameter and with a finite number of transmission conditions. We give formulations of the associated inverse problems such as Titchmarsh-Weyl theorem, Hochstadt-Lieberman theorem and Mochizuki-Trooshin theorem, and prove corresponding uniqueness theorems. The obtained results are generalizations of the similar results for the classical Sturm-Liouville operator on a finite interval.

  3. Exact multiplicity results for quasilinear boundary-value problems with cubic-like nonlinearities

    Directory of Open Access Journals (Sweden)

    Idris Addou

    2000-01-01

    Full Text Available We consider the boundary-value problem $$displaylines{ -(varphi_p (u'' =lambda f(u mbox{ in }(0,1 cr u(0 = u(1 =0,, }$$ where $p>1$, $lambda >0$ and $varphi_p (x =| x|^{p-2}x$. The nonlinearity $f$ is cubic-like with three distinct roots 0=a less than b less than c. By means of a quadrature method, we provide the exact number of solutions for all $lambda >0$. This way we extend a recent result, for $p=2$, by Korman et al. cite{KormanLiOuyang} to the general case $p>1$. We shall prove that when 1less than $pleq 2$ the structure of the solution set is exactly the same as that studied in the case $p=2$ by Korman et al. cite{KormanLiOuyang}, and strictly different in the case $p>2$.

  4. A universal nonlinear relation among boundary states in closed string field theory

    International Nuclear Information System (INIS)

    Kishimoto, Isao; Matsuo, Yutaka; Watanabe, Eitoku

    2004-01-01

    We show that the boundary states satisfy a nonlinear relation (the idempotency equation) with respect to the star product of closed string field theory. This relation is universal in the sense that various D-branes, including the infinitesimally deformed ones, satisfy the same equation, including the coefficient. This paper generalizes our analysis [hep-th/0306189] in the following senses. (1) We present a background-independent formulation based on conformal field theory. It illuminates the geometric nature of the relation and allows us to more systematically analyze the variations around the D-brane background. (2) We show that the Witten-type star product satisfies a similar relation but with a more divergent coefficient. (3) We determine the coefficient of the relation analytically. The result shows that the α parameter can be formally factored out, and the relation becomes universal. We present a conjecture on vacuum theory based on this computation. (author)

  5. Multiple Solutions for a Nonlinear Fractional Boundary Value Problem via Critical Point Theory

    Directory of Open Access Journals (Sweden)

    Yang Wang

    2017-01-01

    Full Text Available This paper is concerned with the existence of multiple solutions for the following nonlinear fractional boundary value problem: DT-αaxD0+αux=fx,ux,  x∈0,T, u0=uT=0, where α∈1/2,1, ax∈L∞0,T with a0=ess  infx∈0,Tax>0, DT-α and D0+α stand for the left and right Riemann-Liouville fractional derivatives of order α, respectively, and f:0,T×R→R is continuous. The existence of infinitely many nontrivial high or small energy solutions is obtained by using variant fountain theorems.

  6. On the Ψ-Conditional Exponential Asymptotic Stability of Nonlinear Lyapunov Matrix Differential Equations

    Directory of Open Access Journals (Sweden)

    Diamandescu Aurel

    2016-07-01

    Full Text Available It is proved (necessary and sufficient conditions for Ψ– conditional exponential asymptotic stability of the trivial solution of nonlinear Lyapunov matrix differential equations

  7. On the Ψ-Conditional Asymptotic Stability of Nonlinear Lyapunov Matrix Differential Equations

    Directory of Open Access Journals (Sweden)

    Diamandescu Aurel

    2015-12-01

    Full Text Available It is proved (necessary and sufficient conditions for Ψ − conditional asymptotic stability of the trivial solution of linear or nonlinear Lyapunov matrix differential equations.

  8. The height of the atmospheric boundary layer during unstable conditions

    Energy Technology Data Exchange (ETDEWEB)

    Gryning, S.E.

    2005-11-01

    The height of the convective atmospheric boundary layer, also called the mixed-layer, is one of the fundamental parameters that characterise the structure of the atmosphere near the ground. It has many theoretical and practical applications such as the prediction of air pollution concentrations, surface temperature and the scaling of turbulence. However, as pointed out by Builtjes (2001) in a review paper on Major Twentieth Century Milestones in Air Pollution Modelling and Its Application, the weakest point in meteorology data is still the determination of the height of the mixed-layer, the so-called mixing height. A simple applied model for the height of the mixed-layer over homogeneous terrain is suggested in chapter 2. It is based on a parameterised budget for the turbulent kinetic energy. In the model basically three terms - the spin-up term and the production of mechanical and convective turbulent kinetic energy - control the growth of the mixed layer. The interplay between the three terms is related to the meteorological conditions and the height of the mixed layer. A stable layer, the so-called entrainment zone, which is confined between the mixed layer and the free air above, caps the mixed layer. A parameterisation of the depth of the entrainment zone is also suggested, and used to devise a combined model for the height of the mixed layer and the entrainment zone. Another important aspect of the mixed layer development exists in coastal areas where an internal boundary layer forms downwind from the coastline. A model for the growth of the internal boundary layer is developed in analogy with the model for mixed layer development over homogeneous terrain. The strength of this model is that it can operate on a very fine spatial resolution with minor computer resources. Chapter 3 deals with the validation of the models. It is based in parts on data from the literature, and on own measurements. For the validation of the formation of the internal boundary layer

  9. MHD convective boundary layer slip flow and heat transfer over nonlinearly stretching cylinder embedded in a thermally stratified medium

    Directory of Open Access Journals (Sweden)

    Muhammad Tamoor

    Full Text Available This article presents a numerical method of solution to laminar axisymmetric hydro magnetic flow of incompressible, electrically conducting and viscous fluid moving over the circular cylinder embedded in a thermally stratified medium. Fluid over the cylinder moves due to the stretching of cylindrical surface. Different physical conditions at the boundary are also considered. With the help of suitable similarity transformation the boundary layer equations are transformed into ordinary differential equations. The resulting nonlinear ordinary differential equations were solved by Runge-Kutta technique with shooting method. Obtained numerical results for different pertinent parameters are graphically shown for velocity distribution and temperature distribution. Due to the industrial applications point of view, it is evaluated that local Nusselt number at the surfaces increases due to the influence of thermal stratification. The skin-friction and heat transfer coefficients have presented in the form of table. Comparison of heat transfer coefficient is also illustrated. Keywords: Shooting method, Thermal stratification, Suction/blowing, Magneto hydrodynamic

  10. Forced convective heat transfer in boundary layer flow of Sisko fluid over a nonlinear stretching sheet.

    Science.gov (United States)

    Munir, Asif; Shahzad, Azeem; Khan, Masood

    2014-01-01

    The major focus of this article is to analyze the forced convective heat transfer in a steady boundary layer flow of Sisko fluid over a nonlinear stretching sheet. Two cases are studied, namely (i) the sheet with variable temperature (PST case) and (ii) the sheet with variable heat flux (PHF case). The heat transfer aspects are investigated for both integer and non-integer values of the power-law index. The governing partial differential equations are reduced to a system of nonlinear ordinary differential equations using appropriate similarity variables and solved numerically. The numerical results are obtained by the shooting method using adaptive Runge Kutta method with Broyden's method in the domain[Formula: see text]. The numerical results for the temperature field are found to be strongly dependent upon the power-law index, stretching parameter, wall temperature parameter, material parameter of the Sisko fluid and Prandtl number. In addition, the local Nusselt number versus wall temperature parameter is also graphed and tabulated for different values of pertaining parameters. Further, numerical results are validated by comparison with exact solutions as well as previously published results in the literature.

  11. Global existence and nonexistence for the viscoelastic wave equation with nonlinear boundary damping-source interaction

    KAUST Repository

    Said-Houari, Belkacem

    2012-09-01

    The goal of this work is to study a model of the viscoelastic wave equation with nonlinear boundary/interior sources and a nonlinear interior damping. First, applying the Faedo-Galerkin approximations combined with the compactness method to obtain existence of regular global solutions to an auxiliary problem with globally Lipschitz source terms and with initial data in the potential well. It is important to emphasize that it is not possible to consider density arguments to pass from regular to weak solutions if one considers regular solutions of our problem where the source terms are locally Lipschitz functions. To overcome this difficulty, we use an approximation method involving truncated sources and adapting the ideas in [13] to show that the existence of weak solutions can still be obtained for our problem. Second, we show that under some restrictions on the initial data and if the interior source dominates the interior damping term, then the solution ceases to exist and blows up in finite time provided that the initial data are large enough.

  12. Forced convective heat transfer in boundary layer flow of Sisko fluid over a nonlinear stretching sheet.

    Directory of Open Access Journals (Sweden)

    Asif Munir

    Full Text Available The major focus of this article is to analyze the forced convective heat transfer in a steady boundary layer flow of Sisko fluid over a nonlinear stretching sheet. Two cases are studied, namely (i the sheet with variable temperature (PST case and (ii the sheet with variable heat flux (PHF case. The heat transfer aspects are investigated for both integer and non-integer values of the power-law index. The governing partial differential equations are reduced to a system of nonlinear ordinary differential equations using appropriate similarity variables and solved numerically. The numerical results are obtained by the shooting method using adaptive Runge Kutta method with Broyden's method in the domain[Formula: see text]. The numerical results for the temperature field are found to be strongly dependent upon the power-law index, stretching parameter, wall temperature parameter, material parameter of the Sisko fluid and Prandtl number. In addition, the local Nusselt number versus wall temperature parameter is also graphed and tabulated for different values of pertaining parameters. Further, numerical results are validated by comparison with exact solutions as well as previously published results in the literature.

  13. Buckling of Monopod Bucket Foundations – Influence of Boundary Conditions and Soil-structure Interaction

    DEFF Research Database (Denmark)

    Madsen, Søren; Pinna, Rodney; Randolph, M. F.

    2015-01-01

    Using large monopod bucket foundations as an alternative to monopiles for offshore wind turbines offers the potential for large cost savings compared to typical piled foundations. In this paper, numerical simulations are carried out to assess the risk of structural buckling during installation of...... is investigated. The effects of including soil restraint and soil–structure interaction on the buckling analysis are also addressed.......Using large monopod bucket foundations as an alternative to monopiles for offshore wind turbines offers the potential for large cost savings compared to typical piled foundations. In this paper, numerical simulations are carried out to assess the risk of structural buckling during installation...... of large-diameter bucket foundations. Since shell structures are generally sensitive to initially imperfect geometries, eigenmode-affine imperfections are introduced in a nonlinear finite-element analysis. The influence of modelling the real lid structure compared to classic boundary conditions...

  14. Partial differential variational inequalities involving nonlocal boundary conditions in Banach spaces

    Science.gov (United States)

    Liu, Zhenhai; Migórski, Stanisław; Zeng, Shengda

    2017-10-01

    In this paper, we firstly introduce a complicated system obtained by mixing a nonlinear evolutionary partial differential equation and a mixed variational inequality in infinite dimensional Banach spaces in the case where the set of constraints is not necessarily bounded and the problem is driven by nonlocal boundary conditions, which is called partial differential variational inequality ((PDVI), for short). Then, we show that the solution set of the mixed variational inequality involved in problem (PDVI) is nonempty, bounded, closed and convex. Moreover, the upper semicontinuity and measurability properties for set-valued mapping U : [ 0 , T ] ×E2 → Cbv (E1) (see (3.7), below) are also established. Finally, several existence results for (PDVI) are obtained by using a fixed point theorem for condensing set-valued operators and theory of measure of noncompactness.

  15. The transient heat transfer analysis of solids with radiative boundary condition using finite element analysis

    International Nuclear Information System (INIS)

    Reddy, B.S.; Sharan, A.M.

    1985-01-01

    The heat transfer process in some of the metallurgical processes is quite involved; for example, during the cooling of castings or heating of ingots before forging. These castings or ingots can be very complicated shapes. Therefore, the solution of heat transfer problems by exact methods is not possible. In such situations, the heat transfer process is studied either by finite difference or finite element method. The heat transfer process in this problem involves all the three modes of heat transfer which are: the conduction, convection and radiation. In this paper, the equations for the heat transfer process of a solid subjected to nonlinear boundary conditions using the finite element analysis have been derived. Then, these equations are solved using the Gauss-Seidel iteration technique. (author)

  16. Solution of a Problem Linear Plane Elasticity with Mixed Boundary Conditions by the Method of Boundary Integrals

    Directory of Open Access Journals (Sweden)

    Nahed S. Hussein

    2014-01-01

    Full Text Available A numerical boundary integral scheme is proposed for the solution to the system of …eld equations of plane. The stresses are prescribed on one-half of the circle, while the displacements are given. The considered problem with mixed boundary conditions in the circle is replaced by two problems with homogeneous boundary conditions, one of each type, having a common solution. The equations are reduced to a system of boundary integral equations, which is then discretized in the usual way, and the problem at this stage is reduced to the solution to a rectangular linear system of algebraic equations. The unknowns in this system of equations are the boundary values of four harmonic functions which define the full elastic solution and the unknown boundary values of stresses or displacements on proper parts of the boundary. On the basis of the obtained results, it is inferred that a stress component has a singularity at each of the two separation points, thought to be of logarithmic type. The results are discussed and boundary plots are given. We have also calculated the unknown functions in the bulk directly from the given boundary conditions using the boundary collocation method. The obtained results in the bulk are discussed and three-dimensional plots are given. A tentative form for the singular solution is proposed and the corresponding singular stresses and displacements are plotted in the bulk. The form of the singular tangential stress is seen to be compatible with the boundary values obtained earlier. The efficiency of the used numerical schemes is discussed.

  17. Fluctuations in the heliospheric hydrogen distribution induced by generalized and time-dependent interstellar boundary conditions

    International Nuclear Information System (INIS)

    Scherer, K.; Fahr, H.J.

    1990-01-01

    It is well known that the neutral component of the local interstellar medium (LISM) can effectively pass through the plasma interface ahead of the solar system and can penetrate deeply into the inner heliosphere. Here we present a newly-developed theoretical approach to describe the distribution function of LISM neutral hydrogen in the heliosphere, also taking into account time-dependent solar and interstellar boundary conditions. For this purpose we start from a Boltzmann-Vlasov equation, Fourier-transformed with respect to space and time coordinates, in connection with correspondingly transformed solar radiation forces and ionization rates, and then arrive at semi-analytic solutions for the transformed hydrogen velocity distribution function. As interstellar boundary conditions we allow for very general, non-Maxwellian and time-dependent distribution functions to account for the case that some LISM turbulence patterns or non-linear wave-like shock structures pass over the solar system. We consider this theoretical approach to be an ideal instrument for the synoptic interpretation of huge data samples on interplanetary Ly-α resonance glow intensities registered from different celestial directions over extended periods of time. In addition we feel that the theoretical approach presented here, when applied to interplanetary resonance glow data, may permit the detection of genuine fluctuations in the local interstellar medium. (author)

  18. Initial-Boundary Value Problem Solution of the Nonlinear Shallow-water Wave Equations

    Science.gov (United States)

    Kanoglu, U.; Aydin, B.

    2014-12-01

    The hodograph transformation solutions of the one-dimensional nonlinear shallow-water wave (NSW) equations are usually obtained through integral transform techniques such as Fourier-Bessel transforms. However, the original formulation of Carrier and Greenspan (1958 J Fluid Mech) and its variant Carrier et al. (2003 J Fluid Mech) involve evaluation integrals. Since elliptic integrals are highly singular as discussed in Carrier et al. (2003), this solution methodology requires either approximation of the associated integrands by smooth functions or selection of regular initial/boundary data. It should be noted that Kanoglu (2004 J Fluid Mech) partly resolves this issue by simplifying the resulting integrals in closed form. Here, the hodograph transform approach is coupled with the classical eigenfunction expansion method rather than integral transform techniques and a new analytical model for nonlinear long wave propagation over a plane beach is derived. This approach is based on the solution methodology used in Aydın & Kanoglu (2007 CMES-Comp Model Eng) for wind set-down relaxation problem. In contrast to classical initial- or boundary-value problem solutions, here, the NSW equations are formulated to yield an initial-boundary value problem (IBVP) solution. In general, initial wave profile with nonzero initial velocity distribution is assumed and the flow variables are given in the form of Fourier-Bessel series. The results reveal that the developed method allows accurate estimation of the spatial and temporal variation of the flow quantities, i.e., free-surface height and depth-averaged velocity, with much less computational effort compared to the integral transform techniques such as Carrier et al. (2003), Kanoglu (2004), Tinti & Tonini (2005 J Fluid Mech), and Kanoglu & Synolakis (2006 Phys Rev Lett). Acknowledgments: This work is funded by project ASTARTE- Assessment, STrategy And Risk Reduction for Tsunamis in Europe. Grant 603839, 7th FP (ENV.2013.6.4-3 ENV

  19. Bifurcation for a free boundary problem modeling the growth of tumors with a drug induced nonlinear proliferation rate

    Science.gov (United States)

    Li, Fengjie; Liu, Bingchen

    2017-12-01

    In this paper, we study a free boundary model describing growth of tumors under action of drugs. To our knowledge, in theoretical discussion for free boundary problems, the proliferation rate in tumor models discussed in previous bifurcation results is a linear function of nutrients and inhibitors. Whereas in this paper we consider the net proliferation rate as a nonlinear function depending on both nutrients and drugs. First, the existence and the uniqueness of radially symmetric stationary solutions are obtained. Second, we prove that symmetry-breaking solutions bifurcate from the radially symmetric stationary solutions when the concentration of drug on the boundary of tumor is less than one in the rescaled model.

  20. Frequency and Time Domain Modeling of Acoustic Liner Boundary Conditions

    Science.gov (United States)

    Bliss, Donald B.

    1982-01-01

    As part of a research program directed at the acoustics of advanced subsonic propulsion systems undertaken at NASA Langley, Duke University was funded to develop a boundary condition model for bulk-reacting nacelle liners. The overall objective of the Langley program was to understand and predict noise from advanced subsonic transport engines and to develop related noise control technology. The overall technical areas included: fan and propeller source noise, acoustics of ducts and duct liners, interior noise, subjective acoustics, and systems noise prediction. The Duke effort was directed toward duct liner acoustics for the development of analytical methods to characterize liner behavior in both frequency domain and time domain. A review of duct acoustics and liner technology can be found in Reference [1]. At that time, NASA Langley was investigating the propulsion concept of an advanced ducted fan, with a large diameter housed inside a relatively short duct. Fan diameters in excess of ten feet were proposed. The lengths of both the inlet and exhaust portions of the duct were to be short, probably less than half the fan diameter. The nacelle itself would be relatively thin-walled for reasons of aerodynamic efficiency. The blade-passage frequency was expected to be less than I kHz, and very likely in the 200 to 300 Hz range. Because of the design constraints of a short duct, a thin nacelle, and long acoustic wavelengths, the application of effective liner technology would be especially challenging. One of the needs of the NASA Langley program was the capability to accurately and efficiently predict the behavior of the acoustic liner. The traditional point impedance method was not an adequate model for proposed liner designs. The method was too restrictive to represent bulk reacting liners and to allow for the characterization of many possible innovative liner concepts. In the research effort at Duke, an alternative method, initially developed to handle bulk

  1. Eigenmode Analysis of Boundary Conditions for One-Dimensional Preconditioned Euler Equations

    Science.gov (United States)

    Darmofal, David L.

    1998-01-01

    An analysis of the effect of local preconditioning on boundary conditions for the subsonic, one-dimensional Euler equations is presented. Decay rates for the eigenmodes of the initial boundary value problem are determined for different boundary conditions. Riemann invariant boundary conditions based on the unpreconditioned Euler equations are shown to be reflective with preconditioning, and, at low Mach numbers, disturbances do not decay. Other boundary conditions are investigated which are non-reflective with preconditioning and numerical results are presented confirming the analysis.

  2. The influence of compressibility on nonlinear spectral energy transfer - Part 2: Effect on hypersonic boundary layer transition

    Science.gov (United States)

    Mittal, Ankita; Girimaji, Sharath

    2017-11-01

    We examine the effect of compressible spectral energy transfer in the nonlinear regime of transition to turbulence of hypersonic boundary layers. The nature of spectral energy transfer between perturbation modes is profoundly influenced by two compressibility mechanisms. First and foremost, the emergence of nonlinear pressure-dilatation mechanism leads to kinetic-internal energy exchange within the perturbation field. Such interchange is absent in incompressible flow as pressure merely reorients the perturbation amplitude vector while conserving kinetic energy. Secondly, the nature of triadic interactions also changes due to variability in density. In this work, we demonstrate that the efficiency of nonlinear spectral energy transfer is diminished in compressible boundary layers. Emergence of new perturbation modes or `broad-banding' of the perturbation field is significantly delayed in comparison to incompressible boundary layer undergoing transition. A significant amount of perturbation energy is transformed to internal energy and thus unavailable for `tripping' the flow into turbulent state. These factors profoundly change the nature of the nonlinear stage of transition in compressible boundary layer leading to delayed onset of full-fledged turbulence.

  3. Global solutions to the initial-boundary value problem for the quasilinear viscoelastic equation with a derivative nonlinearity

    Directory of Open Access Journals (Sweden)

    Mitsuhiro Nakao

    2014-01-01

    Full Text Available We prove the existence and uniqueness of a global decaying solution to the initial boundary value problem for the quasilinear wave equation with Kelvin-Voigt dissipation and a derivative nonlinearity. To derive the required estimates of the solutions we employ a 'loan' method and use a difference inequality on the energy.

  4. Boundary conditions in the Ginzburg Landau Formulation in heavy ...

    African Journals Online (AJOL)

    The linearized gap equation is the basis for the microscopic derivation of the second order terms in the Ginzburg-Landau free energy expansion. However, close to the boundary these second order terms do not have the same form, since the kernel is changed due to quasi-particle scattering. In addition, these boundary ...

  5. Unsteady slip flow of Carreau nanofluid over a wedge with nonlinear radiation and new mass flux condition

    Directory of Open Access Journals (Sweden)

    M. Khan

    Full Text Available This article addresses a numerical investigation for the unsteady 2D slip flow of Carreau nanofluid past a static and/or moving wedge with the nonlinear radiation. A zero nanoparticle mass flux and convective boundary conditions are implemented. Further, the most recently devised model for nanofluid is adopted that incorporates the effects of Brownian motion and thermophoresis. A set of suitable transformation is demonstrated to alter the nonlinear partial differential equations into nonlinear ordinary differential equations and then tackled numerically by employing bvp4c in Matlab package. The numerical computations for the wall heat flux (Nusselt number and wall mass flux (Sherwood number are also performed. Effects of several controlling parameters on the velocity, temperature and nanoparticles concentration are explored and discussed in detail. Our study reveals that the temperature and the associated thermal boundary layer thickness are enhancing function of the temperature ratio parameter for both shear thickening and shear thinning fluids. Moreover, it is noticed that the velocity in case of moving wedge is higher than static wedge. Keywords: Unsteady wedge flow, Carreau nanofluid, Non-linear radiation, Velocity slip and nanoparticles mass flux conditions

  6. Outcome of homogeneous and heterogeneous reactions in Darcy-Forchheimer flow with nonlinear thermal radiation and convective condition

    Directory of Open Access Journals (Sweden)

    T. Hayat

    Full Text Available The present analysis aims to report the consequences of nonlinear radiation, convective condition and heterogeneous-homogeneous reactions in Darcy-Forchheimer flow over a non-linear stretching sheet with variable thickness. Non-uniform magnetic field and nonuniform heat generation/absorption are accounted. The governing boundary layer partial differential equations are converted into a system of nonlinear ordinary differential equations. The computations are organized and the effects of physical variables such as thickness parameter, power index, Hartman number, inertia and porous parameters, radiation parameter, Biot number, Prandtl number, ratio parameter, heat generation parameter and homogeneous-heterogeneous reaction parameter are investigated. The variations of skin friction coefficient and Nusselt number for different interesting variables are plotted and discussed. It is noticed that Biot number and heat generation variable lead to enhance the temperature distribution. The solutal boundary layer thickness decreases for larger homogeneous variable while reverse trend is seen for heterogeneous reaction. Keywords: Variable sheet thickness, Darcy-Forchheimer flow, Homogeneous-heterogeneous reactions, Power-law surface velocity, Convective condition, Heat generation/absorption, Nonlinear radiation

  7. On the instability of a three-dimensional attachment-line boundary layer - Weakly nonlinear theory and a numerical approach

    Science.gov (United States)

    Hall, P.; Malik, M. R.

    1986-01-01

    The instability of a three-dimensional attachment-line boundary layer is considered in the nonlinear regime. Using weakly nonlinear theory, it is found that, apart from a small interval near the (linear) critical Reynolds number, finite-amplitude solutions bifurcate subcritically from the upper branch of the neutral curve. The time-dependent Navier-Stokes equations for the attachment-line flow have been solved using a Fourier-Chebyshev spectral method and the subcritical instability is found at wavenumbers that correspond to the upper branch. Both the theory and the numerical calculations show the existence of supercritical finite-amplitude (equilibrium) states near the lower branch which explains why the observed flow exhibits a preference for the lower branch modes. The effect of blowing and suction on nonlinear stability of the attachment-line boundary layer is also investigated.

  8. On the instability of a 3-dimensional attachment line boundary layer: Weakly nonlinear theory and a numerical approach

    Science.gov (United States)

    Hall, P.; Malik, M. R.

    1984-01-01

    The instability of a three dimensional attachment line boundary layer is considered in the nonlinear regime. Using weakly nonlinear theory, it is found that, apart from a small interval near the (linear) critical Reynolds number, finite amplitude solutions bifurcate subcritically from the upper branch of the neutral curve. The time dependent Navier-Stokes equations for the attachment line flow have been solved using a Fourier-Chebyshev spectral method and the subcritical instability is found at wavenumbers that correspond to the upper branch. Both the theory and the numerical calculations show the existence of supercritical finite amplitude (equilibrium) states near the lower branch which explains why the observed flow exhibits a preference for the lower branch modes. The effect of blowing and suction on nonlinear stability of the attachment line boundary layer is also investigated.

