Unified approach to split absorbing boundary conditions for nonlinear Schrödinger equations.
Zhang, Jiwei; Xu, Zhenli; Wu, Xiaonan
2008-08-01
An efficient method is proposed for numerical solutions of nonlinear Schrödinger equations on an unbounded domain. Through approximating the kinetic energy term by a one-way equation and uniting it with the potential energy equation, absorbing boundary conditions are designed to truncate the unbounded domain, which are in nonlinear form and can perfectly absorb waves outgoing from the boundaries of the truncated computational domain. The stability of the induced initial boundary value problem defined on the computational domain is examined by a normal mode analysis. Numerical examples are given to illustrate the stable and tractable advantages of the method.
Zhang, Jiwei; Xu, Zhenli; Wu, Xiaonan
2009-04-01
This paper aims to design local absorbing boundary conditions (LABCs) for the two-dimensional nonlinear Schrödinger equations on a rectangle by extending the unified approach. Based on the time-splitting idea, the main process of the unified approach is to approximate the kinetic energy part by a one-way equation, unite it with the potential energy equation, and then obtain the well-posed and accurate LABCs on the artificial boundaries. In the corners, we use the (1,1)-Padé approximation to the kinetic term and also unite it with the nonlinear term to give some local corner boundary conditions. Numerical tests are given to verify the stable and tractable advantages of the method.
A comparison of boundary correction methods for Strang splitting
Einkemmer, Lukas
2016-01-01
In this paper we consider splitting methods in the presence of non-homogeneous boundary conditions. In particular, we consider the corrections that have been described and analyzed in Einkemmer, Ostermann 2015 and Alonso-Mallo, Cano, Reguera 2016. The latter method is extended to the non-linear case, and a rigorous convergence analysis is provided. We perform numerical simulations for diffusion-reaction, advection-reaction, and dispersion-reaction equations in order to evaluate the relative performance of these two corrections. Furthermore, we introduce an extension of both methods to obtain order three locally and evaluate under what circumstances this is beneficial.
Boundary induced nonlinearities at small Reynolds numbers
Sbragaglia, M.; Sugiyama, K.
2007-01-01
We investigate the importance of boundary slip at finite Reynolds numbers for mixed boundary conditions. Nonlinear effects are induced by the non-homogeneity of the boundary condition and change the symmetry properties of the flow with an overall mean flow reduction. To explain the observed drag
Local absorbing boundary conditions for nonlinear wave equation on unbounded domain.
Li, Hongwei; Wu, Xiaonan; Zhang, Jiwei
2011-09-01
The numerical solution of the nonlinear wave equation on unbounded spatial domain is considered. The artificial boundary method is introduced to reduce the nonlinear problem on unbounded spatial domain to an initial boundary value problem on a bounded domain. Using the unified approach, which is based on the operator splitting method, we construct the efficient nonlinear local absorbing boundary conditions for the nonlinear wave equation, and give the stability analysis of the resulting boundary conditions. Finally, several numerical examples are given to demonstrate the effectiveness of our method.
Boundary Controllability of Nonlinear Fractional Integrodifferential Systems
Directory of Open Access Journals (Sweden)
Ahmed HamdyM
2010-01-01
Full Text Available Sufficient conditions for boundary controllability of nonlinear fractional integrodifferential systems in Banach space are established. The results are obtained by using fixed point theorems. We also give an application for integropartial differential equations of fractional order.
The nonlinear fixed gravimetric boundary value problem
Institute of Scientific and Technical Information of China (English)
于锦海; 朱灼文
1995-01-01
The properly-posedness of the nonlinear fixed gravimetric boundary value problem is shown with the help of nonlinear functional analysis and a new iterative method to solve the problem is also given, where each step of the iterative program is reduced to solving one and the same kind of oblique derivative boundary value problem with the same type. Furthermore, the convergence of the iterative program is proved with Schauder estimate of elliptic differential equation.
Nonlinear Fracture Mechanics and Plasticity of the Split Cylinder Test
DEFF Research Database (Denmark)
Olesen, John Forbes; Østergaard, Lennart; Stang, Henrik
2006-01-01
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......The split cylinder testis subjected to an analysis combining nonlinear fracture mechanics and plasticity. The fictitious crack model is applied for the analysis of splitting tensile fracture, and the Mohr-Coulomb yield criterion is adopted for modelling the compressive crushing/sliding failure. Two...
Nonlinear Boundary Stabilization of Nonuniform Timoshenko Beam
Institute of Scientific and Technical Information of China (English)
Qing-xu Yan; Hui-chao Zou; De-xing Feng
2003-01-01
In this paper, the stabilization problem of nonuniform Timoshenko beam by some nonlinear boundary feedback controls is considered. By virtue of nonlinear semigroup theory, energy-perturbed approach and exponential multiplier method, it is shown that the vibration of the beam under the proposed control action decays exponentially or in negative power of time t as t →∞.
Writing on Boundaries: The Split Subject in Chinese Canadian Literature
Institute of Scientific and Technical Information of China (English)
Xie Shaobo
2005-01-01
This article provides a conceptual grasp of the corpus of work produced by Chinese Canadian writers and a framework for analysing its tropes and interpreting their political resonance. It defines the Chinese Canadian work as a three-phase counterhegemonic discourse: Writing back into a forbidden past; negotiating into the present; writing on boundaries. For the ambivalent, split diasporic subject to negotiate into the present from the forbidden past is to reinscribe itself as a locus of crisis, a non-identity, a doubling, a third term. Writing on boundaries can be read as a strategy of decolonization deployed by the subaltern in striving for self-vindication and self-fulfilment.
The Benefit of Split Nonlinearity Compensation for Optical Fiber Communications
Lavery, Domanic; Liga, Gabriele; Alvarado, Alex; Savory, Seb J; Bayvel, Polina
2015-01-01
In this Letter we analyze the benefit of digital compensation of fiber nonlinearity, where the digital signal processing is divided between the transmitter and receiver. The application of the Gaussian noise model indicates that, where there are two or more spans, it is always beneficial to split the nonlinearity compensation. The theory is verified via numerical simulations, investigating transmission of single channel 50 GBd polarization division multiplexed 256-ary quadrature amplitude modulation over 100 km standard single mode fiber spans, using lumped amplification. For this case, the additional increase in mutual information achieved over transmitter- or receiver-side nonlinearity compensation is approximately 1 bit for distances greater than 2000 km. Further, it is shown, theoretically, that the SNR gain for long distances and high bandwidth transmission is 1.5 dB versus transmitter- or receiver-based nonlinearity compensation.
