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.)

ADI splitting schemes for a fourth-order nonlinear partial differential equation from image processing

KAUST Repository

Calatroni, Luca

2013-08-01

We present directional operator splitting schemes for the numerical solution of a fourth-order, nonlinear partial differential evolution equation which arises in image processing. This equation constitutes the H -1-gradient flow of the total variation and represents a prototype of higher-order equations of similar type which are popular in imaging for denoising, deblurring and inpainting problems. The efficient numerical solution of this equation is very challenging due to the stiffness of most numerical schemes. We show that the combination of directional splitting schemes with implicit time-stepping provides a stable and computationally cheap numerical realisation of the equation.

ADI splitting schemes for a fourth-order nonlinear partial differential equation from image processing

KAUST Repository

Calatroni, Luca; Dü ring, Bertram; Schö nlieb, Carola-Bibiane

2013-01-01

We present directional operator splitting schemes for the numerical solution of a fourth-order, nonlinear partial differential evolution equation which arises in image processing. This equation constitutes the H -1-gradient flow of the total variation and represents a prototype of higher-order equations of similar type which are popular in imaging for denoising, deblurring and inpainting problems. The efficient numerical solution of this equation is very challenging due to the stiffness of most numerical schemes. We show that the combination of directional splitting schemes with implicit time-stepping provides a stable and computationally cheap numerical realisation of the equation.

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

Effect of plate permeability on nonlinear stability of the asymptotic suction boundary layer.

Science.gov (United States)

Wedin, Håkan; Cherubini, Stefania; Bottaro, Alessandro

2015-07-01

The nonlinear stability of the asymptotic suction boundary layer is studied numerically, searching for finite-amplitude solutions that bifurcate from the laminar flow state. By changing the boundary conditions for disturbances at the plate from the classical no-slip condition to more physically sound ones, the stability characteristics of the flow may change radically, both for the linearized as well as the nonlinear problem. The wall boundary condition takes into account the permeability K̂ of the plate; for very low permeability, it is acceptable to impose the classical boundary condition (K̂=0). This leads to a Reynolds number of approximately Re(c)=54400 for the onset of linearly unstable waves, and close to Re(g)=3200 for the emergence of nonlinear solutions [F. A. Milinazzo and P. G. Saffman, J. Fluid Mech. 160, 281 (1985); J. H. M. Fransson, Ph.D. thesis, Royal Institute of Technology, KTH, Sweden, 2003]. However, for larger values of the plate's permeability, the lower limit for the existence of linear and nonlinear solutions shifts to significantly lower Reynolds numbers. For the largest permeability studied here, the limit values of the Reynolds numbers reduce down to Re(c)=796 and Re(g)=294. For all cases studied, the solutions bifurcate subcritically toward lower Re, and this leads to the conjecture that they may be involved in the very first stages of a transition scenario similar to the classical route of the Blasius boundary layer initiated by Tollmien-Schlichting (TS) waves. The stability of these nonlinear solutions is also investigated, showing a low-frequency main unstable mode whose growth rate decreases with increasing permeability and with the Reynolds number, following a power law Re(-ρ), where the value of ρ depends on the permeability coefficient K̂. The nonlinear dynamics of the flow in the vicinity of the computed finite-amplitude solutions is finally investigated by direct numerical simulations, providing a viable scenario for

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

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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.

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.

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

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)

Inverse Boundary Value Problem for Non-linear Hyperbolic Partial Differential Equations

OpenAIRE

Nakamura, Gen; Vashisth, Manmohan

2017-01-01

In this article we are concerned with an inverse boundary value problem for a non-linear wave equation of divergence form with space dimension $n\\geq 3$. This non-linear wave equation has a trivial solution, i.e. zero solution. By linearizing this equation at the trivial solution, we have the usual linear isotropic wave equation with the speed $\\sqrt{\\gamma(x)}$ at each point $x$ in a given spacial domain. For any small solution $u=u(t,x)$ of this non-linear equation, we have the linear isotr...

Effect of splitting a mixed-model line on shortening the line length under open- and closed-boundary working area settings

Science.gov (United States)

Zhang, Donghao; Matsuura, Haruki; Asada, Akiko

2017-04-01

Some automobile factories have segmented mixed-model production lines into shorter sub-lines according to part group, such as engine, trim, and powertrain. The effects of splitting a line into sub-lines have been reported from the standpoints of worker motivation, productivity improvement, and autonomy based on risk spreading. There has been no mention of the possibility of shortening the line length by altering the product sequence using sub-lines. The purpose of the present paper is to determine the conditions under which sub-lines reduce the line length and the degree to which the line length may be shortened. The line lengths for a non-split line and a line that has been split into sub-lines are compared using three methods for determining the working area, the standard closed boundary, the optimized open boundary, and real-life constant-length stations. The results are discussed by analyzing the upper and lower bounds of the line length. Based on these results, a procedure for deciding whether or not to split a production line is proposed.

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

KAUST Repository

Eleiwi, Fadi; Laleg-Kirati, Taous-Meriem

2015-01-01

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

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.

Response of Non-Linear Shock Absorbers-Boundary Value Problem Analysis

Science.gov (United States)

Rahman, M. A.; Ahmed, U.; Uddin, M. S.

2013-08-01

A nonlinear boundary value problem of two degrees-of-freedom (DOF) untuned vibration damper systems using nonlinear springs and dampers has been numerically studied. As far as untuned damper is concerned, sixteen different combinations of linear and nonlinear springs and dampers have been comprehensively analyzed taking into account transient terms. For different cases, a comparative study is made for response versus time for different spring and damper types at three important frequency ratios: one at r = 1, one at r > 1 and one at r <1. The response of the system is changed because of the spring and damper nonlinearities; the change is different for different cases. Accordingly, an initially stable absorber may become unstable with time and vice versa. The analysis also shows that higher nonlinearity terms make the system more unstable. Numerical simulation includes transient vibrations. Although problems are much more complicated compared to those for a tuned absorber, a comparison of the results generated by the present numerical scheme with the exact one shows quite a reasonable agreement

Analysis of boundary layer flow over a porous nonlinearly stretching sheet with partial slip at

Directory of Open Access Journals (Sweden)

Swati Mukhopadhyay

2013-12-01

Full Text Available The boundary layer flow of a viscous incompressible fluid toward a porous nonlinearly stretching sheet is considered in this analysis. Velocity slip is considered instead of no-slip condition at the boundary. Similarity transformations are used to convert the partial differential equation corresponding to the momentum equation into nonlinear ordinary differential equation. Numerical solution of this equation is obtained by shooting method. It is found that the horizontal velocity decreases with increasing slip parameter.

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.

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)

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

Science.gov (United States)

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

2013-12-01

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.

Existence of solutions to second-order nonlinear coupled systems with nonlinear coupled boundary conditions

Directory of Open Access Journals (Sweden)

Imran Talib

2015-12-01

Full Text Available In this article, study the existence of solutions for the second-order nonlinear coupled system of ordinary differential equations $$\\displaylines{ u''(t=f(t,v(t,\\quad t\\in [0,1],\\cr v''(t=g(t,u(t,\\quad t\\in [0,1], }$$ with nonlinear coupled boundary conditions $$\\displaylines{ \\phi(u(0,v(0,u(1,v(1,u'(0,v'(0=(0,0, \\cr \\psi(u(0,v(0,u(1,v(1,u'(1,v'(1=(0,0, }$$ where $f,g:[0,1]\\times \\mathbb{R}\\to \\mathbb{R}$ and $\\phi,\\psi:\\mathbb{R}^6\\to \\mathbb{R}^2$ are continuous functions. Our main tools are coupled lower and upper solutions, Arzela-Ascoli theorem, and Schauder's fixed point theorem.

Second-order wave diffraction by a circular cylinder using scaled boundary finite element method

International Nuclear Information System (INIS)

Song, H; Tao, L

2010-01-01

The scaled boundary finite element method (SBFEM) has achieved remarkable success in structural mechanics and fluid mechanics, combing the advantage of both FEM and BEM. Most of the previous works focus on linear problems, in which superposition principle is applicable. However, many physical problems in the real world are nonlinear and are described by nonlinear equations, challenging the application of the existing SBFEM model. A popular idea to solve a nonlinear problem is decomposing the nonlinear equation to a number of linear equations, and then solves them individually. In this paper, second-order wave diffraction by a circular cylinder is solved by SBFEM. By splitting the forcing term into two parts, the physical problem is described as two second-order boundary-value problems with different asymptotic behaviour at infinity. Expressing the velocity potentials as a series of depth-eigenfunctions, both of the 3D boundary-value problems are decomposed to a number of 2D boundary-value sub-problems, which are solved semi-analytically by SBFEM. Only the cylinder boundary is discretised with 1D curved finite-elements on the circumference of the cylinder, while the radial differential equation is solved completely analytically. The method can be extended to solve more complex wave-structure interaction problems resulting in direct engineering applications.

Nonlinear $q$-fractional differential equations with nonlocal and sub-strip type boundary conditions

Directory of Open Access Journals (Sweden)

Bashir Ahmad

2014-06-01

Full Text Available This paper is concerned with new boundary value problems of nonlinear $q$-fractional differential equations with nonlocal and sub-strip type boundary conditions. Our results are new in the present setting and rely on the contraction mapping principle and a fixed point theorem due to O'Regan. Some illustrative examples are also presented.

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.

The splitting in potential Crank-Nicolson scheme with discrete transparent boundary conditions for the Schroedinger equation on a semi-infinite strip

International Nuclear Information System (INIS)

Ducomet, Bernard; Zlotnik, Alexander; Zlotnik, Ilya

2014-01-01

We consider an initial-boundary value problem for a generalized 2D time-dependent Schroedinger equation (with variable coefficients) on a semi-infinite strip. For the Crank-Nicolson-type finite-difference scheme with approximate or discrete transparent boundary conditions (TBCs), the Strang-type splitting with respect to the potential is applied. For the resulting method, the unconditional uniform in time L2-stability is proved. Due to the splitting, an effective direct algorithm using FFT is developed now to implement the method with the discrete TBC for general potential. Numerical results on the tunnel effect for rectangular barriers are included together with the detailed practical error analysis confirming nice properties of the method. (authors)

Clutch pressure estimation for a power-split hybrid transmission using nonlinear robust observer

Science.gov (United States)

Zhou, Bin; Zhang, Jianwu; Gao, Ji; Yu, Haisheng; Liu, Dong

2018-06-01

For a power-split hybrid transmission, using the brake clutch to realize the transition from electric drive mode to hybrid drive mode is an available strategy. Since the pressure information of the brake clutch is essential for the mode transition control, this research designs a nonlinear robust reduced-order observer to estimate the brake clutch pressure. Model uncertainties or disturbances are considered as additional inputs, thus the observer is designed in order that the error dynamics is input-to-state stable. The nonlinear characteristics of the system are expressed as the lookup tables in the observer. Moreover, the gain matrix of the observer is solved by two optimization procedures under the constraints of the linear matrix inequalities. The proposed observer is validated by offline simulation and online test, the results have shown that the observer achieves significant performance during the mode transition, as the estimation error is within a reasonable range, more importantly, it is asymptotically stable.

An unconditionally stable, positivity-preserving splitting scheme for nonlinear Black-Scholes equation with transaction costs.

Science.gov (United States)

Guo, Jianqiang; Wang, Wansheng

2014-01-01

This paper deals with the numerical analysis of nonlinear Black-Scholes equation with transaction costs. An unconditionally stable and monotone splitting method, ensuring positive numerical solution and avoiding unstable oscillations, is proposed. This numerical method is based on the LOD-Backward Euler method which allows us to solve the discrete equation explicitly. The numerical results for vanilla call option and for European butterfly spread are provided. It turns out that the proposed scheme is efficient and reliable.

Waveguides with Absorbing Boundaries: Nonlinearity Controlled by an Exceptional Point and Solitons

Science.gov (United States)

Midya, Bikashkali; Konotop, Vladimir V.

2017-07-01

We reveal the existence of continuous families of guided single-mode solitons in planar waveguides with weakly nonlinear active core and absorbing boundaries. Stable propagation of TE and TM-polarized solitons is accompanied by attenuation of all other modes, i.e., the waveguide features properties of conservative and dissipative systems. If the linear spectrum of the waveguide possesses exceptional points, which occurs in the case of TM polarization, an originally focusing (defocusing) material nonlinearity may become effectively defocusing (focusing). This occurs due to the geometric phase of the carried eigenmode when the surface impedance encircles the exceptional point. In its turn, the change of the effective nonlinearity ensures the existence of dark (bright) solitons in spite of focusing (defocusing) Kerr nonlinearity of the core. The existence of an exceptional point can also result in anomalous enhancement of the effective nonlinearity. In terms of practical applications, the nonlinearity of the reported waveguide can be manipulated by controlling the properties of the absorbing cladding.

Nonlinear evolution of Mack modes in a hypersonic boundary layer

Science.gov (United States)

Chokani, Ndaona

2005-01-01

In hypersonic boundary layer flows the nonlinear disturbance evolution occurs relatively slowly over a very long length scale and has a profound effect on boundary layer transition. In the case of low-level freestream disturbances and negligible surface roughness, the transition is due to the modal growth of exponentially growing Mack modes that are destabilized by wall cooling. Cross-bicoherence measurements, derived from hot-wire data acquired in a quiet hypersonic tunnel, are used to identify and quantify phase-locked, quadratic sum and difference interactions involving the Mack modes. In the early stages of the nonlinear disturbance evolution, cross-bicoherence measurements indicate that the energy exchange between the Mack mode and the mean flow first occurs to broaden the sidebands; this is immediately followed by a sum interaction of the Mack mode to generate the first harmonic. In the next stages of the nonlinear disturbance evolution, there is a difference interaction of the first harmonic, which is also thought to contribute to the mean flow distortion. This difference interaction, in the latter stages, is also accompanied by a difference interaction between Mack mode and first harmonic, and a sum interaction, which forces the second harmonic. Analysis using the digital complex demodulation technique, shows that the low-frequency, phase-locked interaction that is identified in the cross bicoherence when the Mack mode and first harmonic have large amplitudes, arises due to the amplitude modulation of Mack mode and first harmonic.

A new fourth-order Fourier-Bessel split-step method for the extended nonlinear Schroedinger equation

International Nuclear Information System (INIS)

Nash, Patrick L.

2008-01-01

Fourier split-step techniques are often used to compute soliton-like numerical solutions of the nonlinear Schroedinger equation. Here, a new fourth-order implementation of the Fourier split-step algorithm is described for problems possessing azimuthal symmetry in 3 + 1-dimensions. This implementation is based, in part, on a finite difference approximation Δ perpendicular FDA of 1/r (∂)/(∂r) r(∂)/(∂r) that possesses an associated exact unitary representation of e i/2λΔ perpendicular FDA . The matrix elements of this unitary matrix are given by special functions known as the associated Bessel functions. Hence the attribute Fourier-Bessel for the method. The Fourier-Bessel algorithm is shown to be unitary and unconditionally stable. The Fourier-Bessel algorithm is employed to simulate the propagation of a periodic series of short laser pulses through a nonlinear medium. This numerical simulation calculates waveform intensity profiles in a sequence of planes that are transverse to the general propagation direction, and labeled by the cylindrical coordinate z. These profiles exhibit a series of isolated pulses that are offset from the time origin by characteristic times, and provide evidence for a physical effect that may be loosely termed normal mode condensation. Normal mode condensation is consistent with experimentally observed pulse filamentation into a packet of short bursts, which may occur as a result of short, intense irradiation of a medium

High order three part split symplectic integrators: Efficient techniques for the long time simulation of the disordered discrete nonlinear Schrödinger equation

Energy Technology Data Exchange (ETDEWEB)

Skokos, Ch., E-mail: haris.skokos@uct.ac.za [Physics Department, Aristotle University of Thessaloniki, GR-54124 Thessaloniki (Greece); Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch 7701 (South Africa); Gerlach, E. [Lohrmann Observatory, Technical University Dresden, D-01062 Dresden (Germany); Bodyfelt, J.D., E-mail: J.Bodyfelt@massey.ac.nz [Centre for Theoretical Chemistry and Physics, The New Zealand Institute for Advanced Study, Massey University, Albany, Private Bag 102904, North Shore City, Auckland 0745 (New Zealand); Papamikos, G. [School of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury, CT2 7NF (United Kingdom); Eggl, S. [IMCCE, Observatoire de Paris, 77 Avenue Denfert-Rochereau, F-75014 Paris (France)

2014-05-01

While symplectic integration methods based on operator splitting are well established in many branches of science, high order methods for Hamiltonian systems that split in more than two parts have not been studied in great detail. Here, we present several high order symplectic integrators for Hamiltonian systems that can be split in exactly three integrable parts. We apply these techniques, as a practical case, for the integration of the disordered, discrete nonlinear Schrödinger equation (DDNLS) and compare their efficiencies. Three part split algorithms provide effective means to numerically study the asymptotic behavior of wave packet spreading in the DDNLS – a hotly debated subject in current scientific literature.

High order three part split symplectic integrators: Efficient techniques for the long time simulation of the disordered discrete nonlinear Schrödinger equation

International Nuclear Information System (INIS)

Skokos, Ch.; Gerlach, E.; Bodyfelt, J.D.; Papamikos, G.; Eggl, S.

2014-01-01

While symplectic integration methods based on operator splitting are well established in many branches of science, high order methods for Hamiltonian systems that split in more than two parts have not been studied in great detail. Here, we present several high order symplectic integrators for Hamiltonian systems that can be split in exactly three integrable parts. We apply these techniques, as a practical case, for the integration of the disordered, discrete nonlinear Schrödinger equation (DDNLS) and compare their efficiencies. Three part split algorithms provide effective means to numerically study the asymptotic behavior of wave packet spreading in the DDNLS – a hotly debated subject in current scientific literature.

Sum-frequency nonlinear Cherenkov radiation generated on the boundary of bulk medium crystal.

Science.gov (United States)

Wang, Xiaojing; Cao, Jianjun; Zhao, Xiaohui; Zheng, Yuanlin; Ren, Huaijin; Deng, Xuewei; Chen, Xianfeng

2015-12-14

We demonstrated experimentally a method to generate the sum-frequency Nonlinear Cherenkov radiation (NCR) on the boundary of bulk medium by using two synchronized laser beam with wavelength of 1300 nm and 800 nm. It is also an evidence that the polarization wave is always confined to the boundary. Critical conditions of surface sum-frequency NCR under normal and anomalous dispersion condition is discussed.

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

OpenAIRE

Belmiloudi, A.; Mahé, F.

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...

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

Directory of Open Access Journals (Sweden)

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.

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.

Adaptive wavelet collocation methods for initial value boundary problems of nonlinear PDE's

Science.gov (United States)

Cai, Wei; Wang, Jian-Zhong

1993-01-01

We have designed a cubic spline wavelet decomposition for the Sobolev space H(sup 2)(sub 0)(I) where I is a bounded interval. Based on a special 'point-wise orthogonality' of the wavelet basis functions, a fast Discrete Wavelet Transform (DWT) is constructed. This DWT transform will map discrete samples of a function to its wavelet expansion coefficients in O(N log N) operations. Using this transform, we propose a collocation method for the initial value boundary problem of nonlinear PDE's. Then, we test the efficiency of the DWT transform and apply the collocation method to solve linear and nonlinear PDE's.

Mixing in thermally stratified nonlinear spin-up with uniform boundary fluxes

International Nuclear Information System (INIS)

Baghdasarian, Meline; Pacheco-Vega, Arturo; Pacheco, J. Rafael; Verzicco, Roberto

2014-01-01

Studies of stratified spin-up experiments in enclosed cylinders have reported the presence of small pockets of well-mixed fluids but quantitative measurements of the mixedness of the fluid has been lacking. Previous numerical simulations have not addressed these measurements. Here we present numerical simulations that explain how the combined effect of spin-up and thermal boundary conditions enhances or hinders mixing of a fluid in a cylinder. The energy of the system is characterized by splitting the potential energy into diabatic and adiabatic components, and measurements of efficiency of mixing are based on both, the ratio of dissipation of available potential energy to forcing and variance of temperature. The numerical simulations of the Navier–Stokes equations for the problem with different sets of thermal boundary conditions at the horizontal walls helped shed some light on the physical mechanisms of mixing, for which a clear explanation was absent

Mixing in thermally stratified nonlinear spin-up with uniform boundary fluxes

Energy Technology Data Exchange (ETDEWEB)

Baghdasarian, Meline; Pacheco-Vega, Arturo [Department of Mechanical Engineering, California State University, Los Angeles, Los Angeles, California 90032 (United States); Pacheco, J. Rafael, E-mail: rpacheco@asu.edu [SAP Americas Inc., Scottsdale, Arizona 85251 (United States); School of Mathematical and Statistical Sciences, Arizona State University, Tempe, Arizona 85287 (United States); Environmental Fluid Dynamics Laboratories, Department of Civil Engineering and Geological Sciences, The University of Notre Dame, South Bend, Indiana 46556 (United States); Verzicco, Roberto [Dipartimento di Ingegneria Meccanica, Universita di Roma “Tor Vergata”, Via del Politecnico 1, 00133, Roma (Italy); PoF, University of Twente, 7500 AE Enschede (Netherlands)

2014-09-15

Studies of stratified spin-up experiments in enclosed cylinders have reported the presence of small pockets of well-mixed fluids but quantitative measurements of the mixedness of the fluid has been lacking. Previous numerical simulations have not addressed these measurements. Here we present numerical simulations that explain how the combined effect of spin-up and thermal boundary conditions enhances or hinders mixing of a fluid in a cylinder. The energy of the system is characterized by splitting the potential energy into diabatic and adiabatic components, and measurements of efficiency of mixing are based on both, the ratio of dissipation of available potential energy to forcing and variance of temperature. The numerical simulations of the Navier–Stokes equations for the problem with different sets of thermal boundary conditions at the horizontal walls helped shed some light on the physical mechanisms of mixing, for which a clear explanation was absent.

Polyharmonic boundary value problems positivity preserving and nonlinear higher order elliptic equations in bounded domains

CERN Document Server

Gazzola, Filippo; Sweers, Guido

2010-01-01

This monograph covers higher order linear and nonlinear elliptic boundary value problems in bounded domains, mainly with the biharmonic or poly-harmonic operator as leading principal part. Underlying models and, in particular, the role of different boundary conditions are explained in detail. As for linear problems, after a brief summary of the existence theory and Lp and Schauder estimates, the focus is on positivity or - since, in contrast to second order equations, a general form of a comparison principle does not exist - on “near positivity.” The required kernel estimates are also presented in detail. As for nonlinear problems, several techniques well-known from second order equations cannot be utilized and have to be replaced by new and different methods. Subcritical, critical and supercritical nonlinearities are discussed and various existence and nonexistence results are proved. The interplay with the positivity topic from the first part is emphasized and, moreover, a far-reaching Gidas-Ni-Nirenbe...

A purely nonlinear route to transition approaching the edge of chaos in a boundary layer

International Nuclear Information System (INIS)

Cherubini, S; De Palma, P; Robinet, J-Ch; Bottaro, A

2012-01-01

The understanding of transition in shear flows has recently progressed along new paradigms based on the central role of coherent flow structures and their nonlinear interactions. We follow such paradigms to identify, by means of a nonlinear optimization of the energy growth at short time, the initial perturbation which most easily induces transition in a boundary layer. Moreover, a bisection procedure has been used to identify localized flow structures living on the edge of chaos, found to be populated by hairpin vortices and streaks. Such an edge structure appears to act as a relative attractor for the trajectory of the laminar base state perturbed by the initial finite-amplitude disturbances, mediating the route to turbulence of the flow, via the triggering of a regeneration cycle of Λ and hairpin structures at different space and time scales. These findings introduce a new, purely nonlinear scenario of transition in a boundary-layer flow. (paper)

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.

Gap solitons in a chain of split-ring resonator dimers

Energy Technology Data Exchange (ETDEWEB)

Cui, Wei-na, E-mail: cuiweinaa@163.com [Department of Applied Physics, Nanjing University of Science and Technology, Nanjing 210094 (China); Li, Hong-xia, E-mail: hxli@njust.edu.cn [Department of Applied Physics, Nanjing University of Science and Technology, Nanjing 210094 (China); Sun, Min [Department of Applied Physics, Nanjing University of Science and Technology, Nanjing 210094 (China); Bu, Ling-bing [Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters, Key Laboratory for Aerosol-Cloud-Precipitation of China Meteorological Administration, Key Laboratory of Meteorological Disaster of Ministry of Education, Nanjing University of Information Science and Technology, Nanjing 210044 (China)

2017-06-21

Dynamics of a chain of split-ring resonator dimers with Kerr nonlinear interaction are investigated. A dimer is built as a pair of coupled split-ring resonators with different size. It is shown that the gap solitons with frequency lying in the gap exist due to the interaction of the discreteness and nonlinearity. Such localized structures are studied in the phase plane and analytical and numerical expressions are also obtained. - Highlights: • The coupling of the two modes is studied in the chain of split-ring resonator dimers with Kerr nonlinear interaction. • The evolution of the localized structures is studied in the phase plane. • This system supports gap solitons with the frequencies lying in the gap.

New implementation method for essential boundary condition to extended element-free Galerkin method. Application to nonlinear problem

International Nuclear Information System (INIS)

Saitoh, Ayumu; Matsui, Nobuyuki; Itoh, Taku; Kamitani, Atsushi; Nakamura, Hiroaki

2011-01-01

A new method has been proposed for implementing essential boundary conditions to the Element-Free Galerkin Method (EFGM) without using the Lagrange multiplier. Furthermore, the performance of the proposed method has been investigated for a nonlinear Poisson problem. The results of computations show that, as interpolation functions become closer to delta functions, the accuracy of the solution is improved on the boundary. In addition, the accuracy of the proposed method is higher than that of the conventional EFGM. Therefore, it might be concluded that the proposed method is useful for solving the nonlinear Poisson problem. (author)

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

Directory of Open Access Journals (Sweden)

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.

Nonlinear Dynamics of Vortices in Different Types of Grain Boundaries

Science.gov (United States)

Sheikhzada, Ahmad K.

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.

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.

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.

Irradiation-induced amorphization in split-dislocation cores

International Nuclear Information System (INIS)

Ovid'ko, I.A.; Rejzis, A.B.

1999-01-01

The model describing special splitting of lattice and grain-boundary dislocations as one of the micromechanisms of solid-phase amorphization in irradiated crystals is proposed. Calculation of energy characteristics of the process of dislocations special splitting is carried out [ru

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.

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.

Convergence Analysis of the Preconditioned Group Splitting Methods in Boundary Value Problems

Directory of Open Access Journals (Sweden)

Norhashidah Hj. Mohd Ali

2012-01-01

Full Text Available The construction of a specific splitting-type preconditioner in block formulation applied to a class of group relaxation iterative methods derived from the centred and rotated (skewed finite difference approximations has been shown to improve the convergence rates of these methods. In this paper, we present some theoretical convergence analysis on this preconditioner specifically applied to the linear systems resulted from these group iterative schemes in solving an elliptic boundary value problem. We will theoretically show the relationship between the spectral radiuses of the iteration matrices of the preconditioned methods which affects the rate of convergence of these methods. We will also show that the spectral radius of the preconditioned matrices is smaller than that of their unpreconditioned counterparts if the relaxation parameter is in a certain optimum range. Numerical experiments will also be presented to confirm the agreement between the theoretical and the experimental results.

Fermat collocation method for the solutions of nonlinear system of second order boundary value problems

Directory of Open Access Journals (Sweden)

Salih Yalcinbas

2016-01-01

Full Text Available In this study, a numerical approach is proposed to obtain approximate solutions of nonlinear system of second order boundary value problem. This technique is essentially based on the truncated Fermat series and its matrix representations with collocation points. Using the matrix method, we reduce the problem system of nonlinear algebraic equations. Numerical examples are also given to demonstrate the validity and applicability of the presented technique. The method is easy to implement and produces accurate results.

Splitting methods in communication, imaging, science, and engineering

CERN Document Server

Osher, Stanley; Yin, Wotao

2016-01-01

This book is about computational methods based on operator splitting. It consists of twenty-three chapters written by recognized splitting method contributors and practitioners, and covers a vast spectrum of topics and application areas, including computational mechanics, computational physics, image processing, wireless communication, nonlinear optics, and finance. Therefore, the book presents very versatile aspects of splitting methods and their applications, motivating the cross-fertilization of ideas. .

Communication: modeling charge-sign asymmetric solvation free energies with nonlinear boundary conditions.

Science.gov (United States)

Bardhan, Jaydeep P; Knepley, Matthew G

2014-10-07

We show that charge-sign-dependent asymmetric hydration can be modeled accurately using linear Poisson theory after replacing the standard electric-displacement boundary condition with a simple nonlinear boundary condition. Using a single multiplicative scaling factor to determine atomic radii from molecular dynamics Lennard-Jones parameters, the new model accurately reproduces MD free-energy calculations of hydration asymmetries for: (i) monatomic ions, (ii) titratable amino acids in both their protonated and unprotonated states, and (iii) the Mobley "bracelet" and "rod" test problems [D. L. Mobley, A. E. Barber II, C. J. Fennell, and K. A. Dill, "Charge asymmetries in hydration of polar solutes," J. Phys. Chem. B 112, 2405-2414 (2008)]. Remarkably, the model also justifies the use of linear response expressions for charging free energies. Our boundary-element method implementation demonstrates the ease with which other continuum-electrostatic solvers can be extended to include asymmetry.

Communication: Modeling charge-sign asymmetric solvation free energies with nonlinear boundary conditions

International Nuclear Information System (INIS)

Bardhan, Jaydeep P.; Knepley, Matthew G.

2014-01-01

We show that charge-sign-dependent asymmetric hydration can be modeled accurately using linear Poisson theory after replacing the standard electric-displacement boundary condition with a simple nonlinear boundary condition. Using a single multiplicative scaling factor to determine atomic radii from molecular dynamics Lennard-Jones parameters, the new model accurately reproduces MD free-energy calculations of hydration asymmetries for: (i) monatomic ions, (ii) titratable amino acids in both their protonated and unprotonated states, and (iii) the Mobley “bracelet” and “rod” test problems [D. L. Mobley, A. E. Barber II, C. J. Fennell, and K. A. Dill, “Charge asymmetries in hydration of polar solutes,” J. Phys. Chem. B 112, 2405–2414 (2008)]. Remarkably, the model also justifies the use of linear response expressions for charging free energies. Our boundary-element method implementation demonstrates the ease with which other continuum-electrostatic solvers can be extended to include asymmetry

Communication: Modeling charge-sign asymmetric solvation free energies with nonlinear boundary conditions

Energy Technology Data Exchange (ETDEWEB)

Bardhan, Jaydeep P. [Department of Mechanical and Industrial Engineering, Northeastern University, Boston, Massachusetts 02115 (United States); Knepley, Matthew G. [Computation Institute, The University of Chicago, Chicago, Illinois 60637 (United States)

2014-10-07

We show that charge-sign-dependent asymmetric hydration can be modeled accurately using linear Poisson theory after replacing the standard electric-displacement boundary condition with a simple nonlinear boundary condition. Using a single multiplicative scaling factor to determine atomic radii from molecular dynamics Lennard-Jones parameters, the new model accurately reproduces MD free-energy calculations of hydration asymmetries for: (i) monatomic ions, (ii) titratable amino acids in both their protonated and unprotonated states, and (iii) the Mobley “bracelet” and “rod” test problems [D. L. Mobley, A. E. Barber II, C. J. Fennell, and K. A. Dill, “Charge asymmetries in hydration of polar solutes,” J. Phys. Chem. B 112, 2405–2414 (2008)]. Remarkably, the model also justifies the use of linear response expressions for charging free energies. Our boundary-element method implementation demonstrates the ease with which other continuum-electrostatic solvers can be extended to include asymmetry.

Positive solutions for a nonlinear periodic boundary-value problem with a parameter

Directory of Open Access Journals (Sweden)

Jingliang Qiu

2012-08-01

Full Text Available Using topological degree theory with a partially ordered structure of space, sufficient conditions for the existence and multiplicity of positive solutions for a second-order nonlinear periodic boundary-value problem are established. Inspired by ideas in Guo and Lakshmikantham [6], we study the dependence of positive periodic solutions as a parameter approaches infinity, $$ lim_{lambdao +infty}|x_{lambda}|=+infty,quadhbox{or}quad lim_{lambdao+infty}|x_{lambda}|=0. $$

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

Communication: Modeling charge-sign asymmetric solvation free energies with nonlinear boundary conditions

Science.gov (United States)

Bardhan, Jaydeep P.; Knepley, Matthew G.

2014-01-01

We show that charge-sign-dependent asymmetric hydration can be modeled accurately using linear Poisson theory after replacing the standard electric-displacement boundary condition with a simple nonlinear boundary condition. Using a single multiplicative scaling factor to determine atomic radii from molecular dynamics Lennard-Jones parameters, the new model accurately reproduces MD free-energy calculations of hydration asymmetries for: (i) monatomic ions, (ii) titratable amino acids in both their protonated and unprotonated states, and (iii) the Mobley “bracelet” and “rod” test problems [D. L. Mobley, A. E. Barber II, C. J. Fennell, and K. A. Dill, “Charge asymmetries in hydration of polar solutes,” J. Phys. Chem. B 112, 2405–2414 (2008)]. Remarkably, the model also justifies the use of linear response expressions for charging free energies. Our boundary-element method implementation demonstrates the ease with which other continuum-electrostatic solvers can be extended to include asymmetry. PMID:25296776

A Hartman–Nagumo inequality for the vector ordinary -Laplacian and applications to nonlinear boundary value problems

Directory of Open Access Journals (Sweden)

Ureña Antonio J

2002-01-01

Full Text Available A generalization of the well-known Hartman–Nagumo inequality to the case of the vector ordinary -Laplacian and classical degree theory provide existence results for some associated nonlinear boundary value problems.

Operator splitting method for simulation of dynamic flows in natural gas pipeline networks

Science.gov (United States)

Dyachenko, Sergey A.; Zlotnik, Anatoly; Korotkevich, Alexander O.; Chertkov, Michael

2017-12-01

We develop an operator splitting method to simulate flows of isothermal compressible natural gas over transmission pipelines. The method solves a system of nonlinear hyperbolic partial differential equations (PDEs) of hydrodynamic type for mass flow and pressure on a metric graph, where turbulent losses of momentum are modeled by phenomenological Darcy-Weisbach friction. Mass flow balance is maintained through the boundary conditions at the network nodes, where natural gas is injected or withdrawn from the system. Gas flow through the network is controlled by compressors boosting pressure at the inlet of the adjoint pipe. Our operator splitting numerical scheme is unconditionally stable and it is second order accurate in space and time. The scheme is explicit, and it is formulated to work with general networks with loops. We test the scheme over range of regimes and network configurations, also comparing its performance with performance of two other state of the art implicit schemes.

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

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.

Nonlinear fractional differential equations and inclusions of arbitrary order and multi-strip boundary conditions

Directory of Open Access Journals (Sweden)

Bashir Ahmad

2012-06-01

Full Text Available We study boundary value problems of nonlinear fractional differential equations and inclusions of order $q in (m-1, m]$, $m ge 2$ with multi-strip boundary conditions. Multi-strip boundary conditions may be regarded as the generalization of multi-point boundary conditions. Our problem is new in the sense that we consider a nonlocal strip condition of the form: $$ x(1=sum_{i=1}^{n-2}alpha_i int^{eta_i}_{zeta_i} x(sds, $$ which can be viewed as an extension of a multi-point nonlocal boundary condition: $$ x(1=sum_{i=1}^{n-2}alpha_i x(eta_i. $$ In fact, the strip condition corresponds to a continuous distribution of the values of the unknown function on arbitrary finite segments $(zeta_i,eta_i$ of the interval $[0,1]$ and the effect of these strips is accumulated at $x=1$. Such problems occur in the applied fields such as wave propagation and geophysics. Some new existence and uniqueness results are obtained by using a variety of fixed point theorems. Some illustrative examples are also discussed.

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

Nonlinear interaction of s-polarized surface waves at the boundary of a semibounded magnetized plasma

International Nuclear Information System (INIS)

Amein, W.H.; El-Siragy, N.M.; Nagy, O.Z.; Sayed, Y.A.

1981-01-01

Nonlinear interaction of S-Polarized surface waves at the boundary of a semibounded magnetized plasma is investigated. The expressions of the amplitudes of the generated waves are found. It is shown that, the generated waves with combined frequencies are equally radiated from the transient layer into plasma and vacuum

Nonlinear Elliptic Differential Equations with Multivalued Nonlinearities

Indian Academy of Sciences (India)

In this paper we study nonlinear elliptic boundary value problems with monotone and nonmonotone multivalued nonlinearities. First we consider the case of monotone nonlinearities. In the first result we assume that the multivalued nonlinearity is defined on all R R . Assuming the existence of an upper and of a lower ...

Nature Inspired Computational Technique for the Numerical Solution of Nonlinear Singular Boundary Value Problems Arising in Physiology

Directory of Open Access Journals (Sweden)

Suheel Abdullah Malik

2014-01-01

Full Text Available We present a hybrid heuristic computing method for the numerical solution of nonlinear singular boundary value problems arising in physiology. The approximate solution is deduced as a linear combination of some log sigmoid basis functions. A fitness function representing the sum of the mean square error of the given nonlinear ordinary differential equation (ODE and its boundary conditions is formulated. The optimization of the unknown adjustable parameters contained in the fitness function is performed by the hybrid heuristic computation algorithm based on genetic algorithm (GA, interior point algorithm (IPA, and active set algorithm (ASA. The efficiency and the viability of the proposed method are confirmed by solving three examples from physiology. The obtained approximate solutions are found in excellent agreement with the exact solutions as well as some conventional numerical solutions.

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,......, some stabilizing controllers are constructed for various cases using Lyapunov design.......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...

Multi-parameter crack tip stress state description for evaluation of nonlinear zone width in silicate composite specimens in component splitting/bending test geometry

Czech Academy of Sciences Publication Activity Database

Veselý, V.; Frantík, P.; Sopek, J.; Malíková, L.; Seitl, Stanislav

2015-01-01

Roč. 38, č. 2 (2015), s. 200-214 ISSN 8756-758X R&D Projects: GA ČR(CZ) GAP104/11/0833 Institutional support: RVO:68081723 Keywords : near-crack tip fields * Williams series * higher-order terms * stress field * failure criterion * nonlinear zone * quasi-brittle fracture * splitting-bending geometry Subject RIV: JL - Materials Fatigue, Friction Mechanics Impact factor: 1.838, year: 2015

Solution of problems with material nonlinearities with a coupled finite element/boundary element scheme using an iterative solver. Yucca Mountain Site Characterization Project

International Nuclear Information System (INIS)

Koteras, J.R.

1996-01-01

The prediction of stresses and displacements around tunnels buried deep within the earth is an important class of geomechanics problems. The material behavior immediately surrounding the tunnel is typically nonlinear. The surrounding mass, even if it is nonlinear, can usually be characterized by a simple linear elastic model. The finite element method is best suited for modeling nonlinear materials of limited volume, while the boundary element method is well suited for modeling large volumes of linear elastic material. A computational scheme that couples the finite element and boundary element methods would seem particularly useful for geomechanics problems. A variety of coupling schemes have been proposed, but they rely on direct solution methods. Direct solution techniques have large storage requirements that become cumbersome for large-scale three-dimensional problems. An alternative to direct solution methods is iterative solution techniques. A scheme has been developed for coupling the finite element and boundary element methods that uses an iterative solution method. This report shows that this coupling scheme is valid for problems where nonlinear material behavior occurs in the finite element region

A uniformly valid approximation algorithm for nonlinear ordinary singular perturbation problems with boundary layer solutions.

Science.gov (United States)

Cengizci, Süleyman; Atay, Mehmet Tarık; Eryılmaz, Aytekin

2016-01-01

This paper is concerned with two-point boundary value problems for singularly perturbed nonlinear ordinary differential equations. The case when the solution only has one boundary layer is examined. An efficient method so called Successive Complementary Expansion Method (SCEM) is used to obtain uniformly valid approximations to this kind of solutions. Four test problems are considered to check the efficiency and accuracy of the proposed method. The numerical results are found in good agreement with exact and existing solutions in literature. The results confirm that SCEM has a superiority over other existing methods in terms of easy-applicability and effectiveness.

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

Directory of Open Access Journals (Sweden)

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.

Nonlinear Fracture Mechanics and Plasticity of the Split Cylinder Test

DEFF Research Database (Denmark)

Olesen, John Forbes; Østergaard, Lennart; Stang, Henrik

2006-01-01

properties. This implies that the linear elastic interpretation of the ultimate splitting force in term of the uniaxial tensile strength of the material is only valid for special situations, e.g. for very large cylinders. Furthermore, the numerical analysis suggests that the split cylinder test is not well...... models are presented, a simple semi-analytical model based on analytical solutions for the crack propagation in a rectangular prismatic body, and a finite element model including plasticity in bulk material as well as crack propagation in interface elements. A numerical study applying these models...... demonstrates the influence of varying geometry or constitutive properties. For a split cylinder test in load control it is shown how the ultimate load is either plasticity dominated or fracture mechanics dominated. The transition between the two modes is related to changes in geometry or constitutive...

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.

Progresses in the studies of adiabatic splitting of charged particle beams by crossing nonlinear resonances

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A. Franchi

2009-01-01

Full Text Available The multiturn extraction from a circular particle accelerator is performed by trapping the beam inside stable islands of the horizontal phase space. In general, by crossing a resonance of order n, n+1 beamlets are created whenever the resonance is stable, whereas if the resonance is unstable the beam is split in n parts. Islands are generated by nonlinear magnetic fields, whereas the trapping is realized by means of a given tune variation so to cross adiabatically a resonance. Experiments at the CERN Proton Synchrotron carried out in 2007 gave the evidence of protons trapped in stable islands while crossing the one-third and one-fifth resonances. Dedicated experiments were also carried out to study the trapping process and its reversibility properties. The results of these measurement campaigns are presented and discussed in this paper.