  9. Boundary conditions for a composite model of leptons and quarks

    International Nuclear Information System (INIS)

    Mainland, G B

    2015-01-01

    Because the existence of families of elements and hadrons was ultimately understood by the realization that atoms and hadrons are composite, an obvious approach to explaining the existence of lepton and quark families is to assume that the particles in these families are also composite. The mass and spin spectra of leptons and quarks suggest that if these particles are composite, they are most likely bound states of a scalar and spin-1/2 fermion interacting via electrodynamics. However, if they are composite, the bound states must be highly relativistic since in each family the least massive member has a small mass compared with the others. Also, composite leptons and quarks must be extremely tightly bound since no internal structure has ever been conclusively detected. Highly relativistic, bound-state, Bethe- Salpeter solutions of a scalar and a spin-1/2 fermion bound by minimal electrodynamics are discussed. These specific solutions cannot describe leptons or quarks as bound states because the magnitude of the charges of the constituents are an order of magnitude larger than e. The boundary conditions, however, allow solutions when the constituents have charges with magnitudes on the order of e. (paper)

  10. CT image segmentation using FEM with optimized boundary condition.

    Directory of Open Access Journals (Sweden)

    Hiroyuki Hishida

    Full Text Available The authors propose a CT image segmentation method using structural analysis that is useful for objects with structural dynamic characteristics. Motivation of our research is from the area of genetic activity. In order to reveal the roles of genes, it is necessary to create mutant mice and measure differences among them by scanning their skeletons with an X-ray CT scanner. The CT image needs to be manually segmented into pieces of the bones. It is a very time consuming to manually segment many mutant mouse models in order to reveal the roles of genes. It is desirable to make this segmentation procedure automatic. Although numerous papers in the past have proposed segmentation techniques, no general segmentation method for skeletons of living creatures has been established. Against this background, the authors propose a segmentation method based on the concept of destruction analogy. To realize this concept, structural analysis is performed using the finite element method (FEM, as structurally weak areas can be expected to break under conditions of stress. The contribution of the method is its novelty, as no studies have so far used structural analysis for image segmentation. The method's implementation involves three steps. First, finite elements are created directly from the pixels of a CT image, and then candidates are also selected in areas where segmentation is thought to be appropriate. The second step involves destruction analogy to find a single candidate with high strain chosen as the segmentation target. The boundary conditions for FEM are also set automatically. Then, destruction analogy is implemented by replacing pixels with high strain as background ones, and this process is iterated until object is decomposed into two parts. Here, CT image segmentation is demonstrated using various types of CT imagery.

  11. Simulation of the steady-state energy transfer in rigid bodies, with convective-radiative boundary conditions, employing a minimum principle

    International Nuclear Information System (INIS)

    Gama, R.M.S. da.

    1992-08-01

    The energy transfer phenomenon in a rigid and opaque body that exchanges energy, with the environment, by convection and by diffuse thermal radiation is studied. The considered phenomenon is described by a partial differential equation, subjected to (nonlinear) boundary conditions. A minimum principle, suitable for a large class of energy transfer problems is presented. Some particular cases are simulated. (author)

  12. Effect of boundary conditions on thermohydraulic behavior of clay buffer used in nuclear waste repository

    International Nuclear Information System (INIS)

    Arul Peter, A.; Murugesan, K.; Mamidi, Ganesh; Sharma, Umesh Kumar; Sharma, D. Akanshu; Arora, Puneet

    2010-01-01

    The use of nuclear energy is increasing dramatically in the world due to the fast depletion of fossil fuels, and hence the nuclear waste disposal and its short and long-term effects are of considerable importance. One of the options considered for nuclear waste disposal is underground nuclear waste repository facility. In this underground nuclear waste disposal system the waste filled canisters are placed in the rock surrounded by an engineered clay barrier and the whole system is buried in the geological formation, which serves as the natural or geological barrier. The important characteristic of the clay barrier is that it should not open up for radiation though it is continuously subjected to heat loading from the canisters. The heat and moisture transport mechanisms through the clay barrier plays an important role in deciding its mechanical strength. Clay behaves as an unsaturated porous material when it is used as a buffer material in nuclear waste facility. The governing equations for heat and moisture transfer through unsaturated porous media are coupled and nonlinear and hence they have to be solved using numerical solution technique. This paper reports the results of a numerical study on heat and moisture transport through a buffer layer made of clay as used in nuclear waste repository. Galerkin's weighted residual finite element method has been employed for the solution of the non-linear coupled governing equations used to represent the heat and moisture transport through unsaturated clay material. A detailed computational procedure has been established for the solution of the non-linear governing equations using Newton-Raphson technique. Initially the code has been validated with available experimental results. Then numerical simulation results were obtained for heat and moisture variations within the buffer material for Dirichlet temperature boundary conditions in the range, 50 deg C 2 2 , with an aim to simulate the boundary conditions which the clay

  13. Nested Bethe Ansatz for Spin Ladder Model with Open Boundary Conditions

    International Nuclear Information System (INIS)

    Wu Junfang; Zhang Chunmin; Yue Ruihong; Li Runling

    2005-01-01

    The nested Bethe ansatz (BA) method is applied to find the eigenvalues and the eigenvectors of the transfer matrix for spin-ladder model with open boundary conditions. Based on the reflection equation, we find the general diagonal solution, which determines the general boundary interaction in the Hamiltonian. We introduce the spin-ladder model with open boundary conditions. By finding the solution K ± of the reflection equation which determines the nontrivial boundary terms in the Hamiltonian, we diagonalize the transfer matrix of the spin-ladder model with open boundary conditions in the framework of nested BA.

  14. Essential Boundary Conditions with Straight C1 Finite Elements in Curved Domains

    International Nuclear Information System (INIS)

    Ferraro, N.M.; Jardin, S.C.; Luo, X.

    2010-01-01

    The implementation of essential boundary conditions in C1 finite element analysis requires proper treatment of both the boundary conditions on second-order differentials of the solution and the curvature of the domain boundary. A method for the imposition of essential boundary conditions using straight elements (where the elements are not deformed to approximate a curved domain) is described. It is shown that pre-multiplication of the matrix equation by the local rotation matrix at each boundary node is not the optimal transformation. The uniquely optimal transformation is found, which does not take the form of a similarity transformation due to the non-orthogonality of the transformation to curved coordinates.

  15. Compressibility effects on the non-linear receptivity of boundary layers to dielectric barrier discharges

    Science.gov (United States)

    Denison, Marie F. C.

    The reduction of drag and aerodynamic heating caused by boundary layer transition is of central interest for the development of hypersonic vehicles. Receptivity to flow perturbation in the form of Tollmien-Schlichting (TS) wave growth often determines the first stage of the transition process, which can be delayed by depositing specific excitations into the boundary layer. Weakly ionized Dielectric Barrier Discharge (DBD) actuators are being investigated as possible sources of such excitations, but little is known today about their interaction with high-speed flows. In this framework, the first part of the thesis is dedicated to a receptivity study of laminar compressible boundary layers over a flat plate by linear stability analysis following an adjoint operator formulation, under DBD representative excitations assumed independent of flow conditions. The second part of the work concentrates on the development of a coupled plasma-Navier and Stokes solver targeted at the study of supersonic flow and compressibility effects on DBD forcing and non-parallel receptivity. The linear receptivity study of quasi-parallel compressible flows reveals several interesting features such as a significant shift of the region of maximum receptivity deeper into the flow at high Mach number and strong wave amplitude reduction compared to incompressible flows. The response to DBD relevant excitation distributions and to variations of the base flow conditions and system length scales follows these trends. Observed absolute amplitude changes and relative sensitivity modifications between source types are related to the evolution of the offset between forcing peak profile and relevant adjoint mode maximum. The analysis highlights the crucial importance of designing and placing the actuator in a way that matches its force field to the position of maximum boundary layer receptivity for the specific flow conditions of interest. In order to address the broad time and length scale spectrum

  16. A Monge–Ampere Equation with an Unusual Boundary Condition

    Directory of Open Access Journals (Sweden)

    Marc Sedjro

    2015-11-01

    Full Text Available We consider a class of Monge–Ampere equations where the convex conjugate of the unknown function is prescribed on a boundary of its domain yet to be determined. We show the existence of a weak solution.

  17. Nonlinear Analysis of Renal Autoregulation Under Broadband Forcing Conditions

    DEFF Research Database (Denmark)

    Marmarelis, V Z; Chon, K H; Chen, Y M

    1994-01-01

    in describing the dynamic pressure-flow relation is found to be important. Furthermore, the dependence of 1st-order kernel waveforms on the power level of broadband pressure forcing indicates the presence of nonlinear feedback (of sigmoid type) based on previously reported analysis of a class of nonlinear...... feedback systems....

  18. Preconditioned characteristic boundary conditions based on artificial compressibility method for solution of incompressible flows

    Science.gov (United States)

    Hejranfar, Kazem; Parseh, Kaveh

    2017-09-01

    The preconditioned characteristic boundary conditions based on the artificial compressibility (AC) method are implemented at artificial boundaries for the solution of two- and three-dimensional incompressible viscous flows in the generalized curvilinear coordinates. The compatibility equations and the corresponding characteristic variables (or the Riemann invariants) are mathematically derived and then applied as suitable boundary conditions in a high-order accurate incompressible flow solver. The spatial discretization of the resulting system of equations is carried out by the fourth-order compact finite-difference (FD) scheme. In the preconditioning applied here, the value of AC parameter in the flow field and also at the far-field boundary is automatically calculated based on the local flow conditions to enhance the robustness and performance of the solution algorithm. The code is fully parallelized using the Concurrency Runtime standard and Parallel Patterns Library (PPL) and its performance on a multi-core CPU is analyzed. The incompressible viscous flows around a 2-D circular cylinder, a 2-D NACA0012 airfoil and also a 3-D wavy cylinder are simulated and the accuracy and performance of the preconditioned characteristic boundary conditions applied at the far-field boundaries are evaluated in comparison to the simplified boundary conditions and the non-preconditioned characteristic boundary conditions. It is indicated that the preconditioned characteristic boundary conditions considerably improve the convergence rate of the solution of incompressible flows compared to the other boundary conditions and the computational costs are significantly decreased.

  19. A simple and efficient outflow boundary condition for the incompressible Navier–Stokes equations

    Directory of Open Access Journals (Sweden)

    Yibao Li

    2017-01-01

    Full Text Available Many researchers have proposed special treatments for outlet boundary conditions owing to lack of information at the outlet. Among them, the simplest method requires a large enough computational domain to prevent or reduce numerical errors at the boundaries. However, an efficient method generally requires special treatment to overcome the problems raised by the outlet boundary condition used. For example, mass flux is not conserved and the fluid field is not divergence-free at the outlet boundary. Overcoming these problems requires additional computational cost. In this paper, we present a simple and efficient outflow boundary condition for the incompressible Navier–Stokes equations, aiming to reduce the computational domain for simulating flow inside a long channel in the streamwise direction. The proposed outflow boundary condition is based on the transparent equation, where a weak formulation is used. The pressure boundary condition is derived by using the Navier–Stokes equations and the outlet flow boundary condition. In the numerical algorithm, a staggered marker-and-cell grid is used and temporal discretization is based on a projection method. The intermediate velocity boundary condition is consistently adopted to handle the velocity–pressure coupling. Characteristic numerical experiments are presented to demonstrate the robustness and accuracy of the proposed numerical scheme. Furthermore, the agreement of computational results from small and large domains suggests that our proposed outflow boundary condition can significantly reduce computational domain sizes.

  20. Reducing slab boundary artifacts in three‐dimensional multislab diffusion MRI using nonlinear inversion for slab profile encoding (NPEN)

    Science.gov (United States)

    Koopmans, Peter J.; Frost, Robert; Miller, Karla L.

    2015-01-01

    Purpose To propose a method to reduce the slab boundary artifacts in three‐dimensional multislab diffusion MRI. Methods Bloch simulation is used to investigate the effects of multiple factors on slab boundary artifacts, including characterization of residual errors on diffusion quantification. A nonlinear inversion method is proposed to simultaneously estimate the slab profile and the underlying (corrected) image. Results Correction results of numerical phantom and in vivo data demonstrate that the method can effectively remove slab boundary artifacts for diffusion data. Notably, the nonlinear inversion is also successful at short TR, a regimen where previously proposed methods (slab profile encoding and weighted average) retain residual artifacts in both diffusion‐weighted images and diffusion metrics (mean diffusion coefficient and fractional anisotropy). Conclusion The nonlinear inversion for removing slab boundary artifacts provides improvements over existing methods, particularly at the short TRs required to maximize SNR efficiency. Magn Reson Med 76:1183–1195, 2016. © 2015 The Authors. Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. PMID:26510172

  1. Reducing slab boundary artifacts in three-dimensional multislab diffusion MRI using nonlinear inversion for slab profile encoding (NPEN).

    Science.gov (United States)

    Wu, Wenchuan; Koopmans, Peter J; Frost, Robert; Miller, Karla L

    2016-10-01

    To propose a method to reduce the slab boundary artifacts in three-dimensional multislab diffusion MRI. Bloch simulation is used to investigate the effects of multiple factors on slab boundary artifacts, including characterization of residual errors on diffusion quantification. A nonlinear inversion method is proposed to simultaneously estimate the slab profile and the underlying (corrected) image. Correction results of numerical phantom and in vivo data demonstrate that the method can effectively remove slab boundary artifacts for diffusion data. Notably, the nonlinear inversion is also successful at short TR, a regimen where previously proposed methods (slab profile encoding and weighted average) retain residual artifacts in both diffusion-weighted images and diffusion metrics (mean diffusion coefficient and fractional anisotropy). The nonlinear inversion for removing slab boundary artifacts provides improvements over existing methods, particularly at the short TRs required to maximize SNR efficiency. Magn Reson Med 76:1183-1195, 2016. © 2015 The Authors. Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. © 2015 The Authors. Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine.

  2. Revisit boundary conditions for the self-adjoint angular flux formulation

    Energy Technology Data Exchange (ETDEWEB)

    Wang, Yaqi [Idaho National Lab. (INL), Idaho Falls, ID (United States); Gleicher, Frederick N. [Idaho National Lab. (INL), Idaho Falls, ID (United States)

    2015-03-01

    We revisit the boundary conditions for SAAF. We derived the equivalent parity variational form ready for coding up. The more rigorous approach of evaluating odd parity should be solving the odd parity equation coupled with the even parity. We proposed a symmetric reflecting boundary condition although neither positive definiteness nor even-odd decoupling is achieved. A simple numerical test verifies the validity of these boundary conditions.

  3. An Existence Theorem for Fractional Hybrid Differential Inclusions of Hadamard Type with Dirichlet Boundary Conditions

    Directory of Open Access Journals (Sweden)

    Bashir Ahmad

    2014-01-01

    Full Text Available This paper studies the existence of solutions for a boundary value problem of nonlinear fractional hybrid differential inclusions by using a fixed point theorem due to Dhage (2006. The main result is illustrated with the aid of an example.

  4. Modeling of solid/porous wall boundary conditions for the validation of computational fluid dynamics codes

    Science.gov (United States)

    Beutner, Thomas J.; Celik, Zeki Z.; Roberts, Leonard

    1992-01-01

    A computational study has been undertaken to investigate method of modeling solid and porous wall boundary conditions in computational fluid dynamics (CFD) codes. The procedure utilizes experimental measurements at the walls to develop a flow field solution based on the method of singularities. This flow field solution is then imposed as a boundary condition in a CFD simulation of the internal flow field. The effectiveness of this method in describing the boundary conditions at the wind tunnel walls using only sparse experimental measurements has been investigated. Position and refinement of experimental measurement locations required to describe porous wall boundary conditions has also been considered.

  5. Effect of initial conditions, boundary conditions and thickness on the moisture buffering capacity of spruce plywood

    Energy Technology Data Exchange (ETDEWEB)

    Osanyintola, O. F.; Talukdar, P.; Simonson, C. J. [Department of Mechanical Engineering, University of Saskatchewan, Saskatoon, Sask. (China)

    2006-07-01

    In this paper, the moisture buffering capacity of spruce plywood is measured by recording the change in mass of a test specimen when the air relative humidity (RH) is changed between 33% RH and 75% RH. The aim is to represent diurnal cycles in indoor humidity with 33% RH maintained for 16 h and 75% RH maintained for 8 h. Measurements are taken using two different apparatuses, which provide different convective transfer coefficients between the air and the plywood, and the results are compared to a numerical model for validation. The validated numerical model is then used to investigate the effect of initial conditions, boundary conditions and thickness on the moisture buffering capacity of plywood. The results show that the buffering capacity of plywood depends on the initial conditions and thickness of the plywood as well as the surface film coefficient and humidity cycle. (author)

  6. Stress and mixed boundary conditions for two-dimensional ...

    Indian Academy of Sciences (India)

    decagonal quasi-crystal (QC) media, the reciprocal theorem and the general solution for. QCs are applied in a novel ... flat plates consists of an interior component significant throughout the plates and a boundary layer component (in ..... important, but whose minimum distance ˜d from E to ˜E is positive and independent of h.

  7. Experimental verification of free-space singular boundary conditions in an invisibility cloak

    International Nuclear Information System (INIS)

    Wu, Qiannan; Gao, Fei; Song, Zhengyong; Lin, Xiao; Zhang, Youming; Zhang, Baile; Chen, Huanyang

    2016-01-01

    A major issue in invisibility cloaking, which caused intense mathematical discussions in the past few years but still remains physically elusive, is the plausible singular boundary conditions associated with the singular metamaterials at the inner boundary of an invisibility cloak. The perfect cloaking phenomenon, as originally proposed by Pendry et al for electromagnetic waves, cannot be treated as physical before a realistic inner boundary of a cloak is demonstrated. Although a recent demonstration has been done in a waveguide environment, the exotic singular boundary conditions should apply to a general environment as in free space. Here we fabricate a metamaterial surface that exhibits the singular boundary conditions and demonstrate its performance in free space. Particularly, the phase information of waves reflected from this metamaterial surface is explicitly measured, confirming the singular responses of boundary conditions for an invisibility cloak. (paper)

  8. Experimental verification of free-space singular boundary conditions in an invisibility cloak

    Science.gov (United States)

    Wu, Qiannan; Gao, Fei; Song, Zhengyong; Lin, Xiao; Zhang, Youming; Chen, Huanyang; Zhang, Baile

    2016-04-01

    A major issue in invisibility cloaking, which caused intense mathematical discussions in the past few years but still remains physically elusive, is the plausible singular boundary conditions associated with the singular metamaterials at the inner boundary of an invisibility cloak. The perfect cloaking phenomenon, as originally proposed by Pendry et al for electromagnetic waves, cannot be treated as physical before a realistic inner boundary of a cloak is demonstrated. Although a recent demonstration has been done in a waveguide environment, the exotic singular boundary conditions should apply to a general environment as in free space. Here we fabricate a metamaterial surface that exhibits the singular boundary conditions and demonstrate its performance in free space. Particularly, the phase information of waves reflected from this metamaterial surface is explicitly measured, confirming the singular responses of boundary conditions for an invisibility cloak.

  9. Absorption and impedance boundary conditions for phased geometrical-acoustics methods

    DEFF Research Database (Denmark)

    Jeong, Cheol-Ho

    2012-01-01

    Defining accurate acoustical boundary conditions is of crucial importance for room acoustic simulations. In predicting sound fields using phased geometrical acoustics methods, both absorption coefficients and surface impedances of the boundary surfaces can be used, but no guideline has been...... developed on which boundary condition produces accurate results. In this study, various boundary conditions in terms of normal, random, and field incidence absorption coefficients and normal incidence surface impedance are used in a phased beam tracing model, and the simulated results are validated...... with boundary element solutions. Two rectangular rooms with uniform and non-uniform absorption distributions are tested. Effects of the neglect of reflection phase shift are also investigated. It is concluded that the impedance, random incidence, and field incidence absorption boundary conditions produce...

  10. Fractional instantons and bions in the O(N) model with twisted boundary conditions

    Energy Technology Data Exchange (ETDEWEB)

    Nitta, Muneto [Department of Physics, and Research and Education Center for Natural Sciences, Keio University,Hiyoshi 4-1-1, Yokohama, Kanagawa 223-8521 (Japan)

    2015-03-20

    Recently, multiple fractional instanton configurations with zero instanton charge, called bions, have been revealed to play important roles in quantum field theories on compactified spacetime. In two dimensions, fractional instantons and bions have been extensively studied in the ℂP{sup N−1} model and the Grassmann sigma model on ℝ{sup 1}×S{sup 1} with the ℤ{sub N} symmetric twisted boundary condition. Fractional instantons in these models are domain walls with a localized U(1) modulus twisted half along their world volume. In this paper, we classify fractional instantons and bions in the O(N) nonlinear sigma model on ℝ{sup N−2}×S{sup 1} with more general twisted boundary conditions in which arbitrary number of fields change sign. We find that fractional instantons have more general composite structures, that is, a global vortex with an Ising spin (or a half-lump vortex), a half sine-Gordon kink on a domain wall, or a half lump on a “space-filling brane” in the O(3) model (ℂP{sup 1} model) on ℝ{sup 1}×S{sup 1}, and a global monopole with an Ising spin (or a half-Skyrmion monopole), a half sine-Gordon kink on a global vortex, a half lump on a domain wall, or a half Skyrmion on a “space-filling brane” in the O(4) model (principal chiral model or Skyrme model) on ℝ{sup 2}×S{sup 1}. We also construct bion configurations in these models.

  11. Wave Height Distribution for Nonlinear Swell Waves in Deep an Depth Limited Wave Conditions

    DEFF Research Database (Denmark)

    Nørgaard, Jørgen Harck; Andersen, Thomas Lykke; Knudsen, Jannie Elkær

    2017-01-01

    This paper presents initial results from an on-going study on the influence from wave nonlinearity on the wave height distribution in deep- and depth-limited nonlinear wave conditions. A fully nonlinear VOF model, IH-2VOF, is applied to model the propagation of irregular waves on a sloping sea bed...... from deep to shallow water, including the effects of wave breaking. Different wave nonlinearities are evaluated in the model and the effects of the wave nonlinearity, described by the so-called Ursell-number, on the wave height distributions along the sloping sea bed are evaluated. The widely used...

  12. A numerical study of magnetohydrodynamics flow in Casson nanofluid combined with Joule heating and slip boundary conditions

    Directory of Open Access Journals (Sweden)

    A. Kamran

    Full Text Available A numerical study of Casson nanofluid past horizontal stretching surface with magnetic effect and Joule heating are presented. Slip and thermal convective boundary conditions are considered in the study. A numerical technique of Keller box is applied to the nonlinear ODEs which are obtained by applying the similarity transformation to the nonlinear partial differential equations. The magnetic field and Joule heating effects are observed graphically. Also the strength of convective heat exchange (Nusselt number and the strength of mass exchange (Sherwood number are analyzed. It is noted that Nusselt number declines whereas Sherwood number rises by increasing Eckert number. The impact of increasing Hartman number resulted in the decrease of both Sherwood and Nusselt number. Keywords: Casson nanofluid, Magnetohydrodynamic, Joule heating, Keller box method

  13. Generating wind fluctuations for Large Eddy Simulation inflow boundary condition

    International Nuclear Information System (INIS)

    Bekele, S.A.; Hangan, H.

    2004-01-01

    Large Eddy Simulation (LES) studies of flows over bluff bodies immersed in a boundary layer wind environment require instantaneous wind characteristics. The influences of the wind environment on the building pressure distribution are a well-established fact in the experimental study of wind engineering. Measured wind data of full or model scale are available only at a limited number of points. A method of obtaining instantaneous wind data at all mesh points of the inlet boundary for LES computation is necessary. Herein previous and new wind inflow generation techniques are presented. The generated wind data is then applied to a LES computation of a channel flow. The characteristics of the generated wind fluctuations in comparison to the measured data and the properties of the flow field computed from these two wind data are discussed. (author)

  14. Conditions affecting boundary response to messages out of awareness.

    Science.gov (United States)

    Fisher, S

    1976-05-01

    Multiple studies evaluated the role of the following parameters in mediating the effects of auditory subliminal inputs upon the body boundary: being made aware that exposure to subliminal stimuli is occurring, nature of the priming preliminary to the input, length of exposure, competing sensory input, use of specialized content messages, tolerance for unrealistic experience, and masculinity-feminity. A test-retest design was typically employed that involved measuring the baseline Barrier score with the Holtzman bolts and then ascertaining the Barrier change when responding to a second series of Holtzman blots at the same time that subliminal input was occurring. Complex results emerged that defined in considerably new detail what facilitates and blocks the boundary-disrupting effects of subliminal messages in men and to a lesser degree in women.

  15. General Considerations of the Electrostatic Boundary Conditions in Oxide Heterostructures

    Energy Technology Data Exchange (ETDEWEB)

    Higuchi, Takuya

    2011-08-19

    When the size of materials is comparable to the characteristic length scale of their physical properties, novel functionalities can emerge. For semiconductors, this is exemplified by the 'superlattice' concept of Esaki and Tsu, where the width of the repeated stacking of different semiconductors is comparable to the 'size' of the electrons, resulting in novel confined states now routinely used in opto-electronics. For metals, a good example is magnetic/non-magnetic multilayer films that are thinner than the spin-scattering length, from which giant magnetoresistance (GMR) emerged, used in the read heads of hard disk drives. For transition metal oxides, a similar research program is currently underway, broadly motivated by the vast array of physical properties that they host. This long-standing notion has been recently invigorated by the development of atomic-scale growth and probe techniques, which enables the study of complex oxide heterostructures approaching the precision idealized in Fig. 1(a). Taking the subset of oxides derived from the perovskite crystal structure, the close lattice match across many transition metal oxides presents the opportunity, in principle, to develop a 'universal' heteroepitaxial materials system. Hand-in-hand with the continual improvements in materials control, an increasingly relevant challenge is to understand the consequences of the electrostatic boundary conditions which arise in these structures. The essence of this issue can be seen in Fig. 1(b), where the charge sequence of the sublayer 'stacks' for various representative perovskites is shown in the ionic limit, in the (001) direction. To truly 'universally' incorporate different properties using different materials components, be it magnetism, ferroelectricity, superconductivity, etc., it is necessary to access and join different charge sequences, labelled here in analogy to the designations 'group IV, III-V, II

  16. Effect of boundary conditions on radial mode structure of whistlers

    International Nuclear Information System (INIS)

    Boswell, R.W.

    1983-01-01

    The dispersion of the radical eigen modes of a cylindrical m=1 whistler wave with Ωsub(i) << ω << Ωsub(e) << ωsub(pe) are investigated for both conducting and insulating boundaries, where Ωsub(e) and Ωsub(i) are the electron and ion gyro frequencies, Ωsub(pe) is the electron plasma frequency. The effects of electron inertia and resistivity on the modes are discussed

  17. Exchange of stability for a column of fluid with variable Rayleigh number under free boundary conditions

    Science.gov (United States)

    Korbly, L.