Topological invariants in nonlinear boundary value problems
Energy Technology Data Exchange (ETDEWEB)
Vinagre, Sandra [Departamento de Matematica, Universidade de Evora, Rua Roma-tilde o Ramalho 59, 7000-671 Evora (Portugal)]. E-mail: smv@uevora.pt; Severino, Ricardo [Departamento de Matematica, Universidade do Minho, Campus de Gualtar, 4710-057 Braga (Portugal)]. E-mail: ricardo@math.uminho.pt; Ramos, J. Sousa [Departamento de Matematica, Instituto Superior Tecnico, Av. Rovisco Pais 1, 1049-001 Lisbon (Portugal)]. E-mail: sramos@math.ist.utl.pt
2005-07-01
We consider a class of boundary value problems for partial differential equations, whose solutions are, basically, characterized by the iteration of a nonlinear function. We apply methods of symbolic dynamics of discrete bimodal maps in the interval in order to give a topological characterization of its solutions.
An almost symmetric Strang splitting scheme for nonlinear evolution equations.
Einkemmer, Lukas; Ostermann, Alexander
2014-07-01
In this paper we consider splitting methods for the time integration of parabolic and certain classes of hyperbolic partial differential equations, where one partial flow cannot be computed exactly. Instead, we use a numerical approximation based on the linearization of the vector field. This is of interest in applications as it allows us to apply splitting methods to a wider class of problems from the sciences. However, in the situation described, the classic Strang splitting scheme, while still being a method of second order, is not longer symmetric. This, in turn, implies that the construction of higher order methods by composition is limited to order three only. To remedy this situation, based on previous work in the context of ordinary differential equations, we construct a class of Strang splitting schemes that are symmetric up to a desired order. We show rigorously that, under suitable assumptions on the nonlinearity, these methods are of second order and can then be used to construct higher order methods by composition. In addition, we illustrate the theoretical results by conducting numerical experiments for the Brusselator system and the KdV equation.
SOLVABILITY FOR NONLINEAR ELLIPTIC EQUATION WITH BOUNDARY PERTURBATION
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The solvability of nonlinear elliptic equation with boundary perturbation is considered. The perturbed solution of original problem is obtained and the uniformly valid expansion of solution is proved.
Differentiability at lateral boundary for fully nonlinear parabolic equations
Ma, Feiyao; Moreira, Diego R.; Wang, Lihe
2017-09-01
For fully nonlinear uniformly parabolic equations, the first derivatives regularity of viscosity solutions at lateral boundary is studied under new Dini type conditions for the boundary, which is called Reifenberg Dini conditions and is weaker than usual Dini conditions.
Black holes in nonlinear electrodynamics: Quasinormal spectra and parity splitting
Chaverra, Eliana; Degollado, Juan Carlos; Moreno, Claudia; Sarbach, Olivier
2016-06-01
We discuss the quasinormal oscillations of black holes which are sourced by a nonlinear electrodynamic field. While previous studies have focused on the computation of quasinormal frequencies for the wave or higher spin equation on a fixed background geometry described by such black holes, here we compute for the first time the quasinormal frequencies for the coupled electromagnetic-gravitational linear perturbations. To this purpose, we consider a parametrized family of Lagrangians for the electromagnetic field which contains the Maxwell Lagrangian as a special case. In the Maxwell case, the unique spherically symmetric black hole solutions are described by the Reissner-Nordström family and in this case it is well known that the quasinormal spectra in the even- and odd-parity sectors are identical to each other. However, when moving away from the Maxwell case, we obtain deformed Reissner-Nordström black holes, and we show that in this case there is a parity splitting in the quasinormal mode spectra. A partial explanation for this phenomena is provided by considering the eikonal (high-frequency) limit.
Asymptotic behavior of solutions to nonlinear parabolic equation with nonlinear boundary conditions
Directory of Open Access Journals (Sweden)
Diabate Nabongo
2008-01-01
Full Text Available We show that solutions of a nonlinear parabolic equation of second order with nonlinear boundary conditions approach zero as t approaches infinity. Also, under additional assumptions, the solutions behave as a function determined here.
Boundary control of long waves in nonlinear dispersive systems
DEFF Research Database (Denmark)
Hasan, Agus; Foss, Bjarne; Aamo, Ole Morten
2011-01-01
Unidirectional propagation of long waves in nonlinear dispersive systems may be modeled by the Benjamin-Bona-Mahony-Burgers equation, a third order partial differential equation incorporating linear dissipative and dispersive terms, as well as a term covering nonlinear wave phenomena. For higher...... orders of the nonlinearity, the equation may have unstable solitary wave solutions. Although it is a one dimensional problem, achieving a global result for this equation is not trivial due to the nonlinearity and the mixed partial derivative. In this paper, two sets of nonlinear boundary control laws...... that achieve global exponential stability and semi-global exponential stability are derived for both linear and nonlinear cases....
Pulse splitting in nonlinear media with anisotropic dispersion properties
DEFF Research Database (Denmark)
Bergé, L.; Juul Rasmussen, J.; Schmidt, M.R.
1998-01-01
to a singularity in the transverse plane. Instead, the pulse spreads out along the direction of negative dispersion and splits up into small-scale cells, which may undergo further splitting events. The analytical results are supported by direct numerical solutions of the three dimensional cubic Schrodinger...
THIRD-ORDER NONLINEAR SINGULARLY PERTURBED BOUNDARY VALUE PROBLEM
Institute of Scientific and Technical Information of China (English)
王国灿; 金丽
2002-01-01
Third order singulary perturbed boundary value problem by means of differential inequality theories is studied. Based on the given results of second order nonlinear boundary value problem, the upper and lower solutions method of third order nonlinear boundary value problems by making use of Volterra type integral operator was established.Specific upper and lower solutions were constructed, and existence and asymptotic estimates of solutions under suitable conditions were obtained.The result shows that it seems to be new to apply these techniques to solving these kinds of third order singularly perturbed boundary value problem. An example is given to demonstrate the applications.
Boundary controllability for a nonlinear beam equation
Directory of Open Access Journals (Sweden)
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.