Progresses in the Studies of Adiabatic Splitting of Charged Particles Beams by Crossing Nonlinear Resonances

CERN Document Server

Franchi, A; Giovannozzi, M; CERN. Geneva. BE Department

2009-01-01

The multi-turn extraction from a circular particle accelerator is performed by trapping the beam inside stable islands of the horizontal phase space. In general, by crossing a resonance of order n, n+1 beamlets are created whenever the resonance is stable, whereas if the resonance is unstable the beam is split in n parts. Islands are generated by non-linear magnetic fields, whereas the trapping is realized by means of a given tune variation so to cross adiabatically a resonance. Experiments at the CERN Proton Synchrotron carried out in 2007 gave the evidence of protons trapped in stable islands while crossing the one-third and one-fifth resonances. Dedicated experiments were also carried out to study the trapping process and its reversibility properties. The results of these measurement campaigns are presented and discussed in this paper.

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

Splitting of turbulent spot in transitional pipe flow

Science.gov (United States)

Wu, Xiaohua; Moin, Parviz; Adrian, Ronald J.

2017-11-01

Recent study (Wu et al., PNAS, 1509451112, 2015) demonstrated the feasibility and accuracy of direct computation of the Osborne Reynolds' pipe transition problem without the unphysical, axially periodic boundary condition. Here we use this approach to study the splitting of turbulent spot in transitional pipe flow, a feature first discovered by E.R. Lindgren (Arkiv Fysik 15, 1959). It has been widely believed that spot splitting is a mysterious stochastic process that has general implications on the lifetime and sustainability of wall turbulence. We address the following two questions: (1) What is the dynamics of turbulent spot splitting in pipe transition? Specifically, we look into any possible connection between the instantaneous strain rate field and the spot splitting. (2) How does the passive scalar field behave during the process of pipe spot splitting. In this study, the turbulent spot is introduced at the inlet plane through a sixty degree wide numerical wedge within which fully-developed turbulent profiles are assigned over a short time interval; and the simulation Reynolds numbers are 2400 for a 500 radii long pipe, and 2300 for a 1000 radii long pipe, respectively. Numerical dye is tagged on the imposed turbulent spot at the inlet. Splitting of the imposed turbulent spot is detected very easily. Preliminary analysis of the DNS results seems to suggest that turbulent spot slitting can be easily understood based on instantaneous strain rate field, and such spot splitting may not be relevant in external flows such as the flat-plate boundary layer.

Angularly symmetric splitting of a light beam upon reflection and refraction at an air-dielectric plane boundary.

Science.gov (United States)

Azzam, R M A

2015-12-01

Conditions for achieving equal and opposite angular deflections of a light beam by reflection and refraction at an air-dielectric boundary are determined. Such angularly symmetric beam splitting (ASBS) is possible only if the angle of incidence is >60° by exactly one third of the angle of refraction. This simple law, plus Snell's law, leads to several analytical results that clarify all aspects of this phenomenon. In particular, it is shown that the intensities of the two symmetrically deflected beams can be equalized by proper choice of the prism refractive index and the azimuth of incident linearly polarized light. ASBS enables a geometrically attractive layout of optical systems that employ multiple prism beam splitters.

Nonlinear traveling waves in rotating Rayleigh-Bacute enard convection: Stability boundaries and phase diffusion

International Nuclear Information System (INIS)

Liu, Y.; Ecke, R.E.

1999-01-01

We present experimental measurements of a sidewall traveling wave in rotating Rayleigh-Bacute enard convection. The fluid, water with Prandtl number about 6.3, was confined in a 1-cm-high cylindrical cell with radius-to-height ratio Γ=5. We used simultaneous optical-shadowgraph, heat-transport, and local temperature measurements to determine the stability and characteristics of the traveling-wave state for dimensionless rotation rates 60<Ω<420. The state is well described by the one-dimensional complex Ginzburg-Landau (CGL) equation for which the linear and nonlinear coefficients were determined for Ω=274. The Eckhaus-Benjamin-Feir-stability boundary was established and the phase-diffusion coefficient and nonlinear group velocity were determined in the stable regime. Higher-order corrections to the CGL equation were also investigated. copyright 1999 The American Physical Society

Pulse splitting of self-focusing-beams in normally dispersive media

DEFF Research Database (Denmark)

Bergé, L.; Juul Rasmussen, J.

1996-01-01

The influence of the normal group-velocity dispersion on anisotropic self-focusing beams in nonlinear Kerr media is studied analytically. It is shown that a light pulse self-focusing in the presence of normal dispersion is split up into several small-scale cells preventing a catastrophic collapse....... The theoretical explanation of this splitting process is revealed....

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

On the removal of boundary errors caused by Runge-Kutta integration of non-linear partial differential equations

Science.gov (United States)

Abarbanel, Saul; Gottlieb, David; Carpenter, Mark H.

1994-01-01

It has been previously shown that the temporal integration of hyperbolic partial differential equations (PDE's) may, because of boundary conditions, lead to deterioration of accuracy of the solution. A procedure for removal of this error in the linear case has been established previously. In the present paper we consider hyperbolic (PDE's) (linear and non-linear) whose boundary treatment is done via the SAT-procedure. A methodology is present for recovery of the full order of accuracy, and has been applied to the case of a 4th order explicit finite difference scheme.

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

Existence of Positive Solutions to a Singular Semipositone Boundary Value Problem of Nonlinear Fractional Differential Systems

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Xiaofeng Zhang

2017-12-01

Full Text Available In this paper, we consider the existence of positive solutions to a singular semipositone boundary value problem of nonlinear fractional differential equations. By applying the fixed point index theorem, some new results for the existence of positive solutions are obtained. In addition, an example is presented to demonstrate the application of our main results.

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.

Stabilization of exact nonlinear Timoshenko beams in space by boundary feedback

Science.gov (United States)

Do, K. D.

2018-05-01

Boundary feedback controllers are designed to stabilize Timoshenko beams with large translational and rotational motions in space under external disturbances. The exact nonlinear partial differential equations governing motion of the beams are derived and used in the control design. The designed controllers guarantee globally practically asymptotically (and locally practically exponentially) stability of the beam motions at the reference state. The control design, well-posedness and stability analysis are based on various relationships between the earth-fixed and body-fixed coordinates, Sobolev embeddings, and a Lyapunov-type theorem developed to study well-posedness and stability for a class of evolution systems in Hilbert space. Simulation results are included to illustrate the effectiveness of the proposed control design.

Pulse splitting in nonlinear media with anisotropic dispersion properties

DEFF Research Database (Denmark)

Bergé, L.; Juul Rasmussen, J.; Schmidt, M.R.

1998-01-01

The nonlinear self-focusing of beams in media with anisotropic (mix-signed) dispersion is investigated. Theoretical predictions employing virial-type arguments and self-similar techniques suggest that a pulse propagating in a nonlinear medium with anisotropic dispersion will not collapse...

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

Nonlinear soil-structure interaction analysis based on the boundary-element method in time domain with application to embedded foundation

International Nuclear Information System (INIS)

Wolf, J.P.; Darbre, G.R.

1985-01-01

The computational procedure of the so-called truncated indirect boundary-element method is derived. The latter, which is non-local in space and time, represents a rigorous generally applicable procedure for taking into account a layered halfspace in a non-linear soil-structure interaction analysis. As an example, the non-linear soil-structure interaction analysis of a structure embedded in a halfspace with partial uplift of the basement and separation of the side wall is investigated. (orig.)

DETECTION OF FLUX EMERGENCE, SPLITTING, MERGING, AND CANCELLATION OF NETWORK FIELD. I. SPLITTING AND MERGING

Energy Technology Data Exchange (ETDEWEB)

Iida, Y.; Yokoyama, T. [Department of Earth and Planetary Science, University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-0033 (Japan); Hagenaar, H. J. [Lockheed Martin Advanced Technology Center, Org. ADBS, Building 252, 3251 Hanover Street, Palo Alto, CA 94304 (United States)

2012-06-20

Frequencies of magnetic patch processes on the supergranule boundary, namely, flux emergence, splitting, merging, and cancellation, are investigated through automatic detection. We use a set of line-of-sight magnetograms taken by the Solar Optical Telescope (SOT) on board the Hinode satellite. We found 1636 positive patches and 1637 negative patches in the data set, whose time duration is 3.5 hr and field of view is 112'' Multiplication-Sign 112''. The total numbers of magnetic processes are as follows: 493 positive and 482 negative splittings, 536 positive and 535 negative mergings, 86 cancellations, and 3 emergences. The total numbers of emergence and cancellation are significantly smaller than those of splitting and merging. Further, the frequency dependence of the merging and splitting processes on the flux content are investigated. Merging has a weak dependence on the flux content with a power-law index of only 0.28. The timescale for splitting is found to be independent of the parent flux content before splitting, which corresponds to {approx}33 minutes. It is also found that patches split into any flux contents with the same probability. This splitting has a power-law distribution of the flux content with an index of -2 as a time-independent solution. These results support that the frequency distribution of the flux content in the analyzed flux range is rapidly maintained by merging and splitting, namely, surface processes. We suggest a model for frequency distributions of cancellation and emergence based on this idea.

Multiple Solutions of Nonlinear Boundary Value Problems of Fractional Order: A New Analytic Iterative Technique

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Omar Abu Arqub

2014-01-01

Full Text Available The purpose of this paper is to present a new kind of analytical method, the so-called residual power series, to predict and represent the multiplicity of solutions to nonlinear boundary value problems of fractional order. The present method is capable of calculating all branches of solutions simultaneously, even if these multiple solutions are very close and thus rather difficult to distinguish even by numerical techniques. To verify the computational efficiency of the designed proposed technique, two nonlinear models are performed, one of them arises in mixed convection flows and the other one arises in heat transfer, which both admit multiple solutions. The results reveal that the method is very effective, straightforward, and powerful for formulating these multiple solutions.

Application of power series to the solution of the boundary value problem for a second order nonlinear differential equation

International Nuclear Information System (INIS)

Semenova, V.N.

2016-01-01

A boundary value problem for a nonlinear second order differential equation has been considered. A numerical method has been proposed to solve this problem using power series. Results of numerical experiments have been presented in the paper [ru

Numerical solution of large nonlinear boundary value problems by quadratic minimization techniques

International Nuclear Information System (INIS)

Glowinski, R.; Le Tallec, P.

1984-01-01

The objective of this paper is to describe the numerical treatment of large highly nonlinear two or three dimensional boundary value problems by quadratic minimization techniques. In all the different situations where these techniques were applied, the methodology remains the same and is organized as follows: 1) derive a variational formulation of the original boundary value problem, and approximate it by Galerkin methods; 2) transform this variational formulation into a quadratic minimization problem (least squares methods) or into a sequence of quadratic minimization problems (augmented lagrangian decomposition); 3) solve each quadratic minimization problem by a conjugate gradient method with preconditioning, the preconditioning matrix being sparse, positive definite, and fixed once for all in the iterative process. This paper will illustrate the methodology above on two different examples: the description of least squares solution methods and their application to the solution of the unsteady Navier-Stokes equations for incompressible viscous fluids; the description of augmented lagrangian decomposition techniques and their application to the solution of equilibrium problems in finite elasticity

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

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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.

Effects of Collisionality on the Nonlinear Characteristics of Boundary Turbulence and Blob/hole Transport in Tokamak Plasmas

Energy Technology Data Exchange (ETDEWEB)

Li, J.; Yasuaki, K., E-mail: lijq@energy.kyoto-u.ac.jp [Kyoto University, Kyoto (Japan); Cheng, J.; Longwen, Y.; Jiaqi, D. [Southwestern Institute of Physics, Chengdu (China)

2012-09-15

Full text: Blob/hole dynamics near tokamak separatrix is of striking importance in determining the boundary transport. Based on simulations using an extended 2-region (edge/SOL) fluid model, we found that blob/hole dynamics are sensitively influenced by the plasma collisionality, i.e., ion-electron and ion-neutral collisions. Namely, the holes are enhanced in highly collisional edge whereas the blobs are weakened at the SOL, causing larger particle convection. These blob/hole dynamics are closely correlated with potential dipoles. The trends are experimentally evidenced on the HL-2A tokamak. Moreover, as the neutral-ion collision increases, the blobs at the SOL tend to develop into streamers propagating outwards with reduced amplitude while the holes inwards are suppressed, showing a key role in nonlinear structure regulation and resultant transport suppression. Results suggest that adjusting the plasma collisionality by fueling, e.g., gas puffing, could serve as a method to nonlinearly select turbulent structures, i.e., blobs, holes or streamers, to access the control of boundary transport. (author)

Boundary controllability for a nonlinear beam equation

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Xiao-Min Cao

2015-09-01

Full Text Available This article concerns a nonlinear system modeling the bending vibrations of a nonlinear beam of length $L>0$. First, we derive the existence of long time solutions near an equilibrium. Then we prove that the nonlinear beam is locally exact controllable around the equilibrium in $H^4(0,L$ and with control functions in $H^2(0,T$. The approach we used are open mapping theorem, local controllability established by linearization, and the induction.

The Efficiency of Split Panel Designs in an Analysis of Variance Model

Science.gov (United States)

Wang, Wei-Guo; Liu, Hai-Jun

2016-01-01

We consider split panel design efficiency in analysis of variance models, that is, the determination of the cross-sections series optimal proportion in all samples, to minimize parametric best linear unbiased estimators of linear combination variances. An orthogonal matrix is constructed to obtain manageable expression of variances. On this basis, we derive a theorem for analyzing split panel design efficiency irrespective of interest and budget parameters. Additionally, relative estimator efficiency based on the split panel to an estimator based on a pure panel or a pure cross-section is present. The analysis shows that the gains from split panel can be quite substantial. We further consider the efficiency of split panel design, given a budget, and transform it to a constrained nonlinear integer programming. Specifically, an efficient algorithm is designed to solve the constrained nonlinear integer programming. Moreover, we combine one at time designs and factorial designs to illustrate the algorithm’s efficiency with an empirical example concerning monthly consumer expenditure on food in 1985, in the Netherlands, and the efficient ranges of the algorithm parameters are given to ensure a good solution. PMID:27163447

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

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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.

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.

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.

Linear and nonlinear development of controlled disturbances in the supersonic boundary layer on a swept wing at Mach 2.5

International Nuclear Information System (INIS)

Kolosov, G L; Kosinov, A D

2016-01-01

Experimental data on the linear and nonlinear wave train development in 3D supersonic boundary layer over a 45° swept-wing at Mach number 2.5 are presented. Travelling artificial disturbances were introduced in the boundary layer by periodical glow discharge at frequencies 10 and 20 kHz. The spatial-temporal and spectral-wave characteristics of the wave train of unstable disturbances in the linear region are obtained. It is shown that the additional peaks in β '-spectra arise for both subharmonic and fundamental frequencies. The experiments indicate the presence of subharmonic resonance mechanism in 3D boundary layer at Mach number 2.5. (paper)

Investigation of nonlinear 2D bottom transportation dynamics in coastal zone on optimal curvilinear boundary adaptive grids

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Sukhinov Alexander

2017-01-01

Full Text Available One of the practically important tasks of hydrophysics for sea coastal systems is the problem of modeling and forecasting bottom sediment transportation. A number of problems connected to ship safety traffic, water medium condition near the coastal line etc. depends on forecasting bottom deposit transportation under natural and technogenic influences. Coastal systems are characterized by a complicated form of coastline - the presence of long, narrow and curvilinear peninsulas and bays. Water currents and waves near the beach are strongly depend on complicated coastal line and in turn, exert on the bottom sediment transportation near the shore. The use of rectangular grids in the construction of discrete models leads to significant errors in both the specification of boundary conditions and in the modeling of hydrophysical processes in the coastal zone. In this paper, we consider the construction of a finite-element approximation of the initial-boundary value problem for the spatially two-dimensional linearized equation of sediment transportation using optimal boundary-adaptive grid. First, the linearization of a spatially two-dimensional nonlinear parabolic equation on the time grid is performed-when the coefficients of the equation that are nonlinearly dependent on the bottom relief function are set on the previous time layer, and the corresponding initial conditions are used on the first time layer. The algorithm for constructing the grid is based on the procedure for minimizing the generalized Dirichlet functional. On the constructed grid, finite element approximation using bilinear basis functions is performed, which completes the construction of a discrete model for the given problem. The using of curvilinear boundary adaptive grids leads to decreasing of total grid number in 5-20 times and respectively the total modeling time and/or it allows to improve modeling accuracy.

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.

Determination of nonlinear nanomechanical resonator-qubit coupling coefficient in a hybrid quantum system.

Science.gov (United States)

Geng, Qi; Zhu, Ka-Di

2016-07-10

We have theoretically investigated a hybrid system that is composed of a traditional optomechanical component and an additional charge qubit (Cooper pair box) that induces a new nonlinear interaction. It is shown that the peak in optomechanically induced transparency has been split by the new nonlinear interaction, and the width of the splitting is proportional to the coupling coefficient of this nonlinear interaction. This may give a way to measure the nanomechanical oscillator-qubit coupling coefficient in hybrid quantum systems.

Multiple Positive Solutions of a Nonlinear Four-Point Singular Boundary Value Problem with a p-Laplacian Operator on Time Scales

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Shihuang Hong

2009-01-01

Full Text Available We present sufficient conditions for the existence of at least twin or triple positive solutions of a nonlinear four-point singular boundary value problem with a p-Laplacian dynamic equation on a time scale. Our results are obtained via some new multiple fixed point theorems.

Electron refrigeration in hybrid structures with spin-split superconductors

Science.gov (United States)

Rouco, M.; Heikkilä, T. T.; Bergeret, F. S.

2018-01-01

Electron tunneling between superconductors and normal metals has been used for an efficient refrigeration of electrons in the latter. Such cooling is a nonlinear effect and usually requires a large voltage. Here we study the electron cooling in heterostructures based on superconductors with a spin-splitting field coupled to normal metals via spin-filtering barriers. The cooling power shows a linear term in the applied voltage. This improves the coefficient of performance of electron refrigeration in the normal metal by shifting its optimum cooling to lower voltage, and also allows for cooling the spin-split superconductor by reverting the sign of the voltage. We also show how tunnel coupling spin-split superconductors with regular ones allows for a highly efficient refrigeration of the latter.

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[.

Boundary-value problems with free boundaries for elliptic systems of equations

CERN Document Server

Monakhov, V N

1983-01-01

This book is concerned with certain classes of nonlinear problems for elliptic systems of partial differential equations: boundary-value problems with free boundaries. The first part has to do with the general theory of boundary-value problems for analytic functions and its applications to hydrodynamics. The second presents the theory of quasiconformal mappings, along with the theory of boundary-value problems for elliptic systems of equations and applications of it to problems in the mechanics of continuous media with free boundaries: problems in subsonic gas dynamics, filtration theory, and problems in elastico-plasticity.

Linear perturbations of a self-similar solution of hydrodynamics with non-linear heat conduction

International Nuclear Information System (INIS)

Dubois-Boudesocque, Carine

2000-01-01

The stability of an ablative flow, where a shock wave is located upstream a thermal front, is of importance in inertial confinement fusion. The present model considers an exact self-similar solution to the hydrodynamic equations with non-linear heat conduction for a semi-infinite slab. For lack of an analytical solution, a high resolution numerical procedure is devised, which couples a finite difference method with a relaxation algorithm using a two-domain pseudo-spectral method. Stability of this solution is studied by introducing linear perturbation method within a Lagrangian-Eulerian framework. The initial and boundary value problem is solved by a splitting of the equations between a hyperbolic system and a parabolic equation. The boundary conditions of the hyperbolic system are treated, in the case of spectral methods, according to Thompson's approach. The parabolic equation is solved by an influence matrix method. These numerical procedures have been tested versus exact solutions. Considering a boundary heat flux perturbation, the space-time evolution of density, velocity and temperature are shown. (author) [fr

PT -symmetric dimer of coupled nonlinear oscillators

Indian Academy of Sciences (India)

We provide a systematic analysis of a prototypical nonlinear oscillator ... recently, a number of nonlinear variants have been explored, like split-ring resonator chain .... Note that these solutions are valid for any value of ǫ (and hence δ) including ǫ ..... [16] M Abramowitz and I A Stegun, Handbook of mathematical functions ...

Single-step digital backpropagation for nonlinearity mitigation

DEFF Research Database (Denmark)

Secondini, Marco; Rommel, Simon; Meloni, Gianluca

2015-01-01

Nonlinearity mitigation based on the enhanced split-step Fourier method (ESSFM) for the implementation of low-complexity digital backpropagation (DBP) is investigated and experimentally demonstrated. After reviewing the main computational aspects of DBP and of the conventional split-step Fourier...... in the computational complexity, power consumption, and latency with respect to a simple feed-forward equalizer for bulk dispersion compensation....

Analysis of factors influencing fire damage to concrete using nonlinear resonance vibration method

Energy Technology Data Exchange (ETDEWEB)

Park, Gang Kyu; Park, Sun Jong; Kwak, Hyo Gyoung [Civil and Environmental Engineering, Korea Advanced Institute of Science and Technology, KAIST, Daejeon (Korea, Republic of); Yim, Hong Jae [Dept. of Construction and Disaster Prevention Engineering, Kyungpook National University, Sangju (Korea, Republic of)

2015-04-15

In this study, the effects of different mix proportions and fire scenarios (exposure temperatures and post-fire-curing periods) on fire-damaged concrete were analyzed using a nonlinear resonance vibration method based on nonlinear acoustics. The hysteretic nonlinearity parameter was obtained, which can sensitively reflect the damage level of fire-damaged concrete. In addition, a splitting tensile strength test was performed on each fire-damaged specimen to evaluate the residual property. Using the results, a prediction model for estimating the residual strength of fire-damaged concrete was proposed on the basis of the correlation between the hysteretic nonlinearity parameter and the ratio of splitting tensile strength.

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 $p>2$.

Operator Splitting Methods for Degenerate Convection-Diffusion Equations I: Convergence and Entropy Estimates

Energy Technology Data Exchange (ETDEWEB)

Holden, Helge; Karlsen, Kenneth H.; Lie, Knut-Andreas

1999-10-01

We present and analyze a numerical method for the solution of a class of scalar, multi-dimensional, nonlinear degenerate convection-diffusion equations. The method is based on operator splitting to separate the convective and the diffusive terms in the governing equation. The nonlinear, convective part is solved using front tracking and dimensional splitting, while the nonlinear diffusion equation is solved by a suitable difference scheme. We verify L{sup 1} compactness of the corresponding set of approximate solutions and derive precise entropy estimates. In particular, these results allow us to pass to the limit in our approximations and recover an entropy solution of the problem in question. The theory presented covers a large class of equations. Important subclasses are hyperbolic conservation laws, porous medium type equations, two-phase reservoir flow equations, and strongly degenerate equations coming from the recent theory of sedimentation-consolidation processes. A thorough numerical investigation of the method analyzed in this paper (and similar methods) is presented in a companion paper. (author)

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.

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

KAUST Repository

Said-Houari, Belkacem; Nascimento, Flá vio A Falcã o

2012-01-01

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.

Sublayer of Prandtl Boundary Layers

Science.gov (United States)

Grenier, Emmanuel; Nguyen, Toan T.

2018-03-01

The aim of this paper is to investigate the stability of Prandtl boundary layers in the vanishing viscosity limit {ν \\to 0} . In Grenier (Commun Pure Appl Math 53(9):1067-1091, 2000), one of the authors proved that there exists no asymptotic expansion involving one of Prandtl's boundary layer, with thickness of order {√{ν}} , which describes the inviscid limit of Navier-Stokes equations. The instability gives rise to a viscous boundary sublayer whose thickness is of order {ν^{3/4}} . In this paper, we point out how the stability of the classical Prandtl's layer is linked to the stability of this sublayer. In particular, we prove that the two layers cannot both be nonlinearly stable in L^∞. That is, either the Prandtl's layer or the boundary sublayer is nonlinearly unstable in the sup norm.

Studies of nonlinear femtosecond pulse propagation in bulk materials

Science.gov (United States)

Eaton, Hilary Kaye

2000-10-01

Femtosecond pulse lasers are finding widespread application in a variety of fields including medical research, optical switching and communications, plasma formation, high harmonic generation, and wavepacket formation and control. As the number of applications for femtosecond pulses increases, so does the need to fully understand the linear and nonlinear processes involved in propagating these pulses through materials under various conditions. Recent advances in pulse measurement techniques, such as frequency-resolved optical gating (FROG), allow measurement of the full electric field of the pulse and have made detailed investigations of short- pulse propagation effects feasible. In this thesis, I present detailed experimental studies of my work involving nonlinear propagation of femtosecond pulses in bulk media. Studies of plane-wave propagation in fused silica extend the SHG form of FROG from a simple pulse diagnostic to a useful method of interrogating the nonlinear response of a material. Studies of nonlinear propagation are also performed in a regime where temporal pulse splitting occurs. Experimental results are compared with a three- dimensional nonlinear Schrödinger equation. This comparison fuels the development of a more complete model for pulse splitting. Experiments are also performed at peak input powers above those at which pulse splitting is observed. At these higher intensities, a broadband continuum is generated. This work presents a detailed study of continuum behavior and power loss as well as the first near-field spatial- spectral measurements of the generated continuum light. Nonlinear plane-wave propagation of short pulses in liquids is also investigated, and a non-instantaneous nonlinearity with a surprisingly short response time of 10 fs is observed in methanol. Experiments in water confirm that this effect in methanol is indeed real. Possible explanations for the observed effect are discussed and several are experimentally rejected. This

The splitted laser beam filamentation in interaction of laser and an exponential decay inhomogeneous underdense plasma

International Nuclear Information System (INIS)

Xia Xiongping; Yi Lin; Xu Bin; Lu Jianduo

2011-01-01

The splitted beam filamentation in interaction of laser and an exponential decay inhomogeneous underdense plasma is investigated. Based on Wentzel-Kramers-Brillouin (WKB) approximation and paraxial/nonparaxial ray theory, simulation results show that the steady beam width and single beam filamentation along the propagation distance in paraxial case is due to the influence of ponderomotive nonlinearity. In nonparaxial case, the influence of the off-axial of α 00 and α 02 (the departure of the beam from the Gaussian nature) and S 02 (the departure from the spherical nature) results in more complicated ponderomotive nonlinearity and changing of the channel density and refractive index, which led to the formation of two/three splitted beam filamentation and the self-distortion of beam width. In addition, influence of several parameters on two/three splitted beam filamentation is discussed.

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)

Aeroelastic Limit-Cycle Oscillations resulting from Aerodynamic Non-Linearities

NARCIS (Netherlands)

van Rooij, A.C.L.M.

2017-01-01

Aerodynamic non-linearities, such as shock waves, boundary layer separation or boundary layer transition, may cause an amplitude limitation of the oscillations induced by the fluid flow around a structure. These aeroelastic limit-cycle oscillations (LCOs) resulting from aerodynamic non-linearities

Boundary Observability and Stabilization for Westervelt Type Wave Equations without Interior Damping

International Nuclear Information System (INIS)

Kaltenbacher, Barbara

2010-01-01

In this paper we show boundary observability and boundary stabilizability by linear feedbacks for a class of nonlinear wave equations including the undamped Westervelt model used in nonlinear acoustics. We prove local existence for undamped generalized Westervelt equations with homogeneous Dirichlet boundary conditions as well as global existence and exponential decay with absorbing type boundary conditions.

Fundaments of transport equation splitting and the eigenvalue problem

International Nuclear Information System (INIS)

Stancic, V.

2000-01-01

In order to remove some singularities concerning the boundary conditions of one dimensional transport equation, a split form of transport equation describing the forward i.e. μ≥0, and a backward μ<0 directed neutrons is being proposed here. The eigenvalue problem has also been considered here (author)

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

Direct approach for solving nonlinear evolution and two-point

Indian Academy of Sciences (India)

Time-delayed nonlinear evolution equations and boundary value problems have a wide range of applications in science and engineering. In this paper, we implement the differential transform method to solve the nonlinear delay differential equation and boundary value problems. Also, we present some numerical examples ...

Analytic Approximate Solutions to the Boundary Layer Flow Equation over a Stretching Wall with Partial Slip at the Boundary.

Science.gov (United States)

Ene, Remus-Daniel; Marinca, Vasile; Marinca, Bogdan

2016-01-01

Analytic approximate solutions using Optimal Homotopy Perturbation Method (OHPM) are given for steady boundary layer flow over a nonlinearly stretching wall in presence of partial slip at the boundary. The governing equations are reduced to nonlinear ordinary differential equation by means of similarity transformations. Some examples are considered and the effects of different parameters are shown. OHPM is a very efficient procedure, ensuring a very rapid convergence of the solutions after only two iterations.

Higher-order modulation instability in nonlinear fiber optics.

Science.gov (United States)

Erkintalo, Miro; Hammani, Kamal; Kibler, Bertrand; Finot, Christophe; Akhmediev, Nail; Dudley, John M; Genty, Goëry

2011-12-16

We report theoretical, numerical, and experimental studies of higher-order modulation instability in the focusing nonlinear Schrödinger equation. This higher-order instability arises from the nonlinear superposition of elementary instabilities, associated with initial single breather evolution followed by a regime of complex, yet deterministic, pulse splitting. We analytically describe the process using the Darboux transformation and compare with experiments in optical fiber. We show how a suitably low frequency modulation on a continuous wave field induces higher-order modulation instability splitting with the pulse characteristics at different phases of evolution related by a simple scaling relationship. We anticipate that similar processes are likely to be observed in many other systems including plasmas, Bose-Einstein condensates, and deep water waves. © 2011 American Physical Society

Controller Design of Complex System Based on Nonlinear Strength

Directory of Open Access Journals (Sweden)

Rongjun Mu

2015-01-01

Full Text Available This paper presents a new idea of controller design for complex systems. The nonlinearity index method was first developed for error propagation of nonlinear system. The nonlinearity indices access the boundary between the strong and the weak nonlinearities of the system model. The algorithm of nonlinearity index according to engineering application is first proposed in this paper. Applying this method on nonlinear systems is an effective way to measure the nonlinear strength of dynamics model over the full flight envelope. The nonlinearity indices access the boundary between the strong and the weak nonlinearities of system model. According to the different nonlinear strength of dynamical model, the control system is designed. The simulation time of dynamical complex system is selected by the maximum value of dynamic nonlinearity indices. Take a missile as example; dynamical system and control characteristic of missile are simulated. The simulation results show that the method is correct and appropriate.

Spectral Action for Torsion with and without Boundaries

DEFF Research Database (Denmark)

Iochum, B.; Levy, Cyril Olivier; Vassilevich, D.

2012-01-01

We derive a commutative spectral triple and study the spectral action for a rather general geometric setting which includes the (skew-symmetric) torsion and the chiral bag conditions on the boundary. The spectral action splits into bulk and boundary parts. In the bulk, we clarify certain issues...... of the boundary conditions, and show that θ = 0 is a critical point of the action in any dimension and at all orders of the expansion....

Classically integrable boundary conditions for symmetric-space sigma models

International Nuclear Information System (INIS)

MacKay, N.J.; Young, C.A.S.

2004-01-01

We investigate boundary conditions for the non-linear sigma model on the compact symmetric space G/H. The Poisson brackets and the classical local conserved charges necessary for integrability are preserved by boundary conditions which correspond to involutions which commute with the involution defining H. Applied to SO(3)/SO(2), the non-linear sigma model on S 2 , these yield the great circles as boundary submanifolds. Applied to GxG/G, they reproduce known results for the principal chiral model

Spline Collocation Method for Nonlinear Multi-Term Fractional Differential Equation

OpenAIRE

Choe, Hui-Chol; Kang, Yong-Suk

2013-01-01

We study an approximation method to solve nonlinear multi-term fractional differential equations with initial conditions or boundary conditions. First, we transform the nonlinear multi-term fractional differential equations with initial conditions and boundary conditions to nonlinear fractional integral equations and consider the relations between them. We present a Spline Collocation Method and prove the existence, uniqueness and convergence of approximate solution as well as error estimatio...

The forced nonlinear Schroedinger equation

International Nuclear Information System (INIS)

Kaup, D.J.; Hansen, P.J.

1985-01-01

The nonlinear Schroedinger equation describes the behaviour of a radio frequency wave in the ionosphere near the reflexion point where nonlinear processes are important. A simple model of this phenomenon leads to the forced nonlinear Schroedinger equation in terms of a nonlinear boundary value problem. A WKB analysis of the time evolution equations for the nonlinear Schroedinger equation in the inverse scattering transform formalism gives a crude order of magnitude estimation of the qualitative behaviour of the solutions. This estimation is compared with the numerical solutions. (D.Gy.)

Renormgroup symmetries in problems of nonlinear geometrical optics

International Nuclear Information System (INIS)

Kovalev, V.F.

1996-01-01

Utilization and further development of the previously announced approach [1,2] enables one to construct renormgroup symmetries for a boundary value problem for the system of equations which describes propagation of a powerful radiation in a nonlinear medium in geometrical optics approximation. With the help of renormgroup symmetries new rigorous and approximate analytical solutions of nonlinear geometrical optics equations are obtained. Explicit analytical expressions are presented that characterize spatial evolution of laser beam which has an arbitrary intensity dependence at the boundary of the nonlinear medium. (author)

Arbitrary-ratio power splitter based on nonlinear multimode interference coupler

International Nuclear Information System (INIS)

Tajaldini, Mehdi; Jafri, Mohd Zubir Mat

2015-01-01

We propose an ultra-compact multimode interference (MMI) power splitter based on nonlinear effects from simulations using nonlinear modal propagation analysis (NMPA) cooperation with finite difference Method (FDM) to access free choice of splitting ratio. Conventional multimode interference power splitter could only obtain a few discrete ratios. The power splitting ratio may be adjusted continuously while the input set power is varying by a tunable laser. In fact, using an ultra- compact MMI with a simple structure that is launched by a tunable nonlinear input fulfills the problem of arbitrary-ratio in integrated photonics circuits. Silicon on insulator (SOI) is used as the offered material due to the high contrast refractive index and Centro symmetric properties. The high-resolution images at the end of the multimode waveguide in the simulated power splitter have a high power balance, whereas access to a free choice of splitting ratio is not possible under the linear regime in the proposed length range except changes in the dimension for any ratio. The compact dimensions and ideal performance of the device are established according to optimized parameters. The proposed regime can be extended to the design of M×N arbitrary power splitters ratio for programmable logic devices in all optical digital signal processing. The results of this study indicate that nonlinear modal propagation analysis solves the miniaturization problem for all-optical devices based on MMI couplers to achieve multiple functions in a compact planar integrated circuit and also overcomes the limitations of previously proposed methods for nonlinear MMI

Arbitrary-ratio power splitter based on nonlinear multimode interference coupler

Energy Technology Data Exchange (ETDEWEB)

Tajaldini, Mehdi [School of Physics, Universiti Sains Malaysia, 11800 Pulau Pinang (Malaysia); Young Researchers and Elite Club, Baft Branch, Islamic Azad University, Baft (Iran, Islamic Republic of); Jafri, Mohd Zubir Mat [School of Physics, Universiti Sains Malaysia, 11800 Pulau Pinang (Malaysia)

2015-04-24

We propose an ultra-compact multimode interference (MMI) power splitter based on nonlinear effects from simulations using nonlinear modal propagation analysis (NMPA) cooperation with finite difference Method (FDM) to access free choice of splitting ratio. Conventional multimode interference power splitter could only obtain a few discrete ratios. The power splitting ratio may be adjusted continuously while the input set power is varying by a tunable laser. In fact, using an ultra- compact MMI with a simple structure that is launched by a tunable nonlinear input fulfills the problem of arbitrary-ratio in integrated photonics circuits. Silicon on insulator (SOI) is used as the offered material due to the high contrast refractive index and Centro symmetric properties. The high-resolution images at the end of the multimode waveguide in the simulated power splitter have a high power balance, whereas access to a free choice of splitting ratio is not possible under the linear regime in the proposed length range except changes in the dimension for any ratio. The compact dimensions and ideal performance of the device are established according to optimized parameters. The proposed regime can be extended to the design of M×N arbitrary power splitters ratio for programmable logic devices in all optical digital signal processing. The results of this study indicate that nonlinear modal propagation analysis solves the miniaturization problem for all-optical devices based on MMI couplers to achieve multiple functions in a compact planar integrated circuit and also overcomes the limitations of previously proposed methods for nonlinear MMI.

Boundary fluxes for nonlocal diffusion

Science.gov (United States)

Cortazar, Carmen; Elgueta, Manuel; Rossi, Julio D.; Wolanski, Noemi

We study a nonlocal diffusion operator in a bounded smooth domain prescribing the flux through the boundary. This problem may be seen as a generalization of the usual Neumann problem for the heat equation. First, we prove existence, uniqueness and a comparison principle. Next, we study the behavior of solutions for some prescribed boundary data including blowing up ones. Finally, we look at a nonlinear flux boundary condition.

Improved algorithm for solving nonlinear parabolized stability equations

International Nuclear Information System (INIS)

Zhao Lei; Zhang Cun-bo; Liu Jian-xin; Luo Ji-sheng

2016-01-01

Due to its high computational efficiency and ability to consider nonparallel and nonlinear effects, nonlinear parabolized stability equations (NPSE) approach has been widely used to study the stability and transition mechanisms. However, it often diverges in hypersonic boundary layers when the amplitude of disturbance reaches a certain level. In this study, an improved algorithm for solving NPSE is developed. In this algorithm, the mean flow distortion is included into the linear operator instead of into the nonlinear forcing terms in NPSE. An under-relaxation factor for computing the nonlinear terms is introduced during the iteration process to guarantee the robustness of the algorithm. Two case studies, the nonlinear development of stationary crossflow vortices and the fundamental resonance of the second mode disturbance in hypersonic boundary layers, are presented to validate the proposed algorithm for NPSE. Results from direct numerical simulation (DNS) are regarded as the baseline for comparison. Good agreement can be found between the proposed algorithm and DNS, which indicates the great potential of the proposed method on studying the crossflow and streamwise instability in hypersonic boundary layers. (paper)

Embryo splitting

Directory of Open Access Journals (Sweden)

Karl Illmensee

2010-04-01

Full Text Available Mammalian embryo splitting has successfully been established in farm animals. Embryo splitting is safely and efficiently used for assisted reproduction in several livestock species. In the mouse, efficient embryo splitting as well as single blastomere cloning have been developed in this animal system. In nonhuman primates embryo splitting has resulted in several pregnancies. Human embryo splitting has been reported recently. Microsurgical embryo splitting under Institutional Review Board approval has been carried out to determine its efficiency for blastocyst development. Embryo splitting at the 6–8 cell stage provided a much higher developmental efficiency compared to splitting at the 2–5 cell stage. Embryo splitting may be advantageous for providing additional embryos to be cryopreserved and for patients with low response to hormonal stimulation in assisted reproduction programs. Social and ethical issues concerning embryo splitting are included regarding ethics committee guidelines. Prognostic perspectives are presented for human embryo splitting in reproductive medicine.

Dynamic relaxation method for nonlinear buckling analysis of moderately thick FG cylindrical panels with various boundary conditions

Energy Technology Data Exchange (ETDEWEB)

Golmakani, M. E.; Far, M. N. Sadraee; Moravej, M. [Dept. of Mechanical Engineering, Mashhad Branch, Islamic Azad University, Mashhad (Iran, Islamic Republic of)

2016-12-15

Using new approach proposed by Dynamic relaxation (DR) method, buckling analysis of moderately thick Functionally graded (FG) cylindrical panels subjected to axial compression is investigated for various boundary conditions. The mechanical properties of FG panel are assumed to vary continuously along the thickness direction by the simple rule of mixture and Mori-Tanaka model. The incremental form of nonlinear formulations are derived based on First-order shear deformation theory (FSDT) and large deflection von Karman equations. The DR method combined with the finite difference discretization technique is employed to solve the incremental form of equilibrium equations. The critical mechanical buckling load is determined based on compressive load-displacement curve by adding the incremental displacements in each load step to the displacements obtained from the previous ones. A detailed parametric study is carried out to investigate the influences of the boundary conditions, rule of mixture, grading index, radius-to-thickness ratio, length-to-radius ratio and panel angle on the mechanical buckling load. The results reveal that with increase of grading index the effect of radius-to-thickness ratio on the buckling load decreases. It is also observed that effect of distribution rules on the buckling load is dependent to the type of boundary conditions.

Helmholtz bright and boundary solitons

International Nuclear Information System (INIS)

Christian, J M; McDonald, G S; Chamorro-Posada, P

2007-01-01

We report, for the first time, exact analytical boundary solitons of a generalized cubic-quintic nonlinear Helmholtz (NLH) equation. These solutions have a linked-plateau topology that is distinct from conventional dark soliton solutions; their amplitude and intensity distributions are spatially delocalized and connect regions of finite and zero wave-field disturbances (suggesting also the classification as 'edge solitons'). Extensive numerical simulations compare the stability properties of recently derived Helmholtz bright solitons, for this type of polynomial nonlinearity, to those of the new boundary solitons. The latter are found to possess a remarkable stability characteristic, exhibiting robustness against perturbations that would otherwise lead to the destabilizing of their bright-soliton counterparts

Recent topics in nonlinear PDE

International Nuclear Information System (INIS)

Mimura, Masayasu; Nishida, Takaaki

1984-01-01

The meeting on the subject of nonlinear partial differential equations was held at Hiroshima University in February, 1983. Leading and active mathematicians were invited to talk on their current research interests in nonlinear pdes occuring in the areas of fluid dynamics, free boundary problems, population dynamics and mathematical physics. This volume contains the theory of nonlinear pdes and the related topics which have been recently developed in Japan. (Auth.)