    1980-01-01

    The exchange of stabilities is demonstrated for a system with harmonic boundary conditions. The motion of fluid in the presence of temperatures gradients is described. It is shown that this principle holds under free, but not rigid or semirigid, boundary conditions.

  18. Trickle-down boundary conditions in aeolian dune-field pattern formation

    Science.gov (United States)

    Ewing, R. C.; Kocurek, G.

    2015-12-01

    One the one hand, wind-blown dune-field patterns emerge within the overarching boundary conditions of climate, tectonics and eustasy implying the presence of these signals in the aeolian geomorphic and stratigraphic record. On the other hand, dune-field patterns are a poster-child of self-organization, in which autogenic processes give rise to patterned landscapes despite remarkable differences in the geologic setting (i.e., Earth, Mars and Titan). How important are climate, tectonics and eustasy in aeolian dune field pattern formation? Here we develop the hypothesis that, in terms of pattern development, dune fields evolve largely independent of the direct influence of 'system-scale' boundary conditions, such as climate, tectonics and eustasy. Rather, these boundary conditions set the stage for smaller-scale, faster-evolving 'event-scale' boundary conditions. This 'trickle-down' effect, in which system-scale boundary conditions indirectly influence the event scale boundary conditions provides the uniqueness and richness of dune-field patterned landscapes. The trickle-down effect means that the architecture of the stratigraphic record of dune-field pattern formation archives boundary conditions, which are spatially and temporally removed from the overarching geologic setting. In contrast, the presence of an aeolian stratigraphic record itself, reflects changes in system-scale boundary conditions that drive accumulation and preservation of aeolian strata.

  19. Eigenstates of a particle in an array of hexagons with periodic boundary condition

    Directory of Open Access Journals (Sweden)

    A Nemati

    2013-10-01

    Full Text Available In this paper the problem of a particle in an array of hexagons with periodic boundary condition is solved. Using the projection operators, we categorize eigenfunctions corresponding to each of the irreducible representations of the symmetry group . Based on these results, the Dirichlet and Neumann boundary conditions are discussed.

  20. The effect of external boundary conditions on condensation heat transfer in rotating heat pipes

    Science.gov (United States)

    Daniels, T. C.; Williams, R. J.

    1979-01-01

    Experimental evidence shows the importance of external boundary conditions on the overall performance of a rotating heat pipe condenser. Data are presented for the boundary conditions of constant heat flux and constant wall temperature for rotating heat pipes containing either pure vapor or a mixture of vapor and noncondensable gas as working fluid.

  1. Existence of Solution, Filippov’s Theorem and Compactness of the Set of Solutions for a Third-Order Differential Inclusion with Three- Point Boundary Conditions

    Directory of Open Access Journals (Sweden)

    Ali Rezaiguia

    2018-03-01

    Full Text Available In this paper, we study a third-order differential inclusion with three-point boundary conditions. We prove the existence of a solution under convexity conditions on the multi-valued right-hand side; the proof is based on a nonlinear alternative of Leray-Schauder type. We also study the compactness of the set of solutions and establish some Filippov’s- type results for this problem.

  2. Numerical-analytic technique for investigation of solutions of some nonlinear equations with Dirichlet conditions

    Czech Academy of Sciences Publication Activity Database

    Rontó, András; Rontó, M.; Holubová, G.; Nečesal, P.

    -, - (2011), s. 58 ISSN 1687-2770 Institutional research plan: CEZ:AV0Z10190503 Keywords : nonlinear boundary value problem * numerical-analytic method * Chebyshev interpolation polynomials Subject RIV: BA - General Mathematics Impact factor: 0.911, year: 2011 http://www.boundaryvalueproblems.com/content/2011/1/58/abstract

  3. Structural acoustic control of plates with variable boundary conditions: design methodology.

    Science.gov (United States)

    Sprofera, Joseph D; Cabell, Randolph H; Gibbs, Gary P; Clark, Robert L

    2007-07-01

    A method for optimizing a structural acoustic control system subject to variations in plate boundary conditions is provided. The assumed modes method is used to build a plate model with varying levels of rotational boundary stiffness to simulate the dynamics of a plate with uncertain edge conditions. A transducer placement scoring process, involving Hankel singular values, is combined with a genetic optimization routine to find spatial locations robust to boundary condition variation. Predicted frequency response characteristics are examined, and theoretically optimized results are discussed in relation to the range of boundary conditions investigated. Modeled results indicate that it is possible to minimize the impact of uncertain boundary conditions in active structural acoustic control by optimizing the placement of transducers with respect to those uncertainties.

  4. The Ritz Method for Boundary Problems with Essential Conditions as Constraints

    Directory of Open Access Journals (Sweden)

    Vojin Jovanovic

    2016-01-01

    Full Text Available We give an elementary derivation of an extension of the Ritz method to trial functions that do not satisfy essential boundary conditions. As in the Babuška-Brezzi approach boundary conditions are treated as variational constraints and Lagrange multipliers are used to remove them. However, we avoid the saddle point reformulation of the problem and therefore do not have to deal with the Babuška-Brezzi inf-sup condition. In higher dimensions boundary weights are used to approximate the boundary conditions, and the assumptions in our convergence proof are stated in terms of completeness of the trial functions and of the boundary weights. These assumptions are much more straightforward to verify than the Babuška-Brezzi condition. We also discuss limitations of the method and implementation issues that follow from our analysis and examine a number of examples, both analytic and numerical.

  5. Zero Forcing Conditions for Nonlinear channel Equalisation using a pre-coding scheme

    International Nuclear Information System (INIS)

    Arfa, Hichem; Belghith, Safya; El Asmi, Sadok

    2009-01-01

    This paper shows how we can present a zero forcing conditions for a nonlinear channel equalisation. These zero forcing conditions based on the rank of nonlinear system are issued from an algebraic approach based on the module theoretical approach, in which the rank of nonlinear channel is clearly defined. In order to improve the performance of equalisation and reduce the complexity of used nonlinear systems, we will apply a pre-coding scheme. Theoretical results are given and computer simulation is used to corroborate the theory .

  6. Eigenvalue Problems for Systems of Nonlinear Boundary Value Problems on Time Scales

    Directory of Open Access Journals (Sweden)

    S. K. Ntouyas

    2008-01-01

    Full Text Available Values of λ are determined for which there exist positive solutions of the system of dynamic equations, uΔΔ(t+λa(tf(v(σ(t=0, vΔΔ(t+λb(tg(u(σ(t=0, for t∈[0,1]T, satisfying the boundary conditions, u(0=0=u(σ2(1, v(0=0=v(σ2(1, where T is a time scale. A Guo-Krasnosel'skii fixed point-theorem is applied.

  7. A quenched study of the Schroedinger functional with chirally rotated boundary conditions. Non-preturbative tuning

    Energy Technology Data Exchange (ETDEWEB)

    Lopez, J. Gonzalez [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Jansen, K. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Renner, D.B. [Jefferson Lab, Newport News, VA (United States); Shindler, A. [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik

    2012-08-23

    The use of chirally rotated boundary conditions provides a formulation of the Schroedinger functional that is compatible with automatic O(a) improvement of Wilson fermions up to O(a) boundary contributions. The elimination of bulk O(a) effects requires the non-perturbative tuning of the critical mass and one additional boundary counterterm. We present the results of such a tuning in a quenched setup for several values of the renormalized gauge coupling, from perturbative to nonperturbative regimes, and for a range of lattice spacings. We also check that the correct boundary conditions and symmetries are restored in the continuum limit. (orig.)

  8. Integral conditions for nonoscillation of second order nonlinear differential equations

    Czech Academy of Sciences Publication Activity Database

    Cecchi, M.; Došlá, Z.; Marini, M.; Vrkoč, Ivo

    2006-01-01

    Roč. 64, č. 6 (2006), s. 1278-1289 ISSN 0362-546X R&D Projects: GA AV ČR(CZ) IAA1163401 Institutional research plan: CEZ:AV0Z10190503 Keywords : change of integration * half-linear differential equation * nonlinear differential equation Subject RIV: BA - General Mathematics Impact factor: 0.677, year: 2006

  9. MHD free convective boundary layer flow of a nanofluid past a flat vertical plate with Newtonian heating boundary condition.

    Science.gov (United States)

    Uddin, Mohammed J; Khan, Waqar A; Ismail, Ahmed I

    2012-01-01

    Steady two dimensional MHD laminar free convective boundary layer flows of an electrically conducting Newtonian nanofluid over a solid stationary vertical plate in a quiescent fluid taking into account the Newtonian heating boundary condition is investigated numerically. A magnetic field can be used to control the motion of an electrically conducting fluid in micro/nano scale systems used for transportation of fluid. The transport equations along with the boundary conditions are first converted into dimensionless form and then using linear group of transformations, the similarity governing equations are developed. The transformed equations are solved numerically using the Runge-Kutta-Fehlberg fourth-fifth order method with shooting technique. The effects of different controlling parameters, namely, Lewis number, Prandtl number, buoyancy ratio, thermophoresis, Brownian motion, magnetic field and Newtonian heating on the flow and heat transfer are investigated. The numerical results for the dimensionless axial velocity, temperature and nanoparticle volume fraction as well as the reduced Nusselt and Sherwood number have been presented graphically and discussed. It is found that the rate of heat and mass transfer increase as Newtonian heating parameter increases. The dimensionless velocity and temperature distributions increase with the increase of Newtonian heating parameter. The results of the reduced heat transfer rate is compared for convective heating boundary condition and found an excellent agreement.

  10. MHD free convective boundary layer flow of a nanofluid past a flat vertical plate with Newtonian heating boundary condition.

    Directory of Open Access Journals (Sweden)

    Mohammed J Uddin

    Full Text Available Steady two dimensional MHD laminar free convective boundary layer flows of an electrically conducting Newtonian nanofluid over a solid stationary vertical plate in a quiescent fluid taking into account the Newtonian heating boundary condition is investigated numerically. A magnetic field can be used to control the motion of an electrically conducting fluid in micro/nano scale systems used for transportation of fluid. The transport equations along with the boundary conditions are first converted into dimensionless form and then using linear group of transformations, the similarity governing equations are developed. The transformed equations are solved numerically using the Runge-Kutta-Fehlberg fourth-fifth order method with shooting technique. The effects of different controlling parameters, namely, Lewis number, Prandtl number, buoyancy ratio, thermophoresis, Brownian motion, magnetic field and Newtonian heating on the flow and heat transfer are investigated. The numerical results for the dimensionless axial velocity, temperature and nanoparticle volume fraction as well as the reduced Nusselt and Sherwood number have been presented graphically and discussed. It is found that the rate of heat and mass transfer increase as Newtonian heating parameter increases. The dimensionless velocity and temperature distributions increase with the increase of Newtonian heating parameter. The results of the reduced heat transfer rate is compared for convective heating boundary condition and found an excellent agreement.

  11. Inferring Lower Boundary Driving Conditions Using Vector Magnetic Field Observations

    Science.gov (United States)

    Schuck, Peter W.; Linton, Mark; Leake, James; MacNeice, Peter; Allred, Joel

    2012-01-01

    Low-beta coronal MHD simulations of realistic CME events require the detailed specification of the magnetic fields, velocities, densities, temperatures, etc., in the low corona. Presently, the most accurate estimates of solar vector magnetic fields are made in the high-beta photosphere. Several techniques have been developed that provide accurate estimates of the associated photospheric plasma velocities such as the Differential Affine Velocity Estimator for Vector Magnetograms and the Poloidal/Toroidal Decomposition. Nominally, these velocities are consistent with the evolution of the radial magnetic field. To evolve the tangential magnetic field radial gradients must be specified. In addition to estimating the photospheric vector magnetic and velocity fields, a further challenge involves incorporating these fields into an MHD simulation. The simulation boundary must be driven, consistent with the numerical boundary equations, with the goal of accurately reproducing the observed magnetic fields and estimated velocities at some height within the simulation. Even if this goal is achieved, many unanswered questions remain. How can the photospheric magnetic fields and velocities be propagated to the low corona through the transition region? At what cadence must we observe the photosphere to realistically simulate the corona? How do we model the magnetic fields and plasma velocities in the quiet Sun? How sensitive are the solutions to other unknowns that must be specified, such as the global solar magnetic field, and the photospheric temperature and density?

  12. Second order bounce back boundary condition for the lattice Boltzmann fluid simulation

    International Nuclear Information System (INIS)

    Kim, In Chan

    2000-01-01

    A new bounce back boundary method of the second order in error is proposed for the lattice Boltzmann fluid simulation. This new method can be used for the arbitrarily irregular lattice geometry of a non-slip boundary. The traditional bounce back boundary condition for the lattice Boltzmann simulation is of the first order in error. Since the lattice Boltzmann method is the second order scheme by itself, a boundary technique of the second order has been desired to replace the first order bounce back method. This study shows that, contrary to the common belief that the bounce back boundary condition is unilaterally of the first order, the second order bounce back boundary condition can be realized. This study also shows that there exists a generalized bounce back technique that can be characterized by a single interpolation parameter. The second order bounce back method can be obtained by proper selection of this parameter in accordance with the detailed lattice geometry of the boundary. For an illustrative purpose, the transient Couette and the plane Poiseuille flows are solved by the lattice Boltzmann simulation with various boundary conditions. The results show that the generalized bounce back method yields the second order behavior in the error of the solution, provided that the interpolation parameter is properly selected. Coupled with its intuitive nature and the ease of implementation, the bounce back method can be as good as any second order boundary method

  13. A novel investigation of a micropolar fluid characterized by nonlinear constitutive diffusion model in boundary layer flow and heat transfer.

    Science.gov (United States)

    Sui, Jize; Zhao, Peng; Cheng, Zhengdong; Zheng, Liancun; Zhang, Xinxin

    2017-02-01

    The rheological and heat-conduction constitutive models of micropolar fluids (MFs), which are important non-Newtonian fluids, have been, until now, characterized by simple linear expressions, and as a consequence, the non-Newtonian performance of such fluids could not be effectively captured. Here, we establish the novel nonlinear constitutive models of a micropolar fluid and apply them to boundary layer flow and heat transfer problems. The nonlinear power law function of angular velocity is represented in the new models by employing generalized " n -diffusion theory," which has successfully described the characteristics of non-Newtonian fluids, such as shear-thinning and shear-thickening fluids. These novel models may offer a new approach to the theoretical understanding of shear-thinning behavior and anomalous heat transfer caused by the collective micro-rotation effects in a MF with shear flow according to recent experiments. The nonlinear similarity equations with a power law form are derived and the approximate analytical solutions are obtained by the homotopy analysis method, which is in good agreement with the numerical solutions. The results indicate that non-Newtonian behaviors involving a MF depend substantially on the power exponent n and the modified material parameter [Formula: see text] introduced by us. Furthermore, the relations of the engineering interest parameters, including local boundary layer thickness, local skin friction, and Nusselt number are found to be fitted by a quadratic polynomial to n with high precision, which enables the extraction of the rapid predictions from a complex nonlinear boundary-layer transport system.

  14. A novel investigation of a micropolar fluid characterized by nonlinear constitutive diffusion model in boundary layer flow and heat transfer

    Science.gov (United States)

    Sui, Jize; Zhao, Peng; Cheng, Zhengdong; Zheng, Liancun; Zhang, Xinxin

    2017-02-01

    The rheological and heat-conduction constitutive models of micropolar fluids (MFs), which are important non-Newtonian fluids, have been, until now, characterized by simple linear expressions, and as a consequence, the non-Newtonian performance of such fluids could not be effectively captured. Here, we establish the novel nonlinear constitutive models of a micropolar fluid and apply them to boundary layer flow and heat transfer problems. The nonlinear power law function of angular velocity is represented in the new models by employing generalized "n-diffusion theory," which has successfully described the characteristics of non-Newtonian fluids, such as shear-thinning and shear-thickening fluids. These novel models may offer a new approach to the theoretical understanding of shear-thinning behavior and anomalous heat transfer caused by the collective micro-rotation effects in a MF with shear flow according to recent experiments. The nonlinear similarity equations with a power law form are derived and the approximate analytical solutions are obtained by the homotopy analysis method, which is in good agreement with the numerical solutions. The results indicate that non-Newtonian behaviors involving a MF depend substantially on the power exponent n and the modified material parameter K 0 introduced by us. Furthermore, the relations of the engineering interest parameters, including local boundary layer thickness, local skin friction, and Nusselt number are found to be fitted by a quadratic polynomial to n with high precision, which enables the extraction of the rapid predictions from a complex nonlinear boundary-layer transport system.

  15. Graph Theory-Based Technique for Isolating Corrupted Boundary Conditions in Continental-Scale River Network Hydrodynamic Simulation

    Science.gov (United States)

    Yu, C. W.; Hodges, B. R.; Liu, F.

    2017-12-01

    Development of continental-scale river network models creates challenges where the massive amount of boundary condition data encounters the sensitivity of a dynamic nu- merical model. The topographic data sets used to define the river channel characteristics may include either corrupt data or complex configurations that cause instabilities in a numerical solution of the Saint-Venant equations. For local-scale river models (e.g. HEC- RAS), modelers typically rely on past experience to make ad hoc boundary condition adjustments that ensure a stable solution - the proof of the adjustment is merely the sta- bility of the solution. To date, there do not exist any formal methodologies or automated procedures for a priori detecting/fixing boundary conditions that cause instabilities in a dynamic model. Formal methodologies for data screening and adjustment are a critical need for simulations with a large number of river reaches that draw their boundary con- dition data from a wide variety of sources. At the continental scale, we simply cannot assume that we will have access to river-channel cross-section data that has been ade- quately analyzed and processed. Herein, we argue that problematic boundary condition data for unsteady dynamic modeling can be identified through numerical modeling with the steady-state Saint-Venant equations. The fragility of numerical stability increases with the complexity of branching in river network system and instabilities (even in an unsteady solution) are typically triggered by the nonlinear advection term in Saint-Venant equations. It follows that the behavior of the simpler steady-state equations (which retain the nonlin- ear term) can be used to screen the boundary condition data for problematic regions. In this research, we propose a graph-theory based method to isolate the location of corrupted boundary condition data in a continental-scale river network and demonstrate its utility with a network of O(10^4) elements. Acknowledgement

  16. The determination of an unknown boundary condition in a fractional diffusion equation

    KAUST Repository

    Rundell, William

    2013-07-01

    In this article we consider an inverse boundary problem, in which the unknown boundary function ∂u/∂v = f(u) is to be determined from overposed data in a time-fractional diffusion equation. Based upon the free space fundamental solution, we derive a representation for the solution f as a nonlinear Volterra integral equation of second kind with a weakly singular kernel. Uniqueness and reconstructibility by iteration is an immediate result of a priori assumption on f and applying the fixed point theorem. Numerical examples are presented to illustrate the validity and effectiveness of the proposed method. © 2013 Copyright Taylor and Francis Group, LLC.

  17. Exact Solution of the Six-Vertex Model with Domain Wall Boundary Conditions. Disordered Phase

    CERN Document Server

    Bleher, P M

    2005-01-01

    The six-vertex model, or the square ice model, with domain wall boundary conditions (DWBC) has been introduced and solved for finite $N$ by Korepin and Izergin. The solution is based on the Yang-Baxter equations and it represents the free energy in terms of an $N\\times N$ Hankel determinant. Paul Zinn-Justin observed that the Izergin-Korepin formula can be re-expressed in terms of the partition function of a random matrix model with a nonpolynomial interaction. We use this observation to obtain the large $N$ asymptotics of the six-vertex model with DWBC in the disordered phase. The solution is based on the Riemann-Hilbert approach and the Deift-Zhou nonlinear steepest descent method. As was noticed by Kuperberg, the problem of enumeration of alternating sign matrices (the ASM problem) is a special case of the the six-vertex model. We compare the obtained exact solution of the six-vertex model with known exact results for the 1, 2, and 3 enumerations of ASMs, and also with the exact solution on the so-called f...

  18. Flow and heat transfer in Sisko fluid with convective boundary condition.

    Science.gov (United States)

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

    2014-01-01

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

  19. An approximate method for solving a melting problem with periodic boundary conditions

    Directory of Open Access Journals (Sweden)

    Qu Liang-Hui

    2014-01-01

    Full Text Available An effective thermal diffusivity method is used to solve one-dimensional melting problem with periodic boundary conditions in a semi-infinite domain. An approximate analytic solution showing the functional relation between the location of the moving boundary and time is obtained by using Laplace transform. The evolution of the moving boundary and the temperature field in the phase change domain are simulated numerically, and the numerical results are compared with previous results in open literature.

  20. Chaotic attractors, chaotic saddles, and fractal basin boundaries : Goodwin's nonlinear accelerator model reconsidered

    NARCIS (Netherlands)

    Lorenz, HW; Nusse, HE

    Goodwin's nonlinear accelerator model with periodic investment outlays is reconsidered and used as an economic example of the emergence of complex motion in nonlinear dynamical systems. In addition to chaotic attractors, the model can possess coexisting attracting periodic orbits or simple

  1. CFD Modeling of Non-Neutral Atmospheric Boundary Layer Conditions

    DEFF Research Database (Denmark)

    Koblitz, Tilman

    . All implementations in the ABL model are tuning free, and except for standard site specific input parameters, no additional model coefficients need to be specified before the simulation. In summary the results show that the implemented modifications are applicable and reproduce the main flow......For wind resource assessment, the wind industry is increasingly relying on Computational Fluid Dynamics models that focus on modeling the airflow in a neutrally stratified surface-layer. Physical processes like the Coriolis force, buoyancy forces and heat transport, that are important...... to the atmospheric boundary-layer, are mostly ignored so far. In order to decrease the uncertainty of wind resource assessment, the present work focuses on atmospheric flows that include atmospheric stability and the Coriolis effect. Within the present work a RANS model framework is developed and implemented...

  2. Boundary Conditions for a New Type of Design Task

    DEFF Research Database (Denmark)

    McAloone, Tim C.

    2011-01-01

    and knowledge associated with the use of the product is increasingly perceived to be the new design object. But how to organise the design of combined products and services, over expanded time domains and new stakeholder boundaries? The design research community is paying increasing attention to this new design......Manufacturing companies have traditionally focused their efforts on developing and producing physical products for the market. Currently, however, many companies are rethinking their business strategies, from selling products to providing services. In place of the product alone, the activity...... object and research paradigm, studying service‐oriented approaches to product development and seeking to understand how to spell the systematic development of these so-called Product/Service‐Systems (PSS). When considering the shift towards PSS in the domain of engineering, it is in...

  3. Implications of a wavepacket formulation for the nonlinear parabolized stability equations to hypersonic boundary layers

    Science.gov (United States)

    Kuehl, Joseph

    2016-11-01

    The parabolized stability equations (PSE) have been developed as an efficient and powerful tool for studying the stability of advection-dominated laminar flows. In this work, a new "wavepacket" formulation of the PSE is presented. This method accounts for the influence of finite-bandwidth-frequency distributions on nonlinear stability calculations. The methodology is motivated by convolution integrals and is found to appropriately represent nonlinear energy transfer between primary modes and harmonics, in particular nonlinear feedback, via a "nonlinear coupling coefficient." It is found that traditional discrete mode formulations overestimate nonlinear feedback by approximately 70%. This results in smaller maximum disturbance amplitudes than those observed experimentally. The new formulation corrects this overestimation, accounts for the generation of side lobes responsible for spectral broadening and results in disturbance saturation amplitudes consistent with experiment. A Mach 6 flared-cone example is presented. Support from the AFOSR Young Investigator Program via Grant FA9550-15-1-0129 is gratefully acknowledges.

  4. Solutions to fourth-order random differential equations with periodic boundary conditions

    Directory of Open Access Journals (Sweden)

    Xiaoling Han

    2012-12-01

    Full Text Available Existence of solutions and of extremal random solutions are proved for periodic boundary-value problems of fourth-order ordinary random differential equations. Our investigation is done in the space of continuous real-valued functions defined on closed and bounded intervals. Also we study the applications of the random version of a nonlinear alternative of Leray-Schauder type and an algebraic random fixed point theorem by Dhage.

  5. On problems with displacement in boundary conditions for hyperbolic equation

    Directory of Open Access Journals (Sweden)

    Elena A. Utkina

    2016-03-01

    Full Text Available We consider three problems for hyperbolic equation on a plane in the characteristic domain. In these problems at least one of the conditions of the Goursat problem is replaced by nonlocal condition on the relevant characteristic. Non-local conditions are the linear combinations of the normal derivatives at points on opposite characteristics. In case of replacement of one condition we solve the problem by reduction to the Goursat problem for which it exists and is unique. To find the unknown Goursat condition author receives the integral equation, rewrite it in operational form and finds its unique solvability cases. To prove the unique solvability of the equation, the author shows the continuous linear operator and the fact, that some degree of the resulting operator is a contraction mapping. It is known that in this case the required Goursat condition can be written as Neumann series. We considered in detail only one of the tasks, but for both the unique solvability theorems are formulated. If the two conditions are changed, the uniqueness of the solution on the assumption that it exists, is proved by the method of a priori estimates. For this purpose, the inner product and the norm in $L_2$ are used. As a result, the conditions were obtained for the coefficients of a hyperbolic equation that ensure the uniqueness of the solution. An example is given, confirming that these conditions are essential. Namely, constructed an equation whose coefficients do not satisfy the conditions of the last theorem, given the conditions on the characteristics and nontrivial solution is built.

  6. Entropy generation due to double diffusive convective flow of Casson fluids over nonlinearity stretching sheets with slip conditions

    Directory of Open Access Journals (Sweden)

    Sameh E. Ahmed

    2017-12-01

    Full Text Available The present paper deals with the effects of slip boundary conditions and chemical reaction on the heat and mass transfer by mixed convective boundary layer flow of a non-Newtonian fluid over a nonlinear stretching sheet. The Casson fluid model is used to characterize the non-Newtonian fluid behavior. First order chemical reactions are considered. Similar solutions are used to convert the partial differential equations governing the problem to ordinary differential equations. The velocity, temperature and concentration profiles are obtained, numerically, using the MATLAB function bvp4c and those are used to compute the entropy generation number. The effect of increasing values of the Casson parameter is found to suppress the velocity field and temperature distribution. But the concentration is enhanced with the increasing of Casson parameter. The viscous dissipation, temperature and concentration irreversibility are determined and discussed in details.