Nonlinear Vibrations of Timoshenko Beams with Various Boundary Conditions
Institute of Scientific and Technical Information of China (English)
郭强; 刘曦; 钟宏志
2004-01-01
This paper is concerned with the effects of boundary conditions on the large-amplitude free vibrations of Timoshenko beams. The effects of nonlinear terms on the frequency of Timoshenko beams with simply supported ends (supported-supported, SS), clamped ends (clamped-clamped, CC) and one end simply supported and the other end clamped (clamped-supported, CS) are discussed in detail. Given a specific vibration amplitude, the change of nonlinear frequency according to the effects of boundary conditions is always in the following descending order: SS, CS, and CC. It is found that the slenderness ratio has a significant influence on the nonlinear frequency. For slender beams, the nonlinear effects of bending curvature and shear strain are negligible regardless of the boundary conditions. For short beams and especially for those of large amplitude vibrations, however, the nonlinear effects of bending curvature and shear strain become noticeable in the following ascending order: SS, CS, and CC.
NONLINEAR BOUNDARY STABILIZATION OF WAVE EQUATIONS WITH VARIABLE C OEFFICIENTS
Institute of Scientific and Technical Information of China (English)
冯绍继; 冯德兴
2003-01-01
The wave equation with variable coefficients with a nonlinear dissipative boundary feedbackis studied. By the Riemannian geometry method and the multiplier technique, it is shown thatthe closed loop system decays exponentially or asymptotically, and hence the relation betweenthe decay rate of the system energy and the nonlinearity behavior of the feedback function isestablished.
Robust Monotone Iterates for Nonlinear Singularly Perturbed Boundary Value Problems
Directory of Open Access Journals (Sweden)
Boglaev Igor
2009-01-01
Full Text Available This paper is concerned with solving nonlinear singularly perturbed boundary value problems. Robust monotone iterates for solving nonlinear difference scheme are constructed. Uniform convergence of the monotone methods is investigated, and convergence rates are estimated. Numerical experiments complement the theoretical results.
BOUNDARY LAYER AND VANISHING DIFFUSION LIMIT FOR NONLINEAR EVOLUTION EQUATIONS
Institute of Scientific and Technical Information of China (English)
彭艳
2014-01-01
In this paper, we consider an initial-boundary value problem for some nonlinear evolution equations with damping and diffusion. The main purpose is to investigate the boundary layer effect and the convergence rates as the diffusion parameterαgoes to zero.
Nonlinear Second-Order Multivalued Boundary Value Problems
Indian Academy of Sciences (India)
Leszek Gasiński; Nikolaos S Papageorgiou
2003-08-01
In this paper we study nonlinear second-order differential inclusions involving the ordinary vector -Laplacian, a multivalued maximal monotone operator and nonlinear multivalued boundary conditions. Our framework is general and unifying and incorporates gradient systems, evolutionary variational inequalities and the classical boundary value problems, namely the Dirichlet, the Neumann and the periodic problems. Using notions and techniques from the nonlinear operatory theory and from multivalued analysis, we obtain solutions for both the `convex' and `nonconvex' problems. Finally, we present the cases of special interest, which fit into our framework, illustrating the generality of our results.
Operator splitting for partial differential equations with Burgers nonlinearity
Holden, Helge; Risebro, Nils Henrik
2011-01-01
We provide a new analytical approach to operator splitting for equations of the type $u_t=Au+u u_x$ where $A$ is a linear differential operator such that the equation is well-posed. Particular examples include the viscous Burgers' equation, the Korteweg-de Vries (KdV) equation, the Benney-Lin equation, and the Kawahara equation. We show that the Strang splitting method converges with the expected rate if the initial data are sufficiently regular. In particular, for the KdV equation we obtain second-order convergence in $H^r$ for initial data in $H^{r+5}$ with arbitrary $r\\ge 1$.
Boundary control of nonlinear coupled heat systems using backstepping
Bendevis, Paul
2016-10-20
A state feedback boundary controller is designed for a 2D coupled PDE system modelling heat transfer in a membrane distillation system for water desalination. Fluid is separated into two compartments with nonlinear coupling at a membrane boundary. The controller sets the temperature on one boundary in order to track a temperature difference across the membrane boundary. The control objective is achieved by an extension of backstepping methods to these coupled equations. Stability of the target system via Lyapunov like methods, and the invertibility of the integral transformation are used to show the stability of the tracking error.
Multi-Symplectic Splitting Method for Two-Dimensional Nonlinear Schriidinger Equation
Institute of Scientific and Technical Information of China (English)
陈亚铭; 朱华君; 宋松和
2011-01-01
Using the idea of splitting numerical methods and the multi-symplectic methods, we propose a multisymplectic splitting （MSS） method to solve the two-dimensional nonlinear Schrodinger equation （2D-NLSE） in this paper. It is further shown that the method constructed in this way preserve the global symplectieity exactly. Numerical experiments for the plane wave solution and singular solution of the 2D-NLSE show the accuracy and effectiveness of the proposed method.
Creating and refining boundaries--church splitting among Pentecostal Vietnamese migrants in Berlin.
Hüwelmeier, Gertrud
2013-06-01
In many parts of the world, Pentecostalism is becoming the fastest growing religious movement. As a result of migration, people from Asia, Africa and Latin America carry religious ideas and practices across borders, in other cases, migrants establish religious networks in the diaspora. However, while embracing newcomers from various backgrounds, Pentecostal believers constantly cross cultural boundaries by incorporating people from different ethnic, national and language backgrounds. While Pentecostal charismatic practitioners blurr boundaries in many situations, simultaneously, they create 'bright boundaries' by rejecting 'traditional' religious practices, imagined as the Other of Pentecostalism and thus to be eliminated. By referring to the concept of boundaries (Barth 1969; Alba (Ethnic and Racial Studies 1:20-69, 2005)) this article argues that charismatic Pentecostal Christianity, alongside its embracing practices with regard to social, ethnic and political boundaries, generates religious boundaries: First, church members reject "traditional" religious practices such as ancestor veneration and spirit possession, practices migrants carry across borders. Second, Pentecostal believers create boundaries towards those who split from the church. By exploring the ambiguities of migrant converts, I will investigate, how some of them subvert and reject control and authority exerted by religious leaders. Therefore, this article, based on ethnographic fieldwork among Vietnamese Pentecostalists, contributes to widely underresearched practices of boundary making and church splitting in the diaspora.
Nonlinear Boundary Dynamics and Chiral Symmetry in Holographic QCD
Albrecht, Dylan; Wilcox, Ronald J
2011-01-01
In the hard-wall model of holographic QCD we find that nonlinear boundary dynamics are required in order to maintain the correct pattern of explicit and spontaneous chiral symmetry breaking beyond leading order in the pion fields. With the help of a field redefinition, we demonstrate that the requisite nonlinear boundary conditions are consistent with the Sturm-Liouville structure required for the Kaluza-Klein decomposition of bulk fields. Observables insensitive to the chiral limit receive only small corrections in the improved description, and classical calculations in the hard-wall model remain surprisingly accurate.