Group invariance in engineering boundary value problems

CERN Document Server

Seshadri, R

1985-01-01

REFEREN CES . 156 9 Transforma.tion of a Boundary Value Problem to an Initial Value Problem . 157 9.0 Introduction . 157 9.1 Blasius Equation in Boundary Layer Flow . 157 9.2 Longitudinal Impact of Nonlinear Viscoplastic Rods . 163 9.3 Summary . 168 REFERENCES . . . . . . . . . . . . . . . . . . 168 . 10 From Nonlinear to Linear Differential Equa.tions Using Transformation Groups. . . . . . . . . . . . . . 169 . 10.1 From Nonlinear to Linear Differential Equations . 170 10.2 Application to Ordinary Differential Equations -Bernoulli's Equation . . . . . . . . . . . 173 10.3 Application to Partial Differential Equations -A Nonlinear Chemical Exchange Process . 178 10.4 Limitations of the Inspectional Group Method . 187 10.5 Summary . 188 REFERENCES . . . . 188 11 Miscellaneous Topics . 190 11.1 Reduction of Differential Equations to Algebraic Equations 190 11.2 Reduction of Order of an Ordinary Differential Equation . 191 11.3 Transformat.ion From Ordinary to Partial Differential Equations-Search for First Inte...

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

KAUST Repository

Graber, Philip Jameson; Said-Houari, Belkacem

2012-01-01

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.

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.

Polarity of translation boundaries in antiferroelectric PbZrO{sub 3}

Energy Technology Data Exchange (ETDEWEB)

Wei, Xian-Kui, E-mail: xiankui.wei@epfl.ch [Ceramics Laboratory, EPFL–Swiss Federal Institute of Technology, Lausanne 1015 (Switzerland); Peter Grünberg Institute and Ernst Ruska Center for Microscopy and Spectroscopy with Electrons, Research Center Jülich, 52425 Jülich (Germany); Jia, Chun-Lin [Peter Grünberg Institute and Ernst Ruska Center for Microscopy and Spectroscopy with Electrons, Research Center Jülich, 52425 Jülich (Germany); International Centre of Dielectric Research, The School of Electronic and Information Engineering, Xi’an Jiaotong University, Xi’an 710049 (China); Roleder, Krystian [Institute of Physics, University of Silesia, Katowice 40007 (Poland); Setter, Nava [Ceramics Laboratory, EPFL–Swiss Federal Institute of Technology, Lausanne 1015 (Switzerland)

2015-02-15

Graphical abstract: Strain-free rigid model and aberration-corrected transmission electron microscopes are used to investigate the polarity of translation boundaries in antiferroelectric PbZrO{sub 3}. - Highlights: • Domain boundaries in antiferroelectric PbZrO{sub 3} show polar and antipolar property. • The antiphase boundary can split into “sub-domains”. • Polarization reversal possibly exists inside the translation boundaries. • Thermal treatment can alter morphology and density of the translation boundaries. - Abstract: The polarity of translation boundaries (TBs) in antiferroelectric PbZrO{sub 3} is investigated. We show that previous experimentally reported polar property of R{sub III-1} type TB can be well approximated by a strain-free rigid model. Based on this, the modeling investigation suggests that there are two additional polar TBs, three antipolar-like TBs and one antipolar antiphase boundary. High-resolution scanning-transmission-electron-microscopy study reveals that the straight R{sub III-1} type TB can split into “sub-domains” with possible polarization reversal, suggesting the occurrence of ferroic orders at the TBs. In addition, dependence of morphology and density of the TBs on thermal treatments is discussed according to our results.

Combined algorithms in nonlinear problems of magnetostatics

International Nuclear Information System (INIS)

Gregus, M.; Khoromskij, B.N.; Mazurkevich, G.E.; Zhidkov, E.P.

1988-01-01

To solve boundary problems of magnetostatics in unbounded two- and three-dimensional regions, we construct combined algorithms based on a combination of the method of boundary integral equations with the grid methods. We study the question of substantiation of the combined method of nonlinear magnetostatic problem without the preliminary discretization of equations and give some results on the convergence of iterative processes that arise in non-linear cases. We also discuss economical iterative processes and algorithms that solve boundary integral equations on certain surfaces. Finally, examples of numerical solutions of magnetostatic problems that arose when modelling the fields of electrophysical installations are given too. 14 refs.; 2 figs.; 1 tab

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.

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.

Improved algorithm for solving nonlinear parabolized stability equations

Science.gov (United States)

Zhao, Lei; Zhang, Cun-bo; Liu, Jian-xin; Luo, Ji-sheng

2016-08-01

Due to its high computational efficiency and ability to consider nonparallel and nonlinear effects, nonlinear parabolized stability equations (NPSE) approach has been widely used to study the stability and transition mechanisms. However, it often diverges in hypersonic boundary layers when the amplitude of disturbance reaches a certain level. In this study, an improved algorithm for solving NPSE is developed. In this algorithm, the mean flow distortion is included into the linear operator instead of into the nonlinear forcing terms in NPSE. An under-relaxation factor for computing the nonlinear terms is introduced during the iteration process to guarantee the robustness of the algorithm. Two case studies, the nonlinear development of stationary crossflow vortices and the fundamental resonance of the second mode disturbance in hypersonic boundary layers, are presented to validate the proposed algorithm for NPSE. Results from direct numerical simulation (DNS) are regarded as the baseline for comparison. Good agreement can be found between the proposed algorithm and DNS, which indicates the great potential of the proposed method on studying the crossflow and streamwise instability in hypersonic boundary layers. Project supported by the National Natural Science Foundation of China (Grant Nos. 11332007 and 11402167).

A numerical solution of a singular boundary value problem arising in boundary layer theory.

Science.gov (United States)

Hu, Jiancheng

2016-01-01

In this paper, a second-order nonlinear singular boundary value problem is presented, which is equivalent to the well-known Falkner-Skan equation. And the one-dimensional third-order boundary value problem on interval [Formula: see text] is equivalently transformed into a second-order boundary value problem on finite interval [Formula: see text]. The finite difference method is utilized to solve the singular boundary value problem, in which the amount of computational effort is significantly less than the other numerical methods. The numerical solutions obtained by the finite difference method are in agreement with those obtained by previous authors.

Helmholtz bright and boundary solitons

Energy Technology Data Exchange (ETDEWEB)

Christian, J M [Joule Physics Laboratory, School of Computing, Science and Engineering, Institute for Materials Research, University of Salford, Salford M5 4WT (United Kingdom); McDonald, G S [Joule Physics Laboratory, School of Computing, Science and Engineering, Institute for Materials Research, University of Salford, Salford M5 4WT (United Kingdom); Chamorro-Posada, P [Departmento de TeorIa de la Senal y Comunicaciones e IngenierIa Telematica, Universidad de Valladolid, ETSI Telecomunicacion, Campus Miguel Delibes s/n, 47011 Valladolid (Spain)

2007-02-16

We report, for the first time, exact analytical boundary solitons of a generalized cubic-quintic nonlinear Helmholtz (NLH) equation. These solutions have a linked-plateau topology that is distinct from conventional dark soliton solutions; their amplitude and intensity distributions are spatially delocalized and connect regions of finite and zero wave-field disturbances (suggesting also the classification as 'edge solitons'). Extensive numerical simulations compare the stability properties of recently derived Helmholtz bright solitons, for this type of polynomial nonlinearity, to those of the new boundary solitons. The latter are found to possess a remarkable stability characteristic, exhibiting robustness against perturbations that would otherwise lead to the destabilizing of their bright-soliton counterparts.

Boundary fluxes for non-local diffusion

OpenAIRE

Cortazar, C.; Elgueta, M.; Rossi, J. D.; Wolanski, N.

2006-01-01

We study a nonlocal diffusion operator in a bounded smooth domain prescribing the flux through the boundary. This problem may be seen as a generalization of the usual Neumann problem for the heat equation. First, we prove existence, uniqueness and a comparison principle. Next, we study the behavior of solutions for some prescribed boundary data including blowing up ones. Finally, we look at a nonlinear flux boundary condition.

Nonlinear second-order multivalued boundary value problems

Indian Academy of Sciences (India)

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

Department of Mathematics, National Technical University, Zografou Campus,. Athens 15780 ... incorporates gradient systems, evolutionary variational inequalities and the classical boundary value ... We are led to an eventual application.

Optimal boundary control and boundary stabilization of hyperbolic systems

CERN Document Server

Gugat, Martin

2015-01-01

This brief considers recent results on optimal control and stabilization of systems governed by hyperbolic partial differential equations, specifically those in which the control action takes place at the boundary.  The wave equation is used as a typical example of a linear system, through which the author explores initial boundary value problems, concepts of exact controllability, optimal exact control, and boundary stabilization.  Nonlinear systems are also covered, with the Korteweg-de Vries and Burgers Equations serving as standard examples.  To keep the presentation as accessible as possible, the author uses the case of a system with a state that is defined on a finite space interval, so that there are only two boundary points where the system can be controlled.  Graduate and post-graduate students as well as researchers in the field will find this to be an accessible introduction to problems of optimal control and stabilization.

Feedback options in nonlinear numerical finance

DEFF Research Database (Denmark)

Hugger, Jens; Mashayekhi, Sima

2012-01-01

on an infinite slab is presented and boundary values on a bounded domain are derived. This bounded, nonlinear, 2 dimensional initial-boundary value problem is solved numerically using a number of standard finite difference schemes and the methods incorporated in the symbolic software Maple™....

The Split Coefficient Matrix method for hyperbolic systems of gasdynamic equations

Science.gov (United States)

Chakravarthy, S. R.; Anderson, D. A.; Salas, M. D.

1980-01-01

The Split Coefficient Matrix (SCM) finite difference method for solving hyperbolic systems of equations is presented. This new method is based on the mathematical theory of characteristics. The development of the method from characteristic theory is presented. Boundary point calculation procedures consistent with the SCM method used at interior points are explained. The split coefficient matrices that define the method for steady supersonic and unsteady inviscid flows are given for several examples. The SCM method is used to compute several flow fields to demonstrate its accuracy and versatility. The similarities and differences between the SCM method and the lambda-scheme are discussed.

Numeric treatment of nonlinear second order multi-point boundary value problems using ANN, GAs and sequential quadratic programming technique

Directory of Open Access Journals (Sweden)

Zulqurnain Sabir

2014-06-01

Full Text Available In this paper, computational intelligence technique are presented for solving multi-point nonlinear boundary value problems based on artificial neural networks, evolutionary computing approach, and active-set technique. The neural network is to provide convenient methods for obtaining useful model based on unsupervised error for the differential equations. The motivation for presenting this work comes actually from the aim of introducing a reliable framework that combines the powerful features of ANN optimized with soft computing frameworks to cope with such challenging system. The applicability and reliability of such methods have been monitored thoroughly for various boundary value problems arises in science, engineering and biotechnology as well. Comprehensive numerical experimentations have been performed to validate the accuracy, convergence, and robustness of the designed scheme. Comparative studies have also been made with available standard solution to analyze the correctness of the proposed scheme.

Reflection of equatorial Kelvin waves at eastern ocean boundaries Part I: hypothetical boundaries

Directory of Open Access Journals (Sweden)

J. Soares

1999-06-01

Full Text Available A baroclinic shallow-water model is developed to investigate the effect of the orientation of the eastern ocean boundary on the behavior of equatorial Kelvin waves. The model is formulated in a spherical polar coordinate system and includes dissipation and non-linear terms, effects which have not been previously included in analytical approaches to the problem. Both equatorial and middle latitude response are considered given the large latitudinal extent used in the model. Baroclinic equatorial Kelvin waves of intraseasonal, seasonal and annual periods are introduced into the domain as pulses of finite width. Their subsequent reflection, transmission and dissipation are investigated. It is found that dissipation is very important for the transmission of wave energy along the boundary and for reflections from the boundary. The dissipation was found to be dependent not only on the presence of the coastal Kelvin waves in the domain, but also on the period of these coastal waves. In particular the dissipation increases with wave period. It is also shown that the equatorial β-plane approximation can allow an anomalous generation of Rossby waves at higher latitudes. Nonlinearities generally have a small effect on the solutions, within the confines of this model.Key words. Oceanography: general (equatorial oceanography; numerical modeling · Oceanography: physical (eastern boundary currents

Immiscible three-dimensional fingering in porous media: A weakly nonlinear analysis

Science.gov (United States)

Brandão, Rodolfo; Dias, Eduardo O.; Miranda, José A.

2018-03-01

We present a weakly nonlinear theory for the development of fingering instabilities that arise at the interface between two immiscible viscous fluids flowing radially outward in a uniform three-dimensional (3D) porous medium. By employing a perturbative second-order mode-coupling scheme, we investigate the linear stability of the system as well as the emergence of intrinsically nonlinear finger branching events in this 3D environment. At the linear stage, we find several differences between the 3D radial fingering and its 2D counterpart (usual Saffman-Taylor flow in radial Hele-Shaw cells). These include the algebraic growth of disturbances and the existence of regions of absolute stability for finite values of viscosity contrast and capillary number in the 3D system. On the nonlinear level, our main focus is to get analytical insight into the physical mechanism resulting in the occurrence of finger tip-splitting phenomena. In this context, we show that the underlying mechanism leading to 3D tip splitting relies on the coupling between the fundamental interface modes and their first harmonics. However, we find that in three dimensions, in contrast to the usual 2D fingering structures normally encountered in radial Hele-Shaw flows, tip splitting into three branches can also be observed.

Nonlinear mechanics of thin-walled structures asymptotics, direct approach and numerical analysis

CERN Document Server

Vetyukov, Yury

2014-01-01

This book presents a hybrid approach to the mechanics of thin bodies. Classical theories of rods, plates and shells with constrained shear are based on asymptotic splitting of the equations and boundary conditions of three-dimensional elasticity. The asymptotic solutions become accurate as the thickness decreases, and the three-dimensional fields of stresses and displacements can be determined. The analysis includes practically important effects of electromechanical coupling and material inhomogeneity. The extension to the geometrically nonlinear range uses the direct approach based on the principle of virtual work. Vibrations and buckling of pre-stressed structures are studied with the help of linearized incremental formulations, and direct tensor calculus rounds out the list of analytical techniques used throughout the book. A novel theory of thin-walled rods of open profile is subsequently developed from the models of rods and shells, and traditionally applied equations are proven to be asymptotically exa...

The periodic structure of the natural record, and nonlinear dynamics.

Science.gov (United States)

Shaw, H.R.

1987-01-01

This paper addresses how nonlinear dynamics can contribute to interpretations of the geologic record and evolutionary processes. Background is given to explain why nonlinear concepts are important. A resume of personal research is offered to illustrate why I think nonlinear processes fit with observations on geological and cosmological time series data. The fabric of universal periodicity arrays generated by nonlinear processes is illustrated by means of a simple computer mode. I conclude with implications concerning patterns of evolution, stratigraphic boundary events, and close correlations of major geologically instantaneous events (such as impacts or massive volcanic episodes) with any sharply defined boundary in the geologic column. - from Author

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

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.

Thermodynamic evaluation of the Kalina split-cycle concepts for waste heat recovery applications

International Nuclear Information System (INIS)

Nguyen, Tuong-Van; Knudsen, Thomas; Larsen, Ulrik; Haglind, Fredrik

2014-01-01

The Kalina split-cycle is a thermodynamic process for converting thermal energy into electrical power. It uses an ammonia–water mixture as a working fluid (like a conventional Kalina cycle) and has a varying ammonia concentration during the pre-heating and evaporation steps. This second feature results in an improved match between the heat source and working fluid temperature profiles, decreasing the entropy generation in the heat recovery system. The present work compares the thermodynamic performance of this power cycle with the conventional Kalina process, and investigates the impact of varying boundary conditions by conducting an exergy analysis. The design parameters of each configuration were determined by performing a multi-variable optimisation. The results indicate that the Kalina split-cycle with reheat presents an exergetic efficiency by 2.8% points higher than a reference Kalina cycle with reheat, and by 4.3% points without reheat. The cycle efficiency varies by 14% points for a variation of the exhaust gas temperature of 100 °C, and by 1% point for a cold water temperature variation of 30 °C. This analysis also pinpoints the large irreversibilities in the low-pressure turbine and condenser, and indicates a reduction of the exergy destruction by about 23% in the heat recovery system compared to the baseline cycle. - Highlights: • The thermodynamic performance of the Kalina split-cycle is assessed. • The Kalina split-cycle is compared to the Kalina cycle, with and without reheat. • An exergy analysis is performed to evaluate its thermodynamic performance. • The impact of varying boundary conditions is investigated. • The Kalina split-cycle displays high exergetic efficiency for low- and medium-temperature applications

Towards realistic molecular dynamics simulations of grain boundary mobility

International Nuclear Information System (INIS)

Zhou, J.; Mohles, V.

2011-01-01

In order to investigate grain boundary migration by molecular dynamics (MD) simulations a new approach involving a crystal orientation-dependent driving force has been developed by imposing an appropriate driving force on grain boundary atoms and enlarging the effective range of driving force. The new approach has been validated by the work of the driving force associated with the motion of grain boundaries. With the new approach the relation between boundary migration velocity and driving force is found to be nonlinear, as was expected from rate theory for large driving forces applied in MD simulations. By evaluating grain boundary mobility nonlinearly for a set of symmetrical tilt boundaries in aluminum at high temperature, high-angle grain boundaries were shown to move much faster than low-angle grain boundaries. This agrees well with experimental findings for recrystallization and grain growth. In comparison with the available data the simulated mobility of a 38.21 o Σ7 boundary was found to be significantly lower than other MD simulation results and comparable with the experimental values. Furthermore, the average volume involved during atomic jumps for boundary migration is determined in MD simulations for the first time. The large magnitude of the volume indicates that grain boundary migration is accomplished by the correlated motion of atom groups.

Nonlinear singular elliptic equations

International Nuclear Information System (INIS)

Dong Minh Duc.

1988-09-01

We improve the Poincare inequality, the Sobolev imbedding theorem and the Trudinger imbedding theorem and prove a Mountain pass theorem. Applying these results we study a nonlinear singular mixed boundary problem. (author). 22 refs

On the wave equation with semilinear porous acoustic boundary conditions

KAUST Repository

Graber, Philip Jameson; Said-Houari, Belkacem

2012-01-01

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.

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.

Metamaterial-Enhanced Nonlinear Terahertz Spectroscopy

Directory of Open Access Journals (Sweden)

Zhang X.

2013-03-01

Full Text Available We demonstrate large nonlinear terahertz responses in the gaps of metamaterial split ring resonators in several materials and use nonlinear THz transmission and THz-pump/THz-probe spectroscopy to study the nonlinear responses and dynamics. We use the field enhancement in the SRR gaps to initiate high-field phenomena at lower incident fields. In vanadium dioxide, we drive the insulator-to-metal phase transition with high-field THz radiation. The film conductivity increases by over two orders of magnitude and the phase transition occurs on a several picosecond timescale. In gallium arsenide, we observe high-field transport phenomena, including mobility saturation and impact ionization. The carrier density increases by up to ten orders of magnitude at high fields. At the highest fields, we demonstrate THz-induced damage in both vanadium dioxide and gallium arsenide.

Experimental evidence of adiabatic splitting of charged particle beams using stable islands of transverse phase space

Directory of Open Access Journals (Sweden)

S. Gilardoni

2006-10-01

Full Text Available Recently, a novel technique to perform multiturn extraction from a circular particle accelerator was proposed. It is based on beam splitting and trapping, induced by a slow crossing of a nonlinear resonance, inside stable islands of transverse phase space. Experiments at the CERN Proton Synchrotron started in 2002 and evidence of beam splitting was obtained by summer 2004. In this paper, the measurement results achieved with both a low- and a high-intensity, single-bunch proton beam are presented.

Determining the boundary of inclusions with known conductivities using a Levenberg–Marquardt algorithm by electrical resistance tomography

International Nuclear Information System (INIS)

Tan, Chao; Xu, Yaoyuan; Dong, Feng

2011-01-01

Electrical resistance tomography (ERT) is a non-intrusive technique to image the electrical conductivity distribution of a closed vessel by injecting exciting current into the vessel and measuring the boundary voltages induced. ERT image reconstruction is characterized as a severely nonlinear and ill-posed inverse problem with many unknowns. In recent years, a growing number of papers have been published which aim to determine the locations and shapes of inclusions by assuming that their conductivities are piecewise constant and isotropic. In this work, the boundary of inclusions is reconstructed by ERT with a boundary element method. The Jacobian matrix of the forward problem is first calculated with a direct linearization method based on the boundary element, and validated through comparison with that determined by the finite element method and analytical method. A boundary reconstruction algorithm is later presented based on the Levenberg–Marquardt (L-M) method. Several numerical simulations and static experiments were conducted to study the reconstruction quality, where much importance was given to the smoothness of boundaries in the reconstruction; thus, a restriction of the curve radius is introduced to adjust the damping parameter for the L-M algorithm. Analytical results on the stability and precision of the boundary reconstruction demonstrate that stable reconstruction can be achieved when the conductivity of the objects differs much from that of the background medium, and convex boundaries can also be precisely reconstructed. Contrarily, the reconstructions for inclusions with similar conductivities to the background medium are not stable. The situation of an incorrect initial estimation of the inclusions' number is numerically studied and the results show that the boundary of inclusions could be correctly reconstructed with a splitting/merging function under the aforementioned proper operation condition of the present algorithm

Sturm-Liouville BVPs with Caratheodory nonlinearities

Directory of Open Access Journals (Sweden)

Abdelhamid Benmezai

2016-11-01

Full Text Available In this article we study the existence and multiplicity of solutions for several classes of Sturm-Liouville boundary value problems having Caratheodory nonlinearities. Many results existing in the literature for such boundary value problems in the continuous framework will find in this work their extensions to the Caratheodory setting.

Stability and boundary stabilization of 1-D hyperbolic systems

CERN Document Server

Bastin, Georges

2016-01-01

This monograph explores the modeling of conservation and balance laws of one-dimensional hyperbolic systems using partial differential equations. It presents typical examples of hyperbolic systems for a wide range of physical engineering applications, allowing readers to understand the concepts in whichever setting is most familiar to them. With these examples, it also illustrates how control boundary conditions may be defined for the most commonly used control devices. The authors begin with the simple case of systems of two linear conservation laws and then consider the stability of systems under more general boundary conditions that may be differential, nonlinear, or switching. They then extend their discussion to the case of nonlinear conservation laws and demonstrate the use of Lyapunov functions in this type of analysis. Systems of balance laws are considered next, starting with the linear variety before they move on to more general cases of nonlinear ones. They go on to show how the problem of boundary...

First and second order operator splitting methods for the phase field crystal equation

International Nuclear Information System (INIS)

Lee, Hyun Geun; Shin, Jaemin; Lee, June-Yub

2015-01-01

In this paper, we present operator splitting methods for solving the phase field crystal equation which is a model for the microstructural evolution of two-phase systems on atomic length and diffusive time scales. A core idea of the methods is to decompose the original equation into linear and nonlinear subequations, in which the linear subequation has a closed-form solution in the Fourier space. We apply a nonlinear Newton-type iterative method to solve the nonlinear subequation at the implicit time level and thus a considerably large time step can be used. By combining these subequations, we achieve the first- and second-order accuracy in time. We present numerical experiments to show the accuracy and efficiency of the proposed methods

Field-Split Preconditioned Inexact Newton Algorithms

KAUST Repository

Liu, Lulu

2015-06-02

The multiplicative Schwarz preconditioned inexact Newton (MSPIN) algorithm is presented as a complement to additive Schwarz preconditioned inexact Newton (ASPIN). At an algebraic level, ASPIN and MSPIN are variants of the same strategy to improve the convergence of systems with unbalanced nonlinearities; however, they have natural complementarity in practice. MSPIN is naturally based on partitioning of degrees of freedom in a nonlinear PDE system by field type rather than by subdomain, where a modest factor of concurrency can be sacrificed for physically motivated convergence robustness. ASPIN, originally introduced for decompositions into subdomains, is natural for high concurrency and reduction of global synchronization. We consider both types of inexact Newton algorithms in the field-split context, and we augment the classical convergence theory of ASPIN for the multiplicative case. Numerical experiments show that MSPIN can be significantly more robust than Newton methods based on global linearizations, and that MSPIN can be more robust than ASPIN and maintain fast convergence even for challenging problems, such as high Reynolds number Navier--Stokes equations.

Field-Split Preconditioned Inexact Newton Algorithms

KAUST Repository

Liu, Lulu; Keyes, David E.

2015-01-01

The multiplicative Schwarz preconditioned inexact Newton (MSPIN) algorithm is presented as a complement to additive Schwarz preconditioned inexact Newton (ASPIN). At an algebraic level, ASPIN and MSPIN are variants of the same strategy to improve the convergence of systems with unbalanced nonlinearities; however, they have natural complementarity in practice. MSPIN is naturally based on partitioning of degrees of freedom in a nonlinear PDE system by field type rather than by subdomain, where a modest factor of concurrency can be sacrificed for physically motivated convergence robustness. ASPIN, originally introduced for decompositions into subdomains, is natural for high concurrency and reduction of global synchronization. We consider both types of inexact Newton algorithms in the field-split context, and we augment the classical convergence theory of ASPIN for the multiplicative case. Numerical experiments show that MSPIN can be significantly more robust than Newton methods based on global linearizations, and that MSPIN can be more robust than ASPIN and maintain fast convergence even for challenging problems, such as high Reynolds number Navier--Stokes equations.

A general boundary capability embedded in an orthogonal mesh

International Nuclear Information System (INIS)

Hewett, D.W.; Yu-Jiuan Chen

1995-01-01

The authors describe how they hold onto orthogonal mesh discretization when dealing with curved boundaries. Special difference operators were constructed to approximate numerical zones split by the domain boundary; the operators are particularly simple for this rectangular mesh. The authors demonstrated that this simple numerical approach, termed Dynamic Alternating Direction Implicit, turned out to be considerably more efficient than more complex grid-adaptive algorithms that were tried previously

SplitDist—Calculating Split-Distances for Sets of Trees

DEFF Research Database (Denmark)

Mailund, T

2004-01-01

We present a tool for comparing a set of input trees, calculating for each pair of trees the split-distances, i.e., the number of splits in one tree not present in the other.......We present a tool for comparing a set of input trees, calculating for each pair of trees the split-distances, i.e., the number of splits in one tree not present in the other....

Nonlinear hydromagnetic Rayleigh-Taylor instability for strong viscous fluids in porous media

CERN Document Server

El-Dib, Y O

2003-01-01

In the present work a weakly nonlinear stability for magnetic fluid is discussed. The research of an interface between two strong viscous homogeneous incompressible fluids through porous medium is investigated theoretically and graphically. The effect of the vertical magnetic field has been demonstrated in this study. The linear form of equation of motion is solved in the light of the nonlinear boundary conditions. The boundary value problem leads to construct nonlinear characteristic equation having complex coefficients in elevation function. The nonlinearity is kept to third-order expansion. The nonlinear characteristic equation leads to derive the well-known nonlinear Schroedinger equation. This equation having complex coefficients of the disturbance amplitude varies in both space and time. Stability criteria have been performed for nonlinear Chanderasekhar dispersion relation including the porous effects. Stability conditions are discussed through the assumption of equal kinematic viscosity. The calculati...

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.

Dynamics of nonlinear dielectric susceptibility of ferroelectrics near the morphotropic phase boundary

International Nuclear Information System (INIS)

Ibrahim, Abdel-Baset M A; Osman, Junaidah

2013-01-01

The dynamics of the nonlinear (NL) dielectric susceptibility of ferroelectrics (FE) near the morphotropic phase boundary (MPB) is theoretically investigated based on the Landau–Devonshire free energy approach and the concept of FE soft modes. To do so, the NL dielectric susceptibility elements of FE material in the tetragonal phase are expressed as functions of optical phonon modes. These are the E modes with normal characteristic frequency ω E 2 and the A modes with ω A 2 . On the one hand, the tetragonal E modes appear to exhibit a double soft-mode character, i.e. the mode softens either when the thermodynamic temperature T approaches the transition temperature T c or when the free energy parameter β 1 approaches β 2 . On the other hand, the A modes exhibit single soft-mode character when T approaches T c . Within this formulation, the dynamics of first-, second- and third-order NL susceptibility elements are investigated. The origin of the anomalous behavior of certain NL elements at the MPB appears to be a manifestation of FE mode-softening. This approach provides a simple yet powerful technique to understand the dynamics of the NL dielectric susceptibility elements of FE material near the MPB. (paper)

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

Directory of Open Access Journals (Sweden)

Qiuju Tuo

2015-01-01

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

Wave Propagation in Linear and Nonlinear Photonic Band-Gap Materials

National Research Council Canada - National Science Library

Venakides, Stephanos

2003-01-01

.... Development of 3D boundary element code for EM scattering off photonic crystal slabs. Development of 2D FDTD code that includes nonlinearities and use in studying resonant phenomena. Nonlinear Effects...

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

Science.gov (United States)

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

1993-01-01

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

Nonlinear analysis of shear deformable beam-columns partially ...

African Journals Online (AJOL)

In this paper, a boundary element method is developed for the nonlinear analysis of shear deformable beam-columns of arbitrary doubly symmetric simply or multiply connected constant cross section, partially supported on tensionless Winkler foundation, undergoing moderate large deflections under general boundary ...

Theory and design of nonlinear metamaterials

Science.gov (United States)

Rose, Alec Daniel

and oscillators. By applying this set of tools and knowledge to microwave metamaterials, I experimentally confirm several novel nonlinear phenomena. Most notably, I construct a backward wave nonlinear medium from varactor-loaded split ring resonators loaded in a rectangular waveguide, capable of generating second-harmonic opposite to conventional nonlinear materials with a conversion efficiency as high as 1.5%. In addition, I confirm nonlinear magnetoelectric coupling in two dual gap varactor-loaded split ring resonator metamaterials through measurement of the amplitude and phase of the second-harmonic generated in the forward and backward directions from a thin slab. I then use the presence of simultaneous nonlinearities in such metamaterials to observe nonlinear interference, manifest as unidirectional difference frequency generation with contrasts of 6 and 12 dB in the forward and backward directions, respectively. Finally, I apply these principles and intuition to several plasmonic platforms with the goal of achieving similar enhancements and configurations at optical frequencies. Using the example of fluorescence enhancement in optical patch antennas, I develop a semi-classical numerical model for the calculation of field-induced enhancements to both excitation and spontaneous emission rates of an embedded fluorophore, showing qualitative agreement with experimental results, with enhancement factors of more than 30,000. Throughout these series of works, I emphasize the indispensability of effective design and retrieval tools in understanding and optimizing both metamaterials and plasmonic systems. Ultimately, when weighed against the disadvantages in fabrication and optical losses, the results presented here provide a context for the application of nonlinear metamaterials within three distinct areas where a competitive advantage over conventional materials might be obtained: fundamental science demonstrations, linear and nonlinear anisotropy engineering, and

Advances in nonlinear vibration analysis of structures. Part-I. Beams

Indian Academy of Sciences (India)

Unknown

element analysis of nonlinear beams under static and dynamic loads. ... linearization, substitution of inplane boundary conditions at element level rather .... Modelling the nonlinear vibration problems using finite elements, albeit with a couple.

Spatiotemporal electromagnetic soliton and spatial ring formation in nonlinear metamaterials

International Nuclear Information System (INIS)

Zhang Jinggui; Wen Shuangchun; Xiang Yuanjiang; Wang Youwen; Luo Hailu

2010-01-01

We present a systematic investigation of ultrashort electromagnetic pulse propagation in metamaterials (MMs) with simultaneous cubic electric and magnetic nonlinearity. We predict that spatiotemporal electromagnetic solitons may exist in the positive-index region of a MM with focusing nonlinearity and anomalous group velocity dispersion (GVD), as well as in the negative-index region of the MM with defocusing nonlinearity and normal GVD. The experimental circumstances for generating and manipulating spatiotemporal electromagnetic solitons can be created by elaborating appropriate MMs. In addition, we find that, in the negative-index region of a MM, a spatial ring may be formed as the electromagnetic pulse propagates for focusing nonlinearity and anomalous GVD; while the phenomenon of temporal splitting of the electromagnetic pulse may appear for the same case except for the defocusing nonlinearity. Finally, we demonstrate that the nonlinear magnetization makes the sign of effective electric nonlinear effect switchable due to the combined action of electric and magnetic nonlinearity, exerting a significant influence on the propagation of electromagnetic pulses.

Splitting method for the combined formulation of fluid-particle problem

International Nuclear Information System (INIS)

Choi, Hyung Gwon; Yoo, Jung Yul; Joseph, D. D.

2000-01-01

A splitting method for the direct numerical simulation of solid-liquid mixtures is presented, where a symmetric pressure equation is newly proposed. Through numerical experiment, it is found that the newly proposed splitting method works well with a matrix-free formulation for some bench mark problems avoiding an erroneous pressure field which appears when using the conventional pressure equation of a splitting method. When deriving a typical pressure equation of a splitting method, the motion of a solid particle has to be approximated by the 'intermediate velocity' instead of treating it as unknowns since it is necessary as a boundary condition. Therefore, the motion of a solid particle is treated in such an explicit way that a particle moves by the known form drag(pressure drag) that is calculated from the pressure equation in the previous step. From the numerical experiment, it was shown that this method gives an erroneous pressure field even for the very small time step size as a particle velocity increases. In this paper, coupling the unknowns of particle velocities in the pressure equation is proposed, where the resulting matrix is reduced to the symmetric one by applying the projector of the combined formulation. It has been tested over some bench mark problems and gives reasonable pressure fields

A modulation model for mode splitting of magnetic perturbations in the Mega Ampere Spherical Tokamak

International Nuclear Information System (INIS)

Hole, M J; Appel, L C

2009-01-01

Recent observations of magnetic fluctuation activity in the Mega Ampere Spherical Tokamak (MAST) reveal the presence of plasmas with bands of both low and high frequency magnetic fluctuations. Such plasmas exhibit a spectrum of low frequency modes with adjacent toroidal mode numbers, for which the measured frequency is near the Doppler shifted rotation frequency of the plasma. These are thought to be tearing modes. Also present are a spectrum of high frequency modes (e.g. Alfven, fishbone and/or ICE). The frequency and mode number of the tearing mode and its harmonics is identical to the frequency and mode number splitting of the high frequency MHD activity, strongly suggesting that the high frequency splitting is produced by modulation of the high and low frequency modes. We describe a strong modulation model, in which the nonlinear terms are fitted to produce the amplitude envelope profile of the tearing mode. A bispectral analysis proves that the low frequency modes are indeed in phase with the fundamental, while Fourier-SVD mode analysis confirms the mode numbers are toroidal harmonics. Employing this model, the sideband amplitude profile of the high frequency modes is predicted, and found to be in good agreement with experimental observations. Also, toroidal mode number splitting of the high frequency activity matches the mode number of the tearing mode. Weak evidence is found to indicate the Alfvenic sidebands are in phase with the Alfven eigenmode fundamental. The findings support predictions of a strong modulation model, and suggest a need to further develop nonlinear MHD theory to predict the amplitude of coupled sidebands, and so corroborate the observed nonlinear plasma response.

Azimuthal asymmetry in processes of nonlinear QED for linearly polarized photon

International Nuclear Information System (INIS)

Bajer, V.N.; Mil'shtejn, A.I.

1994-01-01

Cross sections of nonlinear QED processes (photon-photon scattering, photon splitting in a Coulomb field, and Delbrueck scattering) are considered for linearly polarized initial photon. The cross sections have sizeable azimuthal asymmetry. 15 refs.; 3 figs

Law of nonlinear flow in saturated clays and radial consolidation

Institute of Scientific and Technical Information of China (English)

无

2007-01-01

It was derived that micro-scale amount level of average pore radius of clay changed from 0.01 to 0.1 micron by an equivalent concept of flow in porous media. There is good agreement between the derived results and test ones. Results of experiments show that flow in micro-scale pore of saturated clays follows law of nonlinear flow. Theoretical analyses demonstrate that an interaction of solid-liquid interfaces varies inversely with permeability or porous radius. The interaction is an important reason why nonlinear flow in saturated clays occurs. An exact mathematical model was presented for nonlinear flow in micro-scale pore of saturated clays. Dimension and physical meanings of parameters of it are definite. A new law of nonlinear flow in saturated clays was established. It can describe characteristics of flow curve of the whole process of the nonlinear flow from low hydraulic gradient to high one. Darcy law is a special case of the new law. A mathematical model was presented for consolidation of nonlinear flow in radius direction in saturated clays with constant rate based on the new law of nonlinear flow. Equations of average mass conservation and moving boundary, and formula of excess pore pressure distribution and average degree of consolidation for nonlinear flow in saturated clay were derived by using an idea of viscous boundary layer, a method of steady state in stead of transient state and a method of integral of an equation. Laws of excess pore pressure distribution and changes of average degree of consolidation with time were obtained. Results show that velocity of moving boundary decreases because of the nonlinear flow in saturated clay. The results can provide geology engineering and geotechnical engineering of saturated clay with new scientific bases. Calculations of average degree of consolidation of the Darcy flow are a special case of that of the nonlinear flow.

External boundary effects on simultaneous diffusion and reaction processes

International Nuclear Information System (INIS)

Le Roux, M.N.; Wilhelmsson, H.

1989-01-01

External boundaries influence the spatial and temporal structure of evolution of dynamic systems governed by reaction-diffusion equations. Critical limits, i.e. thresholds for explosive growth or onset of diffusion dominated decay, are found to be caused by the presence of the boundary and to depend on: the position of the boundary, where the density is assumed to be zero at any instant of time: the mutual weights (coefficients) and powers of the nonlinear reaction and diffusion processes; and the initial spatial distribution. However, for particular relations between the nonlinear powers of the reaction and diffusion terms the critical limits do not depend on the initial conditions. The results are obtained by simulation experiment for one, two and three dimensions. Trends in the dynamic evolution of the system with an external boundary imposed are compared with the corresponding analytic results obtained for free boundary. Interesting applications are found in various areas, e.g. in the field of high temperature fusion plasma where the evolution of the temperature profile for the so-called H-mode (constant plasma density) is described

Device Applications of Nonlinear Dynamics

CERN Document Server

Baglio, Salvatore

2006-01-01

This edited book is devoted specifically to the applications of complex nonlinear dynamic phenomena to real systems and device applications. While in the past decades there has been significant progress in the theory of nonlinear phenomena under an assortment of system boundary conditions and preparations, there exist comparatively few devices that actually take this rich behavior into account. "Device Applications of Nonlinear Dynamics" applies and exploits this knowledge to make devices which operate more efficiently and cheaply, while affording the promise of much better performance. Given the current explosion of ideas in areas as diverse as molecular motors, nonlinear filtering theory, noise-enhanced propagation, stochastic resonance and networked systems, the time is right to integrate the progress of complex systems research into real devices.

EFFECTS OF THE NEUTRINO MASS SPLITTING ON THE NONLINEAR MATTER POWER SPECTRUM

International Nuclear Information System (INIS)

Wagner, Christian; Verde, Licia; Jimenez, Raul

2012-01-01

We have performed cosmological N-body simulations which include the effect of the masses of the individual neutrino species. The simulations were aimed at studying the effect of different neutrino hierarchies on the matter power spectrum. Compared to the linear theory predictions, we find that nonlinearities enhance the effect of hierarchy on the matter power spectrum at mildly nonlinear scales. The maximum difference between the different hierarchies is about 0.5% for a sum of neutrino masses of 0.1 eV. Albeit this is a small effect, it is potentially measurable from upcoming surveys. In combination with neutrinoless double-β decay experiments, this opens up the possibility of using the sky to determine if neutrinos are Majorana or Dirac fermions.

Propagation of Quasi-plane Nonlinear Waves in Tubes

Directory of Open Access Journals (Sweden)

P. Koníček

2002-01-01

Full Text Available This paper deals with possibilities of using the generalized Burgers equation and the KZK equation to describe nonlinear waves in circular ducts. A new method for calculating of diffraction effects taking into account boundary layer effects is described. The results of numerical solutions of the model equations are compared. Finally, the limits of validity of the used model equations are discussed with respect to boundary conditions and the radius of the circular duct. The limits of applicability of the KZK equation and the GBE equation for describing nonlinear waves in tubes are discussed.

Collisions of Two Spatial Solitons in Inhomogeneous Nonlinear Media

International Nuclear Information System (INIS)

Zhong Weiping; Yi Lin; Yang Zhengping; Xie Ruihua; Milivoj, Belic; Chen Goong

2008-01-01

Collisions of spatial solitons occurring in the nonlinear Schroeinger equation with harmonic potential are studied, using conservation laws and the split-step Fourier method. We find an analytical solution for the separation distance between the spatial solitons in an inhomogeneous nonlinear medium when the light beam is self-trapped in the transverse dimension. In the self-focusing nonlinear media the spatial solitons can be transmitted stably, and the interaction between spatial solitons is enhanced due to the linear focusing effect (and also diminished for the linear defocusing effect). In the self-defocusing nonlinear media, in the absence of self-trapping or in the presence of linear self-defocusing, no transmission of stable spatial solitons is possible. However, in such media the linear focusing effect can be exactly compensated, and the spatial solitons can propagate through

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

Science.gov (United States)

Warminski, Jerzy

2018-01-01

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

SEACAS Theory Manuals: Part 1. Problem Formulation in Nonlinear Solid Mechancis

Energy Technology Data Exchange (ETDEWEB)

Attaway, S.W.; Laursen, T.A.; Zadoks, R.I.

1998-08-01

This report gives an introduction to the basic concepts and principles involved in the formulation of nonlinear problems in solid mechanics. By way of motivation, the discussion begins with a survey of some of the important sources of nonlinearity in solid mechanics applications, using wherever possible simple one dimensional idealizations to demonstrate the physical concepts. This discussion is then generalized by presenting generic statements of initial/boundary value problems in solid mechanics, using linear elasticity as a template and encompassing such ideas as strong and weak forms of boundary value problems, boundary and initial conditions, and dynamic and quasistatic idealizations. The notational framework used for the linearized problem is then extended to account for finite deformation of possibly inelastic solids, providing the context for the descriptions of nonlinear continuum mechanics, constitutive modeling, and finite element technology given in three companion reports.