  7. MHD boundary layer slip flow and radiative nonlinear heat transfer over a flat plate with variable fluid properties and thermophoresis

    Directory of Open Access Journals (Sweden)

    S.K. Parida

    2015-12-01

    Full Text Available This work considers the two-dimensional steady MHD boundary layer flow of heat and mass transfer over a flat plate with partial slip at the surface subjected to the convective heat flux. The particular attraction lies in searching the effects of variable viscosity and variable thermal diffusivity on the behavior of the flow. In addition, non-linear thermal radiation effects and thermophoresis are taken into account. The governing nonlinear partial differential equations for the flow, heat and mass transfer are transformed into a set of coupled nonlinear ordinary differential equations by using similarity variable, which are solved numerically by applying Runge–Kutta fourth–fifth order integration scheme in association with quasilinear shooting technique. The novel results for the dimensionless velocity, temperature, concentration and ambient Prandtl number within the boundary layer are displayed graphically for various parameters that characterize the flow. The local skin friction, Nusselt number and Sherwood number are shown graphically. The numerical results obtained for the particular case are fairly in good agreement with the result of Rahman [6].

  8. The refined analytic torsion and a well-posed boundary condition for the odd signature operator

    Science.gov (United States)

    Huang, Rung-Tzung; Lee, Yoonweon

    2018-03-01

    In this paper we discuss the refined analytic torsion on an odd dimensional compact oriented Riemannian manifold with boundary under some assumption. For this purpose we introduce two boundary conditions which are complementary to each other and well-posed for the odd signature operator B in the sense of Seeley. We then show that the zeta-determinants of B2 and eta-invariants of B subject to these boundary conditions are well defined by using the method of the asymptotic expansions of the traces of the heat kernels. We use these facts to define the refined analytic torsion on a compact manifold with boundary and show that it is invariant on the change of metrics in the interior of the manifold. We finally describe the refined analytic torsion under these boundary conditions as an element of the determinant line.

  9. The PPP model of alternant cyclic polyenes with modified boundary conditions

    International Nuclear Information System (INIS)

    Bendazzoli, G.L.; Evangelisti, S.

    1995-01-01

    The extension of the PPP Hamiltonian for alternant cyclic polyenes to noninteger values of the pseudomomentum by imposing modified boundary conditions is discussed in detail. It is shown that a computer program for periodic boundary conditions can be easily adapted to the new boundary conditions. Full CI computations are carried out for some low-lying states of the PPP model of alternant cyclic polyenes (CH) N (N even) at half-filling. The energy values obtained by using periodic (Bloch) and antiperiodic (Moebius) orbitals are used to perform energy extrapolations for N → ∞. 38 refs., 2 figs., 5 tabs

  10. Existence and regularity of solutions to the Leray-alpha model with Navier slip boundary conditions

    Directory of Open Access Journals (Sweden)

    Hani Ali

    2016-08-01

    Full Text Available We establish the existence and regularity of a unique weak solution to turbulent flows in a bounded domain $\\Omega\\subset\\mathbb R^3$ governed by the Leray-$\\alpha$ model with Navier slip boundary condition for the velocity. Furthermore, we show that when the filter coefficient $\\alpha$ tends to zero, these weak solutions converge to a suitable weak solution to the incompressible Navier Stokes equations subject to the Navier boundary conditions. Finally, we discuss the relation between the Leray-$\\alpha$ model and the Navier-Stokes equations with homogeneous Dirichlet boundary condition.

  11. Effects of boundary conditions on magnetization switching in kinetic ising models of nanoscale ferromagnets

    DEFF Research Database (Denmark)

    Richards, H.L.; Kolesik, M.; Lindgård, P.-A.

    1997-01-01

    Magnetization switching in highly anisotropic single-domain ferromagnets has been previously shown to be qualitatively described by the droplet theory of metastable decay and simulations of two-dimensional kinetic Ising systems with periodic boundary conditions. In this paper we consider the effe......Magnetization switching in highly anisotropic single-domain ferromagnets has been previously shown to be qualitatively described by the droplet theory of metastable decay and simulations of two-dimensional kinetic Ising systems with periodic boundary conditions. In this paper we consider...... simulations of two-dimensional Ising systems with various system shapes and boundary conditions....

  12. An effective absorbing layer for the boundary condition in acoustic seismic wave simulation

    Science.gov (United States)

    Yao, Gang; da Silva, Nuno V.; Wu, Di

    2018-04-01

    Efficient numerical simulation of seismic wavefields generally involves truncating the Earth model in order to keep computing time and memory requirements down. Absorbing boundary conditions, therefore, are applied to remove the boundary reflections caused by this truncation, thereby allowing for accurate modeling of wavefields. In this paper, we derive an effective absorbing boundary condition for both acoustic and elastic wave simulation, through the simplification of the damping term of the split perfectly matched layer (SPML) boundary condition. This new boundary condition is accurate, cost-effective, and easily implemented, especially for high-performance computing. Stability analysis shows that this boundary condition is effectively as stable as normal (non-absorbing) wave equations for explicit time-stepping finite differences. We found that for full-waveform inversion (FWI), the strengths of the effective absorbing layer—a reduction of the computational and memory cost coupled with a simplistic implementation—significantly outweighs the limitation of incomplete absorption of outgoing waves relative to the SPML. More importantly, we demonstrate that this limitation can easily be overcome through the use of two strategies in FWI, namely variable cell size and model extension thereby fully compensating for the imperfectness of the proposed absorbing boundary condition.

  13. Heat conduction in a plate-type fuel element with time-dependent boundary conditions

    International Nuclear Information System (INIS)

    Faya, A.J.G.; Maiorino, J.R.

    1981-01-01

    A method for the solution of boundary-value problems with variable boundary conditions is applied to solve a heat conduction problem in a plate-type fuel element with time dependent film coefficient. The numerical results show the feasibility of the method in the solution of this class of problems. (Author) [pt

  14. Nonlinear Boundary Value Problem for Concave Capillary Surfaces Occurring in Single Crystal Rod Growth from the Melt

    Directory of Open Access Journals (Sweden)

    Agneta Maria Balint

    2008-12-01

    Full Text Available The boundary value problem z″=((ρ⋅g⋅z−p/γ[1+(z′2]3/2−(1/r⋅[1+(z′2]⋅z′, r∈[r1, r0], z′(r1=−tan⁡(π/2−αg, z′(r0=−tan⁡αc, z(r0=0, and z(r is strictly decreasing on [r1,r0], is considered. Here, 0conditions are given in terms of p for the existence of concave solutions of the above nonlinear boundary value problem (NLBVP. Numerical illustration is given. This kind of results is useful in the experiment planning and technology design of single crystal rod growth from the melt by edge-defined film-fed growth (EFG method. With this aim, this study was undertaken.

  15. Wave Height Distribution for Nonlinear Swell Waves in Deep an Depth-Limited Wave Conditions

    DEFF Research Database (Denmark)

    Nørgaard, Jørgen Harck; Andersen, Thomas Lykke; Knudsen, Jannie Elkær

    2017-01-01

    This paper presents initial results from an on-going study on the influence from wave nonlinearity on the wave height distribution in deep- and depth-limited nonlinear wave conditions. A fully nonlinear VOF model, IH-2VOF, is applied to model the propagation of irregular waves on a sloping sea bed...... Battjes & Groenendijk (2000) shallow water wave height distribution is concluded in the present study to significantly underpredict the low-exceedance wave heights in case of very nonlinear waves. A modification of the Battjess & Groenendijk (2000) distribution is suggested in order to include the effects...... from deep to shallow water, including the effects of wave breaking. Different wave nonlinearities are evaluated in the model and the effects of the wave nonlinearity, described by the so-called Ursell-number, on the wave height distributions along the sloping sea bed are evaluated. The widely used...

  16. Crossing the boundary: numerical investigation of water entry conditions

    Science.gov (United States)

    Angelidis, Dionysios; Sotiropoulos, Fotis

    2017-11-01

    Several engineering and scientific applications involve water impact problems. To accurately capture the dynamics of the cavity formation and the water ejected as a body hits the water, the formidable range of temporal and spatial scales should accurately be resolved with affordable computational cost. We have enhanced the potential of the two-phase flow version of the immersed-boundary adaptive mesh refinement flow solver, developed by our group, to perform high-fidelity two-phase flow calculations on locally refined grids. We employ a level-set method and tackle the computational challenges arise during the explicit solution of a mass-conserving reinitialization equation. In contrast to conventional approaches, we propose a convergence criterion which enables the number of iterations to be self-adjusted based on the values of the distance function. The efficiency of our method is demonstrated by performing two-phase flow calculations including the high-speed water entry of a V-shaped wedge. Our results are found to be in good agreement with experimental measurements and enable us to gain insight into the instability that arises on the onset of the closure phase of the cavity. This material is based upon work supported by the National Science Foundation (CBET-1509071).

  17. A free boundary problem for a reaction-diffusion system with nonlinear memory

    DEFF Research Database (Denmark)

    Lin, Zhigui; Ling, Zhi; Pedersen, Michael

    2013-01-01

    We consider a integro-partial differential equation with a free boundary which appears in the theory of the nuclear dynamics. First, local existence and uniqueness are obtained by using the contraction mapping theorem. Then, the behavior of the free boundary and the blow-up criteria are obtained...

  18. Asymptotic investigation of the nonlinear boundary value dynamic problem for the systems with finite sizes

    International Nuclear Information System (INIS)

    Andrianov, I.V.; Danishevsky, V.V.

    1994-01-01

    Asymptotic approaches for nonlinear dynamics of continual system are developed well for the infinite in spatial variables. For the systems with finite sizes we have an infinite number of resonance, and Poincare-Lighthill-Go method does riot work. Using of averaging procedure or method of multiple scales leads to the infinite systems of nonlinear algebraic or ordinary differential equations systems and then using truncation method. which does not gives possibility to obtain all important properties of the solutions

  19. Boundary Conditions and the Aeolian Sediment State of the Olympia Undae Dune Field, Mars

    Science.gov (United States)

    Middlebrook, W.; Ewing, R. C.; Ayoub, F.; Bridges, N. T.; Smith, I.; Spiga, A.

    2015-05-01

    We evaluate the boundary conditions in Olympia Undae. We map two and three dimensional dune parameters from two locations proximal and distal to Planum Boreum and constrain sediment fluxes. We compare our results with a mesoscale atmospheric model.

  20. On the Ideal Boundary Condition in a General Toroidal Geometry for a Mixed Magnetic Field Representation

    International Nuclear Information System (INIS)

    Tang, X. Z.

    2000-01-01

    Subtleties of implementing the standard perfectly conducting wall boundary condition in a general toroidal geometry are clarified for a mixed scalar magnetic field representation. An iterative scheme based on Ohm's law is given

  1. Experimental validation of the sound transmission of rectangular baffled plates with general elastic boundary conditions.

    Science.gov (United States)

    Ou, Dayi; Mak, Cheuk Ming

    2011-06-01

    Several prediction methods have recently been developed for systematically studying the effects of general boundary conditions on the sound transmission loss (STL) of plate-like structures. But corresponding experimental validation studies remain scarce owing to the difficulty of obtaining accurate boundary conditions for practical structures. This paper presents a convincing experiment conducted on a baffled plate system to validate the STL prediction model in a previous paper by Yu et al. [Noise Control Eng. J. 58(2), 187-200, 2010]. A method is proposed to determine the boundary conditions of this system, and experimental STL compares well with the predictions based on the identified boundary condition. © 2011 Acoustical Society of America

  2. Enhancement of single mode operation in coaxial optical waveguide using DB boundary conditions

    Science.gov (United States)

    Lohia, Pooja; Prajapati, Y.; Saini, J. P.; Rai, B. S.

    2014-11-01

    In this study, a competent numerical strategy to compute the dispersion of optical waveguides is presented and propagation of electromagnetic waves in a coaxial optical waveguide with DB boundary conditions is instigated. For this intend, cylindrical coordinates are here being used to derive the DB boundary conditions and to obtain field components for the modes. The propagation constant for the waveguide to be studied is determined by solving the Bessel and the modified Bessel functions. The cutoff frequencies for various lower order modes have been calculated and their dispersion characteristics are plotted correspondingly. The behavior of the coaxial optical waveguide under DB boundary conditions is shown to be significantly different from that of coaxial optical waveguide and conventional optical waveguide under traditional or tangential boundary conditions. Finally, the effect of waveguide dimensions on the mode cutoff frequencies and fabrication issues are also addressed.

  3. The No-Slip Boundary Condition in Fluid Mechanics

    Indian Academy of Sciences (India)

    Ideas leading to the resolution of the problem of no-slip condition for fluid velocity at a solid surface are traced in this concluding part of the article. In the continuum limit velocity slip being zero is established beyond any doubt now. Even turbulent flows which have a large velocity gradient near a wall have to satisfy the ...

  4. Stokes flow with slip and Kuwabara boundary conditions

    Indian Academy of Sciences (India)

    R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22

    condition under Stokes approximation using particle-in-cell model technique and the result compared with the no-slip case. The corresponding problem of streaming flow past spheroidal particles departing but little in shape from a sphere is also investigated. The explicit expression for the stream function is obtained to the ...

  5. The No-Slip Boundary Condition in Fluid Mechanics

    Indian Academy of Sciences (India)

    Historical Development. A brief and excellent review of this problem of velocity slip in fluid flow is given in the book by Goldstein [1]. We freely borrow from this book adding some explanations and supple- ments based on the earlier discussion in Part 1. We saw that Newton tacitly assumed the no-slip condition in the.

  6. Existence of Solutions of Abstract Nonlinear Mixed Functional Integrodifferential equation with nonlocal conditions

    Directory of Open Access Journals (Sweden)

    Dhakne Machindra B.

    2017-04-01

    Full Text Available In this paper we discuss the existence of mild and strong solutions of abstract nonlinear mixed functional integrodifferential equation with nonlocal condition by using Sadovskii’s fixed point theorem and theory of fractional power of operators.

  7. Numerical analysis of the asymptotic behavior of solutions of a boundary problem for a nonlinear parabolic equation

    International Nuclear Information System (INIS)

    Vasileva, D.P.

    1993-01-01

    Blow-up and global time self-similar solutions of a boundary problem for a nonlinear equation u t = Δ u σ+1 + u β are found in the case β = σ + 1. It is shown that they describe the asymptotic behavior of a wide class of initial perturbations. A numerical investigation of the solutions in the case β>σ + 1 is also made. A hypothesis is done that the behavior for large times of global time solutions is described by the self-similar solutions of the equation without source.(author). 20 refs.; 9 figs

  8. DNS of turbulent heat transfer in a channel flow with streamwisely varying thermal boundary condition

    International Nuclear Information System (INIS)

    Seki, Yohji; Kawamura, Hiroshi

    2005-01-01

    Direct numerical simulation (DNS) have been performed for the turbulent heat transfer in a channel flow. In the present study, effect of thermal boundary condition is examined. DNS has been carried out for streamwisely thermal boundary conditions (Re τ =180) with Pγ=0.71 to obtain statistical mean temperatures, temperature variances, budget terms and time scale ratios etc. The obtained results have indicated that the time scale ratio varies along a streamwise. (author)

  9. Asymptotic stability and blow up for a semilinear damped wave equation with dynamic boundary conditions

    KAUST Repository

    Gerbi, Stéphane

    2011-12-01

    In this paper we consider a multi-dimensional wave equation with dynamic boundary conditions, related to the KelvinVoigt damping. Global existence and asymptotic stability of solutions starting in a stable set are proved. Blow up for solutions of the problem with linear dynamic boundary conditions with initial data in the unstable set is also obtained. © 2011 Elsevier Ltd. All rights reserved.

  10. Strongly nonlinear nonhomogeneous elliptic unilateral problems with L^1 data and no sign conditions

    Directory of Open Access Journals (Sweden)

    Elhoussine Azroul

    2012-05-01

    Full Text Available In this article, we prove the existence of solutions to unilateral problems involving nonlinear operators of the form: $$ Au+H(x,u,abla u=f $$ where $A$ is a Leray Lions operator from $W_0^{1,p(x}(Omega$ into its dual $W^{-1,p'(x}(Omega$ and $H(x,s,xi$ is the nonlinear term satisfying some growth condition but no sign condition. The right hand side $f$ belong to $L^1(Omega$.

  11. Adaptive State Estimation for a Class of Nonlinear Stochastic Systems under Generalized Lipschitz Condition

    Science.gov (United States)

    Miao, Xiu-feng; Li, Long-suo; Yan, Xiu-ming

    2014-11-01

    This paper is concerned with adaptive observer design problem for a class of nonlinear stochastic systems. Unknown constant parameters are assumed to be norm bounded. In order to better use the structural knowledge of the nonlinear part, a generalized Lipschitz condition is introduced to the adaptive observer design for a class of nonlinear stochastic systems for the first time. Based on a Lyapunov-Krasovskii functional approach and stochastic Lyapunov stability theory, we present a new adaptive observer design condition with ultimately exponentially bounded in sense of mean square for errors systems in terms of linear matrix inequality (LMI). A numerical example is exploited to show the validity and feasibility of the results.

  12. Schrödinger functional boundary conditions and improvement for N > 3

    DEFF Research Database (Denmark)

    Hietanen, A.; Karavirta, T.; Vilaseca, P.

    2014-01-01

    The standard method to calculate non-perturbatively the evolution of the running coupling of a SU(N ) gauge theory is based on the Schrodinger functional (SF). In this paper we construct a family of boundary fields for general values of N which enter the standard definition of the SF coupling. We...... provide spatial boundary conditions for fermions in several representations which reduce the condition number of the squared Dirac operator. In addition, we calculate the improvement coefficients for N > 3 needed to remove boundary cutoff effects from the gauge action. After this, residual cutoff effects...

  13. Dirac perturbations on Schwarzschild-anti-de Sitter spacetimes: Generic boundary conditions and new quasinormal modes

    Science.gov (United States)

    Wang, Mengjie; Herdeiro, Carlos; Jing, Jiliang

    2017-11-01

    We study Dirac quasinormal modes of Schwarzschild-anti-de Sitter (Schwarzschild-AdS) black holes, following the generic principle for allowed boundary conditions proposed in [M. Wang, C. Herdeiro, and M. O. P. Sampaio, Phys. Rev. D 92, 124006 (2015)., 10.1103/PhysRevD.92.124006]. After deriving the equations of motion for Dirac fields on the aforementioned background, we impose vanishing energy flux boundary conditions to solve these equations. We find a set of two Robin boundary conditions are allowed. These two boundary conditions are used to calculate Dirac normal modes on empty AdS and quasinormal modes on Schwarzschild-AdS black holes. In the former case, we recover the known normal modes of empty AdS; in the latter case, the two sets of Robin boundary conditions lead to two different branches of quasinormal modes. The impact on these modes of the black hole size, the angular momentum quantum number and the overtone number are discussed. Our results show that vanishing energy flux boundary conditions are a robust principle, applicable not only to bosonic fields but also to fermionic fields.

  14. Effects of Uncertainties in Electric Field Boundary Conditions for Ring Current Simulations

    Science.gov (United States)

    Chen, Margaret W.; O'Brien, T. Paul; Lemon, Colby L.; Guild, Timothy B.

    2018-01-01

    Physics-based simulation results can vary widely depending on the applied boundary conditions. As a first step toward assessing the effect of boundary conditions on ring current simulations, we analyze the uncertainty of cross-polar cap potentials (CPCP) on electric field boundary conditions applied to the Rice Convection Model-Equilibrium (RCM-E). The empirical Weimer model of CPCP is chosen as the reference model and Defense Meteorological Satellite Program CPCP measurements as the reference data. Using temporal correlations from a statistical analysis of the "errors" between the reference model and data, we construct a Monte Carlo CPCP discrete time series model that can be generalized to other model boundary conditions. RCM-E simulations using electric field boundary conditions from the reference model and from 20 randomly generated Monte Carlo discrete time series of CPCP are performed for two large storms. During the 10 August 2000 storm main phase, the proton density at 10 RE at midnight was observed to be low (Dst index is bounded by the simulated Dst values. In contrast, the simulated Dst values during the recovery phases of the 10 August 2000 and 31 August 2005 storms tend to underestimate systematically the observed late Dst recovery. This suggests a need to improve the accuracy of particle loss calculations in the RCM-E model. Application of this technique can aid modelers to make efficient choices on either investing more effort on improving specification of boundary conditions or on improving descriptions of physical processes.

  15. Unsteady boundary layer flow of a nanofluid over a stretching/shrinking sheet with a convective boundary condition

    Directory of Open Access Journals (Sweden)

    Syahira Mansur

    2016-10-01

    Full Text Available The unsteady boundary layer flow of a nanofluid past a stretching/shrinking sheet with a convective surface boundary condition is studied. The effects of the unsteadiness parameter, stretching/shrinking parameter, convective parameter, Brownian motion parameter and thermophoresis parameter on the local Nusselt number are investigated. Numerical solutions to the governing equations are obtained using a shooting method. The results for the local Nusselt number are presented for different values of the governing parameters. The local Nusselt number decreases as the stretching/shrinking parameter increases. The local Nusselt number is consistently higher for higher values of the convective parameter but lower for higher values of the unsteadiness parameter, Brownian motion parameter and thermophoresis parameter.

  16. Molecular dynamics simulations of a fully hydrated dipalmitoyl phosphatidylcholine bilayer with different macroscopic boundary conditions and parameters

    NARCIS (Netherlands)

    Tieleman, D.P; Berendsen, H.J.C.

    1996-01-01

    We compared molecular dynamics simulations of a bilayer of 128 fully hydrated phospholipid (DPPC) molecules, using different parameters and macroscopic boundary conditions. The same system was studied under constant pressure, constant volume, and constant surface tension boundary conditions, with

  17. Structural vibration a uniform accurate solution for laminated beams, plates and shells with general boundary conditions

    CERN Document Server

    Jin, Guoyong; Su, Zhu

    2015-01-01

    This book develops a uniform accurate method which is capable of dealing with vibrations of laminated beams, plates and shells with arbitrary boundary conditions including classical boundaries, elastic supports and their combinations. It also provides numerous solutions for various configurations including various boundary conditions, laminated schemes, geometry and material parameters, which fill certain gaps in this area of reach and may serve as benchmark solutions for the readers. For each case, corresponding fundamental equations in the framework of classical and shear deformation theory are developed. Following the fundamental equations, numerous free vibration results are presented for various configurations including different boundary conditions, laminated sequences and geometry and material properties. The proposed method and corresponding formulations can be readily extended to static analysis.

  18. An energy absorbing far-field boundary condition for the elastic wave equation

    Energy Technology Data Exchange (ETDEWEB)

    Petersson, N A; Sjogreen, B

    2008-07-15

    The authors present an energy absorbing non-reflecting boundary condition of Clayton-Engquist type for the elastic wave equation together with a discretization which is stable for any ratio of compressional to shear wave speed. They prove stability for a second order accurate finite-difference discretization of the elastic wave equation in three space dimensions together with a discretization of the proposed non-reflecting boundary condition. The stability proof is based on a discrete energy estimate and is valid for heterogeneous materials. The proof includes all six boundaries of the computational domain where special discretizations are needed at the edges and corners. The stability proof holds also when a free surface boundary condition is imposed on some sides of the computational domain.

  19. On the Boundary between Nonlinear Jump Phenomenon and Linear Response of Hypoid Gear Dynamics

    Directory of Open Access Journals (Sweden)

    Jun Wang

    2011-01-01

    Full Text Available A nonlinear time-varying (NLTV dynamic model of a hypoid gear pair system with time-dependent mesh point, line-of-action vector, mesh stiffness, mesh damping, and backlash nonlinearity is formulated to analyze the transitional phase between nonlinear jump phenomenon and linear response. It is found that the classical jump discontinuity will occur if the dynamic mesh force exceeds the mean value of tooth mesh force. On the other hand, the propensity for the gear response to jump disappears when the dynamic mesh force is lower than the mean mesh force. Furthermore, the dynamic analysis is able to distinguish the specific tooth impact types from analyzing the behaviors of the dynamic mesh force. The proposed theory is general and also applicable to high-speed spur, helical and spiral bevel gears even though those types of gears are not the primary focus of this paper.

  20. Critical dense polymers with Robin boundary conditions, half-integer Kac labels and Z4 fermions

    Directory of Open Access Journals (Sweden)

    Paul A. Pearce

    2014-12-01

    Full Text Available For general Temperley–Lieb loop models, including the logarithmic minimal models LM(p,p′ with p,p′ coprime integers, we construct an infinite family of Robin boundary conditions on the strip as linear combinations of Neumann and Dirichlet boundary conditions. These boundary conditions are Yang–Baxter integrable and allow loop segments to terminate on the boundary. Algebraically, the Robin boundary conditions are described by the one-boundary Temperley–Lieb algebra. Solvable critical dense polymers is the first member LM(1,2 of the family of logarithmic minimal models and has loop fugacity β=0 and central charge c=−2. Specialising to LM(1,2 with our Robin boundary conditions, we solve the model exactly on strips of arbitrary finite size N and extract the finite-size conformal corrections using an Euler–Maclaurin formula. The key to the solution is an inversion identity satisfied by the commuting double row transfer matrices. This inversion identity is established directly in the Temperley–Lieb algebra. We classify the eigenvalues of the double row transfer matrices using the physical combinatorics of the patterns of zeros in the complex spectral parameter plane and obtain finitised characters related to spaces of coinvariants of Z4 fermions. In the continuum scaling limit, the Robin boundary conditions are associated with irreducible Virasoro Verma modules with conformal weights Δr,s−12=132(L2−4 where L=2s−1−4r, r∈Z, s∈N. These conformal weights populate a Kac table with half-integer Kac labels. Fusion of the corresponding modules with the generators of the Kac fusion algebra is examined and general fusion rules are proposed.

  1. Hydrogeological boundary settings in SR 97. Uncertainties in regional boundary settings and transfer of boundary conditions to site-scale models

    International Nuclear Information System (INIS)

    Follin, S.