Critical Exponents for Fast Diffusion Equations with Nonlinear Boundary Sources
Institute of Scientific and Technical Information of China (English)
WANG LU-SHENG; WANG ZE-JIA
2011-01-01
In this paper, we study the large time behavior of solutions to a class of fast diffusion equations with nonlinear boundary sources on the exterior domain of the unit ball. We are interested in the critical global exponent q0 and the critical Fujita exponent qc for the problem considered, and show that q0 ＝ qc for the multidimensional Non-Newtonian polytropic filtration equation with nonlinear boundary sources, which is quite different from the known results that q0 ＜ qc for the onedimensional case; moreover, the value is different from the slow case.
The benefit of split nonlinearity compensation for single channel optical fiber communications
Lavery, D.; Ives, David J; Liga, Gabriele; Alvarado, A Alex; Savory, SJ; Bayvel, P.
2016-01-01
In this letter, we analyze the benefit of digital compensation of fiber nonlinearity, where the digital signal processing is divided between the transmitter and the receiver. The application of the Gaussian noise model indicates that, where there are two or more spans, it is always beneficial to split the nonlinearity compensation. The theory is verified via numerical simulations, investigating the transmission of a single-channel 50-GBd polarization division multiplexed 4- and 256-ary quadra...
INITIAL BOUNDARY VALUE PROBLEM FOR A DAMPED NONLINEAR HYPERBOLIC EQUATION
Institute of Scientific and Technical Information of China (English)
陈国旺
2003-01-01
In the paper, the existence and uniqueness of the generalized global solution and the classical global solution of the initial boundary value problems for the nonlinear hyperbolic equationare proved by Galerkin method and the sufficient conditions of blow-up of solution in finite time are given.
QUASILINEAR ELLIPTIC BOUNDARY VALUE PROBLEMS WITH DISCONTINUOUS NONLINEARITIES
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
In this paper we shall consider a discontinuous nonlinear nonmonotone elliptic boundary value problem, i.e. a quasilinear elliptic hemivariational inequality. This kind of problems is strongly motivated by various problems in mechanics. By use of the notion of the generalized gradient of Clarke and the theory of pseudomonotone operators, we will prove the existence of solutions.
Chin, Siu A
2007-01-01
Since the kinetic and the potential energy term of the real time nonlinear Schr\\"odinger equation can each be solved exactly, the entire equation can be solved to any order via splitting algorithms. We verified the fourth-order convergence of some well known algorithms by solving the Gross-Pitaevskii equation numerically. All such splitting algorithms suffer from a latent numerical instability even when the total energy is very well conserved. A detail error analysis reveals that the noise, or elementary excitations of the nonlinear Schr\\"odinger, obeys the Bogoliubov spectrum and the instability is due to the exponential growth of high wave number noises caused by the splitting process. For a continuum wave function, this instability is unavoidable no matter how small the time step. For a discrete wave function, the instability can be avoided only for $\\dt k_{max}^2{<\\atop\\sim}2 \\pi$, where $k_{max}=\\pi/\\Delta x$.
Nonlinear Schrodinger equations on the half-line with nonlinear boundary conditions
Directory of Open Access Journals (Sweden)
Ahmet Batal
2016-08-01
Full Text Available In this article, we study the initial boundary value problem for nonlinear Schrodinger equations on the half-line with nonlinear boundary conditions $$ u_x(0,t+\\lambda|u(0,t|^ru(0,t=0,\\quad \\lambda\\in\\mathbb{R}-\\{0\\},\\; r> 0. $$ We discuss the local well-posedness when the initial data $u_0=u(x,0$ belongs to an $L^2$-based inhomogeneous Sobolev space $H^s(\\mathbb{R}_+$ with $s\\in (\\frac{1}{2},\\frac{7}{2}-\\{\\frac{3}{2}\\}$. We deal with the nonlinear boundary condition by first studying the linear Schrodinger equation with a time-dependent inhomogeneous Neumann boundary condition $u_x(0,t=h(t$ where $h\\in H^{\\frac{2s-1}{4}}(0,T$.
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
With the aid of a nonlinear transformation, a class of nonlinear convectiondiffusion PDE in one space dimension is converted into a linear one, the unique solution of a nonlinear boundary-initial value problem for the nonlinear PDE can be exactly expressed by the nonlinear transformation, and several illustrative examples are given
Ramsay, Joseph; Kohler, Monica D.; Davis, Paul M.; Wang, Xinguo; Holt, William; Weeraratne, Dayanthie S.
2016-10-01
SKS arrivals from ocean bottom seismometer (OBS) data from an offshore southern California deployment are analysed for shear wave splitting. The project involved 34 OBSs deployed for 12 months in a region extending up to 500 km west of the coastline into the oceanic Pacific plate. The measurement process consisted of removing the effects of anisotropy using a range of values for splitting fast directions and delay times to minimize energy along the transverse seismometer axis. Computed splitting parameters are unexpectedly similar to onland parameters, exhibiting WSW-ENE fast polarization directions and delays between 0.8 and 1.8 s, even for oceanic plate sites. This is the first SKS splitting study to extend across the entire boundary between the North America and Pacific plates, into the oceanic part of the Pacific plate. The splitting results show that the fast direction of anisotropy on the Pacific plate does not align with absolute plate motion (APM), and they extend the trend of anisotropy in southern California an additional 500 km west, well onto the oceanic Pacific plate. We model the finite strain and anisotropy within the asthenosphere associated with density-buoyancy driven mantle flow and the effects of APM. In the absence of plate motion effects, such buoyancy driven mantle flow would be NE-directed beneath the Pacific plate observations. The best-fit patterns of mantle flow are inferred from the tomography-based models that show primary influences from foundering higher-density zones associated with the history of subduction beneath North America. The new offshore SKS measurements, when combined with measurements onshore within the plate boundary zone, indicate that dramatic lateral variations in density-driven upper-mantle flow are required from offshore California into the plate boundary zone in California and western Basin and Range.