Artificial boundary conditions for certain evolution PDEs with cubic nonlinearity for non-compactly supported initial data

Science.gov (United States)

Vaibhav, V.

2011-04-01

The paper addresses the problem of constructing non-reflecting boundary conditions for two types of one dimensional evolution equations, namely, the cubic nonlinear Schrödinger (NLS) equation, ∂tu+Lu-iχ|u|2u=0 with L≡-i∂x2, and the equation obtained by letting L≡∂x3. The usual restriction of compact support of the initial data is relaxed by allowing it to have a constant amplitude along with a linear phase variation outside a compact domain. We adapt the pseudo-differential approach developed by Antoine et al. (2006) [5] for the NLS equation to the second type of evolution equation, and further, extend the scheme to the aforementioned class of initial data for both of the equations. In addition, we discuss efficient numerical implementation of our scheme and produce the results of several numerical experiments demonstrating its effectiveness.

Initial-boundary value problems associated with the Ablowitz-Ladik system

Science.gov (United States)

Xia, Baoqiang; Fokas, A. S.

2018-02-01

We employ the Ablowitz-Ladik system as an illustrative example in order to demonstrate how to analyze initial-boundary value problems for integrable nonlinear differential-difference equations via the unified transform (Fokas method). In particular, we express the solutions of the integrable discrete nonlinear Schrödinger and integrable discrete modified Korteweg-de Vries equations in terms of the solutions of appropriate matrix Riemann-Hilbert problems. We also discuss in detail, for both the above discrete integrable equations, the associated global relations and the process of eliminating of the unknown boundary values.

Anderson localization of light near boundaries of disordered photonic lattices

International Nuclear Information System (INIS)

Jovic, Dragana M.; Kivshar, Yuri S.; Denz, Cornelia; Belic, Milivoj R.

2011-01-01

We study numerically the effect of boundaries on Anderson localization of light in truncated two-dimensional photonic lattices in a nonlinear medium. We demonstrate suppression of Anderson localization at the edges and corners, so that stronger disorder is needed near the boundaries to obtain the same localization as in the bulk. We find that the level of suppression depends on the location in the lattice (edge vs corner), as well as on the strength of disorder. We also discuss the effect of nonlinearity on various regimes of Anderson localization.

On the vibrations of a simply supported square plate on a weakly nonlinear elastic foundation

NARCIS (Netherlands)

Zarubinskaya, M.A.; Van Horssen, W.T.

2003-01-01

In this paper an initial-boundary value problem for a weakly nonlinear plate equation with a quadratic nonlinearity will be studied. This initial-boundary value problem can be regarded as a simple model describing free oscillations of a simply supported square plate on an elastic foundation. It is

IMPSOR, 3-D Boundary Problems Solution for Thermal Conductivity Calculation

International Nuclear Information System (INIS)

Wilson, D.G.; Williams, M.A.

1994-01-01

1 - Description of program or function: IMPSOR implements finite difference methods for multidimensional moving boundary problems with Dirichlet or Neumann boundary conditions. The geometry of the spatial domain is a rectangular parallelepiped with dimensions specified by the user. Dirichlet or Neumann boundary conditions may be specified on each face of the box independently. The user defines the initial and boundary conditions as well as the thermal and physical properties of the problem and several parameters for the numerical method, e.g. degree of implicitness, time-step size. 2 - Method of solution: The spatial domain is partitioned and the governing equation discretized, which yields a nonlinear system of equations at each time-step. This nonlinear system is solved using a successive over-relaxation (SOR) algorithm. For a given node, the previous iteration's temperature and thermal conductivity values are used for advanced points with current values at previous points. This constitutes a Gauss-Seidel iteration. Most of the computing time used by the numerical method is spent in the iterative solution of the nonlinear system. The SOR scheme employed is designed to accommodate vectorization on a Cray X-MP. 3 - Restrictions on the complexity of the problem: Maximum of 70,000 nodes

Nonlinear Conservation Laws and Finite Volume Methods

Science.gov (United States)

Leveque, Randall J.

Introduction Software Notation Classification of Differential Equations Derivation of Conservation Laws The Euler Equations of Gas Dynamics Dissipative Fluxes Source Terms Radiative Transfer and Isothermal Equations Multi-dimensional Conservation Laws The Shock Tube Problem Mathematical Theory of Hyperbolic Systems Scalar Equations Linear Hyperbolic Systems Nonlinear Systems The Riemann Problem for the Euler Equations Numerical Methods in One Dimension Finite Difference Theory Finite Volume Methods Importance of Conservation Form - Incorrect Shock Speeds Numerical Flux Functions Godunov's Method Approximate Riemann Solvers High-Resolution Methods Other Approaches Boundary Conditions Source Terms and Fractional Steps Unsplit Methods Fractional Step Methods General Formulation of Fractional Step Methods Stiff Source Terms Quasi-stationary Flow and Gravity Multi-dimensional Problems Dimensional Splitting Multi-dimensional Finite Volume Methods Grids and Adaptive Refinement Computational Difficulties Low-Density Flows Discrete Shocks and Viscous Profiles Start-Up Errors Wall Heating Slow-Moving Shocks Grid Orientation Effects Grid-Aligned Shocks Magnetohydrodynamics The MHD Equations One-Dimensional MHD Solving the Riemann Problem Nonstrict Hyperbolicity Stiffness The Divergence of B Riemann Problems in Multi-dimensional MHD Staggered Grids The 8-Wave Riemann Solver Relativistic Hydrodynamics Conservation Laws in Spacetime The Continuity Equation The 4-Momentum of a Particle The Stress-Energy Tensor Finite Volume Methods Multi-dimensional Relativistic Flow Gravitation and General Relativity References

Method of orthogonally splitting imaging pose measurement

Science.gov (United States)

Zhao, Na; Sun, Changku; Wang, Peng; Yang, Qian; Liu, Xintong

2018-01-01

In order to meet the aviation's and machinery manufacturing's pose measurement need of high precision, fast speed and wide measurement range, and to resolve the contradiction between measurement range and resolution of vision sensor, this paper proposes an orthogonally splitting imaging pose measurement method. This paper designs and realizes an orthogonally splitting imaging vision sensor and establishes a pose measurement system. The vision sensor consists of one imaging lens, a beam splitter prism, cylindrical lenses and dual linear CCD. Dual linear CCD respectively acquire one dimensional image coordinate data of the target point, and two data can restore the two dimensional image coordinates of the target point. According to the characteristics of imaging system, this paper establishes the nonlinear distortion model to correct distortion. Based on cross ratio invariability, polynomial equation is established and solved by the least square fitting method. After completing distortion correction, this paper establishes the measurement mathematical model of vision sensor, and determines intrinsic parameters to calibrate. An array of feature points for calibration is built by placing a planar target in any different positions for a few times. An terative optimization method is presented to solve the parameters of model. The experimental results show that the field angle is 52 °, the focus distance is 27.40 mm, image resolution is 5185×5117 pixels, displacement measurement error is less than 0.1mm, and rotation angle measurement error is less than 0.15°. The method of orthogonally splitting imaging pose measurement can satisfy the pose measurement requirement of high precision, fast speed and wide measurement range.

A nonlinear plate control without linearization

Directory of Open Access Journals (Sweden)

Yildirim Kenan

2017-03-01

Full Text Available In this paper, an optimal vibration control problem for a nonlinear plate is considered. In order to obtain the optimal control function, wellposedness and controllability of the nonlinear system is investigated. The performance index functional of the system, to be minimized by minimum level of control, is chosen as the sum of the quadratic 10 functional of the displacement. The velocity of the plate and quadratic functional of the control function is added to the performance index functional as a penalty term. By using a maximum principle, the nonlinear control problem is transformed to solving a system of partial differential equations including state and adjoint variables linked by initial-boundary-terminal conditions. Hence, it is shown that optimal control of the nonlinear systems can be obtained without linearization of the nonlinear term and optimal control function can be obtained analytically for nonlinear systems without linearization.

Strongly nonlinear theory of rapid solidification near absolute stability

Science.gov (United States)

Kowal, Katarzyna N.; Altieri, Anthony L.; Davis, Stephen H.

2017-10-01

We investigate the nonlinear evolution of the morphological deformation of a solid-liquid interface of a binary melt under rapid solidification conditions near two absolute stability limits. The first of these involves the complete stabilization of the system to cellular instabilities as a result of large enough surface energy. We derive nonlinear evolution equations in several limits in this scenario and investigate the effect of interfacial disequilibrium on the nonlinear deformations that arise. In contrast to the morphological stability problem in equilibrium, in which only cellular instabilities appear and only one absolute stability boundary exists, in disequilibrium the system is prone to oscillatory instabilities and a second absolute stability boundary involving attachment kinetics arises. Large enough attachment kinetics stabilize the oscillatory instabilities. We derive a nonlinear evolution equation to describe the nonlinear development of the solid-liquid interface near this oscillatory absolute stability limit. We find that strong asymmetries develop with time. For uniform oscillations, the evolution equation for the interface reduces to the simple form f''+(βf')2+f =0 , where β is the disequilibrium parameter. Lastly, we investigate a distinguished limit near both absolute stability limits in which the system is prone to both cellular and oscillatory instabilities and derive a nonlinear evolution equation that captures the nonlinear deformations in this limit. Common to all these scenarios is the emergence of larger asymmetries in the resulting shapes of the solid-liquid interface with greater departures from equilibrium and larger morphological numbers. The disturbances additionally sharpen near the oscillatory absolute stability boundary, where the interface becomes deep-rooted. The oscillations are time-periodic only for small-enough initial amplitudes and their frequency depends on a single combination of physical parameters, including the

Regional Quasi-Three-Dimensional Unsaturated-Saturated Water Flow Model Based on a Vertical-Horizontal Splitting Concept

Directory of Open Access Journals (Sweden)

Yan Zhu

2016-05-01

Full Text Available Due to the high nonlinearity of the three-dimensional (3-D unsaturated-saturated water flow equation, using a fully 3-D numerical model is computationally expensive for large scale applications. A new unsaturated-saturated water flow model is developed in this paper based on the vertical/horizontal splitting (VHS concept to split the 3-D unsaturated-saturated Richards’ equation into a two-dimensional (2-D horizontal equation and a one-dimensional (1-D vertical equation. The horizontal plane of average head gradient in the triangular prism element is derived to split the 3-D equation into the 2-D equation. The lateral flow in the horizontal plane of average head gradient represented by the 2-D equation is then calculated by the water balance method. The 1-D vertical equation is discretized by the finite difference method. The two equations are solved simultaneously by coupling them into a unified nonlinear system with a single matrix. Three synthetic cases are used to evaluate the developed model code by comparing the modeling results with those of Hydrus1D, SWMS2D and FEFLOW. We further apply the model to regional-scale modeling to simulate groundwater table fluctuations for assessing the model applicability in complex conditions. The proposed modeling method is found to be accurate with respect to measurements.

Nonlinear core deflection in injection molding

Science.gov (United States)

Poungthong, P.; Giacomin, A. J.; Saengow, C.; Kolitawong, C.; Liao, H.-C.; Tseng, S.-C.

2018-05-01

Injection molding of thin slender parts is often complicated by core deflection. This deflection is caused by molten plastics race tracking through the slit between the core and the rigid cavity wall. The pressure of this liquid exerts a lateral force of the slender core causing the core to bend, and this bending is governed by a nonlinear fifth order ordinary differential equation for the deflection that is not directly in the position along the core. Here we subject this differential equation to 6 sets of boundary conditions, corresponding to 6 commercial core constraints. For each such set of boundary conditions, we develop an explicit approximate analytical solution, including both a linear term and a nonlinear term. By comparison with finite difference solutions, we find our new analytical solutions to be accurate. We then use these solutions to derive explicit analytical approximations for maximum deflections and for the core position of these maximum deflections. Our experiments on the base-gated free-tip boundary condition agree closely with our new explicit approximate analytical solution.

Refraction of polarized neutrons on the boundary in thick magnetic film FeAlSi

Energy Technology Data Exchange (ETDEWEB)

Aksenov, V L; Kozhevnikov, S V; Nikitenko, Yu V [Joint Inst. for Nuclear Research, Dubna (Russian Federation). Frank Lab. of Neutron Physics

1999-07-01

Complete text of publication follows. Refraction of polarized neutrons in multilayer structure FeAlSi(20 mkm)/Cr(0.05 mkm)/CaTiO{sub 3}(1000 mkm) has been investigated. An external magnetic field was applied under an angle to the sample surface. Refraction on themagnetic boundaries of two types has been investigated. First type is the boundary vacuum-magnetic film. Second type is magnetic film - non-magnetic substrate CaTiO{sub 3} (thin non-magnetic Cr layer doesn't refract the beam). On the boundary there are spin-flip and beam-splitting. Four spatial splitted beams were observed for different spin transitions on each type of the boundary: '+-', '++', '-+' and '--'. From the experimental values of the glancing angles of refracted beam the following parameters has been derives: the nuclear potentials of the magnetic film and the non-magnetic substrate, the magnitude and the direction of a magnetic induction in the magnetic film. It has been shown that the method of refractometry of polarized neutrons can be used for investigation of thick (about mkm) magnetic films. (author)

Algebraic techniques for diagonalization of a split quaternion matrix in split quaternionic mechanics

International Nuclear Information System (INIS)

Jiang, Tongsong; Jiang, Ziwu; Zhang, Zhaozhong

2015-01-01

In the study of the relation between complexified classical and non-Hermitian quantum mechanics, physicists found that there are links to quaternionic and split quaternionic mechanics, and this leads to the possibility of employing algebraic techniques of split quaternions to tackle some problems in complexified classical and quantum mechanics. This paper, by means of real representation of a split quaternion matrix, studies the problem of diagonalization of a split quaternion matrix and gives algebraic techniques for diagonalization of split quaternion matrices in split quaternionic mechanics

Computation of Nonlinear Backscattering Using a High-Order Numerical Method

Science.gov (United States)

Fibich, G.; Ilan, B.; Tsynkov, S.

2001-01-01

The nonlinear Schrodinger equation (NLS) is the standard model for propagation of intense laser beams in Kerr media. The NLS is derived from the nonlinear Helmholtz equation (NLH) by employing the paraxial approximation and neglecting the backscattered waves. In this study we use a fourth-order finite-difference method supplemented by special two-way artificial boundary conditions (ABCs) to solve the NLH as a boundary value problem. Our numerical methodology allows for a direct comparison of the NLH and NLS models and for an accurate quantitative assessment of the backscattered signal.

A nonsmooth nonlinear conjugate gradient method for interactive contact force problems

DEFF Research Database (Denmark)

Silcowitz, Morten; Abel, Sarah Maria Niebe; Erleben, Kenny

2010-01-01

of a nonlinear complementarity problem (NCP), which can be solved using an iterative splitting method, such as the projected Gauss–Seidel (PGS) method. We present a novel method for solving the NCP problem by applying a Fletcher–Reeves type nonlinear nonsmooth conjugate gradient (NNCG) type method. We analyze...... and present experimental convergence behavior and properties of the new method. Our results show that the NNCG method has at least the same convergence rate as PGS, and in many cases better....

Self-adaptive treatment of time dependent nonlinear nonhomogeneous radial heat flow in reactor components with boundary element method; Samoadaptivno obravnanje spemenljivega nelinearnega nehomogenoga radialnega topltnega toka v reaktorskih komponentah z metodo robnih elementov

Energy Technology Data Exchange (ETDEWEB)

Sarler, B; Alujevic, A [Univerza B. Kardelja, Institut ' Jozef Stefan' , Ljubljana (Yugoslavia)

1988-07-01

The basic principles of self-adaptive algorithm for treatment of transient nonlinear nonhomogeneous radial heat flow, based on direct Boundary Element method formulation, are presented. The indicators of discretization error are developed, together with binary-tree strategy for manipulation with time domain mesh, assuring automatic optimisation of calculation procedure with respect to predetermined error. The developed method is particularly suitable for use in a spectrum of extremely nonlinear cases, occurring in thermal analyses of reactor components.(author)

Use Residual Correction Method and Monotone Iterative Technique to Calculate the Upper and Lower Approximate Solutions of Singularly Perturbed Non-linear Boundary Value Problems

Directory of Open Access Journals (Sweden)

Chi-Chang Wang

2013-09-01

Full Text Available This paper seeks to use the proposed residual correction method in coordination with the monotone iterative technique to obtain upper and lower approximate solutions of singularly perturbed non-linear boundary value problems. First, the monotonicity of a non-linear differential equation is reinforced using the monotone iterative technique, then the cubic-spline method is applied to discretize and convert the differential equation into the mathematical programming problems of an inequation, and finally based on the residual correction concept, complex constraint solution problems are transformed into simpler questions of equational iteration. As verified by the four examples given in this paper, the method proposed hereof can be utilized to fast obtain the upper and lower solutions of questions of this kind, and to easily identify the error range between mean approximate solutions and exact solutions.

A new type of surface acoustic waves in solids due to nonlinear elasticity

International Nuclear Information System (INIS)

Mozhaev, V.G.

1988-12-01

It is shown that in nonlinear elastic semi-infinite medium possessing a property of self focusing of shear waves, besides bulk non-linear shear waves, new surface acoustic waves exist, localization of which near the boundary is entirely due to nonlinear effects. (author). 8 refs

Nonlinear effects of high temperature on buckling of structural elements

International Nuclear Information System (INIS)

Iyengar, N.G.R.

1975-01-01

Structural elements used in nuclear reactors are subjected to high temperatures. Since with increase in temperature there is a gradual fall in the elastic modulus and the stress-strain relationship is nonlinear at these operating load levels, a realistic estimate of the buckling load should include this nonlinearity. In this paper the buckling loads for uniform columns with circular and rectangular cross-sections and different boundary conditions under high temperature environment are estimated. The stress-strain relationship for the material has been assumed to follow inverse Ramberg-Osgood law. In view of the fact that no closed form solutions are possible, approximate methods like perturbation and Galerkin techniques are used. Further, the solution for general value for 'm' is quite involved. Results have been obtained with values for 'm' as 3 and 5. Studies reveal that the influence of material nonlinearity on the buckling load is of the softening type, and it increases with increase in the value of 'm'. The nonlinear effects are more for clamped boundaries than for simply supported boundaries. For the first mode analysis both the methods are powerful. It is, however, felt that for higher modes the Galerkin method might be better in view of its simplicity. This investigation may be considered as a step towards a more general solution

Practical splitting methods for the adaptive integration of nonlinear evolution equations. Part I: Construction of optimized schemes and pairs of schemes

KAUST Repository

Auzinger, Winfried; Hofstä tter, Harald; Ketcheson, David I.; Koch, Othmar

2016-01-01

We present a number of new contributions to the topic of constructing efficient higher-order splitting methods for the numerical integration of evolution equations. Particular schemes are constructed via setup and solution of polynomial systems for the splitting coefficients. To this end we use and modify a recent approach for generating these systems for a large class of splittings. In particular, various types of pairs of schemes intended for use in adaptive integrators are constructed.

Practical splitting methods for the adaptive integration of nonlinear evolution equations. Part I: Construction of optimized schemes and pairs of schemes

KAUST Repository

Auzinger, Winfried

2016-07-28

We present a number of new contributions to the topic of constructing efficient higher-order splitting methods for the numerical integration of evolution equations. Particular schemes are constructed via setup and solution of polynomial systems for the splitting coefficients. To this end we use and modify a recent approach for generating these systems for a large class of splittings. In particular, various types of pairs of schemes intended for use in adaptive integrators are constructed.

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.

ProteinSplit: splitting of multi-domain proteins using prediction of ordered and disordered regions in protein sequences for virtual structural genomics

International Nuclear Information System (INIS)

Wyrwicz, Lucjan S; Koczyk, Grzegorz; Rychlewski, Leszek; Plewczynski, Dariusz

2007-01-01

The annotation of protein folds within newly sequenced genomes is the main target for semi-automated protein structure prediction (virtual structural genomics). A large number of automated methods have been developed recently with very good results in the case of single-domain proteins. Unfortunately, most of these automated methods often fail to properly predict the distant homology between a given multi-domain protein query and structural templates. Therefore a multi-domain protein should be split into domains in order to overcome this limitation. ProteinSplit is designed to identify protein domain boundaries using a novel algorithm that predicts disordered regions in protein sequences. The software utilizes various sequence characteristics to assess the local propensity of a protein to be disordered or ordered in terms of local structure stability. These disordered parts of a protein are likely to create interdomain spacers. Because of its speed and portability, the method was successfully applied to several genome-wide fold annotation experiments. The user can run an automated analysis of sets of proteins or perform semi-automated multiple user projects (saving the results on the server). Additionally the sequences of predicted domains can be sent to the Bioinfo.PL Protein Structure Prediction Meta-Server for further protein three-dimensional structure and function prediction. The program is freely accessible as a web service at http://lucjan.bioinfo.pl/proteinsplit together with detailed benchmark results on the critical assessment of a fully automated structure prediction (CAFASP) set of sequences. The source code of the local version of protein domain boundary prediction is available upon request from the authors

Nonlinear Fourier transforms for the sine-Gordon equation in the quarter plane

Science.gov (United States)

Huang, Lin; Lenells, Jonatan

2018-03-01

Using the Unified Transform, also known as the Fokas method, the solution of the sine-Gordon equation in the quarter plane can be expressed in terms of the solution of a matrix Riemann-Hilbert problem whose definition involves four spectral functions a , b , A , B. The functions a (k) and b (k) are defined via a nonlinear Fourier transform of the initial data, whereas A (k) and B (k) are defined via a nonlinear Fourier transform of the boundary values. In this paper, we provide an extensive study of these nonlinear Fourier transforms and the associated eigenfunctions under weak regularity and decay assumptions on the initial and boundary values. The results can be used to determine the long-time asymptotics of the sine-Gordon quarter-plane solution via nonlinear steepest descent techniques.

NLIE of Dirichlet sine-Gordon model for boundary bound states

International Nuclear Information System (INIS)

Ahn, Changrim; Bajnok, Zoltan; Palla, Laszlo; Ravanini, Francesco

2008-01-01

We investigate boundary bound states of sine-Gordon model on the finite-size strip with Dirichlet boundary conditions. For the purpose we derive the nonlinear integral equation (NLIE) for the boundary excited states from the Bethe ansatz equation of the inhomogeneous XXZ spin 1/2 chain with boundary imaginary roots discovered by Saleur and Skorik. Taking a large volume (IR) limit we calculate boundary energies, boundary reflection factors and boundary Luescher corrections and compare with the excited boundary states of the Dirichlet sine-Gordon model first considered by Dorey and Mattsson. We also consider the short distance limit and relate the IR scattering data with that of the UV conformal field theory

Boundary effects in a quasi-two-dimensional driven granular fluid.

Science.gov (United States)

Smith, N D; Smith, M I

2017-12-01

The effect of a confining boundary on the spatial variations in granular temperature of a driven quasi-two-dimensional layer of particles is investigated experimentally. The radial drop in the relative granular temperature ΔT/T exhibits a maximum at intermediate particle numbers which coincides with a crossover from kinetic to collisional transport of energy. It is also found that at low particle numbers, the distributions of radial velocities are increasingly asymmetric as one approaches the boundary. The radial and tangential granular temperatures split, and in the tails of the radial velocity distribution there is a higher population of fast moving particles traveling away rather than towards the boundary.

Polarization Insensitivity in Double-Split Ring and Triple-Split Ring Terahertz Resonators

International Nuclear Information System (INIS)

Wu Qian-Nan; Lan Feng; Tang Xiao-Pin; Yang Zi-Qiang

2015-01-01

A modified double-split ring resonator and a modified triple-split ring resonator, which offer polarization-insensitive performance, are investigated, designed and fabricated. By displacing the two gaps of the conventional double-split ring resonator away from the center, the second resonant frequency for the 0° polarized wave and the resonant frequency for the 90° polarized wave become increasingly close to each other until they are finally identical. Theoretical and experimental results show that the modified double-split ring resonator and the modified triple-split ring resonator are insensitive to different polarized waves and show strong resonant frequency dips near 433 and 444 GHz, respectively. The results of this work suggest new opportunities for the investigation and design of polarization-dependent terahertz devices based on split ring resonators. (paper)

Heat transfer enhancement in a turbulent natural convection boundary layer along a vertical flat plate

International Nuclear Information System (INIS)

Tsuji, Toshihiro; Kajitani, Tsuyoshi; Nishino, Tatsuhiko

2007-01-01

An experimental study on heat transfer enhancement for a turbulent natural convection boundary layer in air along a vertical flat plate has been performed by inserting a long flat plate in the spanwise direction (simple heat transfer promoter) and short flat plates aligned in the spanwise direction (split heat transfer promoter) with clearances into the near-wall region of the boundary layer. For a simple heat transfer promoter, the heat transfer coefficients increase by a peak value of approximately 37% in the downstream region of the promoter compared with those in the usual turbulent natural convection boundary layer. It is found from flow visualization and simultaneous measurements of the flow and thermal fields with hot- and cold-wires that such increase of heat transfer coefficients is mainly caused by the deflection of flows toward the outer region of the boundary layer and the invasion of low-temperature fluids from the outer region to the near-wall region with large-scale vortex motions riding out the promoter. However, heat transfer coefficients for a split heat transfer promoter exhibit an increase in peak value of approximately 60% in the downstream region of the promoter. Flow visualization and PIV measurements show that such remarkable heat transfer enhancement is attributed to longitudinal vortices generated by flows passing through the clearances of the promoter in addition to large-scale vortex motions riding out the promoter. Consequently, it is concluded that heat transfer enhancement of the turbulent natural convection boundary layer can be substantially achieved in a wide area of the turbulent natural convection boundary layer by employing multiple column split heat transfer promoters. It may be expected that the heat transfer enhancement in excess of approximately 40% can be accomplished by inserting such promoters

Parametrices and exact paralinearization of semi-linear boundary problems

DEFF Research Database (Denmark)

Johnsen, Jon

2008-01-01

The subject is parametrices for semi-linear problems, based on parametrices for linear boundary problems and on non-linearities that decompose into solution-dependent linear operators acting on the solutions. Non-linearities of product type are shown to admit this via exact paralinearization...... of homogeneous distributions, tensor products and halfspace extensions have been revised. Examples include the von Karman equation....

A model of electric breakdown in polycrystalline semiconductors with highly nonlinear I - V characteristics

International Nuclear Information System (INIS)

Yildirim, E.H.; Tanatar, B.; Canessa, E.

1993-07-01

A deterministic algorithm to study the nonlinear current-voltage characteristics of polycrystalline semiconductors, such as ZnO-based metal oxide varistors, under dc bias and at room temperature is developed based on the electrical properties of individual grain boundaries. Assuming a thermionic emission type mechanism between individual grains and a nonuniform distribution of barrier heights at grain boundaries, the set of nonlinear Kirchhoff equations that determines the macroscopic current across the specimen and the nonlinearity coefficient α is solved numerically. The applied voltage dependence of the barrier height is found to be crucial to obtain α values reaching ∼50, indicating high nonlinearity as required by potential commercial applications. (author). 20 refs, 3 figs

A nonlinear free boundary problem with a self-driven Bernoulli condition

OpenAIRE

Dipierro, Serena; Karakhanyan, Aram; Valdinoci, Enrico

2017-01-01

We study a Bernoulli type free boundary problem with two phases J[u]=∫Ω|∇u(x)|2dx+Φ(M−(u),M+(u)),u−u¯∈W1,20(Ω), where u¯∈W1,2(Ω) is a given boundary datum. Here, M1 and M2 are weighted volumes of {u≤0}∩Ω and {u>0}∩Ω, respectively, and Φ is a nonnegative function of two real variables. We show that, for this problem, the Bernoulli constant, which determines the gradient jump condition across the free boundary, is of global type and it is indeed determined by the weighted volumes of the phas...

Bad splits in bilateral sagittal split osteotomy: systematic review of fracture patterns.

Science.gov (United States)

Steenen, S A; Becking, A G

2016-07-01

An unfavourable and unanticipated pattern of the mandibular sagittal split osteotomy is generally referred to as a 'bad split'. Few restorative techniques to manage the situation have been described. In this article, a classification of reported bad split pattern types is proposed and appropriate salvage procedures to manage the different types of undesired fracture are presented. A systematic review was undertaken, yielding a total of 33 studies published between 1971 and 2015. These reported a total of 458 cases of bad splits among 19,527 sagittal ramus osteotomies in 10,271 patients. The total reported incidence of bad split was 2.3% of sagittal splits. The most frequently encountered were buccal plate fractures of the proximal segment (types 1A-F) and lingual fractures of the distal segment (types 2A and 2B). Coronoid fractures (type 3) and condylar neck fractures (type 4) have seldom been reported. The various types of bad split may require different salvage approaches. Copyright © 2016 International Association of Oral and Maxillofacial Surgeons. Published by Elsevier Ltd. All rights reserved.

Constraint-preserving boundary treatment for a harmonic formulation of the Einstein equations

Energy Technology Data Exchange (ETDEWEB)

Seiler, Jennifer; Szilagyi, Bela; Pollney, Denis; Rezzolla, Luciano [Max-Planck-Institut fuer Gravitationsphysik, Albert-Einstein-Institut, Golm (Germany)

2008-09-07

We present a set of well-posed constraint-preserving boundary conditions for a first-order in time, second-order in space, harmonic formulation of the Einstein equations. The boundary conditions are tested using robust stability, linear and nonlinear waves, and are found to be both less reflective and constraint preserving than standard Sommerfeld-type boundary conditions.

Constraint-preserving boundary treatment for a harmonic formulation of the Einstein equations

International Nuclear Information System (INIS)

Seiler, Jennifer; Szilagyi, Bela; Pollney, Denis; Rezzolla, Luciano

2008-01-01

We present a set of well-posed constraint-preserving boundary conditions for a first-order in time, second-order in space, harmonic formulation of the Einstein equations. The boundary conditions are tested using robust stability, linear and nonlinear waves, and are found to be both less reflective and constraint preserving than standard Sommerfeld-type boundary conditions

The influence of beam boundaries and velocity reduction on Pierce instability in laboratory plasmas

International Nuclear Information System (INIS)

Jovanovic, D.

1982-01-01

The influences of the beam-plasma boundary and of weak nonlinearities on the Pierce instability are investigated. It is shown that the finite width of the beam has negligible influence on both the stability of the system and growth rate. In the nonlinear regime the wavelength decreases and enhancement of the wave potential close to the beam inlet boundary is observed. The relationship between this effect and the formation of double layers is discussed. (Auth.)

Finite element solution of quasistationary nonlinear magnetic field

International Nuclear Information System (INIS)

Zlamal, Milos

1982-01-01

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

Nonlinear Displacement Discontinuity Model for Generalized Rayleigh Wave in Contact Interface

Energy Technology Data Exchange (ETDEWEB)

Kim, No Hyu; Yang, Seung Yong [Korea University of Technology and Education, Cheonan (Korea, Republic of)

2007-12-15

Imperfectly jointed interface serves as mechanical waveguide for elastic waves and gives rise to two distinct kinds of guided wave propagating along the interface. Contact acoustic nonlinearity (CAN) is known to plays major role in the generation of these interface waves called generalized Rayleigh waves in non-welded interface. Closed crack is modeled as non-welded interface that has nonlinear discontinuity condition in displacement across its boundary. Mathematical analysis of boundary conditions and wave equation is conducted to investigate the dispersive characteristics of the interface waves. Existence of the generalized Rayleigh wave(interface wave) in nonlinear contact interface is verified in theory where the dispersion equation for the interface wave is formulated and analyzed. It reveals that the interface waves have two distinct modes and that the phase velocity of anti-symmetric wave mode is highly dependent on contact conditions represented by linear and nonlinear dimensionless specific stiffness

Nonlinear Displacement Discontinuity Model for Generalized Rayleigh Wave in Contact Interface

International Nuclear Information System (INIS)

Kim, No Hyu; Yang, Seung Yong

2007-01-01

Imperfectly jointed interface serves as mechanical waveguide for elastic waves and gives rise to two distinct kinds of guided wave propagating along the interface. Contact acoustic nonlinearity (CAN) is known to plays major role in the generation of these interface waves called generalized Rayleigh waves in non-welded interface. Closed crack is modeled as non-welded interface that has nonlinear discontinuity condition in displacement across its boundary. Mathematical analysis of boundary conditions and wave equation is conducted to investigate the dispersive characteristics of the interface waves. Existence of the generalized Rayleigh wave(interface wave) in nonlinear contact interface is verified in theory where the dispersion equation for the interface wave is formulated and analyzed. It reveals that the interface waves have two distinct modes and that the phase velocity of anti-symmetric wave mode is highly dependent on contact conditions represented by linear and nonlinear dimensionless specific stiffness

Nonlinear evolution of tearing and coalescence instability with free boundary conditions

International Nuclear Information System (INIS)

Malara, F.; Veltri, P.; Carbone, V.

1990-01-01

The nonlinear evolution of a reconnection instability in a plane current sheet is described. In particular, the appearance of coalescence instability was studied, which follows the formation of a chain of magnetic islands due to the tearing instability. In order to describe realistically this phonemenon, the time evolution of all the unstable modes which are present in the spectrum at the same time is considered. Moreover, this study allows to investigate the turbulent energy cascade which forms owing to the nonlinear coupling between such modes. (R.P.) 9 refs.; 6 figs

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

76 FR 77008 - Notice of Administrative Boundary Change for Bureau of Land Management Offices in Montana To...

Science.gov (United States)

2011-12-09

... DEPARTMENT OF THE INTERIOR Bureau of Land Management [LLMT930000-12-L18200000-XX0000] Notice of Administrative Boundary Change for Bureau of Land Management Offices in Montana To Eliminate the County Split of... Office The Bureau of Land Management, Butte Field Office administrative boundary now encompasses all of...

On the long run effects of market splitting: Why more price zones might decrease welfare

International Nuclear Information System (INIS)

Grimm, Veronika; Martin, Alexander; Weibelzahl, Martin; Zöttl, Gregor

2016-01-01

In liberalized electricity markets we observe different approaches to congestion management. While nodal pricing is implemented in Canada and some markets in the United States, European markets are split up into a limited number of price zones with uniform prices, in order to at least partially realize the benefits of regional price differentiation. Zonal boundaries often coincide with national borders, but some countries are also split into multiple zones. In this paper we shed light on possible negative welfare effects of market splitting that arise in a model where investment incentives in new generation capacity are taken into account if zones are misspecified. We show that standard approaches to configure price zones – on the basis of projected nodal price differences or congested transmission capacity – may fail to suggest reasonable zone specifications. Also an adjustment of Available Transfer Capacities (ATCs) between zones or a switch to flow-based market splitting does not ensure positive welfare effects. Our analysis suggests that a careful and detailed evaluation of the system is needed to ensure a reasonable zone configuration. - Highlights: •We analyze investment and production in energy only markets with market splitting. •Market splitting can lead to decreased welfare even for reasonably chosen zones. •We identify the reasons for the negative impact of introducing prices zones.

On the Stochastic Wave Equation with Nonlinear Damping

International Nuclear Information System (INIS)

Kim, Jong Uhn

2008-01-01

We discuss an initial boundary value problem for the stochastic wave equation with nonlinear damping. We establish the existence and uniqueness of a solution. Our method for the existence of pathwise solutions consists of regularization of the equation and data, the Galerkin approximation and an elementary measure-theoretic argument. We also prove the existence of an invariant measure when the equation has pure nonlinear damping

Stabilization of the Wave Equation with Boundary Time-Varying Delay

Directory of Open Access Journals (Sweden)

Hao Li

2014-01-01

Full Text Available We study the stabilization of the wave equation with variable coefficients in a bounded domain and a time-varying delay term in the time-varying, weakly nonlinear boundary feedbacks. By the Riemannian geometry methods and a suitable assumption of nonlinearity, we obtain the uniform decay of the energy of the closed loop system.

Nonlinear to Linear Elastic Code Coupling in 2-D Axisymmetric Media.

Energy Technology Data Exchange (ETDEWEB)

Preston, Leiph [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

2017-08-01

Explosions within the earth nonlinearly deform the local media, but at typical seismological observation distances, the seismic waves can be considered linear. Although nonlinear algorithms can simulate explosions in the very near field well, these codes are computationally expensive and inaccurate at propagating these signals to great distances. A linearized wave propagation code, coupled to a nonlinear code, provides an efficient mechanism to both accurately simulate the explosion itself and to propagate these signals to distant receivers. To this end we have coupled Sandia's nonlinear simulation algorithm CTH to a linearized elastic wave propagation code for 2-D axisymmetric media (axiElasti) by passing information from the nonlinear to the linear code via time-varying boundary conditions. In this report, we first develop the 2-D axisymmetric elastic wave equations in cylindrical coordinates. Next we show how we design the time-varying boundary conditions passing information from CTH to axiElasti, and finally we demonstrate the coupling code via a simple study of the elastic radius.

Market Structure and Stock Splits

OpenAIRE

David Michayluk; Paul Kofman

2001-01-01

Enhanced liquidity is one possible motivation for stock splits but empirical research frequently documents declines in liquidity following stock splits. Despite almost thirty years of inquiry, little is known about all the changes in a stock's trading activity following a stock split. We examine how liquidity measures change around more than 2,500 stock splits and find a pervasive decline in most measures. Large stock splits exhibit a more severe liquidity decline than small stock splits, esp...

A nonlinear boundary integral equations method for the solving of quasistatic elastic contact problem with Coulomb friction

Directory of Open Access Journals (Sweden)

Yurii M. Streliaiev

2016-06-01

Full Text Available Three-dimensional quasistatic contact problem of two linearly elastic bodies' interaction with Coulomb friction taken into account is considered. The boundary conditions of the problem have been simplified by the modification of the Coulomb's law of friction. This modification is based on the introducing of a delay in normal contact tractions that bound tangent contact tractions in the Coulomb's law of friction expressions. At this statement the problem is reduced to a sequence of similar systems of nonlinear integral equations describing bodies' interaction at each step of loading. A method for an approximate solution of the integral equations system corresponded to each step of loading is applied. This method consists of system regularization, discretization of regularized system and iterative process application for solving the discretized system. A numerical solution of a contact problem of an elastic sphere with an elastic half-space interaction under increasing and subsequently decreasing normal compressive force has been obtained.

The entropic boundary law in BF theory

Science.gov (United States)

Livine, Etera R.; Terno, Daniel R.

2009-01-01

We compute the entropy of a closed bounded region of space for pure 3d Riemannian gravity formulated as a topological BF theory for the gauge group SU(2) and show its holographic behavior. More precisely, we consider a fixed graph embedded in space and study the flat connection spin network state without and with particle-like topological defects. We regularize and compute exactly the entanglement for a bipartite splitting of the graph and show it scales at leading order with the number of vertices on the boundary (or equivalently with the number of loops crossing the boundary). More generally these results apply to BF theory with any compact gauge group in any space-time dimension.

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.

Development and Breakdown of Goertler Vortices in High Speed Boundary Layers

Science.gov (United States)

Li, Fei; Choudhari, Meelan; Chang, Chau-Lyan; Wu, Minwei; Greene, Ptrick T.

2010-01-01

The nonlinear development of G rtler instability over a concave surface gives rise to a highly distorted stationary flow in the boundary layer that has strong velocity gradients in both spanwise and wall-normal directions. This distorted flow is susceptible to strong, high frequency secondary instability that leads to the onset of transition. For high Mach number flows, the boundary layer is also subject to the second mode instability. The nonlinear development of G rtler vortices and the ensuing growth and breakdown of secondary instability, the G rtler vortex interactions with second mode instabilities as well as oblique second mode interactions are examined in the context of both internal and external hypersonic configurations using nonlinear parabolized stability equations, 2-D eigenvalue analysis and direct numerical simulation. For G rtler vortex development inside the Purdue Mach 6 Ludwieg tube wind tunnel, multiple families of unstable secondary eigenmodes are identified and their linear and nonlinear evolution is examined. The computation of secondary instability is continued past the onset of transition to elucidate the physical mechanisms underlying the laminar breakdown process. Nonlinear breakdown scenarios associated with transition over a Mach 6 compression cone configuration are also explored.

Reflection and Intention: Interpersonal Boundaries in Teaching and Learning

Science.gov (United States)

Schwartz, Harriet L.

2012-01-01

Prior to working on this sourcebook, the author thinks that if asked, she would have responded that the essence of setting boundaries was in the moments "with" students--the moments when she clarifies her availability or make the split-second decision about whether to self-disclose or not. After working with the contributing authors for this book…

The background-quantum split symmetry in two-dimensional σ-models

International Nuclear Information System (INIS)

Blasi, A.; Delduc, F.; Sorella, S.P.

1989-01-01

A generic, non-linear, background-quantum split is translated into a BRS symmetry. The renormalization of the resulting Slavnov-Taylor identity is analyzed in the class of two-dimensional σ-models with Wess-Zumino term which suggests the adoption of a regularization independent method. We discuss the cohomology of the linearized nilpotent operator derived from the Slavnov-Taylor identity. In particular, the cohomology class with zero Faddeev-Popov charge ensures the stability of the action, while the fact that the cohomology class with one unit of Faddeev-Popov charge is empty ensures the absence of anomalies. (orig.)