    1999-06-01

    The SR 97 project presents a performance assessment (PA) of the overall safety of a hypothetical deep repository at three sites in Sweden arbitrarily named Aberg, Beberg and Ceberg. One component of this PA assesses the uncertainties in the hydrogeological modelling. This study focuses on uncertainties in boundary settings (size of model domain and boundary conditions) in the regional and site-scale hydrogeological modelling of the three sites used to simulating the possible transport of radionuclides from the emplacement waste packages through the host rock to the accessible environment. Model uncertainties associated with, for instance, parameter heterogeneity and structural interpretations are addressed in other studies. This study concludes that the regional modelling of the SR 97 project addresses uncertainties in the choice of boundary conditions and size of model domain differently at each site, although the overall handling is acceptable and in accordance with common modelling practice. For example, the treatment of uncertainties with regard to the ongoing post-glacial flushing of the Baltic Shield is creditably addressed although not exhaustive from a modelling point of view. A significant contribution of the performed modelling is the study of nested numerical models, i.e., the numerical interplay between regional and site-scale numerical models. In the site-scale modelling great efforts are made to address problems associated with (i) the telescopic mesh refinement (TMR) technique with regard to the stochastic continuum approach, and (ii) the transfer of boundary conditions between variable-density flow systems and flow systems that are constrained to treat uniform density flow. This study concludes that the efforts made to handle these problems are acceptable with regards to the objectives of the SR 97 project

  2. A generalized Ginzburg-Landau model for nonlinear relaxation oscillation of magnetized plasma boundary with shear flow

    Science.gov (United States)

    Yun, Gunsu; Oh, Youngmin; Lee, Jieun; Hwang, H. J.; Lee, Jaehyun; Leconte, Michael; Kstar Team

    2017-10-01

    The boundary of high-temperature plasma confined by a toroidal magnetic field structure often undergoes quasi-periodic relaxation oscillations between high and low energy states. On the KSTAR tokamak, the oscillation cycle consists of a long quasi-steady state characterized by eigenmode-like filamentary modes, an abrupt transition into non-modal filamentary structure [Lee JE, Sci. Rep. 7, 45075], and its rapid burst (via magnetic reconnection) leading to the boundary collapse. A phenomenological model including the effects of time-varying perpendicular flow shear, turbulent transport, and external heating has been developed to understand the nonlinear oscillation. The model, which has the form of a generalized complex Ginzburg-Landau equation, shows that the flow shear amplitude and the shear layer width determine the nonlinear oscillation. Numerical solutions revealed that there exists a critical flow shear level below which steady states can exist. This result suggests that the abrupt transition to the non-modal unstable state is due to the flow shear increasing above the critical level. The model predicts that high wavenumber (k) modes can coexist with low- k modes at sufficiently low level of flow shear [Lee J, Phys. Rev. Lett. 117, 075001]. Work supported by the National Research Foundation of Korea.

  3. Understanding the Effects of Lower Boundary Conditions and Eddy Diffusion on the Ionosphere-Thermosphere System

    Science.gov (United States)

    Malhotra, G.; Ridley, A. J.; Marsh, D. R.; Wu, C.; Paxton, L. J.

    2017-12-01

    The exchange of energy between lower atmospheric regions with the ionosphere-thermosphere (IT) system is not well understood. A number of studies have observed day-to-day and seasonal variabilities in the difference between data and model output of various IT parameters. It is widely speculated that the forcing from the lower atmosphere, variability in weather systems and gravity waves that propagate upward from troposphere into the upper mesosphere and lower thermosphere (MLT) may be responsible for these spatial and temporal variations in the IT region, but their exact nature is unknown. These variabilities can be interpreted in two ways: variations in state (density, temperature, wind) of the upper mesosphere or spatial and temporal changes in the small-scale mixing, or Eddy diffusion that is parameterized within the model.In this study, firstly, we analyze the sensitivity of the thermospheric and ionospheric states - neutral densities, O/N2, total electron content (TEC), peak electron density, and peak electron height - to various lower boundary conditions in the Global Ionosphere Thermosphere Model (GITM). We use WACCM-X and GSWM to drive the lower atmospheric boundary in GITM at 100 km, and compare the results with the current MSIS-driven version of GITM, analyzing which of these simulations match the measurements from GOCE, GUVI, CHAMP, and GPS-derived TEC best. Secondly, we analyze the effect of eddy diffusion in the IT system. The turbulence due to eddy mixing cannot be directly measured and it is a challenge to completely characterize its linear and non-linear effects from other influences, since the eddy diffusion both influences the composition through direct mixing and the temperature structure due to turbulent conduction changes. In this study we input latitudinal and seasonal profiles of eddy diffusion into GITM and then analyze the changes in the thermospheric and ionospheric parameters. These profiles will be derived from both WACC-X simulations

  4. Multipoint Singular Boundary-Value Problem for Systems of Nonlinear Differential Equations

    Directory of Open Access Journals (Sweden)

    Zdeněk Šmarda

    2009-01-01

    Full Text Available A singular Cauchy-Nicoletti problem for a system of nonlinear ordinary differential equations is considered. With the aid of combination of Ważewski's topological method and Schauder's principle, the theorem concerning the existence of a solution of this problem (having the graph in a prescribed domain is proved.

  5. Pushing the Boundaries : Level-set Methods and Geometrical Nonlinearities in Structural Topology Optimization

    NARCIS (Netherlands)

    Van Dijk, N.P.

    2012-01-01

    This thesis aims at understanding and improving topology optimization techniques focusing on density-based level-set methods and geometrical nonlinearities. Central in this work are the numerical modeling of the mechanical response of a design and the consistency of the optimization process itself.

  6. An outgoing energy flux boundary condition for finite difference ICRP antenna models

    Energy Technology Data Exchange (ETDEWEB)

    Batchelor, D.B.; Carter, M.D.

    1992-11-01

    For antennas at the ion cyclotron range of frequencies (ICRF) modeling in vacuum can now be carried out to a high level of detail such that shaping of the current straps, isolating septa, and discrete Faraday shield structures can be included. An efficient approach would be to solve for the fields in the vacuum region near the antenna in three dimensions by finite methods and to match this solution at the plasma-vacuum interface to a solution obtained in the plasma region in one dimension by Fourier methods. This approach has been difficult to carry out because boundary conditions must be imposed at the edge of the finite difference grid on a point-by-point basis, whereas the condition for outgoing energy flux into the plasma is known only in terms of the Fourier transform of the plasma fields. A technique is presented by which a boundary condition can be imposed on the computational grid of a three-dimensional finite difference, or finite element, code by constraining the discrete Fourier transform of the fields at the boundary points to satisfy an outgoing energy flux condition appropriate for the plasma. The boundary condition at a specific grid point appears as a coupling to other grid points on the boundary, with weighting determined by a kemel calctdated from the plasma surface impedance matrix for the various plasma Fourier modes. This boundary condition has been implemented in a finite difference solution of a simple problem in two dimensions, which can also be solved directly by Fourier transformation. Results are presented, and it is shown that the proposed boundary condition does enforce outgoing energy flux and yields the same solution as is obtained by Fourier methods.

  7. Homogenization of the evolution Stokes equation in a perforated domain with a stochastic Fourier boundary condition

    KAUST Repository

    Bessaih, Hakima

    2015-04-01

    The evolution Stokes equation in a domain containing periodically distributed obstacles subject to Fourier boundary condition on the boundaries is considered. We assume that the dynamic is driven by a stochastic perturbation on the interior of the domain and another stochastic perturbation on the boundaries of the obstacles. We represent the solid obstacles by holes in the fluid domain. The macroscopic (homogenized) equation is derived as another stochastic partial differential equation, defined in the whole non perforated domain. Here, the initial stochastic perturbation on the boundary becomes part of the homogenized equation as another stochastic force. We use the twoscale convergence method after extending the solution with 0 in the holes to pass to the limit. By Itô stochastic calculus, we get uniform estimates on the solution in appropriate spaces. In order to pass to the limit on the boundary integrals, we rewrite them in terms of integrals in the whole domain. In particular, for the stochastic integral on the boundary, we combine the previous idea of rewriting it on the whole domain with the assumption that the Brownian motion is of trace class. Due to the particular boundary condition dealt with, we get that the solution of the stochastic homogenized equation is not divergence free. However, it is coupled with the cell problem that has a divergence free solution. This paper represents an extension of the results of Duan and Wang (Comm. Math. Phys. 275:1508-1527, 2007), where a reaction diffusion equation with a dynamical boundary condition with a noise source term on both the interior of the domain and on the boundary was studied, and through a tightness argument and a pointwise two scale convergence method the homogenized equation was derived. © American Institute of Mathematical Sciences.

  8. Nonlinear activity of acoustically driven gas bubble near a rigid boundary

    Energy Technology Data Exchange (ETDEWEB)

    Maksimov, Alexey [Pacific Oceanological Institute, Vladivostok 690041 (Russian Federation)

    2015-10-28

    The presence of a boundary can produce considerable changes in the oscillation amplitude of the bubble and its scattered echo. The present study fills a gap in the literature, in that it is concerned theoretically with the bubble activity at relatively small distances from the rigid boundary. It was shown that the bi-spherical coordinates provide separation of variables and are more suitable for analysis of the dynamics of these constrained bubbles. Explicit formulas have been derived which describe the dependence of the bubble emission near a rigid wall on its size and the separation distance between the bubble and the boundary. As applications, time reversal technique for gas leakage detection and radiation forces that are induced by an acoustic wave on a constrained bubble were analyzed.

  9. General treatment of a non-linear gauge condition

    International Nuclear Information System (INIS)

    Malleville, C.

    1982-06-01

    A non linear gauge condition is presented in the frame of a non abelian gauge theory broken with the Higgs mechanism. It is shown that this condition already introduced for the standard SU(2) x U(1) model can be generalized for any gauge model with the same type of simplification, namely the suppression of any coupling of the form: massless gauge boson, massive gauge boson, unphysical Higgs [fr

  10. An Outflow Boundary Condition Model for Noninvasive Prediction of Fractional Flow Reserve in Diseased Coronary Arteries.

    Science.gov (United States)

    Fayssal, Iyad A; Moukalled, Fadl; Alam, Samir; Isma'eel, Hussain

    2018-04-01

    This paper reports on a new boundary condition formulation to model the total coronary myocardial flow and resistance characteristics of the myocardial vascular bed for any specific patient when considered for noninvasive diagnosis of ischemia. The developed boundary condition model gives an implicit representation of the downstream truncated coronary bed. Further, it is based on incorporating patient-specific physiological parameters that can be noninvasively extracted to account for blood flow demand to the myocardium at rest and hyperemic conditions. The model is coupled to a steady three-dimensional (3D) collocated pressure-based finite volume flow solver and used to characterize the "functional significance" of a patient diseased coronary artery segment without the need for predicting the hemodynamics of the entire arterial system. Predictions generated with this boundary condition provide a deep understanding of the inherent challenges behind noninvasive image-based diagnostic techniques when applied to human diseased coronary arteries. The overall numerical method and formulated boundary condition model are validated via two computational-based procedures and benchmarked with available measured data. The newly developed boundary condition is used via a designed computational methodology to (a) confirm the need for incorporating patient-specific physiological parameters when modeling the downstream coronary resistance, (b) explain the discrepancies presented in the literature between measured and computed fractional flow reserve (FFRCT), and (c) discuss the current limitations and future challenges in shifting to noninvasive assessment of ischemia.

  11. Universal parity effects in the entanglement entropy of XX chains with open boundary conditions

    International Nuclear Information System (INIS)

    Fagotti, Maurizio; Calabrese, Pasquale

    2011-01-01

    We consider the Rényi entanglement entropies in the one-dimensional XX spin-chains with open boundary conditions in the presence of a magnetic field. In the case of a semi-infinite system and a block starting from the boundary, we derive rigorously the asymptotic behavior for large block sizes on the basis of a recent mathematical theorem for the determinant of Toeplitz plus Hankel matrices. We conjecture a generalized Fisher–Hartwig form for the corrections to the asymptotic behavior of this determinant that allows the exact characterization of the corrections to the scaling at order o(l -1 ) for any n. By combining these results with conformal field theory arguments, we derive exact expressions also in finite chains with open boundary conditions and in the case when the block is detached from the boundary

  12. Continuous Time Random Walks in finite domains and general boundary conditions: some formal considerations

    Energy Technology Data Exchange (ETDEWEB)

    van Milligen, B. Ph. [Asociacion EURATOM-CIEMAT; Calvo, Ivan [CIEMAT, Madrid; Sanchez, Raul [ORNL

    2008-01-01

    The present work studies continuous time random walks (CTRWs) in a finite domain. A broad class of boundary conditions, of which absorbing and reflecting boundaries are particular cases, is considered. It is shown how any CTRW in this class can be mapped to a CTRW in an infinite domain. This may allow applying well-known techniques for infinite CTRWs to the problem of obtaining the fluid limit for finite domain CTRWs, where the fluid limit (or hydrodynamic limit) refers to the partial differential equation describing the long time and large distance behavior of the system. As an illustration, the fluid limit equation and its propagator are obtained explicitly in the case of purely reflecting boundaries. We also derive the modification of the Riemann-Liouville fractional differential operators implementing the reflecting boundary conditions.

  13. Continuous time random walks in finite domains and general boundary conditions: some formal considerations

    Energy Technology Data Exchange (ETDEWEB)

    Milligen, B Ph van; Calvo, I [Asociacion EURATOM-CIEMAT para Fusion, Avda. Complutense 22, 28040 Madrid (Spain); Sanchez, R [Fusion Energy Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831 (United States)], E-mail: boudewijn.vanmilligen@ciemat.es

    2008-05-30

    The present work studies continuous time random walks (CTRWs) in a finite domain. A broad class of boundary conditions, of which absorbing and reflecting boundaries are particular cases, is considered. It is shown how any CTRW in this class can be mapped to a CTRW in an infinite domain. This may allow applying well-known techniques for infinite CTRWs to the problem of obtaining the fluid limit for finite domain CTRWs, where the fluid limit (or hydrodynamic limit) refers to the partial differential equation describing the long time and large distance behaviour of the system. As an illustration, the fluid limit equation and its propagator are obtained explicitly in the case of purely reflecting boundaries. We also derive the modification of the Riemann-Liouville fractional differential operators implementing the reflecting boundary conditions.

  14. Adaptive Neural Control of Nonaffine Nonlinear Systems without Differential Condition for Nonaffine Function

    Directory of Open Access Journals (Sweden)

    Chaojiao Sun

    2016-01-01

    Full Text Available An adaptive neural control scheme is proposed for nonaffine nonlinear system without using the implicit function theorem or mean value theorem. The differential conditions on nonaffine nonlinear functions are removed. The control-gain function is modeled with the nonaffine function probably being indifferentiable. Furthermore, only a semibounded condition for nonaffine nonlinear function is required in the proposed method, and the basic idea of invariant set theory is then constructively introduced to cope with the difficulty in the control design for nonaffine nonlinear systems. It is rigorously proved that all the closed-loop signals are bounded and the tracking error converges to a small residual set asymptotically. Finally, simulation examples are provided to demonstrate the effectiveness of the designed method.

  15. Effects of microscopic boundary conditions on plastic deformations of small-sized single crystals

    DEFF Research Database (Denmark)

    Kuroda, Mitsutoshi; Tvergaard, Viggo

    2009-01-01

    The finite deformation version of the higher-order gradient crystal plasticity model proposed by the authors is applied to solve plane strain boundary value problems, in order to obtain an understanding of the effect of the higher-order boundary conditions. Numerical solutions are carried out...... for uniaxial plane strain compression of a single crystal block and for uniform pure bending of a single crystal foil. The compressed block has loading surfaces that are penetrable or impenetrable to dislocations. This allows for a study of the two types of higher-order boundaries available, and a significant...

  16. SIMILARITY SOLUTION FOR NATURAL CONVECTION FROM A MOVING VERTICAL PLATE WITH INTERNAL HEAT GENERATION AND A CONVECTIVE BOUNDARY CONDITION

    Directory of Open Access Journals (Sweden)

    Oluwole Daniel Makinde

    2011-01-01

    Full Text Available Steady laminar natural convection flow over a semi-infinite moving vertical plate in the presence of internal heat generation and a convective surface boundary condition is examined in this paper. It is assumed that the left surface of the plate is in contact with a hot fluid while the cold fluid on the right surface of the plate contains a heat source that decays exponentially with the classical similarity variable. The governing non-linear partial differential equations have been transformed by a similarity transformation into a system of ordinary differential equations, which are solved numerically by applying shooting iteration technique together with fourth order Runge-Kutta integration scheme. The effects of physical parameters on the dimensionless velocity and temperature profiles are depicted graphically and analyzed in detail. Finally, numerical values of physical quantities, such as the local skin-friction coefficient and the local Nusselt number are presented in tabular form.

  17. Tear film dynamics with evaporation, wetting, and time-dependent flux boundary condition on an eye-shaped domain

    Science.gov (United States)

    Li, Longfei; Braun, R. J.; Maki, K. L.; Henshaw, W. D.; King-Smith, P. E.

    2014-01-01

    We study tear film dynamics with evaporation on a wettable eye-shaped ocular surface using a lubrication model. The mathematical model has a time-dependent flux boundary condition that models the cycles of tear fluid supply and drainage; it mimics blinks on a stationary eye-shaped domain. We generate computational grids and solve the nonlinear governing equations using the OVERTURE computational framework. In vivo experimental results using fluorescent imaging are used to visualize the influx and redistribution of tears for an open eye. Results from the numerical simulations are compared with the experiment. The model captures the flow around the meniscus and other dynamic features of human tear film observed in vivo. PMID:24926191

  18. The nonlocal boundary value problems for strongly singular higher-order nonlinear functional-differential equations

    Czech Academy of Sciences Publication Activity Database

    Mukhigulashvili, Sulkhan

    -, č. 35 (2015), s. 23-50 ISSN 1126-8042 Institutional support: RVO:67985840 Keywords : higher order functional differential equations * Dirichlet boundary value problem * strong singularity Subject RIV: BA - General Mathematics http://ijpam.uniud.it/online_issue/201535/03-Mukhigulashvili.pdf

  19. Atmospheric-radiation boundary conditions for high-frequency waves in time-distance helioseismology

    Science.gov (United States)

    Fournier, D.; Leguèbe, M.; Hanson, C. S.; Gizon, L.; Barucq, H.; Chabassier, J.; Duruflé, M.

    2017-12-01

    The temporal covariance between seismic waves measured at two locations on the solar surface is the fundamental observable in time-distance helioseismology. Above the acoustic cut-off frequency ( 5.3 mHz), waves are not trapped in the solar interior and the covariance function can be used to probe the upper atmosphere. We wish to implement appropriate radiative boundary conditions for computing the propagation of high-frequency waves in the solar atmosphere. We consider recently developed and published radiative boundary conditions for atmospheres in which sound-speed is constant and density decreases exponentially with radius. We compute the cross-covariance function using a finite element method in spherical geometry and in the frequency domain. The ratio between first- and second-skip amplitudes in the time-distance diagram is used as a diagnostic to compare boundary conditions and to compare with observations. We find that a boundary condition applied 500 km above the photosphere and derived under the approximation of small angles of incidence accurately reproduces the "infinite atmosphere" solution for high-frequency waves. When the radiative boundary condition is applied 2 Mm above the photosphere, we find that the choice of atmospheric model affects the time-distance diagram. In particular, the time-distance diagram exhibits double-ridge structure when using a Vernazza Avrett Loeser atmospheric model.

  20. Winkler boundary conditions for three-point bending tests on 1D nanomaterials

    International Nuclear Information System (INIS)

    Gangadean, D; McIlroy, David N; Faulkner, Brian E; Eric Aston, D

    2010-01-01

    Bending tests with atomic force microscopes (AFM) is a common method for elasticity measurements on 1D nanomaterials. Interpretation of the force and deflection data is necessary to determine the Young's modulus of the tested material and has been done assuming either of two classic boundary conditions that represent two extreme possibilities for the rigidity of the sample-anchor interface. The elasticity results from the two boundary conditions differ by a factor of four. Furthermore, both boundary conditions ignore the effects of deflections in the anchors themselves. The Winkler model for beams on elastic foundations is developed here for three-point bending tests to provide a more realistic representation. Equations for computing sample elasticity are derived from two sets of boundary conditions for the Winkler model. Application of this model to interpret the measurement of mechanical stiffness of a silica nanowire at multiple points in a three-point bending is discussed. With the correct choice of boundary conditions, the Winkler model gives a better fit for the observed stiffness profile than the classical beam models while providing a result that differs from both by a factor of two and is comparable to the bulk elasticity.

  1. Conditional independence graph for nonlinear time series and its application to international financial markets

    Science.gov (United States)

    Gao, Wei; Zhao, Hongxia

    2013-05-01

    Conditional independence graphs are proposed for describing the dependence structure of multivariate nonlinear time series, which extend the graphical modeling approach based on partial correlation. The vertexes represent the components of a multivariate time series and edges denote direct dependence between corresponding series. The conditional independence relations between component series are tested efficiently and consistently using conditional mutual information statistics and a bootstrap procedure. Furthermore, a method combining information theory with surrogate data is applied to test the linearity of the conditional dependence. The efficiency of the methods is approved through simulation time series with different linear and nonlinear dependence relations. Finally, we show how the method can be applied to international financial markets to investigate the nonlinear independence structure.

  2. Solving Boundary Value Problem for a Nonlinear Stationary Controllable System with Synthesizing Control

    Directory of Open Access Journals (Sweden)

    Alexander N. Kvitko

    2017-01-01

    Full Text Available An algorithm for constructing a control function that transfers a wide class of stationary nonlinear systems of ordinary differential equations from an initial state to a final state under certain control restrictions is proposed. The algorithm is designed to be convenient for numerical implementation. A constructive criterion of the desired transfer possibility is presented. The problem of an interorbital flight is considered as a test example and it is simulated numerically with the presented method.

  3. On a Mixed Nonlinear One Point Boundary Value Problem for an Integrodifferential Equation

    Directory of Open Access Journals (Sweden)

    Mesloub Said

    2008-01-01

    Full Text Available This paper is devoted to the study of a mixed problem for a nonlinear parabolic integro-differential equation which mainly arise from a one dimensional quasistatic contact problem. We prove the existence and uniqueness of solutions in a weighted Sobolev space. Proofs are based on some a priori estimates and on the Schauder fixed point theorem. we also give a result which helps to establish the regularity of a solution.

  4. Existence of Positive Solutions to Singular -Laplacian General Dirichlet Boundary Value Problems with Sign Changing Nonlinearity

    Directory of Open Access Journals (Sweden)

    Qiying Wei

    2009-01-01

    Full Text Available By using the well-known Schauder fixed point theorem and upper and lower solution method, we present some existence criteria for positive solution of an -point singular -Laplacian dynamic equation on time scales with the sign changing nonlinearity. These results are new even for the corresponding differential (=ℝ and difference equations (=ℤ, as well as in general time scales setting. As an application, an example is given to illustrate the results.

  5. Existence results for boundary problems for uniformly elliptic and parabolic fully nonlinear equations

    Directory of Open Access Journals (Sweden)

    M. G. Crandall

    1999-07-01

    Full Text Available We study existence of continuous weak (viscosity solutions of Dirichlet and Cauchy-Dirichlet problems for fully nonlinear uniformly elliptic and parabolic equations. Two types of results are obtained in contexts where uniqueness of solutions fails or is unknown. For equations with merely measurable coefficients we prove solvability of the problem, while in the continuous case we construct maximal and minimal solutions. Necessary barriers on external cones are also constructed.

  6. A Wavelet Bicoherence-Based Quadratic Nonlinearity Feature for Translational Axis Condition Monitoring

    Directory of Open Access Journals (Sweden)

    Yong Li

    2014-01-01

    Full Text Available The translational axis is one of the most important subsystems in modern machine tools, as its degradation may result in the loss of the product qualification and lower the control precision. Condition-based maintenance (CBM has been considered as one of the advanced maintenance schemes to achieve effective, reliable and cost-effective operation of machine systems, however, current vibration-based maintenance schemes cannot be employed directly in the translational axis system, due to its complex structure and the inefficiency of commonly used condition monitoring features. In this paper, a wavelet bicoherence-based quadratic nonlinearity feature is proposed for translational axis condition monitoring by using the torque signature of the drive servomotor. Firstly, the quadratic nonlinearity of the servomotor torque signature is discussed, and then, a biphase randomization wavelet bicoherence is introduced for its quadratic nonlinear detection. On this basis, a quadratic nonlinearity feature is proposed for condition monitoring of the translational axis. The properties of the proposed quadratic nonlinearity feature are investigated by simulations. Subsequently, this feature is applied to the real-world servomotor torque data collected from the X-axis on a high precision vertical machining centre. All the results show that the performance of the proposed feature is much better than that of original condition monitoring features.

  7. A wavelet bicoherence-based quadratic nonlinearity feature for translational axis condition monitoring.

    Science.gov (United States)

    Li, Yong; Wang, Xiufeng; Lin, Jing; Shi, Shengyu

    2014-01-27

    The translational axis is one of the most important subsystems in modern machine tools, as its degradation may result in the loss of the product qualification and lower the control precision. Condition-based maintenance (CBM) has been considered as one of the advanced maintenance schemes to achieve effective, reliable and cost-effective operation of machine systems, however, current vibration-based maintenance schemes cannot be employed directly in the translational axis system, due to its complex structure and the inefficiency of commonly used condition monitoring features. In this paper, a wavelet bicoherence-based quadratic nonlinearity feature is proposed for translational axis condition monitoring by using the torque signature of the drive servomotor. Firstly, the quadratic nonlinearity of the servomotor torque signature is discussed, and then, a biphase randomization wavelet bicoherence is introduced for its quadratic nonlinear detection. On this basis, a quadratic nonlinearity feature is proposed for condition monitoring of the translational axis. The properties of the proposed quadratic nonlinearity feature are investigated by simulations. Subsequently, this feature is applied to the real-world servomotor torque data collected from the X-axis on a high precision vertical machining centre. All the results show that the performance of the proposed feature is much better than that of original condition monitoring features.

  8. A highly precise frequency-based method for estimating the tension of an inclined cable with unknown boundary conditions

    Science.gov (United States)

    Ma, Lin

    2017-11-01

    This paper develops a method for precisely determining the tension of an inclined cable with unknown boundary conditions. First, the nonlinear motion equation of an inclined cable is derived, and a numerical model of the motion of the cable is proposed using the finite difference method. The proposed numerical model includes the sag-extensibility, flexural stiffness, inclination angle and rotational stiffness at two ends of the cable. Second, the influence of the dynamic parameters of the cable on its frequencies is discussed in detail, and a method for precisely determining the tension of an inclined cable is proposed based on the derivatives of the eigenvalues of the matrices. Finally, a multiparameter identification method is developed that can simultaneously identify multiple parameters, including the rotational stiffness at two ends. This scheme is applicable to inclined cables with varying sag, varying flexural stiffness and unknown boundary conditions. Numerical examples indicate that the method provides good precision. Because the parameters of cables other than tension (e.g., the flexural stiffness and rotational stiffness at the ends) are not accurately known in practical engineering, the multiparameter identification method could further improve the accuracy of cable tension measurements.