Pump induced normal mode splittings in phase conjugation in a Kerr nonlinear waveguide
Indian Academy of Sciences (India)
S Dutta Gupta
2000-03-01
Phase conjugation in a Kerr nonlinear waveguide is studied with counter-propagating normally incident pumps and a probe beam at an arbitrary angle of incidence. Detailed numerical results for the specular and phase conjugated reﬂectivities are obtained with full account of pump depletion. For sufﬁcient strengths of the pump a normal mode splitting is demonstrated in both the specular and the phase conjugated reﬂectivities of the probe wave. The splitting is explained in terms of a simple model under undepleted pump approximation.
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.
Nonlinear interaction of two waves in boundary-layer flows
Nayfeh, A. H.; Bozatli, A. N.
1980-01-01
First-order nonlinear interactions of Tollmien-Schlichting waves of different frequencies and initial amplitudes in boundary-layer flows are analyzed using the method of multiple scales. Numerical results for flow past a flat plate show that the spatial detuning wipes out resonant interactions unless the initial amplitudes are very large. Thus, a wave having a moderate amplitude has little influence on its subharmonic although it has a strong influence on its second harmonic. Moreover, two waves having moderate amplitudes have a strong influence on their difference frequency. The results show that the difference frequency can be very unstable when generated by the nonlinear interaction, even though it may be stable when introduced by itself in the boundary layer.
Controlling near shore nonlinear surging waves through bottom boundary conditions
Mukherjee, Abhik; Kundu, Anjan
2016-01-01
Instead of taking the usual passive view for warning of near shore surging waves including extreme waves like tsunamis, we aim to study the possibility of intervening and controlling nonlinear surface waves through the feedback boundary effect at the bottom. It has been shown through analytic result that the controlled leakage at the bottom may regulate the surface solitary wave amplitude opposing the hazardous variable depth effect. The theoretical results are applied to a real coastal bathymetry in India.
On Nonlinear Approximations to Cosmic Problems with Mixed Boundary Conditions
Mancinelli, Paul J.; Yahil, Amos; Ganon, Galit; Dekel, Avishai
1993-01-01
Nonlinear approximations to problems with mixed boundary conditions are useful for predicting large-scale streaming velocities from the density field, or vice-versa. We evaluate the schemes of Bernardeau \\cite{bernardeau92}, Gramann \\cite{gramann93}, and Nusser \\etal \\cite{nusser91}, using smoothed density and velocity fields obtained from $N$-body simulations of a CDM universe. The approximation of Nusser \\etal is overall the most accurate and robust. For Gaussian smoothing of 1000\\kms\\ the ...
Tracking control of a flexible beam by nonlinear boundary feedback
Directory of Open Access Journals (Sweden)
Bao-Zhu Guo
1995-01-01
Full Text Available This paper is concerned with tracking control of a dynamic model consisting of a flexible beam rotated by a motor in a horizontal plane at the one end and a tip body rigidly attached at the free end. The well-posedness of the closed loop systems considering the dissipative nonlinear boundary feedback is discussed and the asymptotic stability about difference energy of the hybrid system is also investigated.
The Benefit of Split Nonlinearity Compensation for Single-Channel Optical Fiber Communications
Lavery, Domanic; Ives, David; Liga, Gabriele; Alvarado, Alex; Savory, Seb J.; Bayvel, Polina
2016-09-01
In this Letter we analyze the benefit of digital compensation of fiber nonlinearity, where the digital signal processing is divided between the transmitter and receiver. The application of the Gaussian noise model indicates that, where there are two or more spans, it is always beneficial to split the nonlinearity compensation. The theory is verified via numerical simulations, investigating transmission of single channel 50 GBd polarization division multiplexed 256-ary quadrature amplitude modulation over 100 km standard single mode fiber spans, using lumped amplification. For this case, the additional increase in mutual information achieved over transmitter- or receiver-side nonlinearity compensation is approximately 1 bit for distances greater than 2000 km. Further, it is shown, theoretically, that the SNR gain for long distances and high bandwidth transmission is 1.5 dB versus transmitter- or receiver-based nonlinearity compensation.
RESTRICTED NONLINEAR APPROXIMATION AND SINGULAR SOLUTIONS OF BOUNDARY INTEGRAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
Reinhard Hochmuth
2002-01-01
This paper studies several problems, which are potentially relevant for the construction of adaptive numerical schemes. First, biorthogonal spline wavelets on [0,1 ] are chosen as a starting point for characterizations of functions in Besov spaces B , (0,1) with 0＜σ＜∞ and (1+σ)-1＜τ＜∞. Such function spaces are known to be related to nonlinear approximation. Then so called restricted nonlinear approximation procedures with respect to Sobolev space norms are considered. Besides characterization results Jackson type estimates for various tree-type and tresholding algorithms are investigated. Finally known approximation results for geometry induced singularity functions of boundary integeral equations are combined with the characterization results for restricted nonlinear approximation to show Besov space regularity results.
ON NONLINEAR STABILITY IN NONPARALLEL BOUNDARY LAYER FLOW
Institute of Scientific and Technical Information of China (English)
TANG Deng-bin; WANG Wei-zhi
2004-01-01
The nonlinear stability problem in nonparallel boundary layer flow for two-dimensional disturbances was studied by using a newly presented method called Parabolic Stability Equations (PSE). A series of new modes generated by the nonlinear interaction of disturbance waves were tabulately analyzed, and the Mean Flow Distortion (MFD) was numerically given. The computational techniques developed, including the higher-order spectral method and the more effective algebraic mapping, increased greatly the numerical accuracy and the rate of convergence. With the predictor-corrector approach in the marching procedure, the normalization condition was satisfied, and the stability of numerical calculation could be ensured. With different initial amplitudes, the nonlinear stability of disturbance wave was studied. The results of examples show good agreement with the data given by the DNS using the full Navier-Stokes equations.
Asymptotic analysis of a vibrating cantilever with a nonlinear boundary
Institute of Scientific and Technical Information of China (English)
C.; W.; LIM
2009-01-01
Nonlinear vibration of a cantilever in a contact atomic force microscope is analyzed via an asymptotic approach. The asymptotic solution is sought for a beam equation with a nonlinear boundary condition. The steady-state responses are determined in primary resonance and subharmonic resonance. The relations between the response amplitudes and the excitation frequencies and amplitudes are derived from the solvability condition. Multivaluedness occurs in the relations as a consequence of the nonlinearity. The stability of steady-state responses is analyzed by use of the Lyapunov linearized stability theory. The stability analysis predicts the jumping phenomenon for certain parameters. The curves of the response amplitudes changing with the excitation frequencies are numerically compared with those obtained via the method of multiple scales. The calculation results demonstrate that the two methods predict the same varying tendencies while there are small quantitative differences.