Differential quadrature method of nonlinear bending of functionally graded beam

Science.gov (United States)

Gangnian, Xu; Liansheng, Ma; Wang, Youzhi; Quan, Yuan; Weijie, You

2018-02-01

Using the third-order shear deflection beam theory (TBT), nonlinear bending of functionally graded (FG) beams composed with various amounts of ceramic and metal is analyzed utilizing the differential quadrature method (DQM). The properties of beam material are supposed to accord with the power law index along to thickness. First, according to the principle of stationary potential energy, the partial differential control formulae of the FG beams subjected to a distributed lateral force are derived. To obtain numerical results of the nonlinear bending, non-dimensional boundary conditions and control formulae are dispersed by applying the DQM. To verify the present solution, several examples are analyzed for nonlinear bending of homogeneous beams with various edges. A minute parametric research is in progress about the effect of the law index, transverse shear deformation, distributed lateral force and boundary conditions.

Magnetohydrodynamic three-dimensional flow of viscoelastic nanofluid in the presence of nonlinear thermal radiation

Energy Technology Data Exchange (ETDEWEB)

Hayat, T. [Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000 (Pakistan); Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589 (Saudi Arabia); Muhammad, Taseer, E-mail: taseer_qau@yahoo.com [Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000 (Pakistan); Alsaedi, A.; Alhuthali, M.S. [Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589 (Saudi Arabia)

2015-07-01

Magnetohydrodynamic (MHD) three-dimensional flow of couple stress nanofluid in the presence of thermophoresis and Brownian motion effects is analyzed. Energy equation subject to nonlinear thermal radiation is taken into account. The flow is generated by a bidirectional stretching surface. Fluid is electrically conducting in the presence of a constant applied magnetic field. The induced magnetic field is neglected for a small magnetic Reynolds number. Mathematical formulation is performed using boundary layer analysis. Newly proposed boundary condition requiring zero nanoparticle mass flux is employed. The governing nonlinear mathematical problems are first converted into dimensionless expressions and then solved for the series solutions of velocities, temperature and nanoparticles concentration. Convergence of the constructed solutions is verified. Effects of emerging parameters on the temperature and nanoparticles concentration are plotted and discussed. Skin friction coefficients and Nusselt number are also computed and analyzed. It is found that the thermal boundary layer thickness is an increasing function of radiative effect. - Highlights: • Three-dimensional boundary layer flow of viscoelastic nanofluid is examined. • Nonlinear thermal radiation is analyzed. • Brownian motion and thermophoresis effects are present. • Recently developed condition requiring zero nanoparticle mass flux is implemented. • Construction of convergent solutions of nonlinear flow is possible.

Finite frequency shear wave splitting tomography: a model space search approach

Science.gov (United States)

Mondal, P.; Long, M. D.

2017-12-01

Observations of seismic anisotropy provide key constraints on past and present mantle deformation. A common method for upper mantle anisotropy is to measure shear wave splitting parameters (delay time and fast direction). However, the interpretation is not straightforward, because splitting measurements represent an integration of structure along the ray path. A tomographic approach that allows for localization of anisotropy is desirable; however, tomographic inversion for anisotropic structure is a daunting task, since 21 parameters are needed to describe general anisotropy. Such a large parameter space does not allow a straightforward application of tomographic inversion. Building on previous work on finite frequency shear wave splitting tomography, this study aims to develop a framework for SKS splitting tomography with a new parameterization of anisotropy and a model space search approach. We reparameterize the full elastic tensor, reducing the number of parameters to three (a measure of strength based on symmetry considerations for olivine, plus the dip and azimuth of the fast symmetry axis). We compute Born-approximation finite frequency sensitivity kernels relating model perturbations to splitting intensity observations. The strong dependence of the sensitivity kernels on the starting anisotropic model, and thus the strong non-linearity of the inverse problem, makes a linearized inversion infeasible. Therefore, we implement a Markov Chain Monte Carlo technique in the inversion procedure. We have performed tests with synthetic data sets to evaluate computational costs and infer the resolving power of our algorithm for synthetic models with multiple anisotropic layers. Our technique can resolve anisotropic parameters on length scales of ˜50 km for realistic station and event configurations for dense broadband experiments. We are proceeding towards applications to real data sets, with an initial focus on the High Lava Plains of Oregon.

Growth and wall-transpiration control of nonlinear unsteady Görtler vortices forced by free-stream vortical disturbances

Science.gov (United States)

Marensi, Elena; Ricco, Pierre

2017-11-01

The generation, nonlinear evolution, and wall-transpiration control of unsteady Görtler vortices in an incompressible boundary layer over a concave plate is studied theoretically and numerically. Görtler rolls are initiated and driven by free-stream vortical perturbations of which only the low-frequency components are considered because they penetrate the most into the boundary layer. The formation and development of the disturbances are governed by the nonlinear unsteady boundary-region equations with the centrifugal force included. These equations are subject to appropriate initial and outer boundary conditions, which account for the influence of the upstream and free-stream forcing in a rigorous and mutually consistent manner. Numerical solutions show that the stabilizing effect on nonlinearity, which also occurs in flat-plate boundary layers, is significantly enhanced in the presence of centrifugal forces. Sufficiently downstream, the nonlinear vortices excited at different free-stream turbulence intensities Tu saturate at the same level, proving that the initial amplitude of the forcing becomes unimportant. At low Tu, the disturbance exhibits a quasi-exponential growth with the growth rate being intensified for more curved plates and for lower frequencies. At higher Tu, in the typical range of turbomachinery applications, the Görtler vortices do not undergo a modal stage as nonlinearity saturates rapidly, and the wall curvature does not affect the boundary-layer response. Good quantitative agreement with data from direct numerical simulations and experiments is obtained. Steady spanwise-uniform and spanwise-modulated zero-mass-flow-rate wall transpiration is shown to attenuate the growth of the Görtler vortices significantly. A novel modified version of the Fukagata-Iwamoto-Kasagi identity, used for the first time to study a transitional flow, reveals which terms in the streamwise momentum balance are mostly affected by the wall transpiration, thus

Novel phenomena in one-dimensional non-linear transport in long quantum wires

International Nuclear Information System (INIS)

Morimoto, T; Hemmi, M; Naito, R; Tsubaki, K; Park, J-S; Aoki, N; Bird, J P; Ochiai, Y

2006-01-01

We have investigated the non-linear transport properties of split-gate quantum wires of various channel lengths. In this report, we present results on a resonant enhancement of the non-linear conductance that is observed near pinch-off under a finite source-drain bias voltage. The resonant phenomenon exhibits a strong dependence on temperature and in-plane magnetic field. We discuss the possible relationship of this phenomenon to the spin-polarized manybody state that has recently been suggested to occur in quasi-one dimensional systems

Periodic oscillations in linear continuous media coupled with nonlinear discrete systems

International Nuclear Information System (INIS)

Lupini, R.

1998-01-01

A general derivation of partial differential equations with boundary conditions in the form of ordinary differential equations is obtained using the principle of stationary action for a Lagrangian function composed of continuous plus discrete parts in interaction across the boundaries of a 1-dimensional medium. This approach leads directly to the theorem of energy conservation. For linear continuous medium, homogeneous Dirichlet condition at one boundary, and nonlinear oscillator at the other boundary, the entire differential problem reduces to a nonlinear differential-difference equation of neutral type and of the second order. The lag parameter is τ = l/c, where c is the phase speed, l the length of the continuum. The Author investigate the problem of the occurrence of periodic solutions of period integer multiple of the lag (super harmonic solutions) in the case of zero inertia of the boundary system. The problem for such oscillations is shown to reduce to systems of ordinary differential equations with matching conditions in a phase space of lower dimensionality: Phase-plane techniques are used to determine solutions of period 4τ, 8τ and 6τ

Parameter spaces for linear and nonlinear whistler-mode waves

International Nuclear Information System (INIS)

Summers, Danny; Tang, Rongxin; Omura, Yoshiharu; Lee, Dong-Hun

2013-01-01

We examine the growth of magnetospheric whistler-mode waves which comprises a linear growth phase followed by a nonlinear growth phase. We construct time-profiles for the wave amplitude that smoothly match at the transition between linear and nonlinear wave growth. This matching procedure can only take place over a limited “matching region” in (N h /N 0 ,A T )-space, where A T is the electron thermal anisotropy, N h is the hot (energetic) electron number density, and N 0 is the cold (background) electron number density. We construct this matching region and determine how the matching wave amplitude varies throughout the region. Further, we specify a boundary in (N h /N 0 ,A T )-space that separates a region where only linear chorus wave growth can occur from the region in which fully nonlinear chorus growth is possible. We expect that this boundary should prove of practical use in performing computationally expensive full-scale particle simulations, and in interpreting experimental wave data

Splitting Method for Solving the Coarse-Mesh Discretized Low-Order Quasi-Diffusion Equations

International Nuclear Information System (INIS)

Hiruta, Hikaru; Anistratov, Dmitriy Y.; Adams, Marvin L.

2005-01-01

In this paper, the development is presented of a splitting method that can efficiently solve coarse-mesh discretized low-order quasi-diffusion (LOQD) equations. The LOQD problem can reproduce exactly the transport scalar flux and current. To solve the LOQD equations efficiently, a splitting method is proposed. The presented method splits the LOQD problem into two parts: (a) the D problem that captures a significant part of the transport solution in the central parts of assemblies and can be reduced to a diffusion-type equation and (b) the Q problem that accounts for the complicated behavior of the transport solution near assembly boundaries. Independent coarse-mesh discretizations are applied: the D problem equations are approximated by means of a finite element method, whereas the Q problem equations are discretized using a finite volume method. Numerical results demonstrate the efficiency of the methodology presented. This methodology can be used to modify existing diffusion codes for full-core calculations (which already solve a version of the D problem) to account for transport effects

Thermodynamic evaluation of the Kalina split-cycle concepts for waste heat recovery applications

DEFF Research Database (Denmark)

Nguyen, Tuong-Van; Knudsen, Thomas; Larsen, Ulrik

2014-01-01

of varying boundary conditions by conducting an exergy analysis. The design parameters of each configuration were determined by performing a multi-variable optimisation. The results indicate that the Kalina split-cycle with reheat presents an exergetic efficiency by 2.8% points higher than a reference Kalina...... and condenser, and indicates a reduction of the exergy destruction by about 23% in the heat recovery system compared to the baseline cycle....

Predicting Loss-of-Control Boundaries Toward a Piloting Aid

Science.gov (United States)

Barlow, Jonathan; Stepanyan, Vahram; Krishnakumar, Kalmanje

2012-01-01

This work presents an approach to predicting loss-of-control with the goal of providing the pilot a decision aid focused on maintaining the pilot's control action within predicted loss-of-control boundaries. The predictive architecture combines quantitative loss-of-control boundaries, a data-based predictive control boundary estimation algorithm and an adaptive prediction method to estimate Markov model parameters in real-time. The data-based loss-of-control boundary estimation algorithm estimates the boundary of a safe set of control inputs that will keep the aircraft within the loss-of-control boundaries for a specified time horizon. The adaptive prediction model generates estimates of the system Markov Parameters, which are used by the data-based loss-of-control boundary estimation algorithm. The combined algorithm is applied to a nonlinear generic transport aircraft to illustrate the features of the architecture.

The Impact of Dam-Reservoir-Foundation Interaction on Nonlinear Response of Concrete Gravity Dams

International Nuclear Information System (INIS)

Amini, Ali Reza; Motamedi, Mohammad Hossein; Ghaemian, Mohsen

2008-01-01

To study the impact of dam-reservoir-foundation interaction on nonlinear response of concrete gravity dams, a two-dimensional finite element model of a concrete gravity dam including the dam body, a part of its foundation and a part of the reservoir was made. In addition, the proper boundary conditions were used in both reservoir and foundation in order to absorb the energy of outgoing waves at the far end boundaries. Using the finite element method and smeared crack approach, some different seismic nonlinear analyses were done and finally, we came to a conclusion that the consideration of dam-reservoir-foundation interaction in nonlinear analysis of concrete dams is of great importance, because from the performance point of view, this interaction significantly improves the nonlinear response of concrete dams

Nonlinear electrorheological instability of two Rivlin-Ericksen elastico-viscous fluids

CERN Document Server

El-Dib, Y O

2003-01-01

The behaviour of surface waves propagating between two Rivlin-Ericksen elastico-viscous fluids is examined. The investigation is made in the presence of a vertical electric field and a relative horizontal constant velocity. The influence of both surface tension and gravity force is taken into account. Due to the inclusion of streaming flow a mathematical simplification is considered. The viscoelastic contribution is demonstrated in the boundary conditions. From this point of view the approximation equations of motion are solved in the absence of viscoelastic effects. The solutions of the linearized equations of motion under nonlinear boundary conditions lead to derivation of a nonlinear equation governing the interfacial displacement and having damping terms with complex coefficients. This equation is accomplished by utilizing the cubic nonlinearity. The use of the Gardner-Morikawa transformation yields a simplified linear dispersion relation so that the periodic solution for the linear form is utilized. The ...

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.

Splitting methods for split feasibility problems with application to Dantzig selectors

International Nuclear Information System (INIS)

He, Hongjin; Xu, Hong-Kun

2017-01-01

The split feasibility problem (SFP), which refers to the task of finding a point that belongs to a given nonempty, closed and convex set, and whose image under a bounded linear operator belongs to another given nonempty, closed and convex set, has promising applicability in modeling a wide range of inverse problems. Motivated by the increasingly data-driven regularization in the areas of signal/image processing and statistical learning, in this paper, we study the regularized split feasibility problem (RSFP), which provides a unified model for treating many real-world problems. By exploiting the split nature of the RSFP, we shall gainfully employ several efficient splitting methods to solve the model under consideration. A remarkable advantage of our methods lies in their easier subproblems in the sense that the resulting subproblems have closed-form representations or can be efficiently solved up to a high precision. As an interesting application, we apply the proposed algorithms for finding Dantzig selectors, in addition to demonstrating the effectiveness of the splitting methods through some computational results on synthetic and real medical data sets. (paper)

A gradient stable scheme for a phase field model for the moving contact line problem

KAUST Repository

Gao, Min; Wang, Xiao-Ping

2012-01-01

[1,2,4]. The nonlinear version of the scheme is semi-implicit in time and is based on a convex splitting of the Cahn-Hilliard free energy (including the boundary energy) together with a projection method for the Navier-Stokes equations. We show, under

Specific Features of Destabilization of the Wave Profile During Reflection of an Intense Acoustic Beam from a Soft Boundary

Science.gov (United States)

Deryabin, M. S.; Kasyanov, D. A.; Kurin, V. V.; Garasyov, M. A.

2016-05-01

We show that a significant energy redistribution occurs in the spectrum of reflected nonlinear waves, when an intense acoustic beam is reflected from an acoustically soft boundary, which manifests itself at short wave distances from a reflecting boundary. This effect leads to the appearance of extrema in the distributions of the amplitude and intensity of the field of the reflected acoustic beam near the reflecting boundary. The results of physical experiments are confirmed by numerical modeling of the process of transformation of nonlinear waves reflected from an acoustically soft boundary. Numerical modeling was performed by means of the Khokhlov—Zabolotskaya—Kuznetsov (KZK) equation.

Nonlinear interaction of Rayleigh--Taylor and shear instabilities

International Nuclear Information System (INIS)

Finn, J.M.

1993-01-01

Results on the nonlinear behavior of the Rayleigh--Taylor instability and consequent development of shear flow by the shear instability [Phys. Fluids B 4, 488 (1992)] are presented. It is found that the shear flow is generated at sufficient amplitude to reduce greatly the convective transport. For high viscosity, the time-asymptotic state consists of an equilibrium with shear flow and vortex flow (with islands, or ''cat's eyes''), or a relaxation oscillation involving an interplay between the shear instability and the Rayleigh--Taylor instability in the presence of shear. For low viscosity, the dominant feature is a high-frequency nonlinear standing wave consisting of convective vortices localized near the top and bottom boundaries. The localization of these vortices is due to the smaller shear near the boundary regions. The convective transport is largest around these convective vortices near the boundary and there is a region of good confinement near the center. The possible relevance of this behavior to the H mode and edge-localized modes (ELM's) in the tokamak edge region is discussed

Coded Splitting Tree Protocols

DEFF Research Database (Denmark)

Sørensen, Jesper Hemming; Stefanovic, Cedomir; Popovski, Petar

2013-01-01

This paper presents a novel approach to multiple access control called coded splitting tree protocol. The approach builds on the known tree splitting protocols, code structure and successive interference cancellation (SIC). Several instances of the tree splitting protocol are initiated, each...... instance is terminated prematurely and subsequently iterated. The combined set of leaves from all the tree instances can then be viewed as a graph code, which is decodable using belief propagation. The main design problem is determining the order of splitting, which enables successful decoding as early...

Bayesian Statistics and Uncertainty Quantification for Safety Boundary Analysis in Complex Systems

Science.gov (United States)

He, Yuning; Davies, Misty Dawn

2014-01-01

The analysis of a safety-critical system often requires detailed knowledge of safe regions and their highdimensional non-linear boundaries. We present a statistical approach to iteratively detect and characterize the boundaries, which are provided as parameterized shape candidates. Using methods from uncertainty quantification and active learning, we incrementally construct a statistical model from only few simulation runs and obtain statistically sound estimates of the shape parameters for safety boundaries.

Hybrid flux splitting schemes for numerical resolution of two-phase flows

Energy Technology Data Exchange (ETDEWEB)

Flaatten, Tore

2003-07-01

This thesis deals with the construction of numerical schemes for approximating. solutions to a hyperbolic two-phase flow model. Numerical schemes for hyperbolic models are commonly divided in two main classes: Flux Vector Splitting (FVS) schemes which are based on scalar computations and Flux Difference Splitting (FDS) schemes which are based on matrix computations. FVS schemes are more efficient than FDS schemes, but FDS schemes are more accurate. The canonical FDS schemes are the approximate Riemann solvers which are based on a local decomposition of the system into its full wave structure. In this thesis the mathematical structure of the model is exploited to construct a class of hybrid FVS/FDS schemes, denoted as Mixture Flux (MF) schemes. This approach is based on a splitting of the system in two components associated with the pressure and volume fraction variables respectively, and builds upon hybrid FVS/FDS schemes previously developed for one-phase flow models. Through analysis and numerical experiments it is demonstrated that the MF approach provides several desirable features, including (1) Improved efficiency compared to standard approximate Riemann solvers, (2) Robustness under stiff conditions, (3) Accuracy on linear and nonlinear phenomena. In particular it is demonstrated that the framework allows for an efficient weakly implicit implementation, focusing on an accurate resolution of slow transients relevant for the petroleum industry. (author)

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.

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

Science.gov (United States)

Pipkins, Daniel Scott

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

Switching of bound vector solitons for the coupled nonlinear Schrödinger equations with nonhomogenously stochastic perturbations

International Nuclear Information System (INIS)

Sun Zhiyuan; Yu Xin; Liu Ying; Gao Yitian

2012-01-01

We investigate the dynamics of the bound vector solitons (BVSs) for the coupled nonlinear Schrödinger equations with the nonhomogenously stochastic perturbations added on their dispersion terms. Soliton switching (besides soliton breakup) can be observed between the two components of the BVSs. Rate of the maximum switched energy (absolute values) within the fixed propagation distance (about 10 periods of the BVSs) enhances in the sense of statistics when the amplitudes of stochastic perturbations increase. Additionally, it is revealed that the BVSs with enhanced coherence are more robust against the perturbations with nonhomogenous stochasticity. Diagram describing the approximate borders of the splitting and non-splitting areas is also given. Our results might be helpful in dynamics of the BVSs with stochastic noises in nonlinear optical fibers or with stochastic quantum fluctuations in Bose-Einstein condensates.

Switching of bound vector solitons for the coupled nonlinear Schrödinger equations with nonhomogenously stochastic perturbations

Science.gov (United States)

Sun, Zhi-Yuan; Gao, Yi-Tian; Yu, Xin; Liu, Ying

2012-12-01

We investigate the dynamics of the bound vector solitons (BVSs) for the coupled nonlinear Schrödinger equations with the nonhomogenously stochastic perturbations added on their dispersion terms. Soliton switching (besides soliton breakup) can be observed between the two components of the BVSs. Rate of the maximum switched energy (absolute values) within the fixed propagation distance (about 10 periods of the BVSs) enhances in the sense of statistics when the amplitudes of stochastic perturbations increase. Additionally, it is revealed that the BVSs with enhanced coherence are more robust against the perturbations with nonhomogenous stochasticity. Diagram describing the approximate borders of the splitting and non-splitting areas is also given. Our results might be helpful in dynamics of the BVSs with stochastic noises in nonlinear optical fibers or with stochastic quantum fluctuations in Bose-Einstein condensates.

Evaluation of Mandibular Anatomy Associated With Bad Splits in Sagittal Split Ramus Osteotomy of Mandible.

Science.gov (United States)

Wang, Tongyue; Han, Jeong Joon; Oh, Hee-Kyun; Park, Hong-Ju; Jung, Seunggon; Park, Yeong-Joon; Kook, Min-Suk

2016-07-01

This study aimed to identify risk factors associated with bad splits during sagittal split ramus osteotomy by using three-dimensional computed tomography. This study included 8 bad splits and 47 normal patients without bad splits. Mandibular anatomic parameters related to osteotomy line were measured. These included anteroposterior width of the ramus at level of lingula, distance between external oblique ridge and lingula, distance between sigmoid notch and inferior border of mandible, mandibular angle, distance between inferior outer surface of mandibular canal and inferior border of mandible under distal root of second molar (MCEM), buccolingual thickness of the ramus at level of lingula, and buccolingual thickness of the area just distal to first molar (BTM1) and second molar (BTM2). The incidence of bad splits in 625 sagittal split osteotomies was 1.28%. Compared with normal group, bad split group exhibited significantly thinner BTM2 and shorter sigmoid notch and inferior border of mandible (P bad splits. These anatomic data may help surgeons to choose the safest surgical techniques and best osteotomy sites.

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.

A MIT-Based Nonlinear Adaptive Set-Membership Filter for the Ellipsoidal Estimation of Mobile Robots' States

Directory of Open Access Journals (Sweden)

Dalei Song

2012-10-01

Full Text Available The adaptive extended set-membership filter (AESMF for nonlinear ellipsoidal estimation suffers a mismatch between real process noise and its set boundaries, which may result in unstable estimation. In this paper, a MIT method-based adaptive set-membership filter, for the optimization of the set boundaries of process noise, is developed and applied to the nonlinear joint estimation of both time-varying states and parameters. As a result of using the proposed MIT-AESMF, the estimation effectiveness and boundary accuracy of traditional AESMF are substantially improved. Simulation results have shown the efficiency and robustness of the proposed method.

The instability of nonlinear surface waves in an electrified liquid jet

International Nuclear Information System (INIS)

Moatimid, Galal M

2009-01-01

We investigate the weakly nonlinear stability of surface waves of a liquid jet. In this work, the liquids are uniformly streaming through two porous media and the gravitational effects are neglected. The system is acted upon by a uniform tangential electric field, that is parallel to the jet axis. The equations of motion are linearly treated and solved in the light of nonlinear boundary conditions. Therefore, the boundary-value problem leads to a nonlinear characteristic second-order differential equation. This characterized equation has a complex nature. The nonlinearity is kept up to the third degree. It is used to judge the behavior of the surface evolution. According to the linear stability theory, we derive the dispersion relation that accounts for the growth waves. The stability criterion is discussed analytically and a stability picture is identified for a chosen sample system. Several special cases are recovered upon appropriate data choices. In order to derive the Ginsburg-Landau equation for the general case, in the nonlinear approach, we used the method of multiple timescales with the aid of the Taylor expansion. This equation describes the competition between nonlinearity and the linear dispersion relation. As a special case for non-porous media where there is no streaming, we obtained the well-known nonlinear Schroedinger equation as it has been derived by others. The stability criteria are expressed theoretically in terms of various parameters of the problem. Stability diagrams are obtained for a set of physical parameters. We found new instability regions in the parameter space. These regions are due to the nonlinear effects.

Spectral theory and nonlinear analysis with applications to spatial ecology

CERN Document Server

Cano-Casanova, S; Mora-Corral , C

2005-01-01

This volume details some of the latest advances in spectral theory and nonlinear analysis through various cutting-edge theories on algebraic multiplicities, global bifurcation theory, non-linear Schrödinger equations, non-linear boundary value problems, large solutions, metasolutions, dynamical systems, and applications to spatial ecology. The main scope of the book is bringing together a series of topics that have evolved separately during the last decades around the common denominator of spectral theory and nonlinear analysis - from the most abstract developments up to the most concrete applications to population dynamics and socio-biology - in an effort to fill the existing gaps between these fields.

Nonlinear Ion Harmonics in the Paul Trap with Added Octopole Field: Theoretical Characterization and New Insight into Nonlinear Resonance Effect.

Science.gov (United States)

Xiong, Caiqiao; Zhou, Xiaoyu; Zhang, Ning; Zhan, Lingpeng; Chen, Yongtai; Nie, Zongxiu

2016-02-01

The nonlinear harmonics within the ion motion are the fingerprint of the nonlinear fields. They are exclusively introduced by these nonlinear fields and are responsible to some specific nonlinear effects such as nonlinear resonance effect. In this article, the ion motion in the quadrupole field with a weak superimposed octopole component, described by the nonlinear Mathieu equation (NME), was studied by using the analytical harmonic balance (HB) method. Good accuracy of the HB method, which was comparable with that of the numerical fourth-order Runge-Kutta (4th RK), was achieved in the entire first stability region, except for the points at the stability boundary (i.e., β = 1) and at the nonlinear resonance condition (i.e., β = 0.5). Using the HB method, the nonlinear 3β harmonic series introduced by the octopole component and the resultant nonlinear resonance effect were characterized. At nonlinear resonance, obvious resonant peaks were observed in the nonlinear 3β series of ion motion, but were not found in the natural harmonics. In addition, both resonant excitation and absorption peaks could be observed, simultaneously. These are two unique features of the nonlinear resonance, distinguishing it from the normal resonance. Finally, an approximation equation was given to describe the corresponding working parameter, q nr , at nonlinear resonance. This equation can help avoid the sensitivity degradation due to the operation of ion traps at the nonlinear resonance condition.

Propagation of Quasi-plane Nonlinear Waves in Tubes

OpenAIRE

P. Koníček; M. Bednařík; M. Červenka

2002-01-01

This paper deals with possibilities of using the generalized Burgers equation and the KZK equation to describe nonlinear waves in circular ducts. A new method for calculating of diffraction effects taking into account boundary layer effects is described. The results of numerical solutions of the model equations are compared. Finally, the limits of validity of the used model equations are discussed with respect to boundary conditions and the radius of the circular duct. The limits of applicabi...

Propagation dynamics of super-Gaussian beams in fractional Schrödinger equation: from linear to nonlinear regimes.

Science.gov (United States)

Zhang, Lifu; Li, Chuxin; Zhong, Haizhe; Xu, Changwen; Lei, Dajun; Li, Ying; Fan, Dianyuan

2016-06-27

We have investigated the propagation dynamics of super-Gaussian optical beams in fractional Schrödinger equation. We have identified the difference between the propagation dynamics of super-Gaussian beams and that of Gaussian beams. We show that, the linear propagation dynamics of the super-Gaussian beams with order m > 1 undergo an initial compression phase before they split into two sub-beams. The sub-beams with saddle shape separate each other and their interval increases linearly with propagation distance. In the nonlinear regime, the super-Gaussian beams evolve to become a single soliton, breathing soliton or soliton pair depending on the order of super-Gaussian beams, nonlinearity, as well as the Lévy index. In two dimensions, the linear evolution of super-Gaussian beams is similar to that for one dimension case, but the initial compression of the input super-Gaussian beams and the diffraction of the splitting beams are much stronger than that for one dimension case. While the nonlinear propagation of the super-Gaussian beams becomes much more unstable compared with that for the case of one dimension. Our results show the nonlinear effects can be tuned by varying the Lévy index in the fractional Schrödinger equation for a fixed input power.

Magnetohydrodynamic boundary layer on a wedge

International Nuclear Information System (INIS)

Rao, B.N.; Mittal, M.L.

1981-01-01

The effects of the Hall and ionslip currents on the gas-dynamic boundary layer are investigated in view of the increasing prospects for using the MHD principle in electric power generation. The currents are included in the analysis using the generalized Ohm's law (Sherman and Sutton, 1964), and the resulting two nonlinear coupled equations are solved using a modification in the method suggested by Nachtsheim and Swigert (1965), Dewey and Gross (1967), and Steinheuer (1968). Solutions are presented for the incompressible laminar boundary-layer equations in the absence and the presence of the load parameter, and for the pressure gradient parameter for flow separation

Non-reciprocity in nonlinear elastodynamics

Science.gov (United States)

Blanchard, Antoine; Sapsis, Themistoklis P.; Vakakis, Alexander F.

2018-01-01

Reciprocity is a fundamental property of linear time-invariant (LTI) acoustic waveguides governed by self-adjoint operators with symmetric Green's functions. The break of reciprocity in LTI elastodynamics is only possible through the break of time reversal symmetry on the micro-level, and this can be achieved by imposing external biases, adding nonlinearities or allowing for time-varying system properties. We present a Volterra-series based asymptotic analysis for studying spatial non-reciprocity in a class of one-dimensional (1D), time-invariant elastic systems with weak stiffness nonlinearities. We show that nonlinearity is neither necessary nor sufficient for breaking reciprocity in this class of systems; rather, it depends on the boundary conditions, the symmetries of the governing linear and nonlinear operators, and the choice of the spatial points where the non-reciprocity criterion is tested. Extension of the analysis to higher dimensions and time-varying systems is straightforward from a mathematical point of view (but not in terms of new non-reciprocal physical phenomena), whereas the connection of non-reciprocity and time irreversibility can be studied as well. Finally, we show that suitably defined non-reciprocity measures enable optimization, and can provide physical understanding of the nonlinear effects in the dynamics, enabling one to establish regimes of "maximum nonlinearity." We highlight the theoretical developments by means of a numerical example.

Effect of grain boundary complexions on the deformation behavior of Ni bicrystal during bending creep.

Science.gov (United States)

Reddy, K Vijay; Pal, Snehanshu

2018-03-07

The dependence of creep deformation behavior of nickel bicrystal specimens on grain boundary (GB) complexion was investigated by performing a simulated bending creep test using molecular dynamics methods. Strain burst phenomena were observed during the low temperature [500 K, i.e., creep process. Atomic strain and dislocation analyses showed that the time of occurrence of strain burst depends on how easily GB migration happens in bicrystal specimens. Specimens with kite monolayer segregation GB complexion were found to be stable at low temperature (500 K), whereas specimens with split-kite GB complexion were stable at a comparatively higher temperature (900 K). In case of further elevated creep temperatures, e.g., 1100 K and 1300 K, split-kite GB complexion becomes unstable and leads to early failure of the specimen at those temperatures. Additionally, it was observed that split-kite bilayer segregation and normal kite GB complexions exhibit localized increases in elastic modulus during bending creep process, occurring at temperatures of 1100 K and 1300 K, respectively, due to the formation of interpenetrating icosahedral clusters. Graphical abstract Representative creep curves during bending creep deformation of various grain boundary complexions at 900 K.

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.

The Langley Stability and Transition Analysis Code (LASTRAC) : LST, Linear and Nonlinear PSE for 2-D, Axisymmetric, and Infinite Swept Wing Boundary Layers

Science.gov (United States)

Chang, Chau-Lyan

2003-01-01

During the past two decades, our understanding of laminar-turbulent transition flow physics has advanced significantly owing to, in a large part, the NASA program support such as the National Aerospace Plane (NASP), High-speed Civil Transport (HSCT), and Advanced Subsonic Technology (AST). Experimental, theoretical, as well as computational efforts on various issues such as receptivity and linear and nonlinear evolution of instability waves take part in broadening our knowledge base for this intricate flow phenomenon. Despite all these advances, transition prediction remains a nontrivial task for engineers due to the lack of a widely available, robust, and efficient prediction tool. The design and development of the LASTRAC code is aimed at providing one such engineering tool that is easy to use and yet capable of dealing with a broad range of transition related issues. LASTRAC was written from scratch based on the state-of-the-art numerical methods for stability analysis and modem software technologies. At low fidelity, it allows users to perform linear stability analysis and N-factor transition correlation for a broad range of flow regimes and configurations by using either the linear stability theory (LST) or linear parabolized stability equations (LPSE) method. At high fidelity, users may use nonlinear PSE to track finite-amplitude disturbances until the skin friction rise. Coupled with the built-in receptivity model that is currently under development, the nonlinear PSE method offers a synergistic approach to predict transition onset for a given disturbance environment based on first principles. This paper describes the governing equations, numerical methods, code development, and case studies for the current release of LASTRAC. Practical applications of LASTRAC are demonstrated for linear stability calculations, N-factor transition correlation, non-linear breakdown simulations, and controls of stationary crossflow instability in supersonic swept wing boundary

The Split-Brain Phenomenon Revisited: A Single Conscious Agent with Split Perception.

Science.gov (United States)

Pinto, Yair; de Haan, Edward H F; Lamme, Victor A F

2017-11-01

The split-brain phenomenon is caused by the surgical severing of the corpus callosum, the main route of communication between the cerebral hemispheres. The classical view of this syndrome asserts that conscious unity is abolished. The left hemisphere consciously experiences and functions independently of the right hemisphere. This view is a cornerstone of current consciousness research. In this review, we first discuss the evidence for the classical view. We then propose an alternative, the 'conscious unity, split perception' model. This model asserts that a split brain produces one conscious agent who experiences two parallel, unintegrated streams of information. In addition to changing our view of the split-brain phenomenon, this new model also poses a serious challenge for current dominant theories of consciousness. Copyright © 2017 Elsevier Ltd. All rights reserved.

Propagation of optical vortex beams and nucleation of vortex-antivortex pairs in disordered nonlinear photonic lattices

International Nuclear Information System (INIS)

Cho, Yeong-Kwon; Kim, Ki-Hong

2014-01-01

The propagation of optical vortex beams through disordered nonlinear photonic lattices is numerically studied. The vortex beams are generated by using a superposition of several Gaussian laser beams arranged in a radially-symmetric manner. The paraxial nonlinear Schroedinger equation describing the longitudinal propagation of the beam array through nonlinear triangular photonic lattices with two-dimensional disorder is solved numerically by using the split-step Fourier method. We find that due to the spatial disorder, the vortex beam is destabilized after propagating a finite distance and new vortex-antivortex pairs are nucleated at the positions of perfect destructive interference. We also find that in the presence of a self-focusing nonlinearity, the vortex-antivortex pair nucleation is suppressed and the vortex beam becomes more stable, while a self-defocusing nonlinearity enhances the vortex-antivortex pair nucleation.

Nonlinear theory of electroelastic and magnetoelastic interactions

CERN Document Server

Dorfmann, Luis

2014-01-01

This book provides a unified theory of nonlinear electro-magnetomechanical interactions of soft materials capable of large elastic deformations. The authors include an overview of the basic principles of the classical theory of electromagnetism from the fundamental notions of point charges and magnetic dipoles through to distributions of charge and current in a non-deformable continuum, time-dependent electromagnetic fields and Maxwell’s equations. They summarize the basic ingredients of continuum mechanics that are required to account for the deformability of material and present nonlinear constitutive frameworks for electroelastic and magnetoelastic interactions in a highly deformable material. The equations contained in the book are used to formulate and solve a variety of representative boundary-value problems for both nonlinear electroelasticity and magnetoelasticity.

Nonlinear Delta-f Particle Simulations of Collective Effects in High-Intensity Bunched Beams

CERN Document Server

Qin, Hong; Hudson, Stuart R; Startsev, Edward

2005-01-01

The collective effects in high-intensity 3D bunched beams are described self-consistently by the nonlinear Vlasov-Maxwell equations.* The nonlinear delta-f method,** a particle simulation method for solving the nonlinear Vlasov-Maxwell equations, is being used to study the collective effects in high-intensity 3D bunched beams. The delta-f method, as a nonlinear perturbative scheme, splits the distribution function into equilibrium and perturbed parts. The perturbed distribution function is represented as a weighted summation over discrete particles, where the particle orbits are advanced by equations of motion in the focusing field and self-consistent fields, and the particle weights are advanced by the coupling between the perturbed fields and the zero-order distribution function. The nonlinear delta-f method exhibits minimal noise and accuracy problems in comparison with standard particle-in-cell simulations. A self-consistent 3D kinetic equilibrium is first established for high intensity bunched beams. The...

Triadic split-merge sampler

Science.gov (United States)

van Rossum, Anne C.; Lin, Hai Xiang; Dubbeldam, Johan; van der Herik, H. Jaap

2018-04-01

In machine vision typical heuristic methods to extract parameterized objects out of raw data points are the Hough transform and RANSAC. Bayesian models carry the promise to optimally extract such parameterized objects given a correct definition of the model and the type of noise at hand. A category of solvers for Bayesian models are Markov chain Monte Carlo methods. Naive implementations of MCMC methods suffer from slow convergence in machine vision due to the complexity of the parameter space. Towards this blocked Gibbs and split-merge samplers have been developed that assign multiple data points to clusters at once. In this paper we introduce a new split-merge sampler, the triadic split-merge sampler, that perform steps between two and three randomly chosen clusters. This has two advantages. First, it reduces the asymmetry between the split and merge steps. Second, it is able to propose a new cluster that is composed out of data points from two different clusters. Both advantages speed up convergence which we demonstrate on a line extraction problem. We show that the triadic split-merge sampler outperforms the conventional split-merge sampler. Although this new MCMC sampler is demonstrated in this machine vision context, its application extend to the very general domain of statistical inference.

Dispersive shock mediated resonant radiations in defocused nonlinear medium

Science.gov (United States)

Bose, Surajit; Chattopadhyay, Rik; Bhadra, Shyamal Kumar

2018-04-01

We report the evolution of resonant radiation (RR) in a self-defocused nonlinear medium with two zero dispersion wavelengths. RR is generated from dispersive shock wave (DSW) front when the pump pulse is in non-solitonic regime close to first zero dispersion wavelength (ZDW). DSW is responsible for pulse splitting resulting in the generation of blue solitons when leading edge of the pump pulse hits the first ZDW. DSW also generates a red shifted dispersive wave (DW) in the presence of higher order dispersion coefficients. Further, DSW through cross-phase modulation with red shifted dispersive wave (DW) excites a localized radiation. The presence of zero nonlinearity point in the system restricts red-shift of RR and enhances the red shifting of DW. It also helps in the formation of DSW at shorter distance and squeezes the solitonic region beyond second zero dispersion point. Predicted results indicate that the spectral evolution depends on the product of Kerr nonlinearity and group velocity dispersion.

Non-linear analytic and coanalytic problems (Lp-theory, Clifford analysis, examples)

International Nuclear Information System (INIS)

Dubinskii, Yu A; Osipenko, A S

2000-01-01

Two kinds of new mathematical model of variational type are put forward: non-linear analytic and coanalytic problems. The formulation of these non-linear boundary-value problems is based on a decomposition of the complete scale of Sobolev spaces into the 'orthogonal' sum of analytic and coanalytic subspaces. A similar decomposition is considered in the framework of Clifford analysis. Explicit examples are presented

On MHD nonlinear stretching flow of Powell–Eyring nanomaterial

Directory of Open Access Journals (Sweden)

Tasawar Hayat

Full Text Available This communication addresses the magnetohydrodynamic (MHD flow of Powell–Eyring nanomaterial bounded by a nonlinear stretching sheet. Novel features regarding thermophoresis and Brownian motion are taken into consideration. Powell–Eyring fluid is electrically conducted subject to non-uniform applied magnetic field. Assumptions of small magnetic Reynolds number and boundary layer approximation are employed in the mathematical development. Zero nanoparticles mass flux condition at the sheet is selected. Adequate transformation yield nonlinear ordinary differential systems. The developed nonlinear systems have been computed through the homotopic approach. Effects of different pertinent parameters on velocity, temperature and concentration fields are studied and analyzed. Further numerical data of skin friction and heat transfer rate is also tabulated and interpreted. Keywords: Powell–Eyring fluid, Magnetohydrodynamics, Nanomaterial, Nonlinear stretching surface

Nonlinear process generating Tollmien-Schlichting waves in a reattached boundary layer; Hakuri saifuchaku nagare ni okeru T-S hado no hisenkei reiki katei

Energy Technology Data Exchange (ETDEWEB)

Asai, M.; Aiba, K. [Tokyo Metropolitan Institute of Technology, Tokyo (Japan)

1995-09-01

Low-frequency Tollmien-Schlichting (T-S) waves may be thought generated as a result of high-frequency disturbance between two proximity frequency modes grown unstably in a separation shear layer causing secondary nonlinear interference to occur. This fact has been verified by a numerical simulation. A non-compression Navier-Stokes equation was used for the fundamental equation, a tertiary windward difference for the convection term, and a secondary central difference for other differential calculus. The Reynolds number was 200, and the disturbance was introduced by applying `v` variation continuously on the wall face. Non-introduction of the disturbance results in a steady flow. Disturbance frequencies of 0.15 and 0.20 were selected as disturbance frequencies from the relationship between the spatial amplification and the frequency dependency. The structure of the excited disturbance agreed with the intrinsic mode. The difference mode due to nonlinear interference grows as the basic mode was amplified. The basic mode decays sharply in the boundary layer after reattachment, while the difference mode decays slowly. Distribution of the difference mode is a distribution of viscous T-S waves, which may be converted into the intrinsic mode. 8 refs., 7 figs.

Potential-splitting approach applied to the Temkin-Poet model for electron scattering off the hydrogen atom and the helium ion

Science.gov (United States)

Yarevsky, E.; Yakovlev, S. L.; Larson, Å; Elander, N.

2015-06-01

The study of scattering processes in few body systems is a difficult problem especially if long range interactions are involved. In order to solve such problems, we develop here a potential-splitting approach for three-body systems. This approach is based on splitting the reaction potential into a finite range core part and a long range tail part. The solution to the Schrödinger equation for the long range tail Hamiltonian is found analytically, and used as an incoming wave in the three body scattering problem. This reformulation of the scattering problem makes it suitable for treatment by the exterior complex scaling technique in the sense that the problem after the complex dilation is reduced to a boundary value problem with zero boundary conditions. We illustrate the method with calculations on the electron scattering off the hydrogen atom and the positive helium ion in the frame of the Temkin-Poet model.