  9. Nonlinear Chance Constrained Problems: Optimality Conditions, Regularization and Solvers

    Czech Academy of Sciences Publication Activity Database

    Adam, Lukáš; Branda, Martin

    2016-01-01

    Roč. 170, č. 2 (2016), s. 419-436 ISSN 0022-3239 R&D Projects: GA ČR GA15-00735S Institutional support: RVO:67985556 Keywords : Chance constrained programming * Optimality conditions * Regularization * Algorithms * Free MATLAB codes Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 1.289, year: 2016 http://library.utia.cas.cz/separaty/2016/MTR/adam-0460909.pdf

  10. Efficient enforcement of far-field boundary conditions in the Transformed Field Expansions method

    Science.gov (United States)

    Nicholls, David P.

    2011-09-01

    The Method of Transformed Field Expansions (TFE) has been demonstrated to be a robust and highly accurate numerical scheme for simulating solutions of boundary value and free boundary problems from the sciences and engineering. As a Boundary Perturbation Method it builds highly accurate solutions based upon exact solutions in a simple, canonical, geometry and corrects these via Taylor series to fit the actual geometry at hand. The TFE method has significantly enhanced stability properties when compared with other Boundary Perturbation approaches, however, this comes at the cost of requiring a full volumetric discretization as opposed the surface formulation that other methods can realize. In this paper we outline two techniques for ameliorating this shortcoming, first by employing a Legendre Spectral Element Method to implement efficient, graded meshes, and second by utilizing an Artificial Boundary with a Transparent Boundary Condition placed quite close to the boundary of the domain. In this contribution we focus on the specific problem of simulating the Dirichlet-Neumann operator associated to Laplace's equation on a periodic cell (which arises in the water wave problem). While the details of our results are specific to this problem, the general conclusions are valid for the wider class of problems to which the TFE method can be applied. For each technique we discuss implementation details and display numerical results which support the conclusion that each of these techniques can greatly reduce the computational cost of using the TFE method.

  11. Generalized nematohydrodynamic boundary conditions with application to bistable twisted nematic liquid-crystal displays

    KAUST Repository

    Fang, Angbo

    2008-12-08

    Parallel to the highly successful Ericksen-Leslie hydrodynamic theory for the bulk behavior of nematic liquid crystals (NLCs), we derive a set of coupled hydrodynamic boundary conditions to describe the NLC dynamics near NLC-solid interfaces. In our boundary conditions, translational flux (flow slippage) and rotational flux (surface director relaxation) are coupled according to the Onsager variational principle of least energy dissipation. The application of our boundary conditions to the truly bistable π -twist NLC cell reveals a complete picture of the dynamic switching processes. It is found that the thus far overlooked translation-rotation dissipative coupling at solid surfaces can accelerate surface director relaxation and enhance the flow rate. This can be utilized to improve the performance of electro-optical nematic devices by lowering the required switching voltages and reducing the switching times. © 2008 The American Physical Society.

  12. Effects of various thermal boundary conditions on natural convection in porous cavities

    Science.gov (United States)

    Cheong, H. T.; Sivasankaran, S.; Bhuvaneswari, M.; Siri, Z.

    2015-10-01

    The present work analyzes numerically the effects of various thermal boundary conditions and the geometry of the cavity on natural convection in cavities with fluid-saturated porous medium. Cavity of square, right-angled trapezium and right-angled triangle shapes are considered. The different temperature profiles are imposed on the left wall of the cavity and the right wall is maintained at a lower constant temperature. The top and bottom walls are adiabatic. The Darcy model is adopted for the porous medium. The finite difference method is used to solve the governing equations and boundary conditions over a range of Darcy-Rayleigh numbers. Streamlines, isotherms and Nusselt numbers are used for presenting the results. The heat transfer of the square cavity is more enhanced at high Darcy-Rayleigh number for all the thermal boundary conditions considered.

  13. Heat kernel for the elliptic system of linear elasticity with boundary conditions

    Science.gov (United States)

    Taylor, Justin; Kim, Seick; Brown, Russell

    2014-10-01

    We consider the elliptic system of linear elasticity with bounded measurable coefficients in a domain where the second Korn inequality holds. We construct heat kernel of the system subject to Dirichlet, Neumann, or mixed boundary condition under the assumption that weak solutions of the elliptic system are Hölder continuous in the interior. Moreover, we show that if weak solutions of the mixed problem are Hölder continuous up to the boundary, then the corresponding heat kernel has a Gaussian bound. In particular, if the domain is a two dimensional Lipschitz domain satisfying a corkscrew or non-tangential accessibility condition on the set where we specify Dirichlet boundary condition, then we show that the heat kernel has a Gaussian bound. As an application, we construct Green's function for elliptic mixed problem in such a domain.

  14. Reconsidering the boundary conditions for a dynamic, transient mode I crack problem

    KAUST Repository

    Leise, Tanya

    2008-11-01

    A careful examination of a dynamic mode I crack problem leads to the conclusion that the commonly used boundary conditions do not always hold in the case of an applied crack face loading, so that a modification is required to satisfy the equations. In particular, a transient compressive stress wave travels along the crack faces, moving outward from the loading region on the crack face. This does not occur in the quasistatic or steady state problems, and is a special feature of the transient dynamic problem that is important during the time interval immediately following the application of crack face loading. We demonstrate why the usual boundary conditions lead to a prediction of crack face interpenetration, and then examine how to modify the boundary condition for a semi-infinite crack with a cohesive zone. Numerical simulations illustrate the resulting approach.

  15. Explicit formulation for natural frequencies of double-beam system with arbitrary boundary conditions

    Energy Technology Data Exchange (ETDEWEB)

    Mirzabeigy, Alborz; Madoliat, Reza [Iran University of Science and Technology, Narmak, Tehran (Iran, Islamic Republic of); Dabbagh, Vahid [University of Malaya, Kuala Lumpur (Malaysia)

    2017-02-15

    In this paper, free transverse vibration of two parallel beams connected through Winkler type elastic layer is investigated. Euler- Bernoulli beam hypothesis has been applied and it is assumed that boundary conditions of upper and lower beams are similar while arbitrary without any limitation even for non-ideal boundary conditions. Material properties and cross-section geometry of beams could be different from each other. The motion of the system is described by a homogeneous set of two partial differential equations, which is solved by using the classical Bernoulli-Fourier method. Explicit expressions are derived for the natural frequencies. In order to verify accuracy of results, the problem once again solved using modified Adomian decomposition method. Comparison between results indicates excellent accuracy of proposed formulation for any arbitrary boundary conditions. Derived explicit formulation is simplest method to determine natural frequencies of double-beam systems with high level of accuracy in comparison with other methods in literature.

  16. Heat Transfer Boundary Conditions in the RELAP5-3D Code

    Energy Technology Data Exchange (ETDEWEB)

    Richard A. Riemke; Cliff B. Davis; Richard R. Schultz

    2008-05-01

    The heat transfer boundary conditions used in the RELAP5-3D computer program have evolved over the years. Currently, RELAP5-3D has the following options for the heat transfer boundary conditions: (a) heat transfer correlation package option, (b) non-convective option (from radiation/conduction enclosure model or symmetry/insulated conditions), and (c) other options (setting the surface temperature to a volume fraction averaged fluid temperature of the boundary volume, obtaining the surface temperature from a control variable, obtaining the surface temperature from a time-dependent general table, obtaining the heat flux from a time-dependent general table, or obtaining heat transfer coefficients from either a time- or temperature-dependent general table). These options will be discussed, including the more recent ones.

  17. Development of stress boundary conditions in smoothed particle hydrodynamics (SPH) for the modeling of solids deformation

    Science.gov (United States)

    Douillet-Grellier, Thomas; Pramanik, Ranjan; Pan, Kai; Albaiz, Abdulaziz; Jones, Bruce D.; Williams, John R.

    2017-10-01

    This paper develops a method for imposing stress boundary conditions in smoothed particle hydrodynamics (SPH) with and without the need for dummy particles. SPH has been used for simulating phenomena in a number of fields, such as astrophysics and fluid mechanics. More recently, the method has gained traction as a technique for simulation of deformation and fracture in solids, where the meshless property of SPH can be leveraged to represent arbitrary crack paths. Despite this interest, application of boundary conditions within the SPH framework is typically limited to imposed velocity or displacement using fictitious dummy particles to compensate for the lack of particles beyond the boundary interface. While this is enough for a large variety of problems, especially in the case of fluid flow, for problems in solid mechanics there is a clear need to impose stresses upon boundaries. In addition to this, the use of dummy particles to impose a boundary condition is not always suitable or even feasibly, especially for those problems which include internal boundaries. In order to overcome these difficulties, this paper first presents an improved method for applying stress boundary conditions in SPH with dummy particles. This is then followed by a proposal of a formulation which does not require dummy particles. These techniques are then validated against analytical solutions to two common problems in rock mechanics, the Brazilian test and the penny-shaped crack problem both in 2D and 3D. This study highlights the fact that SPH offers a good level of accuracy to solve these problems and that results are reliable. This validation work serves as a foundation for addressing more complex problems involving plasticity and fracture propagation.

  18. Necessary Conditions for Nonlinear Ultrasonic Modulation Generation Given a Localized Fatigue Crack in a Plate-Like Structure

    Directory of Open Access Journals (Sweden)

    Hyung Jin Lim

    2017-02-01

    Full Text Available It has been shown that nonlinear ultrasonics can be more sensitive to local incipient defects, such as a fatigue crack, than conventional linear ultrasonics. Therefore, there is an increasing interest in utilizing nonlinear ultrasonics for structural health monitoring and nondestructive testing applications. While the conditions, which are the necessary conditions that should be satisfied for the generation of nonlinear harmonic components, are extensively studied for distributed material nonlinearity, little work has been done to understand the necessary conditions at the presence of a localized nonlinear source such as a fatigue crack. In this paper, the necessary conditions of nonlinear ultrasonic modulation generation in a plate-like structure are formulated specifically for a localized nonlinear source. Then, the correctness of the formulated necessary conditions is experimentally verified using ultrasounds obtained from aluminum plates.

  19. Representation of boundary conditions in thermal reactor global analysis by diffusion theory employing finite difference approximation

    International Nuclear Information System (INIS)

    Paul, O.P.K.

    1978-01-01

    An approach to simulate the flux vanishing boundary condition in solving the two group coupled neutron diffusion equations in three dimensions (x, y, z) employed to calculate the flux distribution and keff of the reactor is summarised. This is of particular interest when the flux vanishing boundary in x, y, z directions is not an integral multiple of the mesh spacings in these directions. The method assumes the flux to be negative, hypothetically at the mesh points lying outside the boundary and thus the finite difference formalism for Laplacian operator, taking into account six neighbours of a mesh point in a square mesh arrangement, is expressed in a general form so as to account for the boundary mesh points of the system. This approach has been incorporated in a three dimensional diffusion code similar to TAPPS23 and has been used for IRT-2000 reactor and the results are quite satisfactory. (author)

  20. FULL GPU Implementation of Lattice-Boltzmann Methods with Immersed Boundary Conditions for Fast Fluid Simulations

    Directory of Open Access Journals (Sweden)

    G Boroni

    2017-03-01

    Full Text Available Lattice Boltzmann Method (LBM has shown great potential in fluid simulations, but performance issues and difficulties to manage complex boundary conditions have hindered a wider application. The upcoming of Graphic Processing Units (GPU Computing offered a possible solution for the performance issue, and methods like the Immersed Boundary (IB algorithm proved to be a flexible solution to boundaries. Unfortunately, the implicit IB algorithm makes the LBM implementation in GPU a non-trivial task. This work presents a fully parallel GPU implementation of LBM in combination with IB. The fluid-boundary interaction is implemented via GPU kernels, using execution configurations and data structures specifically designed to accelerate each code execution. Simulations were validated against experimental and analytical data showing good agreement and improving the computational time. Substantial reductions of calculation rates were achieved, lowering down the required time to execute the same model in a CPU to about two magnitude orders.

  1. Solving a Local Boundary Value Problem for a Nonlinear Nonstationary System in the Class of Feedback Controls

    Science.gov (United States)

    Kvitko, A. N.

    2018-01-01

    An algorithm convenient for numerical implementation is proposed for constructing differentiable control functions that transfer a wide class of nonlinear nonstationary systems of ordinary differential equations from an initial state to a given point of the phase space. Constructive sufficient conditions imposed on the right-hand side of the controlled system are obtained under which this transfer is possible. The control of a robotic manipulator is considered, and its numerical simulation is performed.

  2. Effects of Boundary Conditions on the Parametric Resonance of Cylindrical Shells under Axial Loading

    Directory of Open Access Journals (Sweden)

    T.Y. Ng

    1998-01-01

    Full Text Available In this paper, a formulation for the dynamic stability analysis of circular cylindrical shells under axial compression with various boundary conditions is presented. The present study uses Love’s first approximation theory for thin shells and the characteristic beam functions as approximate axial modal functions. Applying the Ritz procedure to the Lagrangian energy expression yields a system of Mathieu–Hill equations the stability of which is analyzed using Bolotin’s method. The present study examines the effects of different boundary conditions on the parametric response of homogeneous isotropic cylindrical shells for various transverse modes and length parameters.

  3. The Step-Type Contrast Structure for High Dimensional Tikhonov System with Neumann Boundary Conditions

    Directory of Open Access Journals (Sweden)

    Aifeng Wang

    2016-01-01

    Full Text Available We investigate the step-type contrast structure for high dimensional Tikhonov system with Neumann boundary conditions. We not only propose a key condition with the existence of the number of mutually independent first integrals under which there exists a step-type contrast structure, but also determine where an internal transition time is. Using the method of boundary function, we construct the formal asymptotic solution and give the analytical expression for the higher order terms. At the same time, the uniformly valid asymptotic expansion and the existence of such an available step-type contrast structure are obtained by sewing connection method.

  4. Multiregion, multigroup collision probability method with white boundary condition for light water reactor thermalization calculations

    International Nuclear Information System (INIS)

    Ozgener, B.; Ozgener, H.A.

    2005-01-01

    A multiregion, multigroup collision probability method with white boundary condition is developed for thermalization calculations of light water moderated reactors. Hydrogen scatterings are treated by Nelkin's kernel while scatterings from other nuclei are assumed to obey the free-gas scattering kernel. The isotropic return (white) boundary condition is applied directly by using the appropriate collision probabilities. Comparisons with alternate numerical methods show the validity of the present formulation. Comparisons with some experimental results indicate that the present formulation is capable of calculating disadvantage factors which are closer to the experimental results than alternative methods

  5. Identification of complex model thermal boundary conditions based on exterior temperature measurement

    International Nuclear Information System (INIS)

    Lu Jianming; Ouyang Guangyao; Zhang Ping; Rong Bojun

    2012-01-01

    Combining the advantages of the finite element software in temperature field analyzing with the multivariate function optimization arithmetic, a feasibility method based on the exterior temperature was proposed to get the thermal boundary conditions, which was required in temperature field analyzing. The thermal boundary conditions can be obtained only by some temperature measurement values. Taking the identification of the convection heat transfer coefficient of a high power density diesel engine cylinder head as an example, the calculation result shows that when the temperature measurement error was less than 0.5℃, the maximum relative error was less than 2%. It is shown that the new method was feasible (authors)

  6. Dispersion estimates for spherical Schrödinger equations: the effect of boundary conditions

    Directory of Open Access Journals (Sweden)

    Markus Holzleitner

    2016-01-01

    Full Text Available We investigate the dependence of the \\(L^1\\to L^{\\infty}\\ dispersive estimates for one-dimensional radial Schrödinger operators on boundary conditions at \\(0\\. In contrast to the case of additive perturbations, we show that the change of a boundary condition at zero results in the change of the dispersive decay estimates if the angular momentum is positive, \\(l\\in (0,1/2\\. However, for nonpositive angular momenta, \\(l\\in (-1/2,0]\\, the standard \\(O(|t|^{-1/2}\\ decay remains true for all self-adjoint realizations.

  7. Rate-Independent Processes with Linear Growth Energies and Time-Dependent Boundary Conditions

    Czech Academy of Sciences Publication Activity Database

    Kružík, Martin; Zimmer, J.

    2012-01-01

    Roč. 5, č. 3 (2012), s. 591-604 ISSN 1937-1632 R&D Projects: GA AV ČR IAA100750802 Grant - others:GA ČR(CZ) GAP201/10/0357 Institutional research plan: CEZ:AV0Z10750506 Keywords : concentrations * oscillations * time-dependent boundary conditions * rate-independent evolution Subject RIV: BA - General Mathematics http://library.utia.cas.cz/separaty/2011/MTR/kruzik-rate-independent processes with linear growth energies and time-dependent boundary conditions.pdf

  8. Mathematical analysis of the Navier-Stokes equations with non standard boundary conditions

    Science.gov (United States)

    Tidriri, M. D.

    1995-01-01

    One of the major applications of the domain decomposition time marching algorithm is the coupling of the Navier-Stokes systems with Boltzmann equations in order to compute transitional flows. Another important application is the coupling of a global Navier-Stokes problem with a local one in order to use different modelizations and/or discretizations. Both of these applications involve a global Navier-Stokes system with nonstandard boundary conditions. The purpose of this work is to prove, using the classical Leray-Schauder theory, that these boundary conditions are admissible and lead to a well posed problem.

  9. The Magnetohydrodynamic Boundary Layer Flow of a Nanofluid past a Stretching/Shrinking Sheet with Slip Boundary Conditions

    Directory of Open Access Journals (Sweden)

    Syahira Mansur

    2014-01-01

    Full Text Available The magnetohydrodynamic (MHD boundary layer flow of a nanofluid past a stretching/shrinking sheet with velocity, thermal, and solutal slip boundary conditions is studied. Numerical solutions to the governing equations were obtained using a shooting method. The skin friction coefficient and the local Sherwood number increase as the stretching/shrinking parameter increases. However, the local Nusselt number decreases with increasing the stretching/shrinking parameter. The range of the stretching/shrinking parameter for which the solution exists increases as the velocity slip parameter and the magnetic parameter increase. For the shrinking sheet, the skin friction coefficient increases as the velocity slip parameter and the magnetic parameter increase. For the stretching sheet, it decreases when the velocity slip parameter and the magnetic parameter increase. The local Nusselt number diminishes as the thermal slip parameter increases while the local Sherwood number decreases with increasing the solutal slip parameter. The local Nusselt number is lower for higher values of Lewis number, Brownian motion parameter, and thermophoresis parameter.

  10. Singular and regular second order φ-Laplacian equations on the half-line with functional boundary conditions

    Directory of Open Access Journals (Sweden)

    Joao Fialho

    2017-02-01

    Full Text Available This paper is concerned with the existence of bounded or unbounded solutions to regular and singular second order boundary value problem on the half-line with functional boundary conditions. These functional boundary conditions generalize the usual boundary assumptions and may be applied to a broad number of cases, such as, nonlocal, integro-differential, with delays, with maximum or minimum arguments... The arguments are based on the Schauder fixed point theorem and lower and upper solutions method.

  11. An analytical study of the instability of a superelastic shape memory alloy cylinder subject to practical boundary conditions

    International Nuclear Information System (INIS)

    Dai, Hui-Hui; Wang Jiong; Chen Zhen

    2009-01-01

    In this paper, we study phase transitions in a slender circular cylinder composed of a compressible hyperelastic material with a non-convex strain energy function. We aim to construct asymptotic solutions based on an axisymmetrical three-dimensional setting and use the results to describe the key features observed in the experiments by others. The problem of the solution bifurcations of the governing nonlinear partial differential equations (PDEs) is solved through a novel approach involving coupled series–asymptotic expansions. We derive the normal form equation of the original complicated system of nonlinear PDEs. By writing the normal form equation into a first-order dynamical system and with a phase-plane analysis, we deduce the global bifurcation properties and solve the boundary-value problem analytically. The asymptotic solutions in terms of integrals are obtained. The engineering stress–strain curve plotted from the asymptotic solutions can capture some key features of the curve measured in the experiments. It appears that the asymptotic solutions obtained shed certain light on the instability phenomena associated with phase transitions in a cylinder. Also, an important feature of this work is that we consider the clamped end conditions, which are more practical but rarely used in the literature for phase transition problems

  12. West-WRF Sensitivity to Sea Surface Temperature Boundary Condition in California Precipitation Forecasts of AR Related Events

    Science.gov (United States)

    Zhang, X.; Cornuelle, B. D.; Martin, A.; Weihs, R. R.; Ralph, M.

    2017-12-01

    We evaluated the merit in coastal precipitation forecasts by inclusion of high resolution sea surface temperature (SST) from blended satellite and in situ observations as a boundary condition (BC) to the Weather Research and Forecast (WRF) mesoscale model through simple perturbation tests. Our sensitivity analyses shows that the limited improvement of watershed scale precipitation forecast is credible. When only SST BC is changed, there is an uncertainty introduced because of artificial model state equilibrium and the nonlinear nature of the WRF model system. With the change of SST on the order of a fraction of a degree centigrade, we found that the part of random perturbation forecast response is saturated after 48 hours when it reaches to the order magnitude of the linear response. It is important to update the SST at a shorter time period, so that the independent excited nonlinear modes can cancel each other. The uncertainty in our SST configuration is quantitatively equivalent to adding to a spatially uncorrelated Guasian noise of zero mean and 0.05 degree of standard deviation to the SST. At this random noise perturbation magnitude, the ensemble average behaves well within a convergent range. It is also found that the sensitivity of forecast changes in response to SST changes. This is measured by the ratio of the spatial variability of mean of the ensemble perturbations over the spatial variability of the corresponding forecast. The ratio is about 10% for surface latent heat flux, 5 % for IWV, and less than 1% for surface pressure.

  13. ''Free-space'' boundary conditions for the time-dependent wave equation

    International Nuclear Information System (INIS)

    Lindman, E.L.

    1975-01-01

    Boundary conditions for the discrete wave equation which act like an infinite region of free space in contact with the computational region can be constructed using projection operators. Propagating and evanescent waves coming from within the computational region generate no reflected waves as they cross the boundary. At the same time arbitrary waves may be launched into the computational region. Well known projection operators for one-dimensional waves may be used for this purpose in one dimension. Extensions of these operators to higher dimensions along with numerically efficient approximations to them are described for higher-dimensional problems. The separation of waves into ingoing and outgoing waves inherent in these boundary conditions greatly facilitates diagnostics

  14. Three-Dimensional Vibration Analysis of Rectangular Thick Plates on Pasternak Foundation with Arbitrary Boundary Conditions

    Directory of Open Access Journals (Sweden)

    Huimin Liu

    2017-01-01

    Full Text Available This paper presents the first known vibration characteristic of rectangular thick plates on Pasternak foundation with arbitrary boundary conditions on the basis of the three-dimensional elasticity theory. The arbitrary boundary conditions are obtained by laying out three types of linear springs on all edges. The modified Fourier series are chosen as the basis functions of the admissible function of the thick plates to eliminate all the relevant discontinuities of the displacements and their derivatives at the edges. The exact solution is obtained based on the Rayleigh–Ritz procedure by the energy functions of the thick plate. The excellent accuracy and reliability of current solutions are demonstrated by numerical examples and comparisons with the results available in the literature. In addition, the influence of the foundation coefficients as well as the boundary restraint parameters is also analyzed, which can serve as the benchmark data for the future research technique.

  15. Nonperiodic stochastic boundary conditions for molecular dynamics simulations of materials embedded into a continuum mechanics domain.

    Science.gov (United States)

    Rahimi, Mohammad; Karimi-Varzaneh, Hossein Ali; Böhm, Michael C; Müller-Plathe, Florian; Pfaller, Sebastian; Possart, Gunnar; Steinmann, Paul

    2011-04-21

    A scheme is described for performing molecular dynamics simulations on polymers under nonperiodic, stochastic boundary conditions. It has been designed to allow later the embedding of a particle domain treated by molecular dynamics into a continuum environment treated by finite elements. It combines, in the boundary region, harmonically restrained particles to confine the system with dissipative particle dynamics to dissipate energy and to thermostat the simulation. The equilibrium position of the tethered particles, the so-called anchor points, are well suited for transmitting deformations, forces and force derivatives between the particle and continuum domains. In the present work the particle scheme is tested by comparing results for coarse-grained polystyrene melts under nonperiodic and regular periodic boundary conditions. Excellent agreement is found for thermodynamic, structural, and dynamic properties.

  16. Existence of 2m-1 Positive Solutions for Sturm-Liouville Boundary Value Problems with Linear Functional Boundary Conditions on the Half-Line

    Directory of Open Access Journals (Sweden)

    Yanmei Sun

    2012-01-01

    Full Text Available By using the Leggett-Williams fixed theorem, we establish the existence of multiple positive solutions for second-order nonhomogeneous Sturm-Liouville boundary value problems with linear functional boundary conditions. One explicit example with singularity is presented to demonstrate the application of our main results.

  17. Control design of a nonlinear controller to stabilize the nonlinear ...

    African Journals Online (AJOL)

    This article presents the design of a highly efficient nonlinear0 controller which is a kind of an Active Queue Management (AQM) scheme to stabilize the nonlinear TCP model dynamics. Specific boundary conditions have been considered for stability occurrences and have been compared with other existing Active Queue ...

  18. Nonlinear Dielectric Properties of Yeast Cells Cultured in Different Environmental Conditions

    Science.gov (United States)

    Kawanishi, Gomon; Fukuda, Naoki; Muraji, Masafumi

    The harmonics of the electric current through yeast suspensions, the nonlinear dielectric properties of yeast cells, have particular patterns according to the biological activity of the cells and the measurement of these patterns is a technique for determining the activity of living cells. The concentration of glucose and oxygen in yeast culture medium influences the manifestation of fermentation or respiration of yeast cells. Measurements were made with yeast cells (Saccharomyces cerevisiae) cultured aerobically and anaerobically in sufficient glucose concentration, aerobic fermentation and anaerobic fermentation, and aerobically in limited glucose concentration, respiration. The results showed that the harmonics were barely apparent for yeast cells in aerobic fermentation and respiratory; however, cells in the anaerobic fermentation displayed substantial third and fifth harmonics. We can say that environmental condition affects the yeast cells' nonlinear properties, from another viewpoint, the measurements of the nonlinear properties are available to determine the activity of yeast cells adjusted to the conditions of their cultivation.

  19. Response in atmospheric circulation and sources of Greenland precipitation to glacial boundary conditions

    DEFF Research Database (Denmark)

    Langen, Peter Lang; Vinther, Bo Møllesøe

    2009-01-01

    The response in northern hemisphere atmospheric circulation and the resulting changes in moisture sources for Greenland precipitation to glacial boundary conditions are studied in NCAR's CCM3 atmospheric general circulation model fitted with a moisture tracking functionality. We employ both...... seasonality, condensation temperatures and source temperatures are assessed. Udgivelsesdato: June 2009...