Asymptotic analysis of a vibrating cantilever with a nonlinear boundary
Institute of Scientific and Technical Information of China (English)
CHEN LiQun; C.W.LIM; HU QingQuan; DING Hu
2009-01-01
Nonlinear vibration of a cantilever in a contact atomic force microscope is analyzed via an asymptotic approach.The asymptotic solution is sought for a beam equation with a nonlinear boundary condition.The steady-state responses are determined in primary resonance and subharmonic resonance.The relations between the response amplitudes and the excitation frequencies and amplitudes are derived from the solvability condition.Multivaluedness occurs in the relations as a consequence of the nonlinearity.The stability of steady-state responses is analyzed by use of the Lyapunov linearized sta-bility theory.The stability analysis predicts the jumping phenomenon for certain parameters.The curves of the response amplitudes changing with the excitation frequencies are numerically compared with those obtained via the method of multiple scales.The calculation results demonstrate that the two methods predict the same varying tendencies while there are small quantitative differences.
Asymptotic analysis of a vibrating cantilever with a nonlinear boundary
Chen, Liqun; Lim, C. W.; Hu, Qingquan; Ding, Hu
2009-09-01
Nonlinear vibration of a cantilever in a contact atomic force microscope is analyzed via an asymptotic approach. The asymptotic solution is sought for a beam equation with a nonlinear boundary condition. The steady-state responses are determined in primary resonance and subharmonic resonance. The relations between the response amplitudes and the excitation frequencies and amplitudes are derived from the solvability condition. Multivaluedness occurs in the relations as a consequence of the nonlinearity. The stability of steady-state responses is analyzed by use of the Lyapunov linearized stability theory. The stability analysis predicts the jumping phenomenon for certain parameters. The curves of the response amplitudes changing with the excitation frequencies are numerically compared with those obtained via the method of multiple scales. The calculation results demonstrate that the two methods predict the same varying tendencies while there are small quantitative differences.
2015-06-01
HIGHER-ORDER TREATMENTS OF BOUNDARY CONDITIONS IN SPLIT-STEP FOURIER PARABOLIC EQUATION MODELS by Savas Erdim June 2015 Thesis Advisor...CONDITIONS IN SPLIT-STEP FOURIER PARABOLIC EQUATION MODELS 5. FUNDING NUMBERS 6. AUTHOR(S) Savas Erdim 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES... Parabolic equation models solved using the split-step Fourier (SSF) algorithm, such as the Monterey Miami Parabolic Equation model, are commonly used
Nonlinear Vibration Analysis of Moving Strip with Inertial Boundary Condition
Directory of Open Access Journals (Sweden)
Chong-yi Gao
2015-01-01
Full Text Available According to the movement mechanism of strip and rollers in tandem mill, the strip between two stands was simplified to axially moving Euler beam and the rollers were simplified to the inertial component on the fixed axis rotation, namely, inertial boundary. Nonlinear vibration mechanical model of Euler beam with inertial boundary conditions was established. The transverse and longitudinal motion equations were derived based on Hamilton’s principle. Kantorovich averaging method was employed to discretize the motion equations and the inertial boundary equations, and the solutions were obtained using the modified iteration method. Depending on numerical calculation, the amplitude-frequency responses of Euler beam were determined. The axial velocity, tension, and rotational inertia have strong influences on the vibration characteristics. The results would provide an important theoretical reference to control and analyze the vertical vibration of moving strip in continuous rolling process.
Boundary-Value Problems for Weakly Nonlinear Delay Differential Systems
Directory of Open Access Journals (Sweden)
A. Boichuk
2011-01-01
Full Text Available Conditions are derived of the existence of solutions of nonlinear boundary-value problems for systems of n ordinary differential equations with constant coefficients and single delay (in the linear part and with a finite number of measurable delays of argument in nonlinearity: ż(t=Az(t-τ+g(t+εZ(z(hi(t,t,ε, t∈[a,b], assuming that these solutions satisfy the initial and boundary conditions z(s:=ψ(s if s∉[a,b], lz(⋅=α∈Rm. The use of a delayed matrix exponential and a method of pseudoinverse by Moore-Penrose matrices led to an explicit and analytical form of sufficient conditions for the existence of solutions in a given space and, moreover, to the construction of an iterative process for finding the solutions of such problems in a general case when the number of boundary conditions (defined by a linear vector functional l does not coincide with the number of unknowns in the differential system with a single delay.
Skokos, Ch; Bodyfelt, J D; Papamikos, G; Eggl, S
2013-01-01
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 yet been studied in detail. We demonstrate ways to construct high order symplectic integrators for Hamiltonian systems that can be split in three integrable parts. Using these techniques for the integration of the disordered, discrete nonlinear Schroedinger equation, we show that three part split symplectic integrators are more efficient than other numerical methods for the long time integration of multidimensional systems, with respect to both accuracy and computational time.
A nonlinear wave equation with a nonlinear integral equation involving the boundary value
Directory of Open Access Journals (Sweden)
Thanh Long Nguyen
2004-09-01
Full Text Available We consider the initial-boundary value problem for the nonlinear wave equation $$displaylines{ u_{tt}-u_{xx}+f(u,u_{t}=0,quad xin Omega =(0,1,; 0
Nonlinear interaction of waves in boundary-layer flows
Nayfeh, A. H.; Bozatli, A. N.
1979-01-01
First-order nonlinear interactions of Tollmien-Schlichting waves of different frequencies and initial amplitudes in boundary-layer flows are analyzed by using the method of multiple scales. For the case of two waves, a strong nonlinear interaction exists if one of the frequencies w2 is twice the other frequency w1. Numerical results for flow past a flat plate show that this interaction mechanism is strongly destabilizing even in regions where either the fundamental or its harmonic is damped in the absence of the interaction. For the case of three waves, a strong nonlinear interaction exists when w3 = w2- w1. This combination resonance causes the amplitude of the wave with the difference frequency w3 to multiply many times in magnitude in a short distance even if it is damped in the absence of the interaction. The initial amplitudes play a dominant role in determining the changes in the amplitudes of the waves in both of these mechanisms.
Institute of Scientific and Technical Information of China (English)
莫嘉琪
2003-01-01
The nonlinear predator-prey singularly perturbed Robin initial boundary value problems for reaction diffusion systems were considered. Under suitable conditions, using theory of differential inequalities the existence and asymptotic behavior of solution for initial boundary value problems were studied.