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

Non-linear spectral splitting of Rydberg sodium in external fields

International Nuclear Information System (INIS)

Gao Wei; Yang Hai-Feng; Cheng Hong; Zhang Shan-Shan; Liu Hong-Ping; Liu Dan-Feng

2015-01-01

We have studied highly excited sodium in various electric fields, parallel electric and magnetic fields, with one σ and π photon irradiation, and even in a magnetic field with a complex laser polarization configuration. The σ spectra shows a simple linear Stark effect with the applied electric field, while the π spectra exhibits a strong non-linear dependence on the electric field. The π transitions in parallel fields show a similar behavior to that in a pure electric field but the spectra get more smooth due to the magnetic field. The diamagnetic spectrum with laser polarization angles between 0 and π/2 proves that it can be reproduced by simple linear combination of π and σ components, indicating there is no interference between the π and σ channels. A full quantum calculation considering the quantum defects accounts for all the observations. The quantum defects, especially for the channel np, play an important role in the spectral profile. (paper)

The dimension split element-free Galerkin method for three-dimensional potential problems

Science.gov (United States)

Meng, Z. J.; Cheng, H.; Ma, L. D.; Cheng, Y. M.

2018-02-01

This paper presents the dimension split element-free Galerkin (DSEFG) method for three-dimensional potential problems, and the corresponding formulae are obtained. The main idea of the DSEFG method is that a three-dimensional potential problem can be transformed into a series of two-dimensional problems. For these two-dimensional problems, the improved moving least-squares (IMLS) approximation is applied to construct the shape function, which uses an orthogonal function system with a weight function as the basis functions. The Galerkin weak form is applied to obtain a discretized system equation, and the penalty method is employed to impose the essential boundary condition. The finite difference method is selected in the splitting direction. For the purposes of demonstration, some selected numerical examples are solved using the DSEFG method. The convergence study and error analysis of the DSEFG method are presented. The numerical examples show that the DSEFG method has greater computational precision and computational efficiency than the IEFG method.

Non-linear spin transport in magnetic semiconductor superlattices

International Nuclear Information System (INIS)

Bejar, Manuel; Sanchez, David; Platero, Gloria; MacDonald, A.H.

2004-01-01

The electronic spin dynamics in DC-biased n-doped II-VI semiconductor multiquantum wells doped with magnetic impurities is presented. Under certain range of electronic doping, conventional semiconductor superlattices present self-sustained oscillations. Magnetically doped wells (Mn) present large spin splittings due to the exchange interaction. The interplay between non-linear interwell transport, the electron-electron interaction and the exchange between electrons and the magnetic impurities produces interesting time-dependent features in the spin polarization current tuned by an external magnetic field

Compression, splitting and switching of bright and dark solitons in nonlinear directional coupler

International Nuclear Information System (INIS)

Mandal, Basanti; Chowdhury, A. Roy

2006-01-01

A detailed numerical simulation of the switching, compression and splitting characteristics of various solitary pulses (bright, grey and dark) are carried out by a direct solution of the associated coupled NLS equation. Important physical parameters of the out going pulse such as, intensity distribution, root mean square spatial and temporal width and chirp are calculated. Both the cases of symmetric and asymmetric couplers are considered. The important phenomenon of periodic power transfer from one channel to the other unfolds. The compression varies with the type of pulse launched in the initial channel. It is observed that the chirping of the initial pulse has an optimum value and it vary quite noticeably with the character of the pulse and couplers, symmetric and asymmetric

Nonlinear interactions of counter-travelling waves

International Nuclear Information System (INIS)

Matsuuchi, Kazuo

1980-01-01

Nonlinear interactions between two waves travelling in opposite directions are investigated. When a nonlinear Klein-Gordon equation is adopted as a model equation, it is shown that such a wave system is governed by a simple set of equations for their complex amplitudes. Steady progressive waves governed by this set are investigated for various cases classified according to the signs of the coefficients. It is then found that one wave travelling in one direction appears from a certain point and the other travelling in the opposite direction has a constant amplitude from that point. This phenomenon may be regarded as a sort of reflection in spite of no rigid boundary. (author)

Stabilization of the hypersonic boundary layer by finite-amplitude streaks

Science.gov (United States)

Ren, Jie; Fu, Song; Hanifi, Ardeshir

2016-02-01

Stabilization of two-dimensional disturbances in hypersonic boundary layer flows by finite-amplitude streaks is investigated using nonlinear parabolized stability equations. The boundary-layer flows at Mach numbers 4.5 and 6.0 are studied in which both first and second modes are supported. The streaks considered here are driven either by the so-called optimal perturbations (Klebanoff-type) or the centrifugal instability (Görtler-type). When the streak amplitude is in an appropriate range, i.e., large enough to modulate the laminar boundary layer but low enough to not trigger secondary instability, both first and second modes can effectively be suppressed.

About one counterexample of applying method of splitting in modeling of plating processes

Science.gov (United States)

Solovjev, D. S.; Solovjeva, I. A.; Litovka, Yu V.; Korobova, I. L.

2018-05-01

The paper presents the main factors that affect the uniformity of the thickness distribution of plating on the surface of the product. The experimental search for the optimal values of these factors is expensive and time-consuming. The problem of adequate simulation of coating processes is very relevant. The finite-difference approximation using seven-point and five-point templates in combination with the splitting method is considered as solution methods for the equations of the model. To study the correctness of the solution of equations of the mathematical model by these methods, the experiments were conducted on plating with a flat anode and cathode, which relative position was not changed in the bath. The studies have shown that the solution using the splitting method was up to 1.5 times faster, but it did not give adequate results due to the geometric features of the task under the given boundary conditions.

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........ Finally, we examine the long-time behavior of the global solution. We show that the solution is global and fast if the initial data are small....

An efficient flexible-order model for 3D nonlinear water waves

Science.gov (United States)

Engsig-Karup, A. P.; Bingham, H. B.; Lindberg, O.

2009-04-01

The flexible-order, finite difference based fully nonlinear potential flow model described in [H.B. Bingham, H. Zhang, On the accuracy of finite difference solutions for nonlinear water waves, J. Eng. Math. 58 (2007) 211-228] is extended to three dimensions (3D). In order to obtain an optimal scaling of the solution effort multigrid is employed to precondition a GMRES iterative solution of the discretized Laplace problem. A robust multigrid method based on Gauss-Seidel smoothing is found to require special treatment of the boundary conditions along solid boundaries, and in particular on the sea bottom. A new discretization scheme using one layer of grid points outside the fluid domain is presented and shown to provide convergent solutions over the full physical and discrete parameter space of interest. Linear analysis of the fundamental properties of the scheme with respect to accuracy, robustness and energy conservation are presented together with demonstrations of grid independent iteration count and optimal scaling of the solution effort. Calculations are made for 3D nonlinear wave problems for steep nonlinear waves and a shoaling problem which show good agreement with experimental measurements and other calculations from the literature.

An efficient flexible-order model for 3D nonlinear water waves

International Nuclear Information System (INIS)

Engsig-Karup, A.P.; Bingham, H.B.; Lindberg, O.

2009-01-01

The flexible-order, finite difference based fully nonlinear potential flow model described in [H.B. Bingham, H. Zhang, On the accuracy of finite difference solutions for nonlinear water waves, J. Eng. Math. 58 (2007) 211-228] is extended to three dimensions (3D). In order to obtain an optimal scaling of the solution effort multigrid is employed to precondition a GMRES iterative solution of the discretized Laplace problem. A robust multigrid method based on Gauss-Seidel smoothing is found to require special treatment of the boundary conditions along solid boundaries, and in particular on the sea bottom. A new discretization scheme using one layer of grid points outside the fluid domain is presented and shown to provide convergent solutions over the full physical and discrete parameter space of interest. Linear analysis of the fundamental properties of the scheme with respect to accuracy, robustness and energy conservation are presented together with demonstrations of grid independent iteration count and optimal scaling of the solution effort. Calculations are made for 3D nonlinear wave problems for steep nonlinear waves and a shoaling problem which show good agreement with experimental measurements and other calculations from the literature

Splitting: The Development of a Measure.

Science.gov (United States)

Gerson, Mary-Joan

1984-01-01

Described the development of a scale that measures splitting as a psychological structure. The construct validity of the splitting scale is suggested by the positive relationship between splitting scores and a diagnostic measure of the narcissistic personality disorder, as well as a negative relationship between splitting scores and levels of…

Effect of initial strain and material nonlinearity on the nonlinear static and dynamic response of graphene sheets

Science.gov (United States)

Singh, Sandeep; Patel, B. P.

2018-06-01

Computationally efficient multiscale modelling based on Cauchy-Born rule in conjunction with finite element method is employed to study static and dynamic characteristics of graphene sheets, with/without considering initial strain, involving Green-Lagrange geometric and material nonlinearities. The strain energy density function at continuum level is established by coupling the deformation at continuum level to that at atomic level through Cauchy-Born rule. The atomic interactions between carbon atoms are modelled through Tersoff-Brenner potential. The governing equation of motion obtained using Hamilton's principle is solved through standard Newton-Raphson method for nonlinear static response and Newmark's time integration technique to obtain nonlinear transient response characteristics. Effect of initial strain on the linear free vibration frequencies, nonlinear static and dynamic response characteristics is investigated in detail. The present multiscale modelling based results are found to be in good agreement with those obtained through molecular mechanics simulation. Two different types of boundary constraints generally used in MM simulation are explored in detail and few interesting findings are brought out. The effect of initial strain is found to be greater in linear response when compared to that in nonlinear response.

Nonlinear saturation of the Rayleigh endash Taylor instability

International Nuclear Information System (INIS)

Das, A.; Mahajan, S.; Kaw, P.; Sen, A.; Benkadda, S.; Verga, A.

1997-01-01

A detailed numerical simulation of the nonlinear state of the Rayleigh endash Taylor instability has been carried out. There are three distinct phases of evolution where it is governed by the (i) linear effects, (ii) effects arising from the conventional nonlinear terms and (iii) subtle nonlinear effects arising through the coupling terms. During the third phase of evolution, there is a self-consistent generation of shear flow which saturates the Rayleigh endash Taylor instability even in situations (with periodic boundaries) where, in principle, an infinite amount of gravitational energy can be tapped. The Galerkin approximation is presented to provide an understanding of our numerical findings. Last, there is an attempt to provide a comprehensive understanding of the nonlinear state of the Rayleigh endash Taylor instability by comparing and contrasting this work with earlier studies. copyright 1997 American Institute of Physics

Nonlinear surface waves at ferrite-metamaterial waveguide structure

Science.gov (United States)

Hissi, Nour El Houda; Mokhtari, Bouchra; Eddeqaqi, Noureddine Cherkaoui; Shabat, Mohammed Musa; Atangana, Jacques

2016-09-01

A new ferrite slab made of a metamaterial (MTM), surrounded by a nonlinear cover cladding and a ferrite substrate, was shown to support unusual types of electromagnetic surface waves. We impose the boundary conditions to derive the dispersion relation and others necessary to formulate the proposed structure. We analyse the dispersion properties of the nonlinear surface waves and we calculate the associated propagation index and the film-cover interface nonlinearity. In the calculation, several sets of the permeability of the MTM are considered. Results show that the waves behaviour depends on the values of the permeability of the MTM, the thickness of the waveguide and the film-cover interface nonlinearity. It is also shown that the use of the singular solutions to the electric field equation allows to identify several new properties of surface waves which do not exist in conventional waveguide.

Bad splits in bilateral sagittal split osteotomy: systematic review and meta-analysis of reported risk factors.

Science.gov (United States)

Steenen, S A; van Wijk, A J; Becking, A G

2016-08-01

An unfavourable and unanticipated pattern of the bilateral sagittal split osteotomy (BSSO) is generally referred to as a 'bad split'. Patient factors predictive of a bad split reported in the literature are controversial. Suggested risk factors are reviewed in this article. A systematic review was undertaken, yielding a total of 30 studies published between 1971 and 2015 reporting the incidence of bad split and patient age, and/or surgical technique employed, and/or the presence of third molars. These included 22 retrospective cohort studies, six prospective cohort studies, one matched-pair analysis, and one case series. Spearman's rank correlation showed a statistically significant but weak correlation between increasing average age and increasing occurrence of bad splits in 18 studies (ρ=0.229; Pbad split among the different splitting techniques. A meta-analysis pooling the effect sizes of seven cohort studies showed no significant difference in the incidence of bad split between cohorts of patients with third molars present and concomitantly removed during surgery, and patients in whom third molars were removed at least 6 months preoperatively (odds ratio 1.16, 95% confidence interval 0.73-1.85, Z=0.64, P=0.52). In summary, there is no robust evidence to date to show that any risk factor influences the incidence of bad split. Copyright © 2016 International Association of Oral and Maxillofacial Surgeons. Published by Elsevier Ltd. All rights reserved.

Three-dimensional boundary layer stability and transition

Science.gov (United States)

Malik, M. R.; Li, F.

1992-01-01

Nonparallel and nonlinear stability of a three-dimensional boundary layer, subject to crossflow instability, is investigated using parabolized stability equations (PSEs). Both traveling and stationary disturbances are considered and nonparallel effect on crossflow instability is found to be destabilizing. Our linear PSE results for stationary disturbances agree well with the results from direct solution of Navier-Stokes equations obtained by Spalart (1989). Nonlinear calculations have been carried out for stationary vortices and the computed wall vorticity pattern results in streamwise streaks which resemble remarkably well with the surface oil-flow visualizations in swept-wing experiments. Other features of the stationary vortex development (half-mushroom structure, inflected velocity profiles, vortex doubling, etc.) are also captured in our nonlinear calculations. Nonlinear interaction of the stationary amplitude of the stationary vortex is large as compared to the traveling mode, and the stationary vortex dominates most of the downstream development. When the two modes have the same initial amplitude, the traveling mode dominates the downstream development owing to its higher growth rate, and there is a tendency for the stationary mode to be suppressed. The effect of nonlinear wave development on the skin-friction coefficient is also computed.

On some nonlinear problems arising in the physics of ionized gases

International Nuclear Information System (INIS)

Hilhorst-Goldman, D.

1981-01-01

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

From modular invariants to graphs: the modular splitting method

International Nuclear Information System (INIS)

Isasi, E; Schieber, G

2007-01-01

We start with a given modular invariant M of a two-dimensional su-hat(n) k conformal field theory (CFT) and present a general method for solving the Ocneanu modular splitting equation and then determine, in a step-by-step explicit construction (1) the generalized partition functions corresponding to the introduction of boundary conditions and defect lines; (2) the quantum symmetries of the higher ADE graph G associated with the initial modular invariant M. Note that one does not suppose here that the graph G is already known, since it appears as a by-product of the calculations. We analyse several su-hat(3) k exceptional cases at levels 5 and 9

Shocks, singularities and oscillations in nonlinear optics and fluid mechanics

CERN Document Server

Santo, Daniele; Lannes, David

2017-01-01

The book collects the most relevant results from the INdAM Workshop "Shocks, Singularities and Oscillations in Nonlinear Optics and Fluid Mechanics" held in Rome, September 14-18, 2015. The contributions discuss recent major advances in the study of nonlinear hyperbolic systems, addressing general theoretical issues such as symmetrizability, singularities, low regularity or dispersive perturbations. It also investigates several physical phenomena where such systems are relevant, such as nonlinear optics, shock theory (stability, relaxation) and fluid mechanics (boundary layers, water waves, Euler equations, geophysical flows, etc.). It is a valuable resource for researchers in these fields. .

Positive solutions of boundary value problem for singular positone and semi-positone third-order difference equations

Directory of Open Access Journals (Sweden)

Gai Gongqi

2011-01-01

Full Text Available Abstract This article studies the boundary value problems for the third-order nonlinear singular difference equations Δ 3 u ( i - 2 + λ a ( i f ( i , u ( i = 0 , i ∈ [ 2 , T + 2 ] , satisfying five kinds of different boundary value conditions. This article shows the existence of positive solutions for positone and semi-positone type. The nonlinear term may be singular. Two examples are also given to illustrate the main results. The arguments are based upon fixed point theorems in a cone. MSC [2008]: 34B15; 39A10.

Split Malcev algebras

Indian Academy of Sciences (India)

project of the Spanish Ministerio de Educación y Ciencia MTM2007-60333. References. [1] Calderón A J, On split Lie algebras with symmetric root systems, Proc. Indian. Acad. Sci (Math. Sci.) 118(2008) 351–356. [2] Calderón A J, On split Lie triple systems, Proc. Indian. Acad. Sci (Math. Sci.) 119(2009). 165–177.

Unbounded Perturbations of Nonlinear Second-Order Difference Equations at Resonance

Directory of Open Access Journals (Sweden)

Ma Ruyun

2007-01-01

Full Text Available We study the existence of solutions of nonlinear discrete boundary value problems , , , where is the first eigenvalue of the linear problem , , , satisfies some “asymptotic nonuniform” resonance conditions, and for .

Two-Loop Splitting Amplitudes

International Nuclear Information System (INIS)

Bern, Z.

2004-01-01

Splitting amplitudes govern the behavior of scattering amplitudes at the momenta of external legs become collinear. In this talk we outline the calculation of two-loop splitting amplitudes via the unitarity sewing method. This method retains the simple factorization properties of light-cone gauge, but avoids the need for prescriptions such as the principal value or Mandelstam-Leibbrandt ones. The encountered loop momentum integrals are then evaluated using integration-by-parts and Lorentz invariance identities. We outline a variety of applications for these splitting amplitudes

Two-loop splitting amplitudes

International Nuclear Information System (INIS)

Bern, Z.; Dixon, L.J.; Kosower, D.A.

2004-01-01

Splitting amplitudes govern the behavior of scattering amplitudes at the momenta of external legs become collinear. In this talk we outline the calculation of two-loop splitting amplitudes via the unitarity sewing method. This method retains the simple factorization properties of light-cone gauge, but avoids the need for prescriptions such as the principal value or Mandelstam-Leibbrandt ones. The encountered loop momentum integrals are then evaluated using integration-by-parts and Lorentz invariance identities. We outline a variety of applications for these splitting amplitudes

Positive Solutions for Coupled Nonlinear Fractional Differential Equations

Directory of Open Access Journals (Sweden)

Wenning Liu

2014-01-01

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

Bottom boundary layer forced by finite amplitude long and short surface waves motions

Science.gov (United States)

Elsafty, H.; Lynett, P.

2018-04-01

A multiple-scale perturbation approach is implemented to solve the Navier-Stokes equations while including bottom boundary layer effects under a single wave and under two interacting waves. In this approach, fluid velocities and the pressure field are decomposed into two components: a potential component and a rotational component. In this study, the two components are exist throughout the entire water column and each is scaled with appropriate length and time scales. A one-way coupling between the two components is implemented. The potential component is assumed to be known analytically or numerically a prior, and the rotational component is forced by the potential component. Through order of magnitude analysis, it is found that the leading-order coupling between the two components occurs through the vertical convective acceleration. It is shown that this coupling plays an important role in the bottom boundary layer behavior. Its effect on the results is discussed for different wave-forcing conditions: purely harmonic forcing and impurely harmonic forcing. The approach is then applied to derive the governing equations for the bottom boundary layer developed under two interacting wave motions. Both motions-the shorter and the longer wave-are decomposed into two components, potential and rotational, as it is done in the single wave. Test cases are presented wherein two different wave forcings are simulated: (1) two periodic oscillatory motions and (2) short waves interacting with a solitary wave. The analysis of the two periodic motions indicates that nonlinear effects in the rotational solution may be significant even though nonlinear effects are negligible in the potential forcing. The local differences in the rotational velocity due to the nonlinear vertical convection coupling term are found to be on the order of 30% of the maximum boundary layer velocity for the cases simulated in this paper. This difference is expected to increase with the increase in wave

On a new series of integrable nonlinear evolution equations

International Nuclear Information System (INIS)

Ichikawa, Y.H.; Wadati, Miki; Konno, Kimiaki; Shimizu, Tohru.

1980-10-01

Recent results of our research are surveyed in this report. The derivative nonlinear Schroedinger equation for the circular polarized Alfven wave admits the spiky soliton solutions for the plane wave boundary condition. The nonlinear equation for complex amplitude associated with the carrier wave is shown to be a generalized nonlinear Schroedinger equation, having the ordinary cubic nonlinear term and the derivative of cubic nonlinear term. A generalized scheme of the inverse scattering transformation has confirmed that superposition of the A-K-N-S scheme and the K-N scheme for the component equations valids for the generalized nonlinear Schroedinger equation. Then, two types of new integrable nonlinear evolution equation have been derived from our scheme of the inverse scattering transformation. One is the type of nonlinear Schroedinger equation, while the other is the type of Korteweg-de Vries equation. Brief discussions are presented for physical phenomena, which could be accounted by the second type of the new integrable nonlinear evolution equation. Lastly, the stationary solitary wave solutions have been constructed for the integrable nonlinear evolution equation of the second type. These solutions have peculiar structure that they are singular and discrete. It is a new challenge to construct singular potentials by the inverse scattering transformation. (author)

A nonlinear approach of elastic reflection waveform inversion

KAUST Repository

Guo, Qiang

2016-09-06

Elastic full waveform inversion (EFWI) embodies the original intention of waveform inversion at its inception as it is a better representation of the mostly solid Earth. However, compared with the acoustic P-wave assumption, EFWI for P- and S-wave velocities using multi-component data admitted mixed results. Full waveform inversion (FWI) is a highly nonlinear problem and this nonlinearity only increases under the elastic assumption. Reflection waveform inversion (RWI) can mitigate the nonlinearity by relying on transmissions from reflections focused on inverting low wavenumber components of the model. In our elastic endeavor, we split the P- and S-wave velocities into low wavenumber and perturbation components and propose a nonlinear approach to invert for both of them. The new optimization problem is built on an objective function that depends on both background and perturbation models. We utilize an equivalent stress source based on the model perturbation to generate reflection instead of demigrating from an image, which is applied in conventional RWI. Application on a slice of an ocean-bottom data shows that our method can efficiently update the low wavenumber parts of the model, but more so, obtain perturbations that can be added to the low wavenumbers for a high resolution output.

A nonlinear approach of elastic reflection waveform inversion

KAUST Repository

Guo, Qiang; Alkhalifah, Tariq Ali

2016-01-01

Elastic full waveform inversion (EFWI) embodies the original intention of waveform inversion at its inception as it is a better representation of the mostly solid Earth. However, compared with the acoustic P-wave assumption, EFWI for P- and S-wave velocities using multi-component data admitted mixed results. Full waveform inversion (FWI) is a highly nonlinear problem and this nonlinearity only increases under the elastic assumption. Reflection waveform inversion (RWI) can mitigate the nonlinearity by relying on transmissions from reflections focused on inverting low wavenumber components of the model. In our elastic endeavor, we split the P- and S-wave velocities into low wavenumber and perturbation components and propose a nonlinear approach to invert for both of them. The new optimization problem is built on an objective function that depends on both background and perturbation models. We utilize an equivalent stress source based on the model perturbation to generate reflection instead of demigrating from an image, which is applied in conventional RWI. Application on a slice of an ocean-bottom data shows that our method can efficiently update the low wavenumber parts of the model, but more so, obtain perturbations that can be added to the low wavenumbers for a high resolution output.

Concentric Split Flow Filter

Science.gov (United States)

Stapleton, Thomas J. (Inventor)

2015-01-01

A concentric split flow filter may be configured to remove odor and/or bacteria from pumped air used to collect urine and fecal waste products. For instance, filter may be designed to effectively fill the volume that was previously considered wasted surrounding the transport tube of a waste management system. The concentric split flow filter may be configured to split the air flow, with substantially half of the air flow to be treated traveling through a first bed of filter media and substantially the other half of the air flow to be treated traveling through the second bed of filter media. This split flow design reduces the air velocity by 50%. In this way, the pressure drop of filter may be reduced by as much as a factor of 4 as compare to the conventional design.

Load Sharing Multiobjective Optimization Design of a Split Torque Helicopter Transmission

Directory of Open Access Journals (Sweden)

Chenxi Fu

2015-01-01

Full Text Available Split torque designs can offer significant advantages over the traditional planetary designs for helicopter transmissions. However, it has two unique properties, gap and phase differences, which result in the risk of unequal load sharing. Various methods have been proposed to eliminate the effect of gap and promote load sharing to a certain extent. In this paper, system design parameters will be optimized to change the phase difference, thereby further improving load sharing. A nonlinear dynamic model is established to measure the load sharing with dynamic mesh forces quantitatively. Afterwards, a multiobjective optimization of a reference split torque design is conducted with the promoting of load sharing property, lightweight, and safety considered as the objectives. The load sharing property, which is measured by load sharing coefficient, is evaluated under multiple operating conditions with dynamic analysis method. To solve the multiobjective model with NSGA-II, an improvement is done to overcome the problem of time consuming. Finally, a satisfied optimal solution is picked up as the final design from the Pareto optimal front, which achieves improvements in all the three objectives compared with the reference design.

Non-linear analytic and coanalytic problems ( L_p-theory, Clifford analysis, examples)

Science.gov (United States)

Dubinskii, Yu A.; Osipenko, A. S.

2000-02-01

Two kinds of new mathematical model of variational type are put forward: non-linear analytic and coanalytic problems. The formulation of these non-linear boundary-value problems is based on a decomposition of the complete scale of Sobolev spaces into the "orthogonal" sum of analytic and coanalytic subspaces. A similar decomposition is considered in the framework of Clifford analysis. Explicit examples are presented.

Use of Green's functions in the numerical solution of two-point boundary value problems

Science.gov (United States)

Gallaher, L. J.; Perlin, I. E.

1974-01-01

This study investigates the use of Green's functions in the numerical solution of the two-point boundary value problem. The first part deals with the role of the Green's function in solving both linear and nonlinear second order ordinary differential equations with boundary conditions and systems of such equations. The second part describes procedures for numerical construction of Green's functions and considers briefly the conditions for their existence. Finally, there is a description of some numerical experiments using nonlinear problems for which the known existence, uniqueness or convergence theorems do not apply. Examples here include some problems in finding rendezvous orbits of the restricted three body system.

An Operator-Integration-Factor Splitting (OIFS) method for Incompressible Flows in Moving Domains

Energy Technology Data Exchange (ETDEWEB)

Patel, Saumil S. [Argonne National Lab. (ANL), Argonne, IL (United States); Fischer, Paul F. [Argonne National Lab. (ANL), Argonne, IL (United States); Univ. of Illinois, Urbana-Champaign, IL (United States); Min, Misun [Argonne National Lab. (ANL), Argonne, IL (United States); Tomboulides, Ananias G [Argonne National Lab. (ANL), Argonne, IL (United States); Aristotle Univ., Thessaloniki (Greece)

2017-10-21

In this paper, we present a characteristic-based numerical procedure for simulating incompressible flows in domains with moving boundaries. Our approach utilizes an operator-integration-factor splitting technique to help produce an effcient and stable numerical scheme. Using the spectral element method and an arbitrary Lagrangian-Eulerian formulation, we investigate flows where the convective acceleration effects are non-negligible. Several examples, ranging from laminar to turbulent flows, are considered. Comparisons with a standard, semi-implicit time-stepping procedure illustrate the improved performance of the scheme.

Numerical reconstruction of wave field spatial distributions at the output and input planes of nonlinear medium with use of digital holography

International Nuclear Information System (INIS)

Nalegaev, S S; Petrov, N V; Bespalov, V G

2014-01-01

A numerical reconstruction of spatial distributions of optical radiation propagating through a volume of nonlinear medium at input and output planes of the medium was demonstrated using a scheme of digital holography. A nonlinear Schrodinger equation with Fourier Split-Step method was used as a tool to propagate wavefront in the volume of the medium. Time dependence of the refractive index change was not taken into account.

A nonlinear dynamics for the scalar field in Randers spacetime

Energy Technology Data Exchange (ETDEWEB)

Silva, J.E.G. [Universidade Federal do Cariri (UFCA), Instituto de formação de professores, Rua Olegário Emídio de Araújo, Brejo Santo, CE, 63.260.000 (Brazil); Maluf, R.V. [Universidade Federal do Ceará (UFC), Departamento de Física, Campus do Pici, Fortaleza, CE, C.P. 6030, 60455-760 (Brazil); Almeida, C.A.S., E-mail: carlos@fisica.ufc.br [Universidade Federal do Ceará (UFC), Departamento de Física, Campus do Pici, Fortaleza, CE, C.P. 6030, 60455-760 (Brazil)

2017-03-10

We investigate the properties of a real scalar field in the Finslerian Randers spacetime, where the local Lorentz violation is driven by a geometrical background vector. We propose a dynamics for the scalar field by a minimal coupling of the scalar field and the Finsler metric. The coupling is intrinsically defined on the Randers spacetime, and it leads to a non-canonical kinetic term for the scalar field. The nonlinear dynamics can be split into a linear and nonlinear regimes, which depend perturbatively on the even and odd powers of the Lorentz-violating parameter, respectively. We analyze the plane-waves solutions and the modified dispersion relations, and it turns out that the spectrum is free of tachyons up to second-order.

Nonlinear saturation of the Rayleigh Taylor instability

International Nuclear Information System (INIS)

Das, A.; Mahajan, S.; Kaw, P.; Sen, A.; Benkadda, S.; Verga, A.

1997-01-01

The problem of the nonlinear saturation of the 2 dimensional Rayleigh Taylor instability is re-examined to put various earlier results in a proper perspective. The existence of a variety of final states can be attributed to the differences in the choice of boundary conditions and initial conditions in earlier numerical modeling studies. Our own numerical simulations indicate that the RT instability saturates by the self consistent generation of shear flow even in situations (with periodic boundaries) where, in principle, an infinite amount of gravitational energy can be tapped. Such final states can be achieved for suitable values of the Prandtl number. (author)

Quantum osp-invariant non-linear Schroedinger equation

International Nuclear Information System (INIS)

Kulish, P.P.

1985-04-01

The generalizations of the non-linear Schroedinger equation (NS) associated with the orthosymplectic superalgebras are formulated. The simplest osp(1/2)-NS model is solved by the quantum inverse scattering method on a finite interval under periodic boundary conditions as well as on the wholeline in the case of a finite number of excitations. (author)

Experimental implementation of a nonlinear beamsplitter based on a phase-sensitive parametric amplifier

Energy Technology Data Exchange (ETDEWEB)

Fang, Yami; Feng, Jingliang; Cao, Leiming; Wang, Yaxian; Jing, Jietai, E-mail: jtjing@phy.ecnu.edu.cn [State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062 (China)

2016-03-28

Beamsplitters have played an important role in quantum optics experiments. They are often used to split and combine two beams, especially in the construct of an interferometer. In this letter, we experimentally implement a nonlinear beamsplitter using a phase-sensitive parametric amplifier, which is based on four-wave mixing in hot rubidium vapor. Here we show that, despite the different frequencies of the two input beams, the output ports of the nonlinear beamsplitter exhibit interference phenomena. We make measurements of the interference fringe visibility and study how various parameters, such as the intensity gain of the amplifier, the intensity ratio of the two input beams, and the one and two photon detunings, affect the behavior of the nonlinear beamsplitter. It may find potential applications in quantum metrology and quantum information processing.

DNS of Laminar-Turbulent Transition in Swept-Wing Boundary Layers

Science.gov (United States)

Duan, L.; Choudhari, M.; Li, F.

2014-01-01

Direct numerical simulation (DNS) is performed to examine laminar to turbulent transition due to high-frequency secondary instability of stationary crossflow vortices in a subsonic swept-wing boundary layer for a realistic natural-laminar-flow airfoil configuration. The secondary instability is introduced via inflow forcing and the mode selected for forcing corresponds to the most amplified secondary instability mode that, in this case, derives a majority of its growth from energy production mechanisms associated with the wall-normal shear of the stationary basic state. An inlet boundary condition is carefully designed to allow for accurate injection of instability wave modes and minimize acoustic reflections at numerical boundaries. Nonlinear parabolized stability equation (PSE) predictions compare well with the DNS in terms of modal amplitudes and modal shape during the strongly nonlinear phase of the secondary instability mode. During the transition process, the skin friction coefficient rises rather rapidly and the wall-shear distribution shows a sawtooth pattern that is analogous to the previously documented surface flow visualizations of transition due to stationary crossflow instability. Fully turbulent features are observed in the downstream region of the flow.

A split operator method for transient problems

International Nuclear Information System (INIS)

Belytschko, T.B.

1983-01-01

Numerous techniques have been developed for improving the computational efficiency of transient analysis: mesh partitioning, subcycling procedures and operator splitting methods. In mesh partitioning methods, the model is divided into subdomains which are integrated by different time integrators, typically implicit and explicit. Any stiff portions of the model are integrated by the implicit operator so that the size of the time step can be increased. In subcycling procedures, the stiff portions are integrated by smaller time steps, yielding similar benefits. However, in models for which the governing partial differential equations are basically of a parabolic character, explicit methods can become quite expensive for refined models because the size of the stable time step decreases with the square of the minimum element dimension. Thus explicit methods, whether employed alone or with partitioning or subcycling, have inherent limitations in these problems. A new procedure is here described for the element-by-element semi-implicit method of Hughes and coworkers which requires the solution of only small systems of equations. This procedure is described for a family of uniform gradient or strain elements which are widely used in nonlinear transient analysis. The diffusion equation and the equations of motion for both shells and continua have been treated, but only the former is considered herein. Results are presented for several examples which show the potential of this method for improving the efficiency of a large-scale linear and nonlinear computations. (orig./RW)

Boundary terms in the Nambu-Goto string action

Science.gov (United States)

Hadasz, Leszek; Wȩgrzyn, Paweł

1995-03-01

We investigate classical strings defined by the Nambu-Goto action with the boundary term added. We demonstrate that the latter term has a significant bearing on the string dynamics. It is confirmed that new action terms that depend on higher order derivatives of string coordinates cannot be considered as continuous perturbations from the starting string functional. In the case when the boundary term reduces to the Gauss-Bonnet term, a stability analysis is performed on the rotating rigid string solution. We determine the most generic solution that the fluctuations grow to. Longitudinal string excitations are found. The Regge trajectories are nonlinear.

Boundary terms in the Nambu-Goto string action

International Nuclear Information System (INIS)

Hadasz, L.; Wegrzyn, P.

1995-01-01

We investigate classical strings defined by the Nambu-Goto action with the boundary term added. We demonstrate that the latter term has a significant bearing on the string dynamics. It is confirmed that new action terms that depend on higher order derivatives of string coordinates cannot be considered as continuous perturbations from the starting string functional. In the case when the boundary term reduces to the Gauss-Bonnet term, a stability analysis is performed on the rotating rigid string solution. We determine the most generic solution that the fluctuations grow to. Longitudinal string excitations are found. The Regge trajectories are nonlinear

Imperfection Sensitivity of Nonlinear Vibration of Curved Single-Walled Carbon Nanotubes Based on Nonlocal Timoshenko Beam Theory

Directory of Open Access Journals (Sweden)

Iman Eshraghi

2016-09-01

Full Text Available Imperfection sensitivity of large amplitude vibration of curved single-walled carbon nanotubes (SWCNTs is considered in this study. The SWCNT is modeled as a Timoshenko nano-beam and its curved shape is included as an initial geometric imperfection term in the displacement field. Geometric nonlinearities of von Kármán type and nonlocal elasticity theory of Eringen are employed to derive governing equations of motion. Spatial discretization of governing equations and associated boundary conditions is performed using differential quadrature (DQ method and the corresponding nonlinear eigenvalue problem is iteratively solved. Effects of amplitude and location of the geometric imperfection, and the nonlocal small-scale parameter on the nonlinear frequency for various boundary conditions are investigated. The results show that the geometric imperfection and non-locality play a significant role in the nonlinear vibration characteristics of curved SWCNTs.

On the Approximate Controllability of Some Semilinear Parabolic Boundary-Value Problems

International Nuclear Information System (INIS)

Diaz, J. I.; Henry, J.; Ramos, A. M.

1998-01-01

We prove the approximate controllability of several nonlinear parabolic boundary-value problems by means of two different methods: the first one can be called a Cancellation method and the second one uses the Kakutani fixed-point theorem

Modified Differential Transform Method for Two Singular Boundary Values Problems

Directory of Open Access Journals (Sweden)

Yinwei Lin

2014-01-01

Full Text Available This paper deals with the two singular boundary values problems of second order. Two singular points are both boundary values points of the differential equation. The numerical solutions are developed by modified differential transform method (DTM for expanded point. Linear and nonlinear models are solved by this method to get more reliable and efficient numerical results. It can also solve ordinary differential equations where the traditional one fails. Besides, we give the convergence of this new method.

Split-illumination electron holography

Energy Technology Data Exchange (ETDEWEB)

Tanigaki, Toshiaki; Aizawa, Shinji; Suzuki, Takahiro; Park, Hyun Soon [Advanced Science Institute, RIKEN, Hirosawa 2-1, Wako, Saitama 351-0198 (Japan); Inada, Yoshikatsu [Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, Katahira 2-1-1, Sendai 980-8577 (Japan); Matsuda, Tsuyoshi [Japan Science and Technology Agency, Kawaguchi, Saitama 332-0012 (Japan); Taniyama, Akira [Corporate Research and Development Laboratories, Sumitomo Metal Industries, Ltd., Amagasaki, Hyogo 660-0891 (Japan); Shindo, Daisuke [Advanced Science Institute, RIKEN, Hirosawa 2-1, Wako, Saitama 351-0198 (Japan); Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, Katahira 2-1-1, Sendai 980-8577 (Japan); Tonomura, Akira [Advanced Science Institute, RIKEN, Hirosawa 2-1, Wako, Saitama 351-0198 (Japan); Okinawa Institute of Science and Technology, Graduate University, Onna-son, Okinawa 904-0495 (Japan); Central Research Laboratory, Hitachi, Ltd., Hatoyama, Saitama 350-0395 (Japan)

2012-07-23

We developed a split-illumination electron holography that uses an electron biprism in the illuminating system and two biprisms (applicable to one biprism) in the imaging system, enabling holographic interference micrographs of regions far from the sample edge to be obtained. Using a condenser biprism, we split an electron wave into two coherent electron waves: one wave is to illuminate an observation area far from the sample edge in the sample plane and the other wave to pass through a vacuum space outside the sample. The split-illumination holography has the potential to greatly expand the breadth of applications of electron holography.

Split-illumination electron holography

International Nuclear Information System (INIS)

Tanigaki, Toshiaki; Aizawa, Shinji; Suzuki, Takahiro; Park, Hyun Soon; Inada, Yoshikatsu; Matsuda, Tsuyoshi; Taniyama, Akira; Shindo, Daisuke; Tonomura, Akira

2012-01-01

We developed a split-illumination electron holography that uses an electron biprism in the illuminating system and two biprisms (applicable to one biprism) in the imaging system, enabling holographic interference micrographs of regions far from the sample edge to be obtained. Using a condenser biprism, we split an electron wave into two coherent electron waves: one wave is to illuminate an observation area far from the sample edge in the sample plane and the other wave to pass through a vacuum space outside the sample. The split-illumination holography has the potential to greatly expand the breadth of applications of electron holography.

Field-theoretical investigations in nonlinear realizations of gauge symmetry

International Nuclear Information System (INIS)

Lee, Chenhan.

1989-01-01

A review of both linear realization and non-linear realization of gauge symmetries is given and the connection between the two recipes is carefully examined. The author then constructs both linear and non-linear realizations for of supersymmetric theories. The supermultiplets of the Goldstone modes contain Goldstone bosons, quasi-Goldstone bosons and quasi-Goldstone fermions. He makes an attempt to construct a specific model of a supersymmetric non-linear realization for the Nambu-Goldstone superfields and the quasi-Goldstone fermions are identified with the quarks and leptons. Further, he discusses a mechanism by which the components of the Nambu-Goldstone supermultiplets are given non-zero mass splittings by the coupling to a hidden sector. Next, he turns to anti-symmetric tensor gauge theories, which are shown to be classically equivalent to the non-linear models describing the complete symmetry breakdown. To study the quantum mechanical equivalence of these two models, he carries out the tensor gauge fixing and the quantization procedures for the anti-symmetric tensor theories and establish the global symmetry currents which connect the two models. He then builds the supersymmetric extensions of the anti-symmetric tensor gauge theories in both abelian and non-abelian versions. Such super-tensor gauge theories are shown, by using the superfield equations of motion, to be equivalent to the fully doubled supersymmetric non-linear models of complete symmetry breakdown

Propagation of electromagnetic waves in stratified media with nonlinearity in both dielectric and magnetic responses.

Science.gov (United States)

Kim, Kihong; Phung, D K; Rotermund, F; Lim, H

2008-01-21

We develop a generalized version of the invariant imbedding method, which allows us to solve the electromagnetic wave equations in arbitrarily inhomogeneous stratified media where both the dielectric permittivity and magnetic permeability depend on the strengths of the electric and magnetic fields, in a numerically accurate and efficient manner. We apply our method to a uniform nonlinear slab and find that in the presence of strong external radiation, an initially uniform medium of positive refractive index can spontaneously change into a highly inhomogeneous medium where regions of positive or negative refractive index as well as metallic regions appear. We also study the wave transmission properties of periodic nonlinear media and the influence of nonlinearity on the mode conversion phenomena in inhomogeneous plasmas. We argue that our theory is very useful in the study of the optical properties of a variety of nonlinear media including nonlinear negative index media fabricated using wires and split-ring resonators.

Simulations of nonlinear continuous wave pressure fields in FOCUS

Science.gov (United States)

Zhao, Xiaofeng; Hamilton, Mark F.; McGough, Robert J.