  20. Boundary conditions in Ginsburg Landau theory and critical temperature of high-T superconductors

    Science.gov (United States)

    Lykov, A. N.

    2008-06-01

    New mixed boundary conditions to the Ginsburg-Landau equations are found to limit the critical temperature ( T) of high- T superconductors. Moreover, the value of the pseudogap in these superconductors can be explained by using the method. As a result, the macroscopic approach is proposed to increase T of cuprate superconductors.

  1. Boundary conditions in Ginsburg-Landau theory and critical temperature of high-Tc superconductors

    International Nuclear Information System (INIS)

    Lykov, A.N.

    2008-01-01

    New mixed boundary conditions to the Ginsburg-Landau equations are found to limit the critical temperature (T c ) of high-T c superconductors. Moreover, the value of the pseudogap in these superconductors can be explained by using the method. As a result, the macroscopic approach is proposed to increase T c of cuprate superconductors

  2. Element stacking method for topology optimization with material-dependent boundary and loading conditions

    DEFF Research Database (Denmark)

    Yoon, Gil Ho; Park, Y.K.; Kim, Y.Y.

    2007-01-01

    A new topology optimization scheme, called the element stacking method, is developed to better handle design optimization involving material-dependent boundary conditions and selection of elements of different types. If these problems are solved by existing standard approaches, complicated finite...

  3. Existence of Solutions for Fractional Differential Inclusions with Separated Boundary Conditions in Banach Space

    Directory of Open Access Journals (Sweden)

    Mabrouk Bragdi

    2013-01-01

    Full Text Available We discuss the existence of solutions for a class of some separated boundary differential inclusions of fractional orders 2<α<3 involving the Caputo derivative. In order to obtain necessary conditions for the existence result, we apply the fixed point technique, fractional calculus, and multivalued analysis.

  4. Modeling of Hydrophobic Surfaces by the Stokes Problem With the Stick–Slip Boundary Conditions

    Czech Academy of Sciences Publication Activity Database

    Kučera, R.; Šátek, V.; Haslinger, Jaroslav; Fialová, S.; Pochylý, F.

    2017-01-01

    Roč. 139, č. 1 (2017), č. článku 011202. ISSN 0098-2202 Institutional support: RVO:68145535 Keywords : algebra * boundary conditions * hydrophobicity * Lagrange multipliers * Navier Stokes equations Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 1.437, year: 2016 http://fluidsengineering.asmedigitalcollection.asme.org/article.aspx?articleid=2536532

  5. Evidence for Cretaceous-Paleogene boundary bolide “impact winter” conditions from New Jersey, USA

    NARCIS (Netherlands)

    Vellekoop, J.; Esmeray-Senlet, S.; Miller, K.G.; Browning, J.V.; Sluijs, A.; van de Schootbrugge, B.; Sinninghe Damsté, J.S.; Brinkhuis, H.

    2016-01-01

    Abrupt and short-lived “impact winter” conditions have commonly been implicated as the main mechanism leading to the mass extinction at the Cretaceous-Paleogene (K-Pg) boundary (ca. 66 Ma), marking the end of the reign of the non-avian dinosaurs. However, so far only limited evidence has been

  6. Evidence for Cretaceous-Paleogene boundary bolide "impact winter" conditions from New Jersey, USA

    NARCIS (Netherlands)

    Vellekoop, J.; Esmeray-Senlet, S.; Miller, K.G.; Browning, J.V.; Sluijs, A.|info:eu-repo/dai/nl/311474748; van de Schootbrugge, B.|info:eu-repo/dai/nl/376758562; Sinninghe Damsté, J.S.|info:eu-repo/dai/nl/07401370X; Brinkhuis, H.|info:eu-repo/dai/nl/095046097

    2016-01-01

    Abrupt and short-lived “impact winter” conditions have commonly been implicated as the main mechanism leading to the mass extinction at the Cretaceous-Paleogene (K-Pg) boundary (ca. 66 Ma), marking the end of the reign of the non-avian dinosaurs. However, so far only limited evidence has been

  7. Current Percolation in Medium with Boundaries under Quantum Hall Effect Conditions

    Directory of Open Access Journals (Sweden)

    M. U. Malakeeva

    2012-01-01

    Full Text Available The current percolation has been considered in the medium with boundaries under quantum Hall effect conditions. It has been shown that in that case the effective Hall conductivity has a nonzero value due to percolation of the Hall current through the finite number of singular points (in our model these are corners at the phase joints.

  8. Construction of the Nuclear Effective Interaction from Energy Eigenstates and Boundary Conditions

    Science.gov (United States)

    McElvain, Kenneth; Haxton, Wick

    2017-01-01

    The original Harmonic Oscillator Based Effective Theory (HOBET) work by Haxton and Luu reduced H = T +VNN , with VNN a realistic potential, to Heff in a small basis defined by projection operator P while correctly including all scattering by H through an excluded space Q. Scattering by T is analytically included to all orders, leaving the ET expansion focused on the short range VNN. Results do not depend on the size P as the effect of scattering through Q is fully included, also distinguishing HOBET from other methods. In this talk we abandon VNN and determine the LECs of the ET expansion from energy levels and boundary conditions. In the infinite volume continuum case every energy is an eigenvalue of H with an associated scattering state. In the LQCD context boundary conditions are periodic. In either case the ET LECs can be determined from energy, boundary condition pairs. We show that the Cartesian HO ET LECs can be expressed in terms of the spherical ones, giving a spherical, infinite volume ET, bypassing the use of Luscher's method. The approach cleanly isolates operator mixing induced by the finite box, sequestering effects that vanish in the continuum limit in a Green's function constrained to match the boundary conditions. Supported by the DOE under contracts DE-SC00046548 and DE-AC02-98CH10886.

  9. The Sturm-Liouville inverse spectral problem with boundary conditions depending on the spectral parameter

    Directory of Open Access Journals (Sweden)

    Cornelis van der Mee

    2005-01-01

    Full Text Available We present the complete version including proofs of the results announced in [van der Mee C., Pivovarchik V.: A Sturm-Liouville spectral problem with boundary conditions depending on the spectral parameter. Funct. Anal. Appl. 36 (2002, 315–317 [Funkts. Anal. Prilozh. 36 (2002, 74–77 (Russian

  10. In-plane vibration analysis of annular plates with arbitrary boundary conditions.

    Science.gov (United States)

    Shi, Xianjie; Shi, Dongyan; Qin, Zhengrong; Wang, Qingshan

    2014-01-01

    In comparison with the out-of-plane vibrations of annular plates, far less attention has been paid to the in-plane vibrations which may also play a vital important role in affecting the sound radiation from and power flows in a built-up structure. In this investigation, a generalized Fourier series method is proposed for the in-plane vibration analysis of annular plates with arbitrary boundary conditions along each of its edges. Regardless of the boundary conditions, the in-plane displacement fields are invariantly expressed as a new form of trigonometric series expansions with a drastically improved convergence as compared with the conventional Fourier series. All the unknown expansion coefficients are treated as the generalized coordinates and determined using the Rayleigh-Ritz technique. Unlike most of the existing studies, the presented method can be readily and universally applied to a wide spectrum of in-plane vibration problems involving different boundary conditions, varying material, and geometric properties with no need of modifying the basic functions or adapting solution procedures. Several numerical examples are presented to demonstrate the effectiveness and reliability of the current solution for predicting the in-plane vibration characteristics of annular plates subjected to different boundary conditions.

  11. In-Plane Vibration Analysis of Annular Plates with Arbitrary Boundary Conditions

    Directory of Open Access Journals (Sweden)

    Xianjie Shi

    2014-01-01

    Full Text Available In comparison with the out-of-plane vibrations of annular plates, far less attention has been paid to the in-plane vibrations which may also play a vital important role in affecting the sound radiation from and power flows in a built-up structure. In this investigation, a generalized Fourier series method is proposed for the in-plane vibration analysis of annular plates with arbitrary boundary conditions along each of its edges. Regardless of the boundary conditions, the in-plane displacement fields are invariantly expressed as a new form of trigonometric series expansions with a drastically improved convergence as compared with the conventional Fourier series. All the unknown expansion coefficients are treated as the generalized coordinates and determined using the Rayleigh-Ritz technique. Unlike most of the existing studies, the presented method can be readily and universally applied to a wide spectrum of in-plane vibration problems involving different boundary conditions, varying material, and geometric properties with no need of modifying the basic functions or adapting solution procedures. Several numerical examples are presented to demonstrate the effectiveness and reliability of the current solution for predicting the in-plane vibration characteristics of annular plates subjected to different boundary conditions.

  12. Boundary conditions for the use of personal ventilation over mixing ventilation in open plan offices

    DEFF Research Database (Denmark)

    Petersen, Steffen; Hviid, Christian Anker

    2013-01-01

    This paper investigates the boundary conditions for choosing a combined Personal Ventilation (PV) and Mixing Ventilation (MV) over conventional mixing ventilation in an office with multiple workers. A simplified procedure for annual performance assessment of PV/MV systems in terms of air quality,...

  13. Kelvin--Helmholtz-like instability of a shear layer subject to free boundary conditions

    International Nuclear Information System (INIS)

    Mjolsness, R.C.

    1979-01-01

    For free boundary conditions a shear layer with linear velocity profile supports irrotational disturbances, one mode being unstable when its wavelength lambda>2.619 times the thickness h of the shear layer. For long wavelengths the dispersion relation of the mode approaches the Kelvin--Helmholtz form

  14. Optimal trajectory generation for generalization of discrete movements with boundary condition

    DEFF Research Database (Denmark)

    Herzog, Sebastian; Wörgötter, Florentin; Kulvicius, Tomas

    2016-01-01

    Trajectory generation methods play an important role in robotics since they are essential for the execution of actions. In this paper we present a novel trajectory generation method for generalization of accurate movements with boundary conditions. Our approach originates from optimal control the...

  15. A stable penalty method for the compressible Navier-Stokes equations: I. Open boundary conditions

    DEFF Research Database (Denmark)

    Hesthaven, Jan; Gottlieb, D.

    1996-01-01

    The purpose of this paper is to present asymptotically stable open boundary conditions for the numerical approximation of the compressible Navier-Stokes equations in three spatial dimensions. The treatment uses the conservation form of the Navier-Stokes equations and utilizes linearization...

  16. Transformational leadership climate : Performance linkages, mechanisms, and boundary conditions at the organizational level

    NARCIS (Netherlands)

    Menges, J.; Walter, F.; Vogel, B.; Bruch, H.

    2011-01-01

    Transformational leadership (TFL) climate describes the degree to which leaders throughout an organization engage in TFL behaviors. In this study, we investigate performance linkages, mechanisms, and boundary conditions of TFL climate at the organizational level of analysis. In a sample of 158

  17. Semilinear Evolution Problems with Ventcel-Type Conditions on Fractal Boundaries

    Directory of Open Access Journals (Sweden)

    Maria Rosaria Lancia

    2014-01-01

    Full Text Available A semilinear parabolic transmission problem with Ventcel's boundary conditions on a fractal interface S or the corresponding prefractal interface Sh is studied. Regularity results for the solution in both cases are proved. The asymptotic behaviour of the solutions of the approximating problems to the solution of limit fractal problem is analyzed.

  18. Stability properties of a heat equation with state-dependent parameters and asymmetric boundary conditions

    DEFF Research Database (Denmark)

    Backi, Christoph Josef; Bendtsen, Jan Dimon; Leth, John

    2015-01-01

    In this work the stability properties of a partial differential equation (PDE) with state-dependent parameters and asymmetric boundary conditions are investigated. The PDE describes the temperature distribution inside foodstuff, but can also hold for other applications and phenomena. We show...

  19. Multiplicity of solutions for Dirichlet boundary conditions of second-order quasilinear equations with impulsive effects

    Directory of Open Access Journals (Sweden)

    Tengfei Shen

    2015-12-01

    Full Text Available This paper deals with the multiplicity of solutions for Dirichlet boundary conditions of second-order quasilinear equations with impulsive effects. By using critical point theory, a new result is obtained. An example is given to illustrate the main result.

  20. Application of impedance boundary conditions to numerical solution of corrugated circular horns

    DEFF Research Database (Denmark)

    Iskander, K; Shafai, L; Frandsen, Aksel

    1982-01-01

    An integral equation method is used to formulate the problem of scattering by rotationally symmetric horn antennas. The excitation is assumed to be due to an infinitesimal dipole antenna, while the secondary field is obtained by assuming anisotropic impedance boundary conditions on the horn surfa...

  1. Non-reflecting boundary conditions and tensile instability in smooth particle hydrodynamics

    OpenAIRE

    Powell, Seimon

    2012-01-01

    This thesis aimed at the understanding and further development of smoothed particle hydrodynamics (SPH). The first part described the implementations of non-reflecting boundary conditions for elastic- waves in SPH. The second part contains a stability analysis of the semi-discrete SPH equations and a new method for stabilising basic SPH in tension.

  2. Dynamic response of tube bundles with time-dependent boundary conditions

    International Nuclear Information System (INIS)

    Chaushioung Yeh; Ingtzer Hwang

    1993-01-01

    For the problems of dynamic response of tube bundles in incompressible fluid, the fluid-inertia loading must be included in the governing equations of coupled motion of array of tubes. This inertia loading (hydrodynamic force) can be formulated as an added mass matrix by using boundary element technique for whatever shapes of tubes in an arbitrary array. To deal with the vibration of tube bundles with time-dependent boundary conditions, a general method is established. The complete solution of this linear partial differential equation can be divided into two parts; quasi-static and dynamic solutions, each satisfies the non-homogeneous boundary conditions and homogeneous conditions, respectively. In this paper, a method based on Betti's law and developed by Yeh and Liaw is adopted to find the solution without pursuing the quasistatic solution explicitly. The effects of the time-dependent boundary conditions on the responses of tube bundles of different shapes and arrays are analyzed and discussed in this paper

  3. Effects of physical boundary conditions on the transverse vibration of single-layer graphene sheets

    Science.gov (United States)

    Sadeghzadeh, S.; Khatibi, M. M.

    2016-09-01

    The effects of various approaches for a comprehensive application of boundary conditions on the molecular dynamics of graphene nanosheets were studied in this paper. Fixing more than two rows of carbon atoms was tested for satisfaction of clamped boundary condition in dynamics problems, and it was demonstrated that a completely different view should be taken for clamped boundary conditions. To do this, through the frequency domain decomposition approach, operational modal analysis has been developed to carry out the Laboratory of Nanometric Operational Modal Analysis on a molecular dynamics platform. The theory of the mentioned approach was introduced, and some comparisons were made with experimental works. The modeling results have shown that for graphene sheets with simply supported edges, fixing two or more rows leads to the same response as fixing one row. For clamped edges, the use of a flexible base as a substrate satisfies the boundary condition with the best possible. At the end, as an example, it has been demonstrated that the second and third natural vibration frequencies increase with the increase in aspect ratio, while the first frequency remains unchanged.

  4. A laser Doppler system for the remote sensing of boundary layer winds in clear air conditions

    Science.gov (United States)

    Lawrence, T. R.; Krause, M. C.; Craven, C. E.; Morrison, L. K.; Thomson, J. A. L.; Cliff, W. C.; Huffaker, R. M.

    1975-01-01

    The system discussed uses a laser Doppler radar in combination with a velocity azimuth display mode of scanning to determine the three-dimensional wind field in the atmospheric boundary layer. An attractive feature of this CW monostatic system is that the ambient aerosol provides a 'sufficient' scattering target to permit operation under clear air conditions. Spatial resolution is achieved by focusing.

  5. Inference and testing on the boundary in extended constant conditional correlation GARCH models

    DEFF Research Database (Denmark)

    Pedersen, Rasmus Søndergaard

    2017-01-01

    We consider inference and testing in extended constant conditional correlation GARCH models in the case where the true parameter vector is a boundary point of the parameter space. This is of particular importance when testing for volatility spillovers in the model. The large-sample properties of ...... for (no) volatility spillovers between foreign exchange rates....

  6. Correlation equations for classical continuous systems: finite-volume solutions for tempered boundary conditions

    International Nuclear Information System (INIS)

    Zagrebnov, V.A.

    1980-01-01

    Using resolvents for Kirkwood-Zalburg, Kirkwood-Ruelle and Meier-Montroll operators, solutions of the finite-volume correlation equations for tempered boundary conditions are obtained explicity. The uniqueness theorem is proved. A connection of the correlation equations with the Dobrushin-Landford-Ruelle equations for the Gibbs probability measure is discussed

  7. Conformal field theory of dipolar SLE with the Dirichlet boundary condition

    Science.gov (United States)

    Kang, Nam-Gyu; Tak, Hee-Joon

    2013-12-01

    We develop a version of dipolar conformal field theory based on the central charge modification of the Gaussian free field with the Dirichlet boundary condition and prove that correlators of certain family of fields in this theory are martingale-observables for dipolar SLE. We prove the restriction property of dipolar SLE(8/3) and Friedrich-Werner's formula in the dipolar case.

  8. Comparison of Extreme Pressure Additive Treat Rates in Soybean and Mineral Oils Under Boundary Lubrication Conditions

    Science.gov (United States)

    Traditionally, it is considered that, under boundary lubrication conditions, the reduction in friction and wear is mostly dependent on Extreme Pressure (EP) additives, rather than the basestock. However, several studies indicate that vegetable oils also contribute to the lubricity under this regime...

  9. Single particle nonlocality, geometric phases and time-dependent boundary conditions

    Science.gov (United States)

    Matzkin, A.

    2018-03-01

    We investigate the issue of single particle nonlocality in a quantum system subjected to time-dependent boundary conditions. We discuss earlier claims according to which the quantum state of a particle remaining localized at the center of an infinite well with moving walls would be specifically modified by the change in boundary conditions due to the wall’s motion. We first prove that the evolution of an initially localized Gaussian state is not affected nonlocally by a linearly moving wall: as long as the quantum state has negligible amplitude near the wall, the boundary motion has no effect. This result is further extended to related confined time-dependent oscillators in which the boundary’s motion is known to give rise to geometric phases: for a Gaussian state remaining localized far from the boundaries, the effect of the geometric phases is washed out and the particle dynamics shows no traces of a nonlocal influence that would be induced by the moving boundaries.

  10. Nonlinear physical segmentation algorithm for determining the layer boundary from lidar signal.

    Science.gov (United States)

    Mao, Feiyue; Li, Jun; Li, Chen; Gong, Wei; Min, Qilong; Wang, Wei

    2015-11-30

    Layer boundary (base and top) detection is a basic problem in lidar data processing, the results of which are used as inputs of optical properties retrieval. However, traditional algorithms not only require manual intervention but also rely heavily on the signal-to-noise ratio. Therefore, we propose a robust and automatic algorithm for layer detection based on a novel algorithm for lidar signal segmentation and representation. Our algorithm is based on the lidar equation and avoids most of the limitations of the traditional algorithms. Testing of the simulated and real signals shows that the algorithm is able to position the base and top accurately even with a low signal to noise ratio. Furthermore, the results of the classification are accurate and satisfactory. The experimental results confirm that our algorithm can be used for automatic detection, retrieval, and analysis of lidar data sets.

  11. Combined effects of surface conditions, boundary layer dynamics and chemistry on diurnal SOA evolution

    Directory of Open Access Journals (Sweden)

    R. H. H. Janssen

    2012-08-01

    Full Text Available We study the combined effects of land surface conditions, atmospheric boundary layer dynamics and chemistry on the diurnal evolution of biogenic secondary organic aerosol in the atmospheric boundary layer, using a model that contains the essentials of all these components. First, we evaluate the model for a case study in Hyytiälä, Finland, and find that it is able to satisfactorily reproduce the observed dynamics and gas-phase chemistry. We show that the exchange of organic aerosol between the free troposphere and the boundary layer (entrainment must be taken into account in order to explain the observed diurnal cycle in organic aerosol (OA concentration. An examination of the budgets of organic aerosol and terpene concentrations show that the former is dominated by entrainment, while the latter is mainly driven by emission and chemical transformation. We systematically investigate the role of the land surface, which governs both the surface energy balance partitioning and terpene emissions, and the large-scale atmospheric process of vertical subsidence. Entrainment is especially important for the dilution of organic aerosol concentrations under conditions of dry soils and low terpene emissions. Subsidence suppresses boundary layer growth while enhancing entrainment. Therefore, it influences the relationship between organic aerosol and terpene concentrations. Our findings indicate that the diurnal evolution of secondary organic aerosols (SOA in the boundary layer is the result of coupled effects of the land surface, dynamics of the atmospheric boundary layer, chemistry, and free troposphere conditions. This has potentially some consequences for the design of both field campaigns and large-scale modeling studies.

  12. An Implementation of Hydrostatic Boundary Conditions for Variable Density Lattice Boltzmann Methods

    Science.gov (United States)

    Bardsley, K. J.; Thorne, D. T.; Lee, J. S.; Sukop, M. C.

    2006-12-01

    Lattice Boltzmann Methods (LBMs) have been under development for the last two decades and have become another capable numerical method for simulating fluid flow. Recent advances in lattice Boltzmann applications involve simulation of density-dependent fluid flow in closed (Dixit and Babu, 2006; D'Orazio et al., 2004) or periodic (Guo and Zhao, 2005) domains. However, standard pressure boundary conditions (BCs) are incompatible with concentration-dependent density flow simulations that use a body force for gravity. An implementation of hydrostatic BCs for use under these conditions is proposed here. The basis of this new implementation is an additional term in the pressure BC. It is derived to account for the incorporation of gravity as a body force and the effect of varying concentration in the fluid. The hydrostatic BC expands the potential of density-dependent LBM to simulate domains with boundaries other than the closed or periodic boundaries that have appeared in previous literature on LBM simulations. With this new implementation, LBM will be able to simulate complex concentration-dependent density flows, such as salt water intrusion in the classic Henry and Henry-Hilleke problems. This is demonstrated using various examples, beginning with a closed box system, and ending with a system containing two solid walls, one velocity boundary and one pressure boundary, as in the Henry problem. References Dixit, H. N., V. Babu, (2006), Simulation of high Rayleigh number natural convection in a square cavity using the lattice Boltzmann method, Int. J. Heat Mass Transfer, 49, 727-739. D'Orazio, A., M. Corcione, G.P. Celata, (2004), Application to natural convection enclosed flows of a lattice Boltzmann BGK model coupled with a general purpose thermal boundary conditions, Int. J. Thermal Sci., 43, 575-586. Gou, Z., T.S. Zhao, (2005), Lattice Boltzmann simulation of natural convection with temperature-dependant viscosity in a porous cavity, Numerical Heat Transfer, Part B

  13. Solvability of second-order boundary-value problems at resonance involving integral conditions

    Directory of Open Access Journals (Sweden)

    Yujun Cui

    2012-03-01

    Full Text Available This article concerns the second-order differential equation with integral boundary conditions $$displaylines{ x''(t=f(t,x(t,x'(t,quad tin (0,1,cr x(0=int_0^1x(sdalpha(s,quad x(1=int_0^1x(sdeta(s. }$$ Under the resonance conditions, we construct a projector and then applying coincidence degree theory to establish the existence of solutions.

  14. Scalar field dynamics in a BTZ background with generic boundary conditions

    International Nuclear Information System (INIS)

    Garbarz, Alan; La Madrid, Joan; Leston, Mauricio

    2017-01-01

    We revisit the dynamics of a massive scalar field in a Banados, Teitelboim, and Zanelli background taking into account the lack of global hyperbolicity of the spacetime. We approach this issue using the strategy of Ishibashi and Wald which finds a unique smooth solution as the causal evolution of initial data, each possible evolution corresponding to a positive self-adjoint extension of certain operator in a Hilbert space on the initial surface. Moreover, solutions obtained this way are the most general ones satisfying a few physically sensible requirements. This procedure is intimately related to the choice of boundary conditions and the existence of bound states. We find that the scalar field dynamics in the (effective) mass window -3/4 ≤ m e 2 l 2 < 0 can be well defined within a one-parametric family of distinct boundary conditions (-3/4 being the conformally coupled case), while for m e 2 l 2 ≥ 0 the boundary condition is unique (only one self-adjoint extension is possible). It is argued that there is no sensible evolution possible for m e 2 l 2 < -1, and also it is shown that in the range m e 2 l 2 element of [-1, -3/4) there is a U(1) family of allowed boundary conditions, however, the positivity of the self-adjoint extensions is only motivated but not proven. We focus mainly on describing the dynamics of such evolutions given the initial data and all possible boundary conditions, and in particular we show the energy is always positive and conserved. (orig.)

  15. On the Exit Boundary Condition for One-Dimensional Calculations of Pulsed Detonation Engine Performance

    Science.gov (United States)

    Wilson, Jack; Paxson, Daniel E.

    2002-01-01

    In one-dimensional calculations of pulsed detonation engine (PDE) performance, the exit boundary condition is frequently taken to be a constant static pressure. In reality, for an isolated detonation tube, after the detonation wave arrives at the exit plane, there will be a region of high pressure, which will gradually return to ambient pressure as an almost spherical shock wave expands away from the exit, and weakens. Initially, the flow is supersonic, unaffected by external pressure, but later becomes subsonic. Previous authors have accounted for this situation either by assuming the subsonic pressure decay to be a relaxation phenomenon, or by running a two-dimensional calculation first, including a domain external to the detonation tube, and using the resulting exit pressure temporal distribution as the boundary condition for one-dimensional calculations. These calculations show that the increased pressure does affect the PDE performance. In the present work, a simple model of the exit process is used to estimate the pressure decay time. The planar shock wave emerging from the tube is assumed to transform into a spherical shock wave. The initial strength of the spherical shock wave is determined from comparison with experimental results. Its subsequent propagation, and resulting pressure at the tube exit, is given by a numerical blast wave calculation. The model agrees reasonably well with other, limited, results. Finally, the model was used as the exit boundary condition for a one-dimensional calculation of PDE performance to obtain the thrust wall pressure for a hydrogen-air detonation in tubes of length to diameter ratio (L/D) of 4, and 10, as well as for the original, constant pressure boundary condition. The modified boundary condition had no performance impact for values of L/D > 10, and moderate impact for L/D = 4.