THREE POINT BOUNDARY VALUE PROBLEMS FOR NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
Mujeeb ur Rehman; Rahmat Ali Khan; Naseer Ahmad Asif
2011-01-01
In this paper,we study existence and uniqueness of solutions to nonlinear three point boundary value problems for fractional differential equation of the type cDδ0+u(t) =f(t,u(t),cDσ0+u(t)),t ∈[0,T],u(0) =αu(η),u(T) =βu(η),where1 ＜δ＜2,0＜σ＜ 1,α,β∈R,η∈(0,T),αη(1-β)+(1-α)(T-βη) ≠0 and cDoδ+,cDσ0+ are the Caputo fractional derivatives.We use Schauder fixed point theorem and contraction mapping principle to obtain existence and uniqueness results.Examples are also included to show the applicability of our results.
Nonlinear Vibrations of Multiwalled Carbon Nanotubes under Various Boundary Conditions
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Hossein Aminikhah
2011-01-01
Full Text Available The present work deals with applying the homotopy perturbation method to the problem of the nonlinear oscillations of multiwalled carbon nanotubes embedded in an elastic medium under various boundary conditions. A multiple-beam model is utilized in which the governing equations of each layer are coupled with those of its adjacent ones via the van der Waals interlayer forces. The amplitude-frequency curves for large-amplitude vibrations of single-walled, double-walled, and triple-walled carbon nanotubes are obtained. The influences of some commonly used boundary conditions, changes in material constant of the surrounding elastic medium, and variations of the nanotubes geometrical parameters on the vibration characteristics of multiwalled carbon nanotubes are discussed. The comparison of the generated results with those from the open literature illustrates that the solutions obtained are of very high accuracy and clarifies the capability and the simplicity of the present method. It is worthwhile to say that the results generated are new and can be served as a benchmark for future works.
Institute of Scientific and Technical Information of China (English)
崔霞
2002-01-01
Alternating direction finite element (ADFE) scheme for d-dimensional nonlinear system of parabolic integro-differential equations is studied. By using a local approximation based on patches of finite elements to treat the capacity term qi(u), decomposition of the coefficient matrix is realized; by using alternating direction, the multi-dimensional problem is reduced to a family of single space variable problems, calculation work is simplified; by using finite element method, high accuracy for space variant is kept; by using inductive hypothesis reasoning, the difficulty coming from the nonlinearity of the coefficients and boundary conditions is treated; by introducing Ritz-Volterra projection, the difficulty coming from the memory term is solved. Finally, by using various techniques for priori estimate for differential equations, the unique resolvability and convergence properties for both FE and ADFE schemes are rigorously demonstrated, and optimal H1 and L2norm space estimates and O((△t)2) estimate for time variant are obtained.
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.
Initial-boundary value problems for a class of nonlinear thermoelastic plate equations
Institute of Scientific and Technical Information of China (English)
Zhang Jian-Wen; Rong Xiao-Liang; Wu Run-Heng
2009-01-01
This paper studies initial-boundary value problems for a class of nonlinear thermoelastic plate equations. Under some certain initial data and boundary conditions,it obtains an existence and uniqueness theorem of global weak solutions of the nonlinear thermoelstic plate equations,by means of the Galerkin method. Moreover,it also proves the existence of strong and classical solutions.
A splitting approach for the fully nonlinear and weakly dispersive Green-Naghdi model
Bonneton, Philippe; Lannes, David; Marche, Fabien; Tissier, Marion
2010-01-01
The fully nonlinear and weakly dispersive Green-Naghdi model for shallow water waves of large amplitude is studied. The original model is first recast under a new formulation more suitable for numerical resolution. An hybrid finite volume and finite difference splitting approach is then proposed. The hyperbolic part of the equations is handled with a high-order finite volume scheme allowing for breaking waves and dry areas. The dispersive part is treated with a classical finite difference approach. Extensive numerical validations are then performed in one horizontal dimension, relying both on analytical solutions and experimental data. The results show that our approach gives a good account of all the processes of wave transformation in coastal areas: shoaling, wave breaking and run-up.
Stochastic viscosity solution for stochastic PDIEs with nonlinear Neumann boundary condition
Aman, Auguste
2010-01-01
This paper is an attempt to extend the notion of viscosity solution to nonlinear stochastic partial differential integral equations with nonlinear Neumann boundary condition. Using the recently developed theory on generalized backward doubly stochastic differential equations driven by a L\\'evy process, we prove the existence of the stochastic viscosity solution, and further extend the nonlinear Feynman-Kac formula.
Institute of Scientific and Technical Information of China (English)
SU XIN-WEI
2011-01-01
This paper is devoted to study the existence and uniqueness of solutions to a boundary value problem of nonlinear fractional differential equation with impulsive effects. The arguments are based upon Schauder and Banach fixed-point theorems. We improve and generalize the results presented in [B. Ahmad, S. Sivasundaram, Existence results for nonlinear impulsive hybrid boundary value problems involving fractional differential equations, Nonlinear Analysis: Hybrid Systems, 3(2009), 251258].
Positive solutions of quasilinear parabolic systems with nonlinear boundary conditions
Pao, C. V.; Ruan, W. H.
2007-09-01
The aim of this paper is to investigate the existence, uniqueness, and asymptotic behavior of solutions for a coupled system of quasilinear parabolic equations under nonlinear boundary conditions, including a system of quasilinear parabolic and ordinary differential equations. Also investigated is the existence of positive maximal and minimal solutions of the corresponding quasilinear elliptic system as well as the uniqueness of a positive steady-state solution. The elliptic operators in both systems are allowed to be degenerate in the sense that the density-dependent diffusion coefficients Di(ui) may have the property Di(0)=0 for some or all i. Our approach to the problem is by the method of upper and lower solutions and its associated monotone iterations. It is shown that the time-dependent solution converges to the maximal solution for one class of initial functions and it converges to the minimal solution for another class of initial functions; and if the maximal and minimal solutions coincide then the steady-state solution is unique and the time-dependent solution converges to the unique solution. Applications of these results are given to three model problems, including a porous medium type of problem, a heat-transfer problem, and a two-component competition model in ecology. These applications illustrate some very interesting distinctive behavior of the time-dependent solutions between density-independent and density-dependent diffusions.