2017-03-01

The Khokhlov - Zabolotskaya - Kuznetsov (KZK) equation is a parabolic approximation to the Westervelt equation that models the effects of diffraction, attenuation, and nonlinearity. Although the KZK equation is only valid in the far field of the paraxial region for mildly focused or unfocused transducers, the KZK equation is widely applied in medical ultrasound simulations. For a continuous wave input, the KZK equation is effectively modeled by the Bergen Code [J. Berntsen, Numerical Calculations of Finite Amplitude Sound Beams, in M. F. Hamilton and D. T. Blackstock, editors, Frontiers of Nonlinear Acoustics: Proceedings of 12th ISNA, Elsevier, 1990], which is a finite difference model that utilizes operator splitting. Similar C++ routines have been developed for FOCUS, the `Fast Object-Oriented C++ Ultrasound Simulator' (http://www.egr.msu.edu/˜fultras-web) to calculate nonlinear pressure fields generated by axisymmetric flat circular and spherically focused ultrasound transducers. This new routine complements an existing FOCUS program that models nonlinear ultrasound propagation with the angular spectrum approach [P. T. Christopher and K. J. Parker, J. Acoust. Soc. Am. 90, 488-499 (1991)]. Results obtained from these two nonlinear ultrasound simulation approaches are evaluated and compared for continuous wave linear simulations. The simulation results match closely in the farfield of the paraxial region, but the results differ in the nearfield. The nonlinear pressure field generated by a spherically focused transducer with a peak surface pressure of 0.2MPa radiating in a lossy medium with β = 3.5 is simulated, and the computation times are also evaluated. The nonlinear simulation results demonstrate acceptable agreement in the focal zone. These two related nonlinear simulation approaches are now included with FOCUS to enable convenient simulations of nonlinear pressure fields on desktop and laptop computers.

Performance improvement of 64-QAM coherent optical communication system by optimizing symbol decision boundary based on support vector machine

Science.gov (United States)

Chen, Wei; Zhang, Junfeng; Gao, Mingyi; Shen, Gangxiang

2018-03-01

High-order modulation signals are suited for high-capacity communication systems because of their high spectral efficiency, but they are more vulnerable to various impairments. For the signals that experience degradation, when symbol points overlap on the constellation diagram, the original linear decision boundary cannot be used to distinguish the classification of symbol. Therefore, it is advantageous to create an optimum symbol decision boundary for the degraded signals. In this work, we experimentally demonstrated the 64-quadrature-amplitude modulation (64-QAM) coherent optical communication system using support-vector machine (SVM) decision boundary algorithm to create the optimum symbol decision boundary for improving the system performance. We investigated the influence of various impairments on the 64-QAM coherent optical communication systems, such as the impairments caused by modulator nonlinearity, phase skew between in-phase (I) arm and quadrature-phase (Q) arm of the modulator, fiber Kerr nonlinearity and amplified spontaneous emission (ASE) noise. We measured the bit-error-ratio (BER) performance of 75-Gb/s 64-QAM signals in the back-to-back and 50-km transmission. By using SVM to optimize symbol decision boundary, the impairments caused by I/Q phase skew of the modulator, fiber Kerr nonlinearity and ASE noise are greatly mitigated.

Cool covered sky-splitting spectrum-splitting FK

Energy Technology Data Exchange (ETDEWEB)

Mohedano, Rubén; Chaves, Julio; Falicoff, Waqidi; Hernandez, Maikel; Sorgato, Simone [LPI, Altadena, CA, USA and Madrid (Spain); Miñano, Juan C.; Benitez, Pablo [LPI, Altadena, CA, USA and Madrid, Spain and Universidad Politécnica de Madrid (UPM), Madrid (Spain); Buljan, Marina [Universidad Politécnica de Madrid (UPM), Madrid (Spain)

2014-09-26

Placing a plane mirror between the primary lens and the receiver in a Fresnel Köhler (FK) concentrator gives birth to a quite different CPV system where all the high-tech components sit on a common plane, that of the primary lens panels. The idea enables not only a thinner device (a half of the original) but also a low cost 1-step manufacturing process for the optics, automatic alignment of primary and secondary lenses, and cell/wiring protection. The concept is also compatible with two different techniques to increase the module efficiency: spectrum splitting between a 3J and a BPC Silicon cell for better usage of Direct Normal Irradiance DNI, and sky splitting to harvest the energy of the diffuse radiation and higher energy production throughout the year. Simple calculations forecast the module would convert 45% of the DNI into electricity.

Bad split during bilateral sagittal split osteotomy of the mandible with separators: a retrospective study of 427 patients.

Science.gov (United States)

Mensink, Gertjan; Verweij, Jop P; Frank, Michael D; Eelco Bergsma, J; Richard van Merkesteyn, J P

2013-09-01

An unfavourable fracture, known as a bad split, is a common operative complication in bilateral sagittal split osteotomy (BSSO). The reported incidence ranges from 0.5 to 5.5%/site. Since 1994 we have used sagittal splitters and separators instead of chisels for BSSO in our clinic in an attempt to prevent postoperative hypoaesthesia. Theoretically an increased percentage of bad splits could be expected with this technique. In this retrospective study we aimed to find out the incidence of bad splits associated with BSSO done with splitters and separators. We also assessed the risk factors for bad splits. The study group comprised 427 consecutive patients among whom the incidence of bad splits was 2.0%/site, which is well within the reported range. The only predictive factor for a bad split was the removal of third molars at the same time as BSSO. There was no significant association between bad splits and age, sex, class of occlusion, or the experience of the surgeon. We think that doing a BSSO with splitters and separators instead of chisels does not increase the risk of a bad split, and is therefore safe with predictable results. Copyright © 2012 The British Association of Oral and Maxillofacial Surgeons. Published by Elsevier Ltd. All rights reserved.

Indentification and analysis of nonlinear transition scenarios using NOLOT/PSE

Energy Technology Data Exchange (ETDEWEB)

Hein, S.; Stolte, A.; Dallmann, U.C. (Goettingen Univ. (Germany). Inst. fuer Stroemungsmechanik)

1999-01-01

Laminar-turbulent transition of quasi-three-dimensional boundary-layer flows is investigated by nonlinear nonlocal instability theory based on parabolized stability equations (PSE). A strong TS-CF interaction scenario is described, which leads to a rapid rise in skin-friction coefficient indicating imminent breakdown of the laminar flow. The CF-CF interaction studies reproduce amplitude saturation observed in experiment, but do not provide an explanation for the final breakdown in crossflow-dominated boundary layers yet. (orig.)

Indentification and analysis of nonlinear transition scenarios using NOLOT/PSE

Energy Technology Data Exchange (ETDEWEB)

Hein, S.; Stolte, A.; Dallmann, U.C. [Goettingen Univ. (Germany). Inst. fuer Stroemungsmechanik

1999-12-01

Laminar-turbulent transition of quasi-three-dimensional boundary-layer flows is investigated by nonlinear nonlocal instability theory based on parabolized stability equations (PSE). A strong TS-CF interaction scenario is described, which leads to a rapid rise in skin-friction coefficient indicating imminent breakdown of the laminar flow. The CF-CF interaction studies reproduce amplitude saturation observed in experiment, but do not provide an explanation for the final breakdown in crossflow-dominated boundary layers yet. (orig.)

Splittings, coalescence, bunch and snake patterns in the 3D nonlinear Schrödinger equation with anisotropic dispersion

DEFF Research Database (Denmark)

Germaschewski, K.; Grauer, R.; Bergé, L.

2001-01-01

compression and are shown to split into two symmetric peaks. These peaks can sequentially decay into smaller-scale structures developing near the front edge of a shock, as long as their individual power remains above threshold, until the final dispersion of the wave. Their phase and amplitude dynamics...

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.

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.

Existence of weak solutions to a nonlinear reaction-diffusion system with singular sources

Directory of Open Access Journals (Sweden)

Ida de Bonis

2017-09-01

Full Text Available We discuss the existence of a class of weak solutions to a nonlinear parabolic system of reaction-diffusion type endowed with singular production terms by reaction. The singularity is due to a potential occurrence of quenching localized to the domain boundary. The kind of quenching we have in mind is due to a twofold contribution: (i the choice of boundary conditions, modeling in our case the contact with an infinite reservoir filled with ready-to-react chemicals and (ii the use of a particular nonlinear, non-Lipschitz structure of the reaction kinetics. Our working techniques use fine energy estimates for approximating non-singular problems and uniform control on the set where singularities are localizing.

Superdiffusions and positive solutions of nonlinear partial differential equations

CERN Document Server

Dynkin, E B

2004-01-01

This book is devoted to the applications of probability theory to the theory of nonlinear partial differential equations. More precisely, it is shown that all positive solutions for a class of nonlinear elliptic equations in a domain are described in terms of their traces on the boundary of the domain. The main probabilistic tool is the theory of superdiffusions, which describes a random evolution of a cloud of particles. A substantial enhancement of this theory is presented that can be of interest for everybody who works on applications of probabilistic methods to mathematical analysis.

Self-Similar Nanocavity Design with Ultrasmall Mode Volume for Single-Photon Nonlinearities

DEFF Research Database (Denmark)

Choi, Hyeongrak; Heuck, Mikkel; Englund, Dirk R.

2017-01-01

We propose a photonic crystal nanocavity design with self-similar electromagnetic boundary conditions, achieving ultrasmall mode volume (V-eff). The electric energy density of a cavity mode can be maximized in the air or dielectric region, depending on the choice of boundary conditions. We illust...... at the single-photon level. These features open new directions in cavity quantum electrodynamics, spectroscopy, and quantum nonlinear optics....

Turing instability in reaction-diffusion systems with nonlinear diffusion

Energy Technology Data Exchange (ETDEWEB)

Zemskov, E. P., E-mail: zemskov@ccas.ru [Russian Academy of Sciences, Dorodnicyn Computing Center (Russian Federation)

2013-10-15

The Turing instability is studied in two-component reaction-diffusion systems with nonlinear diffusion terms, and the regions in parametric space where Turing patterns can form are determined. The boundaries between super- and subcritical bifurcations are found. Calculations are performed for one-dimensional brusselator and oregonator models.

Dynamic nonlinear thermal optical effects in coupled ring resonators

Directory of Open Access Journals (Sweden)

Chenguang Huang

2012-09-01

Full Text Available We investigate the dynamic nonlinear thermal optical effects in a photonic system of two coupled ring resonators. A bus waveguide is used to couple light in and out of one of the coupled resonators. Based on the coupling from the bus to the resonator, the coupling between the resonators and the intrinsic loss of each individual resonator, the system transmission spectrum can be classified by three different categories: coupled-resonator-induced absorption, coupled-resonator-induced transparency and over coupled resonance splitting. Dynamic thermal optical effects due to linear absorption have been analyzed for each category as a function of the input power. The heat power in each resonator determines the thermal dynamics in this coupled resonator system. Multiple “shark fins” and power competition between resonators can be foreseen. Also, the nonlinear absorption induced thermal effects have been discussed.

Nonlinear Schrödinger approach to European option pricing

Science.gov (United States)

Wróblewski, Marcin

2017-05-01

This paper deals with numerical option pricing methods based on a Schrödinger model rather than the Black-Scholes model. Nonlinear Schrödinger boundary value problems seem to be alternatives to linear models which better reflect the complexity and behavior of real markets. Therefore, based on the nonlinear Schrödinger option pricing model proposed in the literature, in this paper a model augmented by external atomic potentials is proposed and numerically tested. In terms of statistical physics the developed model describes the option in analogy to a pair of two identical quantum particles occupying the same state. The proposed model is used to price European call options on a stock index. the model is calibrated using the Levenberg-Marquardt algorithm based on market data. A Runge-Kutta method is used to solve the discretized boundary value problem numerically. Numerical results are provided and discussed. It seems that our proposal more accurately models phenomena observed in the real market than do linear models.

Geometrical splitting in Monte Carlo

International Nuclear Information System (INIS)

Dubi, A.; Elperin, T.; Dudziak, D.J.

1982-01-01

A statistical model is presented by which a direct statistical approach yielded an analytic expression for the second moment, the variance ratio, and the benefit function in a model of an n surface-splitting Monte Carlo game. In addition to the insight into the dependence of the second moment on the splitting parameters the main importance of the expressions developed lies in their potential to become a basis for in-code optimization of splitting through a general algorithm. Refs

Innovative wedge axe in making split firewood

International Nuclear Information System (INIS)

Mutikainen, A.

1998-01-01

Interteam Oy, a company located in Espoo, has developed a new method for making split firewood. The tools on which the patented System Logmatic are based are wedge axe and cylindrical splitting-carrying frame. The equipment costs about 495 FIM. The block of wood to be split is placed inside the upright carrying frame and split in a series of splitting actions using the innovative wedge axe. The finished split firewood remains in the carrying frame, which (as its name indicates) also serves as the means for carrying the firewood. This innovative wedge-axe method was compared with the conventional splitting of wood using an axe (Fiskars -handy 1400 splitting axe costing about 200 FIM) in a study conducted at TTS-Institute. There were eight test subjects involved in the study. In the case of the wedge-axe method, handling of the blocks to be split and of the finished firewood was a little quicker, but in actual splitting it was a little slower than the conventional axe method. The average productivity of splitting the wood and of the work stages related to it was about 0.4 m 3 per effective hour in both methods. The methods were also equivalent of one another in terms of the load imposed by the work when measured in terms of the heart rate. As regards work safety, the wedge-axe method was superior to the conventional method, but the continuous striking action and jolting transmitted to the arms were unpleasant (orig.)

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”

TMD splitting functions in kT factorization. The real contribution to the gluon-to-gluon splitting

International Nuclear Information System (INIS)

Hentschinski, M.; Kusina, A.; Kutak, K.; Serino, M.

2018-01-01

We calculate the transverse momentum dependent gluon-to-gluon splitting function within k T -factorization, generalizing the framework employed in the calculation of the quark splitting functions in Hautmann et al. (Nucl Phys B 865:54-66, arXiv:1205.1759, 2012), Gituliar et al. (JHEP 01:181, arXiv:1511.08439, 2016), Hentschinski et al. (Phys Rev D 94(11):114013, arXiv:1607.01507, 2016) and demonstrate at the same time the consistency of the extended formalism with previous results. While existing versions of k T factorized evolution equations contain already a gluon-to-gluon splitting function i.e. the leading order Balitsky-Fadin-Kuraev-Lipatov (BFKL) kernel or the Ciafaloni-Catani-Fiorani-Marchesini (CCFM) kernel, the obtained splitting function has the important property that it reduces both to the leading order BFKL kernel in the high energy limit, to the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) gluon-to-gluon splitting function in the collinear limit as well as to the CCFM kernel in the soft limit. At the same time we demonstrate that this splitting kernel can be obtained from a direct calculation of the QCD Feynman diagrams, based on a combined implementation of the Curci-Furmanski-Petronzio formalism for the calculation of the collinear splitting functions and the framework of high energy factorization. (orig.)

Compressible stability of growing boundary layers using parabolized stability equations

Science.gov (United States)

Chang, Chau-Lyan; Malik, Mujeeb R.; Erlebacher, Gordon; Hussaini, M. Y.

1991-01-01

The parabolized stability equation (PSE) approach is employed to study linear and nonlinear compressible stability with an eye to providing a capability for boundary-layer transition prediction in both 'quiet' and 'disturbed' environments. The governing compressible stability equations are solved by a rational parabolizing approximation in the streamwise direction. Nonparallel flow effects are studied for both the first- and second-mode disturbances. For oblique waves of the first-mode type, the departure from the parallel results is more pronounced as compared to that for the two-dimensional waves. Results for the Mach 4.5 case show that flow nonparallelism has more influence on the first mode than on the second. The disturbance growth rate is shown to be a strong function of the wall-normal distance due to either flow nonparallelism or nonlinear interactions. The subharmonic and fundamental types of breakdown are found to be similar to the ones in incompressible boundary layers.

An efficient strongly coupled immersed boundary method for deforming bodies

Science.gov (United States)

Goza, Andres; Colonius, Tim

2016-11-01

Immersed boundary methods treat the fluid and immersed solid with separate domains. As a result, a nonlinear interface constraint must be satisfied when these methods are applied to flow-structure interaction problems. This typically results in a large nonlinear system of equations that is difficult to solve efficiently. Often, this system is solved with a block Gauss-Seidel procedure, which is easy to implement but can require many iterations to converge for small solid-to-fluid mass ratios. Alternatively, a Newton-Raphson procedure can be used to solve the nonlinear system. This typically leads to convergence in a small number of iterations for arbitrary mass ratios, but involves the use of large Jacobian matrices. We present an immersed boundary formulation that, like the Newton-Raphson approach, uses a linearization of the system to perform iterations. It therefore inherits the same favorable convergence behavior. However, we avoid large Jacobian matrices by using a block LU factorization of the linearized system. We derive our method for general deforming surfaces and perform verification on 2D test problems of flow past beams. These test problems involve large amplitude flapping and a wide range of mass ratios. This work was partially supported by the Jet Propulsion Laboratory and Air Force Office of Scientific Research.

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.

Multiple solutions for inhomogeneous nonlinear elliptic problems arising in astrophyiscs

Directory of Open Access Journals (Sweden)

Marco Calahorrano

2004-04-01

Full Text Available Using variational methods we prove the existence and multiplicity of solutions for some nonlinear inhomogeneous elliptic problems on a bounded domain in $mathbb{R}^n$, with $ngeq 2$ and a smooth boundary, and when the domain is $mathbb{R}_+^n$

Non-linear calculation of PCRV using dynamic relaxation

International Nuclear Information System (INIS)

Schnellenbach, G.

1979-01-01

A brief review is presented of a numerical method called the dynamic relaxation method for stress analysis of the concrete in prestressed concrete pressure vessels. By this method the three-dimensional elliptic differential equations of the continuum are changed into the four-dimensional hyperbolic differential equations known as wave equations. The boundary value problem of the static system is changed into an initial and boundary value problem for which a solution exists if the physical system is defined at time t=0. The effect of non-linear stress-strain behaviour of the material as well as creep and cracking are considered

On the Existence of a Free Boundary for a Class of Reaction-Diffusion Systems.

Science.gov (United States)

1982-02-01

I. Diaz. "Soluciones con soporte compacto para alguno. problemas semilineales". Collect. Math. 30 (1979), 141-179. -26- [121 J. I. Diaz. Tecnica de ...supersoluciones locales para problemas estacionarios no lineales: applicacion al estudio de flujoe subsonicos. Memory of the Real Academia de Ciencias...nonlinearity, nonlinear boundary conditions, dead core set, chemical reactions Work Unit Number I - Applied Analysis (1) Seccion de Matematicas

Urban pattern: Layout design by hierarchical domain splitting

KAUST Repository

Yang, Yongliang; Wang, Jun; Vouga, Etienne; Wonka, Peter

2013-01-01

We present a framework for generating street networks and parcel layouts. Our goal is the generation of high-quality layouts that can be used for urban planning and virtual environments. We propose a solution based on hierarchical domain splitting using two splitting types: streamline-based splitting, which splits a region along one or multiple streamlines of a cross field, and template-based splitting, which warps pre-designed templates to a region and uses the interior geometry of the template as the splitting lines. We combine these two splitting approaches into a hierarchical framework, providing automatic and interactive tools to explore the design space.

Urban pattern: Layout design by hierarchical domain splitting

KAUST Repository

Yang, Yongliang

2013-11-06

We present a framework for generating street networks and parcel layouts. Our goal is the generation of high-quality layouts that can be used for urban planning and virtual environments. We propose a solution based on hierarchical domain splitting using two splitting types: streamline-based splitting, which splits a region along one or multiple streamlines of a cross field, and template-based splitting, which warps pre-designed templates to a region and uses the interior geometry of the template as the splitting lines. We combine these two splitting approaches into a hierarchical framework, providing automatic and interactive tools to explore the design space.

A boundary integral approach to unstable solidification

International Nuclear Information System (INIS)

Strain, J.

1989-01-01

We consider the supercooled Stefan problem with a general anisotropic curvature- and velocity-dependent boundary condition on the moving interface. We present numerical methods, based on an integral equation formulation and including a new algorithm for moving curves with curvature-dependent velocity. These methods compute a periodic interface with O(Δt) accuracy, where Δt is the time step. Previous work has been limited to short time spans and achieved slightly less than O(Δt 1/2 ) accuracy. Accurate numerical results are seen to agree with the predictions of linear stability theory. This agreement has eluded previous authors, because their numerical methods suffered from grid effects and their linear stability theory was incorrect. We study the long-time evolution of an unstable interface. Our computations exhibit the beginnings of a sidebranching instability when the boundary condition includes anisotropy and tip-splitting in the isotropic case. copyright 1989 Academic Press, Inc

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.

On magnetohydrodynamic flow of second grade nanofluid over a nonlinear stretching sheet

Energy Technology Data Exchange (ETDEWEB)

Hayat, Tasawar [Department of Mathematics, Quaid-I-Azam University, Islamabad 44000 (Pakistan); Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589 (Saudi Arabia); Aziz, Arsalan [Department of Mathematics, Quaid-I-Azam University, Islamabad 44000 (Pakistan); Muhammad, Taseer, E-mail: taseer_qau@yahoo.com [Department of Mathematics, Quaid-I-Azam University, Islamabad 44000 (Pakistan); Ahmad, Bashir [Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589 (Saudi Arabia)

2016-06-15

This research article addresses the magnetohydrodynamic (MHD) flow of second grade nanofluid over a nonlinear stretching sheet. Heat and mass transfer aspects are investigated through the thermophoresis and Brownian motion effects. Second grade fluid is assumed electrically conducting through a non-uniform applied magnetic field. Mathematical formulation is developed subject to small magnetic Reynolds number and boundary layer assumptions. Newly constructed condition having zero mass flux of nanoparticles at the boundary is incorporated. Transformations have been invoked for the reduction of partial differential systems into the set of nonlinear ordinary differential systems. The governing nonlinear systems have been solved for local behavior. Graphical results of different influential parameters are studied and discussed in detail. Computations for skin friction coefficient and local Nusselt number have been carried out. It is observed that the effects of thermophoresis parameter on the temperature and nanoparticles concentration distributions are qualitatively similar. The temperature and nanoparticles concentration distributions are enhanced for the larger magnetic parameter. - Highlights: • Constitutive relation for second grade fluid is employed. • Flow is caused by a nonlinear stretching surface. • Magnetic field applied is in transverse direction. • Nanofluid model consists of Brownian motion and thermophoresis. • Magnetic Reynolds number is assumed small.

On magnetohydrodynamic flow of second grade nanofluid over a nonlinear stretching sheet

International Nuclear Information System (INIS)

Hayat, Tasawar; Aziz, Arsalan; Muhammad, Taseer; Ahmad, Bashir

2016-01-01

This research article addresses the magnetohydrodynamic (MHD) flow of second grade nanofluid over a nonlinear stretching sheet. Heat and mass transfer aspects are investigated through the thermophoresis and Brownian motion effects. Second grade fluid is assumed electrically conducting through a non-uniform applied magnetic field. Mathematical formulation is developed subject to small magnetic Reynolds number and boundary layer assumptions. Newly constructed condition having zero mass flux of nanoparticles at the boundary is incorporated. Transformations have been invoked for the reduction of partial differential systems into the set of nonlinear ordinary differential systems. The governing nonlinear systems have been solved for local behavior. Graphical results of different influential parameters are studied and discussed in detail. Computations for skin friction coefficient and local Nusselt number have been carried out. It is observed that the effects of thermophoresis parameter on the temperature and nanoparticles concentration distributions are qualitatively similar. The temperature and nanoparticles concentration distributions are enhanced for the larger magnetic parameter. - Highlights: • Constitutive relation for second grade fluid is employed. • Flow is caused by a nonlinear stretching surface. • Magnetic field applied is in transverse direction. • Nanofluid model consists of Brownian motion and thermophoresis. • Magnetic Reynolds number is assumed small.

Boundary controllability of integrodifferential systems in Banach ...

Indian Academy of Sciences (India)

solution to state space system, the control must be taken in a space of ... this paper is to study the boundary controllability of nonlinear integrodifferential systems ... be a linear closed and densely defined operator with Dً'ق E and let ( be a linear ... (iv) For all t 2 ً0; bٹ and u 2 U, TًtقBu 2 DًAق. ... The construction of the bounded.

Run-up on a body in waves and current. Fully nonlinear and finite-order calculations

DEFF Research Database (Denmark)

Büchmann, Bjarne; Ferrant, P.; Skourup, J.

2001-01-01

Run-up on a large fixed body in waves and current have been calculated using both a fully nonlinear time-domain boundary element model and a finite-order time-domain boundary element model, the latter being correct to second order in the wave steepness and to first-order in the current strength...

Relationship between mandibular anatomy and the occurrence of a bad split upon sagittal split osteotomy.

Science.gov (United States)

Aarabi, Mohammadali; Tabrizi, Reza; Hekmat, Mina; Shahidi, Shoaleh; Puzesh, Ayatollah

2014-12-01

A bad split is a troublesome complication of the sagittal split osteotomy (SSO). The aim of this study was to evaluate the relation between the occurrence of a bad split and mandibular anatomy in SSO using cone-beam computed tomography. The authors designed a cohort retrospective study. Forty-eight patients (96 SSO sites) were studied. The buccolingual thickness of the retromandibular area (BLR), the buccolingual thickness of the ramus at the level of the lingula (BLTR), the height of the mandible from the alveolar crest to the inferior border of the mandible, (ACIB), the distance between the sigmoid notch and the inferior border of the mandible (SIBM), and the anteroposterior width of the ramus (APWR) were measured. The independent t test was applied to compare anatomic measurements between the group with and the group without bad splits. The receiver operating characteristic (ROC) test was used to find a cutoff point in anatomic size for various parts of the mandible related to the occurrence of bad splits. The mean SIBM was 47.05±6.33 mm in group 1 (with bad splits) versus 40.66±2.44 mm in group 2 (without bad splits; P=.01). The mean BLTR was 5.74±1.11 mm in group 1 versus 3.19±0.55 mm in group 2 (P=.04). The mean BLR was 14.98±2.78 mm in group 1 versus 11.21±1.29 mm in group 2 (P=.001). No statistically significant difference was found for APWR and ACIB between the 2 groups. The ROC test showed cutoff points of 10.17 mm for BLR, 36.69 mm for SIBM, and 4.06 mm for BLTR. This study showed that certain mandibular anatomic differences can increase the risk of a bad split during SSO surgery. Copyright © 2014 American Association of Oral and Maxillofacial Surgeons. Published by Elsevier Inc. All rights reserved.

SplitRacer - a new Semi-Automatic Tool to Quantify And Interpret Teleseismic Shear-Wave Splitting

Science.gov (United States)

Reiss, M. C.; Rumpker, G.

2017-12-01

We have developed a semi-automatic, MATLAB-based GUI to combine standard seismological tasks such as the analysis and interpretation of teleseismic shear-wave splitting. Shear-wave splitting analysis is widely used to infer seismic anisotropy, which can be interpreted in terms of lattice-preferred orientation of mantle minerals, shape-preferred orientation caused by fluid-filled cracks or alternating layers. Seismic anisotropy provides a unique link between directly observable surface structures and the more elusive dynamic processes in the mantle below. Thus, resolving the seismic anisotropy of the lithosphere/asthenosphere is of particular importance for geodynamic modeling and interpretations. The increasing number of seismic stations from temporary experiments and permanent installations creates a new basis for comprehensive studies of seismic anisotropy world-wide. However, the increasingly large data sets pose new challenges for the rapid and reliably analysis of teleseismic waveforms and for the interpretation of the measurements. Well-established routines and programs are available but are often impractical for analyzing large data sets from hundreds of stations. Additionally, shear wave splitting results are seldom evaluated using the same well-defined quality criteria which may complicate comparison with results from different studies. SplitRacer has been designed to overcome these challenges by incorporation of the following processing steps: i) downloading of waveform data from multiple stations in mseed-format using FDSNWS tools; ii) automated initial screening and categorizing of XKS-waveforms using a pre-set SNR-threshold; iii) particle-motion analysis of selected phases at longer periods to detect and correct for sensor misalignment; iv) splitting analysis of selected phases based on transverse-energy minimization for multiple, randomly-selected, relevant time windows; v) one and two-layer joint-splitting analysis for all phases at one station by

Nonlinear ion-acoustic cnoidal waves in a dense relativistic degenerate magnetoplasma.

Science.gov (United States)

El-Shamy, E F

2015-03-01

The complex pattern and propagation characteristics of nonlinear periodic ion-acoustic waves, namely, ion-acoustic cnoidal waves, in a dense relativistic degenerate magnetoplasma consisting of relativistic degenerate electrons and nondegenerate cold ions are investigated. By means of the reductive perturbation method and appropriate boundary conditions for nonlinear periodic waves, a nonlinear modified Korteweg-de Vries (KdV) equation is derived and its cnoidal wave is analyzed. The various solutions of nonlinear ion-acoustic cnoidal and solitary waves are presented numerically with the Sagdeev potential approach. The analytical solution and numerical simulation of nonlinear ion-acoustic cnoidal waves of the nonlinear modified KdV equation are studied. Clearly, it is found that the features (amplitude and width) of nonlinear ion-acoustic cnoidal waves are proportional to plasma number density, ion cyclotron frequency, and direction cosines. The numerical results are applied to high density astrophysical situations, such as in superdense white dwarfs. This research will be helpful in understanding the properties of compact astrophysical objects containing cold ions with relativistic degenerate electrons.

Transition due to streamwise streaks in a supersonic flat plate boundary layer

Science.gov (United States)

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

2016-12-01

Transition induced by stationary streaks undergoing transient growth in a supersonic flat plate boundary layer flow is studied using numerical computations. While the possibility of strong transient growth of small-amplitude stationary perturbations in supersonic boundary layer flows has been demonstrated in previous works, its relation to laminar-turbulent transition cannot be established within the framework of linear disturbances. Therefore, this paper investigates the nonlinear evolution of initially linear optimal disturbances that evolve into finite amplitude streaks in the downstream region, and then studies the modal instability of those streaks as a likely cause for the onset of bypass transition. The nonmodal evolution of linearly optimal stationary perturbations in a supersonic, Mach 3 flat plate boundary layer is computed via the nonlinear plane-marching parabolized stability equations (PSE) for stationary perturbations, or equivalently, the perturbation form of parabolized Navier-Stokes equations. To assess the effect of the nonlinear finite-amplitude streaks on transition, the linear form of plane-marching PSE is used to investigate the instability of the boundary layer flow modified by the spanwise periodic streaks. The onset of transition is estimated using an N -factor criterion based on modal amplification of the secondary instabilities of the streaks. In the absence of transient growth disturbances, first mode instabilities in a Mach 3, zero pressure gradient boundary layer reach N =10 at Rex≈107 . However, secondary instability modes of the stationary streaks undergoing transient growth are able to achieve the same N -factor at Rex<2 ×106 when the initial streak amplitude is sufficiently large. In contrast to the streak instabilities in incompressible flows, subharmonic instability modes with twice the fundamental spanwise wavelength of the streaks are found to have higher amplification ratios than the streak instabilities at fundamental

Nonlinear dynamics of rotating shallow water methods and advances

CERN Document Server

Zeitlin, Vladimir

2007-01-01

The rotating shallow water (RSW) model is of wide use as a conceptual tool in geophysical fluid dynamics (GFD), because, in spite of its simplicity, it contains all essential ingredients of atmosphere and ocean dynamics at the synoptic scale, especially in its two- (or multi-) layer version. The book describes recent advances in understanding (in the framework of RSW and related models) of some fundamental GFD problems, such as existence of the slow manifold, dynamical splitting of fast (inertia-gravity waves) and slow (vortices, Rossby waves) motions, nonlinear geostrophic adjustment and wa

Probabilistic estimation of splitting coefficients of normal modes of the Earth, and their uncertainties, using an autoregressive technique

Science.gov (United States)

Pachhai, S.; Masters, G.; Laske, G.

2017-12-01

Earth's normal-mode spectra are crucial to studying the long wavelength structure of the Earth. Such observations have been used extensively to estimate "splitting coefficients" which, in turn, can be used to determine the three-dimensional velocity and density structure. Most past studies apply a non-linear iterative inversion to estimate the splitting coefficients which requires that the earthquake source is known. However, it is challenging to know the source details, particularly for big events as used in normal-mode analyses. Additionally, the final solution of the non-linear inversion can depend on the choice of damping parameter and starting model. To circumvent the need to know the source, a two-step linear inversion has been developed and successfully applied to many mantle and core sensitive modes. The first step takes combinations of the data from a single event to produce spectra known as "receiver strips". The autoregressive nature of the receiver strips can then be used to estimate the structure coefficients without the need to know the source. Based on this approach, we recently employed a neighborhood algorithm to measure the splitting coefficients for an isolated inner-core sensitive mode (13S2). This approach explores the parameter space efficiently without any need of regularization and finds the structure coefficients which best fit the observed strips. Here, we implement a Bayesian approach to data collected for earthquakes from early 2000 and more recent. This approach combines the data (through likelihood) and prior information to provide rigorous parameter values and their uncertainties for both isolated and coupled modes. The likelihood function is derived from the inferred errors of the receiver strips which allows us to retrieve proper uncertainties. Finally, we apply model selection criteria that balance the trade-offs between fit (likelihood) and model complexity to investigate the degree and type of structure (elastic and anelastic

Internal differential rotation of the Sun: the P-modes frequency splitting in the measurements of brightness oscillations

International Nuclear Information System (INIS)

Didkovskij, L.V.

1989-01-01

a 12-DAY SERIES OF TWO-DIMNIONAL IMAGES OF SOLAR BRIGHTNESS OSCILLATIONS EIGENFREQUENCIES in the range of 6-32 degrees. The rotational frequency splitting of separate modes as a function of inner turn-points radius of acoustic waves is found. The results of the analysis shw fast rotation of the central region of the Sun and non-monotonous trend of angular rotation velocity varitions with radius of the boundary of solar core

Simulation of nonlinear wave run-up with a high-order Boussinesq model

DEFF Research Database (Denmark)

Fuhrman, David R.; Madsen, Per A.

2008-01-01

This paper considers the numerical simulation of nonlinear wave run-up within a highly accurate Boussinesq-type model. Moving wet–dry boundary algorithms based on so-called extrapolating boundary techniques are utilized, and a new variant of this approach is proposed in two horizontal dimensions....... As validation, computed results involving the nonlinear run-up of periodic as well as transient waves on a sloping beach are considered in a single horizontal dimension, demonstrating excellent agreement with analytical solutions for both the free surface and horizontal velocity. In two horizontal dimensions...... cases involving long wave resonance in a parabolic basin, solitary wave evolution in a triangular channel, and solitary wave run-up on a circular conical island are considered. In each case the computed results compare well against available analytical solutions or experimental measurements. The ability...

DG-FEM solution for nonlinear wave-structure interaction using Boussinesq-type equations

DEFF Research Database (Denmark)

Engsig-Karup, Allan Peter; Hesthaven, Jan; Bingham, Harry B.

2008-01-01

equations in complex and curvilinear geometries which amends the application range of previous numerical models that have been based on structured Cartesian grids. The Boussinesq method provides the basis for the accurate description of fully nonlinear and dispersive water waves in both shallow and deep...... waters within the breaking limit. To demonstrate the current applicability of the model both linear and mildly nonlinear test cases are considered in two horizontal dimensions where the water waves interact with bottom-mounted fully reflecting structures. It is established that, by simple symmetry...... considerations combined with a mirror principle, it is possible to impose weak slip boundary conditions for both structured and general curvilinear wall boundaries while maintaining the accuracy of the scheme. As is standard for current high-order Boussinesq-type models, arbitrary waves can be generated...

On discrete maximum principles for nonlinear elliptic problems

Czech Academy of Sciences Publication Activity Database

Karátson, J.; Korotov, S.; Křížek, Michal

2007-01-01

Roč. 76, č. 1 (2007), s. 99-108 ISSN 0378-4754 R&D Projects: GA MŠk 1P05ME749; GA AV ČR IAA1019201 Institutional research plan: CEZ:AV0Z10190503 Keywords : nonlinear elliptic problem * mixed boundary conditions * finite element method Subject RIV: BA - General Mathematics Impact factor: 0.738, year: 2007

Existence and Nonexistence of Positive Solutions for Coupled Riemann-Liouville Fractional Boundary Value Problems

Directory of Open Access Journals (Sweden)

Johnny Henderson

2016-01-01

Full Text Available We investigate the existence and nonexistence of positive solutions for a system of nonlinear Riemann-Liouville fractional differential equations with two parameters, subject to coupled integral boundary conditions.

Convexity and Weighted Integral Inequalities for Energy Decay Rates of Nonlinear Dissipative Hyperbolic Systems

International Nuclear Information System (INIS)

Alabau-Boussouira, Fatiha

2005-01-01

This work is concerned with the stabilization of hyperbolic systems by a nonlinear feedback which can be localized on a part of the boundary or locally distributed. We show that general weighted integral inequalities together with convexity arguments allow us to produce a general semi-explicit formula which leads to decay rates of the energy in terms of the behavior of the nonlinear feedback close to the origin. This formula allows us to unify for instance the cases where the feedback has a polynomial growth at the origin, with the cases where it goes exponentially fast to zero at the origin. We also give three other significant examples of nonpolynomial growth at the origin. We also prove the optimality of our results for the one-dimensional wave equation with nonlinear boundary dissipation. The key property for obtaining our general energy decay formula is the understanding between convexity properties of an explicit function connected to the feedback and the dissipation of energy

Boundary value problem for Caputo-Hadamard fractional differential equations

Directory of Open Access Journals (Sweden)

Yacine Arioua

2017-09-01

Full Text Available The aim of this work is to study the existence and uniqueness solutions for boundary value problem of nonlinear fractional differential equations with Caputo-Hadamard derivative in bounded domain. We used the standard and Krasnoselskii's fixed point theorems. Some new results of existence and uniqueness solutions for Caputo-Hadamard fractional equations are obtained.

Fast simulation of non-linear pulsed ultrasound fields using an angular spectrum approach

DEFF Research Database (Denmark)

Du, Yigang; Jensen, Jørgen Arendt

2013-01-01

A fast non-linear pulsed ultrasound field simulation is presented. It is implemented based on an angular spectrum approach (ASA), which analytically solves the non-linear wave equation. The ASA solution to the Westervelt equation is derived in detail. The calculation speed is significantly...... increased compared to a numerical solution using an operator splitting method (OSM). The ASA has been modified and extended to pulsed non-linear ultrasound fields in combination with Field II, where any array transducer with arbitrary geometry, excitation, focusing and apodization can be simulated...... with a center frequency of 5 MHz. The speed is increased approximately by a factor of 140 and the calculation time is 12 min with a standard PC, when simulating the second harmonic pulse at the focal point. For the second harmonic point spread function the full width error is 1.5% at 6 dB and 6.4% at 12 d...

Non-linearity consideration when analyzing reactor noise statistical characteristics. [BWR

Energy Technology Data Exchange (ETDEWEB)

Kebadze, B V; Adamovski, L A

1975-06-01

Statistical characteristics of boiling water reactor noise in the vicinity of stability threshold are studied. The reactor is considered as a non-linear system affected by random perturbations. To solve a non-linear problem the principle of statistical linearization is used. It is shown that the halfwidth of resonance peak in neutron power noise spectrum density as well as the reciprocal of noise dispersion, which are used in predicting a stable operation theshold, are different from zero both within and beyond the stability boundary the determination of which was based on linear criteria.

Are Ducted Mini-Splits Worth It?

Energy Technology Data Exchange (ETDEWEB)

Winkler, Jonathan M [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Maguire, Jeffrey B [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Metzger, Cheryn E. [Pacific Northwest National Laboratory; Zhang, Jason [Pacific Northwest National Laboratory

2018-02-01

Ducted mini-split heat pumps are gaining popularity in some regions of the country due to their energy-efficient specifications and their ability to be hidden from sight. Although product and install costs are typically higher than the ductless mini-split heat pumps, this technology is well worth the premium for some homeowners who do not like to see an indoor unit in their living area. Due to the interest in this technology by local utilities and homeowners, the Bonneville Power Administration (BPA) has funded the Pacific Northwest National Laboratory (PNNL) and the National Renewable Energy Laboratory (NREL) to develop capabilities within the Building Energy Optimization (BEopt) tool to model ducted mini-split heat pumps. After the fundamental capabilities were added, energy-use results could be compared to other technologies that were already in BEopt, such as zonal electric resistance heat, central air source heat pumps, and ductless mini-split heat pumps. Each of these technologies was then compared using five prototype configurations in three different BPA heating zones to determine how the ducted mini-split technology would perform under different scenarios. The result of this project was a set of EnergyPlus models representing the various prototype configurations in each climate zone. Overall, the ducted mini-split heat pumps saved about 33-60% compared to zonal electric resistance heat (with window AC systems modeled in the summer). The results also showed that the ducted mini-split systems used about 4% more energy than the ductless mini-split systems, which saved about 37-64% compared to electric zonal heat (depending on the prototype and climate).

Nonlinear-optical generation of short-wavelength radiation controlled by laser-induced interference structures

International Nuclear Information System (INIS)

Popov, A K; Kimberg, V V

1998-01-01

A study is reported of the combined influence of laser-induced resonances in the energy continuum, of splitting of discrete resonances in the field of several strong radiations, and of absorption of the initial and generated radiations on totally resonant parametric conversion to the short-wavelength range. It is shown that the radiation power can be increased considerably by interference processes involving quantum transitions. (nonlinear optical phenomena and devices)

Power laws and elastic nonlinearity in materials with complex microstructure

Energy Technology Data Exchange (ETDEWEB)

Scalerandi, M., E-mail: marco.scalerandi@infm.polito.it

2016-01-28

Nonlinear ultrasonic methods have been widely used to characterize the microstructure of damaged solids and consolidated granular media. Besides distinguishing between materials exhibiting classical nonlinear behaviors from those exhibiting hysteresis, it could be of importance the discrimination between ultrasonic indications from different physical sources (scatterers). Elastic hysteresis could indeed be due to dislocations, grain boundaries, stick-slip at interfaces, etc. Analyzing data obtained on various concrete samples, we show that the power law behavior of the nonlinear indicator vs. the energy of excitation could be used to classify different microscopic features. In particular, the power law exponent ranges between 1 and 3, depending on the nature of nonlinearity. We also provide a theoretical interpretation of the collected data using models for clapping and hysteretic nonlinearities. - Highlights: • Several materials exhibit a nontrivial nonlinear elastic behavior which can be ascribed to different physical sources. • The quantitative nonlinear response is dependent on the type of microstructure present in the material. • A nonlinear indicator could be defined which depends on the excitation energy of the sample. • Assuming a power law dependence, the exponent depends on the microstructure of the material and could evolve in time. • Experimental results on concrete are discussed and a theoretical description is proposed.