  16. Scalar field dynamics in a BTZ background with generic boundary conditions

    Energy Technology Data Exchange (ETDEWEB)

    Garbarz, Alan; La Madrid, Joan [UBA y IFIBA, CONICET, Departamento de Fisica, FCEyN, Buenos Aires (Argentina); Leston, Mauricio [Pabellon IAFE-CONICET, Instituto de Astronomia y Fisica del Espacio, Buenos Aires (Argentina)

    2017-11-15

    We revisit the dynamics of a massive scalar field in a Banados, Teitelboim, and Zanelli background taking into account the lack of global hyperbolicity of the spacetime. We approach this issue using the strategy of Ishibashi and Wald which finds a unique smooth solution as the causal evolution of initial data, each possible evolution corresponding to a positive self-adjoint extension of certain operator in a Hilbert space on the initial surface. Moreover, solutions obtained this way are the most general ones satisfying a few physically sensible requirements. This procedure is intimately related to the choice of boundary conditions and the existence of bound states. We find that the scalar field dynamics in the (effective) mass window -3/4 ≤ m{sub e}{sup 2}l{sup 2} < 0 can be well defined within a one-parametric family of distinct boundary conditions (-3/4 being the conformally coupled case), while for m{sub e}{sup 2}l{sup 2} ≥ 0 the boundary condition is unique (only one self-adjoint extension is possible). It is argued that there is no sensible evolution possible for m{sub e}{sup 2}l{sup 2} < -1, and also it is shown that in the range m{sub e}{sup 2}l{sup 2} element of [-1, -3/4) there is a U(1) family of allowed boundary conditions, however, the positivity of the self-adjoint extensions is only motivated but not proven. We focus mainly on describing the dynamics of such evolutions given the initial data and all possible boundary conditions, and in particular we show the energy is always positive and conserved. (orig.)

  17. Approximate source conditions for nonlinear ill-posed problems—chances and limitations

    International Nuclear Information System (INIS)

    Hein, Torsten; Hofmann, Bernd

    2009-01-01

    In the recent past the authors, with collaborators, have published convergence rate results for regularized solutions of linear ill-posed operator equations by avoiding the usual assumption that the solutions satisfy prescribed source conditions. Instead the degree of violation of such source conditions is expressed by distance functions d(R) depending on a radius R ≥ 0 which is an upper bound of the norm of source elements under consideration. If d(R) tends to zero as R → ∞ an appropriate balancing of occurring regularization error terms yields convergence rates results. This approach was called the method of approximate source conditions, originally developed in a Hilbert space setting. The goal of this paper is to formulate chances and limitations of an application of this method to nonlinear ill-posed problems in reflexive Banach spaces and to complement the field of low order convergence rates results in nonlinear regularization theory. In particular, we are going to establish convergence rates for a variant of Tikhonov regularization. To keep structural nonlinearity conditions simple, we update the concept of degree of nonlinearity in Hilbert spaces to a Bregman distance setting in Banach spaces

  18. Prescribing transient and asymptotic behaviour of non-linear systems with stochastic initial conditions

    NARCIS (Netherlands)

    Dresscher, Martijn; Jayawardhana, Bayu

    2017-01-01

    We study a control design problem for nonlinear affine systems whose initial condition is a random variable with known distribution. In this control problem, the control objectives are two-folds: (i). the closed-loop system attains a minimum cumulative distribution over a prescribed containment set

  19. Global existence and exponential growth for a viscoelastic wave equation with dynamic boundary conditions

    KAUST Repository

    Gerbi, Stéphane

    2013-01-15

    The goal of this work is to study a model of the wave equation with dynamic boundary conditions and a viscoelastic term. First, applying the Faedo-Galerkin method combined with the fixed point theorem, we show the existence and uniqueness of a local in time solution. Second, we show that under some restrictions on the initial data, the solution continues to exist globally in time. On the other hand, if the interior source dominates the boundary damping, then the solution is unbounded and grows as an exponential function. In addition, in the absence of the strong damping, then the solution ceases to exist and blows up in finite time.

  20. Nonlinear finite element simulations of injuries with free boundaries: application to surgical wounds.

    Science.gov (United States)

    Valero, C; Javierre, E; García-Aznar, J M; Gómez-Benito, M J

    2014-06-01

    Wound healing is a process driven by biochemical and mechanical variables in which a new tissue is synthesised to recover original tissue functionality. Wound morphology plays a crucial role in this process, as the skin behaviour is not uniform along different directions. In this work, we simulate the contraction of surgical wounds, which can be characterised as elongated and deep wounds. Because of the regularity of this morphology, we approximate the evolution of the wound through its cross section, adopting a plane strain hypothesis. This simplification reduces the complexity of the computational problem; while allows for a thorough analysis of the role of wound depth in the healing process, an aspect of medical and computational relevance that has not yet been addressed. To reproduce wound contraction, we consider the role of fibroblasts, myofibroblasts, collagen and a generic growth factor. The contraction phenomenon is driven by cell-generated forces. We postulate that these forces are adjusted to the mechanical environment of the tissue where cells are embedded through a mechanosensing and mechanotransduction mechanism. To solve the nonlinear problem, we use the finite element method (FEM) and an updated Lagrangian approach to represent the change in the geometry. To elucidate the role of wound depth and width on the contraction pattern and evolution of the involved species, we analyse different wound geometries with the same wound area. We find that deeper wounds contract less and reach a maximum contraction rate earlier than superficial wounds. Copyright © 2014 John Wiley & Sons, Ltd.

  1. Involving the Navier-Stokes equations in the derivation of boundary conditions for the lattice Boltzmann method.

    Science.gov (United States)

    Verschaeve, Joris C G

    2011-06-13

    By means of the continuity equation of the incompressible Navier-Stokes equations, additional physical arguments for the derivation of a formulation of the no-slip boundary condition for the lattice Boltzmann method for straight walls at rest are obtained. This leads to a boundary condition that is second-order accurate with respect to the grid spacing and conserves mass. In addition, the boundary condition is stable for relaxation frequencies close to two.

  2. Dynamic stability analysis of fluid-filled cylindrical shells with top end-fixed boundary condition

    International Nuclear Information System (INIS)

    Xu, Y.H.; Tsukimori, K.

    1995-01-01

    This study is aimed at understanding the dynamic instability mechanism of fluid-filled cylindrical shells with top end-fixed boundary condition under seismic excitation. The fluid-structure interaction problem is formulated using the concept of added mass. The contribution of each individual fluid pressure components are identified. A Galerkin/Finite Element discretization is applied to obtain the governing matrix equations. The model coupling among the various combinations of axial and circumferential modes are identified. For dynamic stability analysis, the matrix equations are cast into a set of coupled Hill's equations by employing an orthogonality transformation. The application of this method and the discussion on dynamic buckling behaviors of different boundary conditions are presented. The following comments are found: (1) Strong effect of added mass to the first beam mode frequency is observed in the top end-fixed case and the effect depends on the level of filled fluid and the ratio of shall radius to height; (2) The static and dynamic pressure acting on the bottom plate increase the axial frequency for n=2... N and the critical instability parameter ε cr in the top end-fixed case, respectively; (3) Strong effect of shell top boundary, open or closed, to axial frequencies for mode (i,n) (n=2... N) and instability behaviors is observed for fluid-filled tanks with bottom-fixed boundary condition. (author)

  3. Transducer placement for robustness to variations in boundary conditions for active structural acoustic control

    Science.gov (United States)

    Sprofera, Joseph D.; Clark, Robert L.; Gibbs, Gary P.; Cabell, Randolph H.

    2003-10-01

    The study of control strategies aimed at the reduction of turbulent boundary layer noise transmission into the fuselage of an aircraft has been a topic of academic and industrial research for several years. In this work we focus on an approach that will attempt to address a practical application issue: the impact of uncertainty in boundary conditions on the choice of actuator and sensor locations for structural acoustic control. The selection of an optimized set of transducers and the creation of a suitably adjustable test system is used to demonstrate that robustness to bounded variations in boundary conditions of a plate is achievable in active structural acoustic control. This robustness is achieved through the optimization of transducer placement with respect to maximizing control of structural acoustic radiation over the desired range of boundary conditions. This project incorporates energy based modeling of the structure, electromechanical piezo coupling, radiation filter modeling, and control analysis through the use of Hankel Singular Value (HSV) estimates and optimization based upon the genetic algorithm. Testing in a transmission loss facility will be used to validate the selected transducer placements and demonstrate a reduction in radiated sound power. [Work supported by NASA.

  4. Program Code Generator for Cardiac Electrophysiology Simulation with Automatic PDE Boundary Condition Handling.

    Directory of Open Access Journals (Sweden)

    Florencio Rusty Punzalan

    Full Text Available Clinical and experimental studies involving human hearts can have certain limitations. Methods such as computer simulations can be an important alternative or supplemental tool. Physiological simulation at the tissue or organ level typically involves the handling of partial differential equations (PDEs. Boundary conditions and distributed parameters, such as those used in pharmacokinetics simulation, add to the complexity of the PDE solution. These factors can tailor PDE solutions and their corresponding program code to specific problems. Boundary condition and parameter changes in the customized code are usually prone to errors and time-consuming. We propose a general approach for handling PDEs and boundary conditions in computational models using a replacement scheme for discretization. This study is an extension of a program generator that we introduced in a previous publication. The program generator can generate code for multi-cell simulations of cardiac electrophysiology. Improvements to the system allow it to handle simultaneous equations in the biological function model as well as implicit PDE numerical schemes. The replacement scheme involves substituting all partial differential terms with numerical solution equations. Once the model and boundary equations are discretized with the numerical solution scheme, instances of the equations are generated to undergo dependency analysis. The result of the dependency analysis is then used to generate the program code. The resulting program code are in Java or C programming language. To validate the automatic handling of boundary conditions in the program code generator, we generated simulation code using the FHN, Luo-Rudy 1, and Hund-Rudy cell models and run cell-to-cell coupling and action potential propagation simulations. One of the simulations is based on a published experiment and simulation results are compared with the experimental data. We conclude that the proposed program code

  5. Improved Delay-Dependent Stability Conditions for MIMO Networked Control Systems with Nonlinear Perturbations

    Science.gov (United States)

    2014-01-01

    This paper provides improved time delay-dependent stability criteria for multi-input and multi-output (MIMO) network control systems (NCSs) with nonlinear perturbations. Without the stability assumption on the neutral operator after the descriptor approach, the new proposed stability theory is less conservative than the existing stability condition. Theoretical proof is given in this paper to demonstrate the effectiveness of the proposed stability condition. PMID:24744679

  6. Magnetohydrodynamics (MHD flow of a tangent hyperbolic fluid with nanoparticles past a stretching sheet with second order slip and convective boundary condition

    Directory of Open Access Journals (Sweden)

    Wubshet Ibrahim

    Full Text Available This article presents the effect of thermal radiation on magnetohydrodynamic flow of tangent hyperbolic fluid with nanoparticle past an enlarging sheet with second order slip and convective boundary condition. Condition of zero normal flux of nanoparticles at the wall is used for the concentration boundary condition, which is the current topic that have yet to be studied extensively. The solution for the velocity, temperature and nanoparticle concentration is governed by parameters viz. power-law index (n, Weissenberg number We, Biot number Bi, Prandtl number Pr, velocity slip parameters δ and γ, Lewis number Le, Brownian motion parameter Nb and the thermophoresis parameter Nt. Similarity transformation is used to metamorphosed the governing non-linear boundary-value problem into coupled higher order non-linear ordinary differential equation. The succeeding equations were numerically solved using the function bvp4c from the matlab for different values of emerging parameters. Numerical results are deliberated through graphs and tables for velocity, temperature, concentration, the skin friction coefficient and local Nusselt number. The results designate that the skin friction coefficient Cf deplete as the values of Weissenberg number We, slip parameters γ and δ upturn and it rises as the values of power-law index n increase. The local Nusselt number -θ′(0 decreases as slip parameters γ and δ, radiation parameter Nr, Weissenberg number We, thermophoresis parameter Nt and power-law index n increase. However, the local Nusselt number increases as the Biot number Bi increase. Keywords: Tangent hyperbolic fluid, Second order slip flow, MHD, Convective boundary condition, Radiation effect, Passive control of nanoparticles

  7. Nonlinear Gulf Stream Interaction with the Deep Western Boundary Current System: Observations and a Numerical Simulation

    Science.gov (United States)

    Dietrich, David E.; Mehra, Avichal; Haney, Robert L.; Bowman, Malcolm J.; Tseng, Yu-Heng

    2003-01-01

    Gulf Stream (GS) separation near its observed Cape Hatteras (CH) separation location, and its ensuing path and dynamics, is a challenging ocean modeling problem. If a model GS separates much farther north than CH, then northward GS meanders, which pinch off warm core eddies (rings), are not possible or are strongly constrained by the Grand Banks shelfbreak. Cold core rings pinch off the southward GS meanders. The rings are often re-absorbed by the GS. The important warm core rings enhance heat exchange and, especially, affect the northern GS branch after GS bifurcation near the New England Seamount Chain. This northern branch gains heat by contact with the southern branch water upstream of bifurcation, and warms the Arctic Ocean and northern seas, thus playing a major role in ice dynamics, thermohaline circulation and possible global climate warming. These rings transport heat northward between the separated GS and shelf slope/Deep Western Boundary Current system (DWBC). This region has nearly level time mean isopycnals. The eddy heat transport convergence/divergence enhances the shelfbreak and GS front intensities and thus also increases watermass transformation. The fronts are maintained by warm advection by the Florida Current and cool advection by the DWBC. Thus, the GS interaction with the DWBC through the intermediate eddy field is climatologically important.

  8. Moment-based boundary conditions for lattice Boltzmann simulations of natural convection in cavities

    KAUST Repository

    Allen, Rebecca

    2016-06-29

    We study a multiple relaxation time lattice Boltzmann model for natural convection with moment-based boundary conditions. The unknown primary variables of the algorithm at a boundary are found by imposing conditions directly upon hydrodynamic moments, which are then translated into conditions for the discrete velocity distribution functions. The method is formulated so that it is consistent with the second order implementation of the discrete velocity Boltzmann equations for fluid flow and temperature. Natural convection in square cavities is studied for Rayleigh numbers ranging from 103 to 108. An excellent agreement with benchmark data is observed and the flow fields are shown to converge with second order accuracy. Copyright © 2016 Inderscience Enterprises Ltd.

  9. Scalar field dynamics in a BTZ background with generic boundary conditions

    Science.gov (United States)

    Garbarz, Alan; La Madrid, Joan; Leston, Mauricio

    2017-11-01

    We revisit the dynamics of a massive scalar field in a Banados, Teitelboim, and Zanelli background taking into account the lack of global hyperbolicity of the spacetime. We approach this issue using the strategy of Ishibashi and Wald which finds a unique smooth solution as the causal evolution of initial data, each possible evolution corresponding to a positive self-adjoint extension of certain operator in a Hilbert space on the initial surface. Moreover, solutions obtained this way are the most general ones satisfying a few physically sensible requirements. This procedure is intimately related to the choice of boundary conditions and the existence of bound states. We find that the scalar field dynamics in the (effective) mass window -3/4≤ m_e^2ℓ ^2conditions (-3/4 being the conformally coupled case), while for m_e^2ℓ ^2≥ 0 the boundary condition is unique (only one self-adjoint extension is possible). It is argued that there is no sensible evolution possible for m_e^2ℓ ^2conditions, however, the positivity of the self-adjoint extensions is only motivated but not proven. We focus mainly on describing the dynamics of such evolutions given the initial data and all possible boundary conditions, and in particular we show the energy is always positive and conserved.

  10. Air Quality and Meteorological Boundary Conditions during the MCMA-2003 Field Campaign

    Science.gov (United States)

    Sosa, G.; Arriaga, J.; Vega, E.; Magaña, V.; Caetano, E.; de Foy, B.; Molina, L. T.; Molina, M. J.; Ramos, R.; Retama, A.; Zaragoza, J.; Martínez, A. P.; Márquez, C.; Cárdenas, B.; Lamb, B.; Velasco, E.; Allwine, E.; Pressley, S.; Westberg, H.; Reyes, R.

    2004-12-01

    A comprehensive field campaign to characterize photochemical smog in the Mexico City Metropolitan Area (MCMA) was conducted during April 2003. An important number of equipment was deployed all around the urban core and its surroundings to measure gas and particles composition from the various sources and receptor sites. In addition to air quality measurements, meteorology variables were also taken by regular weather meteorological stations, tethered balloons, radiosondes, sodars and lidars. One important issue with regard to the field campaign was the characterization of the boundary conditions in order to feed meteorological and air quality models. Four boundary sites were selected to measure continuously criteria pollutants, VOC and meteorological variables at surface level. Vertical meteorological profiles were measured at three other sites : radiosondes in Tacubaya site were launched every six hours daily; tethered balloons were launched at CENICA and FES-Cuautitlan sites according to the weather conditions, and one sodar was deployed at UNAM site in the south of the city. Additionally to these measurements, two fixed meteorological monitoring networks deployed along the city were available to complement these measurements. In general, we observed that transport of pollutants from the city to the boundary sites changes every day, according to the coupling between synoptic and local winds. This effect were less important at elevated sites such as Cerro de la Catedral and ININ, where synoptic wind were more dominant during the field campaign. Also, local sources nearby boundary sites hide the influence of pollution coming from the city some days, particularly at the La Reforma site.

  11. CFD Analysis of the Human Exhalation Flow using Different Boundary Conditions and Ventilation Strategies

    DEFF Research Database (Denmark)

    Villafruela, J.M.; Olmedo, Inés; Ruiz de Adana, M.

    2013-01-01

    This paper analyses the dispersion of the exhaled contaminants by humans in indoor environments, with special attention to the exhalation jet and its interaction with the indoor airflow pattern in both mixing and displacement ventilation conditions. The way in which three different numerical...... different environmental conditions and to validate whether a steady boundary condition of the exhalation flow may simulate human breathing in an effective and accurate way. The results show a very good agreement of the numerical results obtained for Test a and the experimental data. This fact confirms...

  12. Influence of the Outer Boundary Condition on models of AGB stars

    Science.gov (United States)

    Wagstaff, G.; Weiss, A.

    2018-04-01

    Current implementations of the stellar atmosphere typically derive boundary conditions for the interior model from either grey plane-parallel atmospheres or scaled solar atmospheres, neither of which can be considered to have appropriate underlying assumptions for the Thermally Pulsing Asymptotic Giant Branch (TP-AGB). This paper discusses the treatment and influence of the outer boundary condition within stellar evolution codes, and the resulting effects on the AGB evolution. The complex interaction of processes, such as the third dredge up and mass loss, governing the TP-AGB can be affected by varying the treatment of this boundary condition. Presented here are the results from altering the geometry, opacities and the implementation of a grid of MARCS/COMARCS model atmospheres in order to improve this treatment. Although there are changes in the TP-AGB evolution, observable quantities, such as the final core mass, are not significantly altered as a result of the change of atmospheric treatment. During the course of the investigation, a previously unseen phenomena in the AGB models was observed and further investigated. This is believed to be physical, although arising from specific conditions which make its presence unlikely. If it were present in stars, this phenomenon would increase the carbon-star lifetime above 10Myr and increase the final core mass by ˜0.1M⊙ in the narrow initial-mass range where it was observed (˜2 - 2.3M⊙).

  13. Modification of the Riemann problem and the application for the boundary conditions in computational fluid dynamics

    Directory of Open Access Journals (Sweden)

    Kyncl Martin

    2017-01-01

    Full Text Available We work with the system of partial differential equations describing the non-stationary compressible turbulent fluid flow. It is a characteristic feature of the hyperbolic equations, that there is a possible raise of discontinuities in solutions, even in the case when the initial conditions are smooth. The fundamental problem in this area is the solution of the so-called Riemann problem for the split Euler equations. It is the elementary problem of the one-dimensional conservation laws with the given initial conditions (LIC - left-hand side, and RIC - right-hand side. The solution of this problem is required in many numerical methods dealing with the 2D/3D fluid flow. The exact (entropy weak solution of this hyperbolical problem cannot be expressed in a closed form, and has to be computed by an iterative process (to given accuracy, therefore various approximations of this solution are being used. The complicated Riemann problem has to be further modified at the close vicinity of boundary, where the LIC is given, while the RIC is not known. Usually, this boundary problem is being linearized, or roughly approximated. The inaccuracies implied by these simplifications may be small, but these have a huge impact on the solution in the whole studied area, especially for the non-stationary flow. Using the thorough analysis of the Riemann problem we show, that the RIC for the local problem can be partially replaced by the suitable complementary conditions. We suggest such complementary conditions accordingly to the desired preference. This way it is possible to construct the boundary conditions by the preference of total values, by preference of pressure, velocity, mass flow, temperature. Further, using the suitable complementary conditions, it is possible to simulate the flow in the vicinity of the diffusible barrier. On the contrary to the initial-value Riemann problem, the solution of such modified problems can be written in the closed form for some

  14. Nonlinear Creep Model for Deep Rock under High Stress and High Pore Water Pressure Condition

    Directory of Open Access Journals (Sweden)

    Xie Yuanguang

    2016-05-01

    Full Text Available Conventional triaxial compression creep experiments for deep sandstone under high confining pressure and high pore water pressure were carried out, in order to predict the creep response of deep rock under these conditions. A nonlinear viscoelastic-plastic creep constitutive model was proposed based on the experimental results. The theory of component model was used as a basis for the formulation of this model. First, by using mathematical fitting and analogy, a new nonlinear viscous component was introduced based on the properties of the creep curves during the tertiary stage. Second, a timer component to judge whether the creep can get into the tertiary stage was presented. Finally, a nonlinear creep model was proposed. Results showed good agreement between theory curves from the nonlinear creep model and experimental data. This model can be applied to predict deep rock creep responses under high stress and high pore water pressure conditions. Hence, the obtained conclusions in this study are beneficial to deep rock engineering.

  15. Sea slugs, subliminal pictures and vegetative state patients: Boundaries of consciousness in classical conditioning.

    Directory of Open Access Journals (Sweden)

    Tristan A Bekinschtein

    2011-12-01

    Full Text Available Classical (trace conditioning is a specific variant of associative learning in which a neutral stimulus leads to the subsequent prediction of an emotionally charged or noxious stimulus after a temporal gap. When conditioning is concurrent with a distraction task, only participants who can report the relationship (the contingency between stimuli explicitly show associative learning. This suggests that consciousness is a prerequisite for trace conditioning. We review and question three main controversies concerning this view. Firstly, virtually all animals, even invertebrate sea slugs, show this type of learning; secondly, unconsciously perceived stimuli may elicit trace conditioning; and thirdly, some vegetative state patients show trace learning. We discuss and analyze these seemingly contradictory arguments to find the theoretical boundaries of consciousness in classical conditioning. We conclude that trace conditioning remains one of the best measures to test conscious processing in the absence of explicit reports.

  16. Influence of Contact Angle Boundary Condition on CFD Simulation of T-Junction

    Science.gov (United States)

    Arias, S.; Montlaur, A.

    2018-03-01

    In this work, we study the influence of the contact angle boundary condition on 3D CFD simulations of the bubble generation process occurring in a capillary T-junction. Numerical simulations have been performed with the commercial Computational Fluid Dynamics solver ANSYS Fluent v15.0.7. Experimental results serve as a reference to validate numerical results for four independent parameters: the bubble generation frequency, volume, velocity and length. CFD simulations accurately reproduce experimental results both from qualitative and quantitative points of view. Numerical results are very sensitive to the gas-liquid-wall contact angle boundary conditions, confirming that this is a fundamental parameter to obtain accurate CFD results for simulations of this kind of problems.

  17. Imposition of Dirichlet Boundary Conditions in Element Free Galerkin Method through an Object-Oriented Implementation

    Directory of Open Access Journals (Sweden)

    Samira Hosseini

    Full Text Available Abstract One of the main drawbacks of Element Free Galerkin (EFG method is its dependence on moving least square shape functions which don’t satisfy the Kronecker Delta property, so in this method it’s not possible to apply Dirichlet boundary conditions directly. The aim of the present paper is to discuss different aspects of three widely used methods of applying Dirichlet boundary conditions in EFG method, called Lagrange multipliers, penalty method, and coupling with finite element method. Numerical simulations are presented to compare the results of these methods form the perspective of accuracy, convergence and computational expense. These methods have been implemented in an object oriented programing environment, called INSANE, and the results are presented and compared with the analytical solutions.

  18. New method for solving the bending problem of rectangular plates with mixed boundary conditions

    Directory of Open Access Journals (Sweden)

    Liu Xin Min

    2016-01-01

    Full Text Available A new method is used to solve the rectangular plate bending problem with mixed boundary conditions. The method overcomes the complicated derivation of the classical solution by Fourth-order differential problem into integrating question. Under uniform loading rectangular plate bending problem with one side fixed the opposite side half simply supported half fixed the other two sides free rectangular plate, one side simply supported the opposite side half simply supported half fixed the other two sides free rectangular plate is systematically solved. According to the actual boundary conditions of the rectangular plate, the corresponding characteristic equation can easily be set up. It is presented deflection curve equation and the numerical calculation. By compared the results of the equation to the finite element program, we are able to demonstrate the correctness of the method. So the method not only has certain theoretical value, but also can be directly applied to engineering practice.

  19. Two transparent boundary conditions for the electromagnetic scattering from two-dimensional overfilled cavities

    Science.gov (United States)

    Du, Kui

    2011-07-01

    We consider electromagnetic scattering from two-dimensional (2D) overfilled cavities embedded in an infinite ground plane. The unbounded computational domain is truncated to a bounded one by using a transparent boundary condition (TBC) proposed on a semi-ellipse. For overfilled rectangular cavities with homogeneous media, another TBC is introduced on the cavity apertures, which produces a smaller computational domain. The existence and uniqueness of the solutions of the variational formulations for the transverse magnetic and transverse electric polarizations are established. In the exterior domain, the 2D scattering problem is solved in the elliptic coordinate system using the Mathieu functions. In the interior domain, the problem is solved by a finite element method. Numerical experiments show the efficiency and accuracy of the new boundary conditions.

  20. Effect of reactor finiteness on the boundary condition at the surface of a booster section

    International Nuclear Information System (INIS)

    Wassef, W.A.

    1982-01-01

    Effect of reactor finiteness on the boundary condition at the surface of an absorbing booster embedded in the reactor core is studied and formulated. The model used in these calculations depends on the Pl-Transport coupling technique. This method takes into consideration the rigorous neutron transport behavior inside the booster medium, while the Pl-approximation in the bulk of the scattering medium surrounding the booster which can be considered infinite in most practical applications. The neutron flux gradient parallel to the surface of the booster is considered. The geometrical configuration of the reactor core cross section is circular or rectangular. Finiteness of the reactor is introduced in the general formulation through its dimensions or buckling. Extensive numerical results are given to demonstrate the dependence of the boundary condition at the surface of the booster section on the reactor finiteness and the different physical parameters