Global existence and uniform stabilization of a generalized dissipative Klein-Gordon equation type with boundary damping

International Nuclear Information System (INIS)

Zhang Zaiyun; Miao Xiujin; Chen Yuezhong; Liu Zhenhai

2011-01-01

In this paper, we prove the existence, uniqueness, and uniform stability of strong and weak solutions of the nonlinear generalized Klein-Gordon equation (1.1) 1 (see Sec. I) in bounded domains with nonlinear damped boundary conditions given by (1.1) 3 (see Sec. I) with some restrictions on function f(u), h(∇u), g(u t ), and b(x), we prove the existence and uniqueness by means of nonlinear semigroup method and obtain the uniform stabilization by using the multiplier technique.

Particulate photocatalysts for overall water splitting

Science.gov (United States)

Chen, Shanshan; Takata, Tsuyoshi; Domen, Kazunari

2017-10-01

The conversion of solar energy to chemical energy is a promising way of generating renewable energy. Hydrogen production by means of water splitting over semiconductor photocatalysts is a simple, cost-effective approach to large-scale solar hydrogen synthesis. Since the discovery of the Honda-Fujishima effect, considerable progress has been made in this field, and numerous photocatalytic materials and water-splitting systems have been developed. In this Review, we summarize existing water-splitting systems based on particulate photocatalysts, focusing on the main components: light-harvesting semiconductors and co-catalysts. The essential design principles of the materials employed for overall water-splitting systems based on one-step and two-step photoexcitation are also discussed, concentrating on three elementary processes: photoabsorption, charge transfer and surface catalytic reactions. Finally, we outline challenges and potential advances associated with solar water splitting by particulate photocatalysts for future commercial applications.

Nonlinear Klein-Gordon soliton mechanics

International Nuclear Information System (INIS)

Reinisch, G.

1992-01-01

Nonlinear Klein-Gordon solitary waves - or solitons in a loose sense - in n+1 dimensions, driven by very general external fields which must only satisfy continuity - together with regularity conditions at the boundaries of the system, obey a quite simple equation of motion. This equation is the exact generalization to this dynamical system of infinite number of degrees of freedom - which may be conservative or not - of the second Newton's law setting the basis of material point mechanics. In the restricted case of conservative nonlinear Klein-Gordon systems, where the external driving force is derivable from a potential energy, we recover the generalized Ehrenfest theorem which was itself the extension to such systems of the well-known Ehrenfest theorem in quantum mechanics. This review paper first displays a few (of one-dimensional sine-Gordon type) typical examples of the basic difficulties related to the trial construction of solitary-waves is proved and the derivation of the previous sine-Gordon examples from this theorem is displayed. Two-dimensional nonlinear solitary-wave patterns are considered, as well as a special emphasis is put on the applications to space-time complexity of 1-dim. sine-Gordon systems

Nonlinear saturation of E x B instability in a plasma slab

International Nuclear Information System (INIS)

Alfsen, K.H.; Holter, Oe.

1984-09-01

The saturation of the E bar x B bar instability is investigated in the nonlinear regime. The governing equations are studied analytically and numerically by using a spectral method with mode truncation. The nonlinear stabilization is due to modifications of the background density- and potential profiles. In the time asymptotic limit a stationary solution, which is independent of the initial conditions is obtained. The asymptotic state is characterized by a splitting of the interacting modes into two almost non-interacting groups, where the modes with even mode number sum; i.e. the modes driven by the linearly most unstable mode, is found to dominate the system. For this group fixed point calculations are performed analytically with six interacting modes. Comparison with numerical calculations indicates excellent agreement far into the unstable region. (Auth.)

(O)Mega split

Energy Technology Data Exchange (ETDEWEB)

Benakli, Karim; Darmé, Luc; Goodsell, Mark D. [Sorbonne Universités, UPMC Univ Paris 06, UMR 7589,LPTHE, F-75005, Paris (France); CNRS, UMR 7589,LPTHE, F-75005, Paris (France)

2015-11-16

We study two realisations of the Fake Split Supersymmetry Model (FSSM), the simplest model that can easily reproduce the experimental value of the Higgs mass for an arbitrarily high supersymmetry scale M{sub S}, as a consequence of swapping higgsinos for equivalent states, fake higgsinos, with suppressed Yukawa couplings. If the LSP is identified as the main Dark matter component, then a standard thermal history of the Universe implies upper bounds on M{sub S}, which we derive. On the other hand, we show that renormalisation group running of soft masses aboveM{sub S} barely constrains the model — in stark contrast to Split Supersymmetry — and hence we can have a “Mega Split” spectrum even with all of these assumptions and constraints, which include the requirements of a correct relic abundance, a gluino life-time compatible with Big Bang Nucleosynthesis and absence of signals in present direct detection experiments of inelastic dark matter. In an appendix we describe a related scenario, Fake Split Extended Supersymmetry, which enjoys similar properties.

Quadratic soliton self-reflection at a quadratically nonlinear interface

Science.gov (United States)

Jankovic, Ladislav; Kim, Hongki; Stegeman, George; Carrasco, Silvia; Torner, Lluis; Katz, Mordechai

2003-11-01

The reflection of bulk quadratic solutions incident onto a quadratically nonlinear interface in periodically poled potassium titanyl phosphate was observed. The interface consisted of the boundary between two quasi-phase-matched regions displaced from each other by a half-period. At high intensities and small angles of incidence the soliton is reflected.

Coupling nonlinear Stokes and Darcy flow using mortar finite elements

KAUST Repository

Ervin, Vincent J.

2011-11-01

We study a system composed of a nonlinear Stokes flow in one subdomain coupled with a nonlinear porous medium flow in another subdomain. Special attention is paid to the mathematical consequence of the shear-dependent fluid viscosity for the Stokes flow and the velocity-dependent effective viscosity for the Darcy flow. Motivated by the physical setting, we consider the case where only flow rates are specified on the inflow and outflow boundaries in both subdomains. We recast the coupled Stokes-Darcy system as a reduced matching problem on the interface using a mortar space approach. We prove a number of properties of the nonlinear interface operator associated with the reduced problem, which directly yield the existence, uniqueness and regularity of a variational solution to the system. We further propose and analyze a numerical algorithm based on mortar finite elements for the interface problem and conforming finite elements for the subdomain problems. Optimal a priori error estimates are established for the interface and subdomain problems, and a number of compatibility conditions for the finite element spaces used are discussed. Numerical simulations are presented to illustrate the algorithm and to compare two treatments of the defective boundary conditions. © 2010 Published by Elsevier B.V. on behalf of IMACS.

Symbolic computation of analytic approximate solutions for nonlinear fractional differential equations

Science.gov (United States)

Lin, Yezhi; Liu, Yinping; Li, Zhibin

2013-01-01

The Adomian decomposition method (ADM) is one of the most effective methods to construct analytic approximate solutions for nonlinear differential equations. In this paper, based on the new definition of the Adomian polynomials, Rach (2008) [22], the Adomian decomposition method and the Padé approximants technique, a new algorithm is proposed to construct analytic approximate solutions for nonlinear fractional differential equations with initial or boundary conditions. Furthermore, a MAPLE software package is developed to implement this new algorithm, which is user-friendly and efficient. One only needs to input the system equation, initial or boundary conditions and several necessary parameters, then our package will automatically deliver the analytic approximate solutions within a few seconds. Several different types of examples are given to illustrate the scope and demonstrate the validity of our package, especially for non-smooth initial value problems. Our package provides a helpful and easy-to-use tool in science and engineering simulations. Program summaryProgram title: ADMP Catalogue identifier: AENE_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENE_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 12011 No. of bytes in distributed program, including test data, etc.: 575551 Distribution format: tar.gz Programming language: MAPLE R15. Computer: PCs. Operating system: Windows XP/7. RAM: 2 Gbytes Classification: 4.3. Nature of problem: Constructing analytic approximate solutions of nonlinear fractional differential equations with initial or boundary conditions. Non-smooth initial value problems can be solved by this program. Solution method: Based on the new definition of the Adomian polynomials [1], the Adomian decomposition method and the Pad

Nonlinear dynamics in the perceptual grouping of connected surfaces.

Science.gov (United States)

Hock, Howard S; Schöner, Gregor

2016-09-01

Evidence obtained using the dynamic grouping method has shown that the grouping of an object's connected surfaces has properties characteristic of a nonlinear dynamical system. When a surface's luminance changes, one of its boundaries is perceived moving across the surface. The direction of this dynamic grouping (DG) motion indicates which of two flanking surfaces has been grouped with the changing surface. A quantitative measure of overall grouping strength (affinity) for adjacent surfaces is provided by the frequency of DG motion perception in directions promoted by the grouping variables. It was found that: (1) variables affecting surface grouping for three-surface objects evolve over time, settling at stable levels within a single fixation, (2) how often DG motion is perceived when a surface's luminance is perturbed (changed) depends on the pre-perturbation affinity state of the surface grouping, (3) grouping variables promoting the same surface grouping combine cooperatively and nonlinearly (super-additively) in determining the surface grouping's affinity, (4) different DG motion directions during different trials indicate that surface grouping can be bistable, which implies that inhibitory interactions have stabilized one of two alternative surface groupings, and (5) when alternative surface groupings have identical affinity, stochastic fluctuations can break the symmetry and inhibitory interactions can then stabilize one of the surface groupings, providing affinity levels are not too high (which results in bidirectional DG motion). A surface-grouping network is proposed within which boundaries vary in salience. Low salience or suppressed boundaries instantiate surface grouping, and DG motion results from changes in boundary salience. Copyright © 2015 Elsevier Ltd. All rights reserved.

Splitting efficiency and interference effects in a Cooper pair splitter based on a triple quantum dot with ferromagnetic contacts

Science.gov (United States)

Bocian, Kacper; Rudziński, Wojciech; Weymann, Ireneusz

2018-05-01

We theoretically study the spin-resolved subgap transport properties of a Cooper pair splitter based on a triple quantum dot attached to superconducting and ferromagnetic leads. Using the Keldysh Green's function formalism, we analyze the dependence of the Andreev conductance, Cooper pair splitting efficiency, and tunnel magnetoresistance on the gate and bias voltages applied to the system. We show that the system's transport properties are strongly affected by spin dependence of tunneling processes and quantum interference between different local and nonlocal Andreev reflections. We also study the effects of finite hopping between the side quantum dots on the Andreev current. This allows for identifying the optimal conditions for enhancing the Cooper pair splitting efficiency of the device. We find that the splitting efficiency exhibits a nonmonotonic dependence on the degree of spin polarization of the leads and the magnitude and type of hopping between the dots. An almost perfect splitting efficiency is predicted in the nonlinear response regime when the energies of the side quantum dots are tuned to the energies of the corresponding Andreev bound states. In addition, we analyzed features of the tunnel magnetoresistance (TMR) for a wide range of the gate and bias voltages, as well as for different model parameters, finding the corresponding sign changes of the TMR in certain transport regimes. The mechanisms leading to these effects are thoroughly discussed.

Existence of positive solutions for boundary value problems of fractional functional differential equations

Directory of Open Access Journals (Sweden)

Chuanzhi Bai

2010-06-01

Full Text Available This paper deals with the existence of positive solutions for a boundary value problem involving a nonlinear functional differential equation of fractional order $\\alpha$ given by $ D^{\\alpha} u(t + f(t, u_t = 0$, $t \\in (0, 1$, $2 < \\alpha \\le 3$, $ u^{\\prime}(0 = 0$, $u^{\\prime}(1 = b u^{\\prime}(\\eta$, $u_0 = \\phi$. Our results are based on the nonlinear alternative of Leray-Schauder type and Krasnosel'skii fixed point theorem.

An algorithm for the split-feasibility problems with application to the split-equality problem.

Science.gov (United States)

Chuang, Chih-Sheng; Chen, Chi-Ming

2017-01-01

In this paper, we study the split-feasibility problem in Hilbert spaces by using the projected reflected gradient algorithm. As applications, we study the convex linear inverse problem and the split-equality problem in Hilbert spaces, and we give new algorithms for these problems. Finally, numerical results are given for our main results.

Acceleration of the AFEN method by two-node nonlinear iteration

Energy Technology Data Exchange (ETDEWEB)

Moon, Kap Suk; Cho, Nam Zin; Noh, Jae Man; Hong, Ser Gi [Korea Advanced Institute of Science and Technology, Taejon (Korea, Republic of)

1999-12-31

A nonlinear iterative scheme developed to reduce the computing time of the AFEN method was tested and applied to two benchmark problems. The new nonlinear method for the AFEN method is based on solving two-node problems and use of two nonlinear correction factors at every interface instead of one factor in the conventional scheme. The use of two correction factors provides higher-order accurate interface fluxes as well as currents which are used as the boundary conditions of the two-node problem. The numerical results show that this new method gives exactly the same solution as that of the original AFEN method and the computing time is significantly reduced in comparison with the original AFEN method. 7 refs., 1 fig., 1 tab. (Author)

Acceleration of the AFEN method by two-node nonlinear iteration

Energy Technology Data Exchange (ETDEWEB)

Moon, Kap Suk; Cho, Nam Zin; Noh, Jae Man; Hong, Ser Gi [Korea Advanced Institute of Science and Technology, Taejon (Korea, Republic of)

1998-12-31

A nonlinear iterative scheme developed to reduce the computing time of the AFEN method was tested and applied to two benchmark problems. The new nonlinear method for the AFEN method is based on solving two-node problems and use of two nonlinear correction factors at every interface instead of one factor in the conventional scheme. The use of two correction factors provides higher-order accurate interface fluxes as well as currents which are used as the boundary conditions of the two-node problem. The numerical results show that this new method gives exactly the same solution as that of the original AFEN method and the computing time is significantly reduced in comparison with the original AFEN method. 7 refs., 1 fig., 1 tab. (Author)

Nonlinear dynamic response of electro-thermo-mechanically loaded piezoelectric cylindrical shell reinforced with BNNTs

International Nuclear Information System (INIS)

Yang, J H; Yang, J; Kitipornchai, S

2012-01-01

This paper presents an investigation on the nonlinear dynamic response of piezoelectric cylindrical shells reinforced with boron nitride nanotubes (BNNTs) under a combined axisymmetric electro-thermo-mechanical loading. By employing the classical Donnell shell theory, the von Kármán–Donnell kinematic relationship, and a piezo-elastic constitutive law including thermal effects, the nonlinear governing equations of motion of the shell are derived through the Reissner variational principle. The finite difference method and a time-integration scheme are used to obtain the nonlinear dynamic response of the BNNT-reinforced piezoelectric shell. A parametric study is conducted, showing the effects of geometrically nonlinear deformation, applied voltage, temperature change, mechanical load, BNNT volume fraction and boundary conditions on the nonlinear dynamic response. (paper)

Ducks in space: from nonlinear absolute instability to noise-sustained structures in a pattern-forming system

Science.gov (United States)

Avitabile, D.; Desroches, M.; Knobloch, E.; Krupa, M.

2017-11-01

A subcritical pattern-forming system with nonlinear advection in a bounded domain is recast as a slow-fast system in space and studied using a combination of geometric singular perturbation theory and numerical continuation. Two types of solutions describing the possible location of stationary fronts are identified, whose origin is traced to the onset of convective and absolute instability when the system is unbounded. The former are present only for non-zero upstream boundary conditions and provide a quantitative understanding of noise-sustained structures in systems of this type. The latter correspond to the onset of a global mode and are present even with zero upstream boundary conditions. The role of canard trajectories in the nonlinear transition between these states is clarified and the stability properties of the resulting spatial structures are determined. Front location in the convective regime is highly sensitive to the upstream boundary condition, and its dependence on this boundary condition is studied using a combination of numerical continuation and Monte Carlo simulations of the partial differential equation. Statistical properties of the system subjected to random or stochastic boundary conditions at the inlet are interpreted using the deterministic slow-fast spatial dynamical system.

Stochastic split determinant algorithms

International Nuclear Information System (INIS)

Horvatha, Ivan

2000-01-01

I propose a large class of stochastic Markov processes associated with probability distributions analogous to that of lattice gauge theory with dynamical fermions. The construction incorporates the idea of approximate spectral split of the determinant through local loop action, and the idea of treating the infrared part of the split through explicit diagonalizations. I suggest that exact algorithms of practical relevance might be based on Markov processes so constructed

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 Mathematics Impact factor: 0.926, year: 2016 http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=5302

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

M-Split: A Graphical User Interface to Analyze Multilayered Anisotropy from Shear Wave Splitting

Science.gov (United States)

Abgarmi, Bizhan; Ozacar, A. Arda

2017-04-01

Shear wave splitting analysis are commonly used to infer deep anisotropic structure. For simple cases, obtained delay times and fast-axis orientations are averaged from reliable results to define anisotropy beneath recording seismic stations. However, splitting parameters show systematic variations with back azimuth in the presence of complex anisotropy and cannot be represented by average time delay and fast axis orientation. Previous researchers had identified anisotropic complexities at different tectonic settings and applied various approaches to model them. Most commonly, such complexities are modeled by using multiple anisotropic layers with priori constraints from geologic data. In this study, a graphical user interface called M-Split is developed to easily process and model multilayered anisotropy with capabilities to properly address the inherited non-uniqueness. M-Split program runs user defined grid searches through the model parameter space for two-layer anisotropy using formulation of Silver and Savage (1994) and creates sensitivity contour plots to locate local maximas and analyze all possible models with parameter tradeoffs. In order to minimize model ambiguity and identify the robust model parameters, various misfit calculation procedures are also developed and embedded to M-Split which can be used depending on the quality of the observations and their back-azimuthal coverage. Case studies carried out to evaluate the reliability of the program using real noisy data and for this purpose stations from two different networks are utilized. First seismic network is the Kandilli Observatory and Earthquake research institute (KOERI) which includes long term running permanent stations and second network comprises seismic stations deployed temporary as part of the "Continental Dynamics-Central Anatolian Tectonics (CD-CAT)" project funded by NSF. It is also worth to note that M-Split is designed as open source program which can be modified by users for

Size effects in non-linear heat conduction with flux-limited behaviors

Science.gov (United States)

Li, Shu-Nan; Cao, Bing-Yang

2017-11-01

Size effects are discussed for several non-linear heat conduction models with flux-limited behaviors, including the phonon hydrodynamic, Lagrange multiplier, hierarchy moment, nonlinear phonon hydrodynamic, tempered diffusion, thermon gas and generalized nonlinear models. For the phonon hydrodynamic, Lagrange multiplier and tempered diffusion models, heat flux will not exist in problems with sufficiently small scale. The existence of heat flux needs the sizes of heat conduction larger than their corresponding critical sizes, which are determined by the physical properties and boundary temperatures. The critical sizes can be regarded as the theoretical limits of the applicable ranges for these non-linear heat conduction models with flux-limited behaviors. For sufficiently small scale heat conduction, the phonon hydrodynamic and Lagrange multiplier models can also predict the theoretical possibility of violating the second law and multiplicity. Comparisons are also made between these non-Fourier models and non-linear Fourier heat conduction in the type of fast diffusion, which can also predict flux-limited behaviors.

Hydromagnetic nonlinear thermally radiative nanoliquid flow with Newtonian heat and mass conditions

Directory of Open Access Journals (Sweden)

Muhammad Ijaz Khan

Full Text Available This paper communicates the analysis of MHD three-dimensional flow of Jeffrey nanoliquid over a stretchable surface. Flow due to a bidirectional surface is considered. Heat and mass transfer subject to volume fraction of nanoparticles, heat generation and nonlinear solar radiation are examined. Newtonian heat and mass transportation conditions are employed at surface. Concept of boundary layer is utilized to developed the mathematical problem. The boundary value problem is dictated by ten physical parameters: Deborah number, Hartman number, ratio of stretching rates, thermophoretic parameter, Brownian motion parameter, Prandtl number, temperature ratio parameter, conjugate heat and mass parameters and Lewis number. Convergent solutions are obtained using homotopic procedure. Convergence zone for obtained results is explicitly identified. The obtained solutions are interpreted physically. Keywords: Hydromagnetic flow, Viscoelastic nanofluid, Thermophoretic and Brownian moment, Nonlinear thermal radiation, Heat generation

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

Solution of a few nonlinear problems in aerodynamics by the finite elements and functional least squares methods. Ph.D. Thesis - Paris Univ.; [mathematical models of transonic flow using nonlinear equations

Science.gov (United States)

Periaux, J.

1979-01-01

The numerical simulation of the transonic flows of idealized fluids and of incompressible viscous fluids, by the nonlinear least squares methods is presented. The nonlinear equations, the boundary conditions, and the various constraints controlling the two types of flow are described. The standard iterative methods for solving a quasi elliptical nonlinear equation with partial derivatives are reviewed with emphasis placed on two examples: the fixed point method applied to the Gelder functional in the case of compressible subsonic flows and the Newton method used in the technique of decomposition of the lifting potential. The new abstract least squares method is discussed. It consists of substituting the nonlinear equation by a problem of minimization in a H to the minus 1 type Sobolev functional space.

Angularly symmetric splitting of a light beam upon reflection and refraction at an air-dielectric plane boundary: reply.

Science.gov (United States)

Azzam, R M A

2016-05-01

The simplified explicit expressions derived by Andersen [J. Opt. Soc. Am. A33, 984 (2016)JOAOD60740-323210.1364/JOSAA.32.000984], that relate to angularly symmetric beam splitting by reflection and refraction at an air-dielectric interface recently described by Azzam [J. Opt. Soc. Am. A32, 2436 (2015)JOAOD60740-323210.1364/JOSAA.32.002436], are welcome. A few additional remarks are also included in my reply to Andersen's comment.

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

International Nuclear Information System (INIS)

Kolesov, Andrei Yu; Rozov, Nikolai Kh

2002-01-01

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

Design of HIFU Transducers for Generating Specified Nonlinear Ultrasound Fields.

Science.gov (United States)

Rosnitskiy, Pavel B; Yuldashev, Petr V; Sapozhnikov, Oleg A; Maxwell, Adam D; Kreider, Wayne; Bailey, Michael R; Khokhlova, Vera A

2017-02-01

Various clinical applications of high-intensity focused ultrasound have different requirements for the pressure levels and degree of nonlinear waveform distortion at the focus. The goal of this paper is to determine transducer design parameters that produce either a specified shock amplitude in the focal waveform or specified peak pressures while still maintaining quasi-linear conditions at the focus. Multiparametric nonlinear modeling based on the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation with an equivalent source boundary condition was employed. Peak pressures, shock amplitudes at the focus, and corresponding source outputs were determined for different transducer geometries and levels of nonlinear distortion. The results are presented in terms of the parameters of an equivalent single-element spherically shaped transducer. The accuracy of the method and its applicability to cases of strongly focused transducers were validated by comparing the KZK modeling data with measurements and nonlinear full diffraction simulations for a single-element source and arrays with 7 and 256 elements. The results provide look-up data for evaluating nonlinear distortions at the focus of existing therapeutic systems as well as for guiding the design of new transducers that generate specified nonlinear fields.

Validation of three-dimensional incompressible spatial direct numerical simulation code: A comparison with linear stability and parabolic stability equation theories for boundary-layer transition on a flat plate

Science.gov (United States)

Joslin, Ronald D.; Streett, Craig L.; Chang, Chau-Lyan

1992-01-01

Spatially evolving instabilities in a boundary layer on a flat plate are computed by direct numerical simulation (DNS) of the incompressible Navier-Stokes equations. In a truncated physical domain, a nonstaggered mesh is used for the grid. A Chebyshev-collocation method is used normal to the wall; finite difference and compact difference methods are used in the streamwise direction; and a Fourier series is used in the spanwise direction. For time stepping, implicit Crank-Nicolson and explicit Runge-Kutta schemes are used to the time-splitting method. The influence-matrix technique is used to solve the pressure equation. At the outflow boundary, the buffer-domain technique is used to prevent convective wave reflection or upstream propagation of information from the boundary. Results of the DNS are compared with those from both linear stability theory (LST) and parabolized stability equation (PSE) theory. Computed disturbance amplitudes and phases are in very good agreement with those of LST (for small inflow disturbance amplitudes). A measure of the sensitivity of the inflow condition is demonstrated with both LST and PSE theory used to approximate inflows. Although the DNS numerics are very different than those of PSE theory, the results are in good agreement. A small discrepancy in the results that does occur is likely a result of the variation in PSE boundary condition treatment in the far field. Finally, a small-amplitude wave triad is forced at the inflow, and simulation results are compared with those of LST. Again, very good agreement is found between DNS and LST results for the 3-D simulations, the implication being that the disturbance amplitudes are sufficiently small that nonlinear interactions are negligible.

Delineation of peatland lagg boundaries from airborne LiDAR

Science.gov (United States)

Langlois, Melanie N.; Richardson, Murray C.; Price, Jonathan S.

2017-09-01

In Canada, peatlands are the most common type of wetland, but boundary delineation in peatland complexes has received little attention in the scientific literature. Typically, peatland boundaries are mapped as crisp, absolute features, and the transitional lagg zone—the ecotone found between a raised bog and the surrounding mineral land—is often overlooked. In this study, we aim (1) to advance existing approaches for detecting and locating laggs and lagg boundaries using airborne LiDAR surveys and (2) to describe the spatial distribution of laggs around raised bog peatlands. Two contrasting spatial analytical approaches for lagg detection were tested using five LiDAR-derived topographic and vegetation indices: topography, vegetation height, topographic wetness index, the standard deviation of the vegetation's height (as a proxy for the complexity of the vegetation's structure), and local indices of elevation variance. Using a dissimilarity approach (edge-detection, split-moving window analysis), no one variable accurately depicted both the lagg-mineral land and bog-lagg boundaries. Some indicators were better at predicting the bog-lagg boundary (i.e., vegetation height) and others at finding the lagg-mineral land boundary (i.e., topography). Dissimilarity analysis reinforces the usefulness of derived variables (e.g., wetness indices) in locating laggs, especially for those with weak topographic and vegetation gradients. When the lagg was confined between the bog and the adjacent upland, it took a linear form, parallel to the peatland's edge and was easier to predict. When the adjacent mineral land was flat or sloping away from the peatland, the lagg was discontinuous and intermittent and more difficult to predict.

Nonlinear closed-loop control theory

International Nuclear Information System (INIS)

Perez, R.B.; Otaduy, P.J.; Abdalla, M.

1992-01-01

Traditionally, the control of nuclear power plants has been implemented by the use of proportional-integral (PI) control systems. PI controllers are both simple and, within their calibration range, highly reliable. However, PIs provide little performance information that could be used to diagnose out-of-range events or the nature of unanticipated transients that may occur in the plant. To go beyond the PI controller, the new control algorithms must deal with the physical system nonlinearities and with the reality of uncertain dynamics terms in its mathematical model. The tool to develop a new kind of control algorithm is provided by Optimal Control Theory. In this theory, a norm is minimized which incorporates the constraint that the model equations should be satisfied at all times by means of the Lagrange multipliers. Optimal control algorithms consist of two sets of coupled equations: (1) the model equations, integrated forward in time; and (2) the equations for the Lagrange multipliers (adjoints), integrated backwards in time. There are two challenges: dealing with large sets of coupled nonlinear equations and with a two-point boundary value problem that must be solved iteratively. In this paper, the rigorous conversion of the two-point boundary value problem into an initial value problem is presented. In addition, the incorporation into the control algorithm of ''real world'' constraints such as sensors and actuators, dynamic response functions and time lags introduced by the digitalization of analog signals is presented. (Author)

A numerical analysis for non-linear radiation in MHD flow around a cylindrical surface with chemically reactive species

Directory of Open Access Journals (Sweden)

Junaid Ahmad Khan

2018-03-01

Full Text Available Boundary layer flow around a stretchable rough cylinder is modeled by taking into account boundary slip and transverse magnetic field effects. The main concern is to resolve heat/mass transfer problem considering non-linear radiative heat transfer and temperature/concentration jump aspects. Using conventional similarity approach, the equations of motion and heat transfer are converted into a boundary value problem whose solution is computed by shooting method for broad range of slip coefficients. The proposed numerical scheme appears to improve as the strengths of magnetic field and slip coefficients are enhanced. Axial velocity and temperature are considerably influenced by a parameter M which is inversely proportional to the radius of cylinder. A significant change in temperature profile is depicted for growing wall to ambient temperature ratio. Relevant physical quantities such as wall shear stress, local Nusselt number and local Sherwood number are elucidated in detail. Keywords: Stretchable boundary, Thermal radiation, Chemical reaction, Mathematical modeling, Non-linear differential system, Mass transfer

Nonlinear Schroedinger equation with U(p,q) isotopical group

International Nuclear Information System (INIS)

Makhankov, V.G.; Pashaev, O.K.

1981-01-01

The properties of the nonlinear Schroedinger equation (NLS) with U(1,1) isogroup are considered in detail. This example illustrates the essential difference between the system and the well-known ''vector'' NLS, i.e. the large set of allowed boundary conditions on the fields that leads to a rich set of solutions of the system. Four types of boundary conditions and related soliton solutions are considered. The Bohr-Sommerfeld quantization allows to interpret them in terms of ''drops'' and ''bubbles'' as bound states of a large number of constituent bosons subject to the thermodynamical relations for gas mixtures. The U(1,1) system under the vanishing boundary conditions may be considered as continuous analog of the Hubbard model and therefore the paper is concluded by studying the inverse scattering equations for this case [ru

Additive operator-difference schemes splitting schemes

CERN Document Server

Vabishchevich, Petr N

2013-01-01

Applied mathematical modeling isconcerned with solving unsteady problems. This bookshows how toconstruct additive difference schemes to solve approximately unsteady multi-dimensional problems for PDEs. Two classes of schemes are highlighted: methods of splitting with respect to spatial variables (alternating direction methods) and schemes of splitting into physical processes. Also regionally additive schemes (domain decomposition methods)and unconditionally stable additive schemes of multi-component splitting are considered for evolutionary equations of first and second order as well as for sy

Alteration of split renal function during Captopril treatment

International Nuclear Information System (INIS)

Aburano, Tamio; Takayama, Teruhiko; Nakajima, Kenichi; Tonami, Norihisa; Hisada, Kinichi; Yasuhara, Shuichirou; Miyamori, Isamu; Takeda, Ryoyu

1987-01-01

Two different methods to evaluate the alteration of split renal function following continued Captopril treatment were studied in a total of 21 patients with hypertension. Eight patients with renovascular hypertension (five with unilateral renal artery stenosis and three with bilateral renal artery stenoses), three patients with diabetic nephropathy, one patient with primary aldosteronism, and nine patients with essential hypertension were included. The studies were performed the day prior to receiving Captopril (baseline), and 6th or 7th day following continued Captopril treatment (37.5 mg or 75 mg/day). Split effective renal plasma flow (ERPF) and glomerular filtration rate (GFR) after injections of I-131 hippuran and Tc-99m DTPA were measured using kidney counting corrected for depth and dose, described by Schlegel and Gates. In the patients with renovascular hypertension, split GFR in the stenotic kidney was significantly decreased 6th or 7th day following continued Captopril treatment compared to a baseline value. And split ERPF in the stenotic kidney was slightly increased although significant increase of split ERPF was not shown. In the patients with diabetic nephropathy, primary aldosteronism or essential hypertension, on the other hand, split GFR was not changed and split ERPF was slightly increased. These findings suggest that the Captopril induced alterations of split renal function may be of importance for the diagnosis of renovascular hypertension. For this purpose, split GFR determination is more useful than split ERPF determination. (author)

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

Science.gov (United States)

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

1993-04-01

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

The role of acoustic nonlinearity in tissue heating behind a rib cage using a high-intensity focused ultrasound phased array

Science.gov (United States)

Yuldashev, Petr V.; Shmeleva, Svetlana M.; Ilyin, Sergey A.; Sapozhnikov, Oleg A.; Gavrilov, Leonid R.; Khokhlova, Vera A.

2013-04-01

The goal of this study was to investigate theoretically the effects of nonlinear propagation in a high-intensity focused ultrasound (HIFU) field produced by a therapeutic phased array and the resultant heating of tissue behind a rib cage. Three configurations of focusing were simulated: in water, in water with ribs in the beam path and in water with ribs backed by a layer of soft tissue. The Westervelt equation was used to model the nonlinear HIFU field, and a 1 MHz phased array consisting of 254 circular elements was used as a boundary condition to the model. The temperature rise in tissue was modelled using the bioheat equation, and thermally necrosed volumes were calculated using the thermal dose formulation. The shapes of lesions predicted by the modelling were compared with those previously obtained in in vitro experiments at low-power sonications. Intensity levels at the face of the array elements that corresponded to the formation of high-amplitude shock fronts in the focal region were determined as 10 W cm-2 in the free field in water and 40 W cm-2 in the presence of ribs. It was shown that exposures with shocks provided a substantial increase in tissue heating, and its better spatial localization in the main focal region only. The relative effects of overheating ribs and splitting of the focus due to the periodic structure of the ribs were therefore reduced. These results suggest that utilizing nonlinear propagation and shock formation effects can be beneficial for inducing confined HIFU lesions when irradiating through obstructions such as ribs. Design of compact therapeutic arrays to provide maximum power outputs with lower intensity levels at the elements is necessary to achieve shock wave regimes for clinically relevant sonication depths in tissue.

Spin Splitting in Different Semiconductor Quantum Wells

International Nuclear Information System (INIS)

Hao Yafei

2012-01-01

We theoretically investigate the spin splitting in four undoped asymmetric quantum wells in the absence of external electric field and magnetic field. The quantum well geometry dependence of spin splitting is studied with the Rashba and the Dresselhaus spin-orbit coupling included. The results show that the structure of quantum well plays an important role in spin splitting. The Rashba and the Dresselhaus spin splitting in four asymmetric quantum wells are quite different. The origin of the distinction is discussed in this work. (condensed matter: electronic structure, electrical, magnetic, and optical properties)

Splitting Ward identity

Energy Technology Data Exchange (ETDEWEB)

Safari, Mahmoud [Institute for Research in Fundamental Sciences (IPM), School of Particles and Accelerators, P.O. Box 19395-5531, Tehran (Iran, Islamic Republic of)

2016-04-15

Within the background-field framework we present a path integral derivation of the splitting Ward identity for the one-particle irreducible effective action in the presence of an infrared regulator, and make connection with earlier works on the subject. The approach is general in the sense that it does not rely on how the splitting is performed. This identity is then used to address the problem of background dependence of the effective action at an arbitrary energy scale. We next introduce the modified master equation and emphasize its role in constraining the effective action. Finally, application to general gauge theories within the geometric approach is discussed. (orig.)

Splitting Ward identity

International Nuclear Information System (INIS)

Safari, Mahmoud

2016-01-01

Within the background-field framework we present a path integral derivation of the splitting Ward identity for the one-particle irreducible effective action in the presence of an infrared regulator, and make connection with earlier works on the subject. The approach is general in the sense that it does not rely on how the splitting is performed. This identity is then used to address the problem of background dependence of the effective action at an arbitrary energy scale. We next introduce the modified master equation and emphasize its role in constraining the effective action. Finally, application to general gauge theories within the geometric approach is discussed. (orig.)

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

Shear at Twin Domain Boundaries in YBa2Cu3O7-x

Science.gov (United States)

Caldwell, W. A.; Tamura, N.; Celestre, R. S.; MacDowell, A. A.; Padmore, H. A.; Geballe, T. H.; Koster, G.; Batterman, B. W.; Patel, J. R.

2004-05-01

The microstructure and strain state of twin domains in YBa2Cu3O7-x are discussed based upon synchrotron white-beam x-ray microdiffraction measurements. Intensity variations of the fourfold twin splitting of Laue diffraction peaks are used to determine the twin domain structure. Strain analysis shows that interfaces between neighboring twin domains are strained in shear, whereas the interior of these domains are regions of low strain. These measurements are consistent with the orientation relationships of twin boundaries within and across domains and show that basal plane shear stresses can exceed 100MPa where twin domains meet. Our results support stress field pinning of magnetic flux vortices by twin domain boundaries.

Pharmaceutical counselling about different types of tablet-splitting methods based on the results of weighing tests and mechanical development of splitting devices.

Science.gov (United States)

Somogyi, O; Meskó, A; Csorba, L; Szabó, P; Zelkó, R

2017-08-30

The division of tablets and adequate methods of splitting them are a complex problem in all sectors of health care. Although tablet-splitting is often required, this procedure can be difficult for patients. Four tablets were investigated with different external features (shape, score-line, film-coat and size). The influencing effect of these features and the splitting methods was investigated according to the precision and "weight loss" of splitting techniques. All four types of tablets were halved by four methods: by hand, with a kitchen knife, with an original manufactured splitting device and with a modified tablet splitter based on a self-developed mechanical model. The mechanical parameters (harness and friability) of the products were measured during the study. The "weight loss" and precision of splitting methods were determined and compared by statistical analysis. On the basis of the results, the external features (geometry), the mechanical parameters of tablets and the mechanical structure of splitting devices can influence the "weight loss" and precision of tablet-splitting. Accordingly, a new decision-making scheme was developed for the selection of splitting methods. In addition, the skills of patients and the specialties of therapy should be considered so that pharmaceutical counselling can be more effective regarding tablet-splitting. Copyright © 2017 Elsevier B.V. All rights reserved.

Iterative Splitting Methods for Differential Equations

CERN Document Server

Geiser, Juergen

2011-01-01

Iterative Splitting Methods for Differential Equations explains how to solve evolution equations via novel iterative-based splitting methods that efficiently use computational and memory resources. It focuses on systems of parabolic and hyperbolic equations, including convection-diffusion-reaction equations, heat equations, and wave equations. In the theoretical part of the book, the author discusses the main theorems and results of the stability and consistency analysis for ordinary differential equations. He then presents extensions of the iterative splitting methods to partial differential

[Nonlinear magnetohydrodynamics

International Nuclear Information System (INIS)

1994-01-01

Resistive MHD equilibrium, even for small resistivity, differs greatly from ideal equilibrium, as do the dynamical consequences of its instabilities. The requirement, imposed by Faraday's law, that time independent magnetic fields imply curl-free electric fields, greatly restricts the electric fields allowed inside a finite-resistivity plasma. If there is no flow and the implications of the Ohm's law are taken into account (and they need not be, for ideal equilibria), the electric field must equal the resistivity times the current density. The vanishing of the divergence of the current density then provides a partial differential equation which, together with boundary conditions, uniquely determines the scalar potential, the electric field, and the current density, for any given resistivity profile. The situation parallels closely that of driven shear flows in hydrodynamics, in that while dissipative steady states are somewhat more complex than ideal ones, there are vastly fewer of them to consider. Seen in this light, the vast majority of ideal MHD equilibria are just irrelevant, incapable of being set up in the first place. The steady state whose stability thresholds and nonlinear behavior needs to be investigated ceases to be an arbitrary ad hoc exercise dependent upon the whim of the investigator, but is determined by boundary conditions and choice of resistivity profile

Direct numerical simulation of a compressible boundary-layer flow past an isolated three-dimensional hump in a high-speed subsonic regime

Science.gov (United States)

De Grazia, D.; Moxey, D.; Sherwin, S. J.; Kravtsova, M. A.; Ruban, A. I.

2018-02-01

In this paper we study the boundary-layer separation produced in a high-speed subsonic boundary layer by a small wall roughness. Specifically, we present a direct numerical simulation (DNS) of a two-dimensional boundary-layer flow over a flat plate encountering a three-dimensional Gaussian-shaped hump. This work was motivated by the lack of DNS data of boundary-layer flows past roughness elements in a similar regime which is typical of civil aviation. The Mach and Reynolds numbers are chosen to be relevant for aeronautical applications when considering small imperfections at the leading edge of wings. We analyze different heights of the hump: The smaller heights result in a weakly nonlinear regime, while the larger result in a fully nonlinear regime with an increasing laminar separation bubble arising downstream of the roughness element and the formation of a pair of streamwise counterrotating vortices which appear to support themselves.

Nonlinear parabolic problems with Neumann-type boundary conditions and L^1-data

Directory of Open Access Journals (Sweden)

Abderrahmane El Hachimi

2007-11-01

$$ \\frac{\\partial u}{\\partial t}-\\triangle_{p}u+\\alpha(u=f \\quad \\text{in } ]0,\\ T[\\times\\Omega, $$ with Neumann-type boundary conditions and initial data in $L^1$. Our approach is based essentially on the time discretization technique by Euler forward scheme.

2-Photon tandem device for water splitting

DEFF Research Database (Denmark)

Seger, Brian; Castelli, Ivano Eligio; Vesborg, Peter Christian Kjærgaard

2014-01-01

Within the field Of photocatalytic water splitting there are several strategies to achieve the goal of efficient and cheap photocatalytic water splitting. This work examines one particular strategy by focusing on monolithically stacked, two-photon photoelectrochemical cells. The overall aim...... for photocatalytic water splitting by using a large bandgap photocathode and a low bandgap photoanode with attached protection layers....

Machine learning control taming nonlinear dynamics and turbulence

CERN Document Server

Duriez, Thomas; Noack, Bernd R