On Nonlinear Approximations to Cosmic Problems with Mixed Boundary Conditions
Mancinelli, P J; Ganon, G; Dekel, A; Mancinelli, Paul J.; Yahil, Amos; Ganon, Galit; Dekel, Avishai
1993-01-01
Nonlinear approximations to problems with mixed boundary conditions are useful for predicting large-scale streaming velocities from the density field, or vice-versa. We evaluate the schemes of Bernardeau \\cite{bernardeau92}, Gramann \\cite{gramann93}, and Nusser \\etal \\cite{nusser91}, using smoothed density and velocity fields obtained from $N$-body simulations of a CDM universe. The approximation of Nusser \\etal is overall the most accurate and robust. For Gaussian smoothing of 1000\\kms\\ the mean error in the approximated relative density perturbation, $\\delta$, is smaller than 0.06, and the dispersion is 0.1. The \\rms\\ error in the estimated velocity is smaller than 60\\kms, and the dispersion is 40\\kms. For smoothing of 500\\kms\\ these numbers increase by about a factor $\\sim 2$ for $\\delta < 4-5$, but deteriorate at higher densities. The other approximations are comparable to those of Nusser \\etal for smoothing of 1000\\kms, but are much less successful for the smaller smoothing of 500\\kms.
Nonlinear Simulations of Coalescence Instability Using a Flux Difference Splitting Method
Ma, Jun; Qin, Hong; Yu, Zhi; Li, Dehui
2016-07-01
A flux difference splitting numerical scheme based on the finite volume method is applied to study ideal/resistive magnetohydrodynamics. The ideal/resistive MHD equations are cast as a set of hyperbolic conservation laws, and we develop a numerical capability to solve the weak solutions of these hyperbolic conservation laws by combining a multi-state Harten-Lax-Van Leer approximate Riemann solver with the hyperbolic divergence cleaning technique, high order shock-capturing reconstruction schemes, and a third order total variance diminishing Runge-Kutta time evolving scheme. The developed simulation code is applied to study the long time nonlinear evolution of the coalescence instability. It is verified that small structures in the instability oscillate with time and then merge into medium structures in a coherent manner. The medium structures then evolve and merge into large structures, and this trend continues through all scale-lengths. The physics of this interesting nonlinear dynamics is numerically analyzed. supported by the National Magnetic Confinement Fusion Science Program of China (Nos. 2013GB111002, 2013GB105003, 2013GB111000, 2014GB124005, 2015GB111003), National Natural Science Foundation of China (Nos. 11305171, 11405208), JSPS-NRF-NSFC A3 Foresight Program in the field of Plasma Physics (NSFC-11261140328), the Science Foundation of the Institute of Plasma Physics, Chinese Academy of Sciences (DSJJ-15-JC02) and the CAS Program for the Interdisciplinary Collaboration Team
Asymptotic stability for a class of boundary control systems with non-linear damping
Zwart, Heiko J.; Ramirez, Hector; Le Gorrec, Yann
2016-01-01
The asymptotic stability of boundary controlled port-Hamiltonian systems defined on a 1D spatial domain interconnected to a class of non-linear boundary damping is addressed. It is shown that if the port-Hamiltonian system is approximately observable, then any boundary damping which behaves linear
Asymptotic stability for a class of boundary control systems with non-linear damping
Zwart, Heiko J.; Ramirez, Hector; Le Gorrec, Yann
2016-01-01
The asymptotic stability of boundary controlled port-Hamiltonian systems defined on a 1D spatial domain interconnected to a class of non-linear boundary damping is addressed. It is shown that if the port-Hamiltonian system is approximately observable, then any boundary damping which behaves linear for small velocities asymptotically stabilizes the system.
Directory of Open Access Journals (Sweden)
Juan Carlos Ceballos V.
2005-10-01
Full Text Available The exact boundary controllability of the higher order nonlinear Schrodinger equation with constant coefficients on a bounded domain with various boundary conditions is studied. We derive the exact boundary controllability for this equation for sufficiently small initial and final states.
Gauckler, Ludwig
2016-06-01
The near-conservation of energy on long time intervals in numerical discretizations of Hamiltonian partial differential equations is discussed using the cubic nonlinear Schrödinger equation and its discretization by the split-step Fourier method as a model problem.
Analysis on Forced Vibration of Thin-Wall Cylindrical Shell with Nonlinear Boundary Condition
Directory of Open Access Journals (Sweden)
Qiansheng Tang
2016-01-01
Full Text Available Forced vibration of thin-wall cylindrical shell under nonlinear boundary condition was discussed in this paper. The nonlinear boundary was modeled as supported clearance in one end of shell and the restraint was assumed as linearly elastic in the radial direction. Based on Sanders’ shell theory, Lagrange equation was utilized to derive the nonlinear governing equations of cylindrical shell. The displacements in three directions were represented by beam functions and trigonometric functions. In the study of nonlinear dynamic responses of thin-wall cylindrical shell with supported clearance under external loads, the Newmark method is used to obtain time history, frequency spectrum plot, phase portraits, Poincare section, bifurcation diagrams, and three-dimensional spectrum plot with different parameters. The effects of external loads, supported clearance, and support stiffness on nonlinear dynamics behaviors of cylindrical shell with nonlinear boundary condition were discussed.
Zia, Haider
2017-06-01
This paper describes an updated exponential Fourier based split-step method that can be applied to a greater class of partial differential equations than previous methods would allow. These equations arise in physics and engineering, a notable example being the generalized derivative non-linear Schrödinger equation that arises in non-linear optics with self-steepening terms. These differential equations feature terms that were previously inaccessible to model accurately with low computational resources. The new method maintains a 3rd order error even with these additional terms and models the equation in all three spatial dimensions and time. The class of non-linear differential equations that this method applies to is shown. The method is fully derived and implementation of the method in the split-step architecture is shown. This paper lays the mathematical ground work for an upcoming paper employing this method in white-light generation simulations in bulk material.
Energy Technology Data Exchange (ETDEWEB)
Zou, Li [Dalian Univ. of Technology, Dalian City (China). State Key Lab. of Structural Analysis for Industrial Equipment; Liang, Songxin; Li, Yawei [Dalian Univ. of Technology, Dalian City (China). School of Mathematical Sciences; Jeffrey, David J. [Univ. of Western Ontario, London (Canada). Dept. of Applied Mathematics
2017-06-01
Nonlinear boundary value problems arise frequently in physical and mechanical sciences. An effective analytic approach with two parameters is first proposed for solving nonlinear boundary value problems. It is demonstrated that solutions given by the two-parameter method are more accurate than solutions given by the Adomian decomposition method (ADM). It is further demonstrated that solutions given by the ADM can also be recovered from the solutions given by the two-parameter method. The effectiveness of this method is demonstrated by solving some nonlinear boundary value problems modeling beam-type nano-electromechanical systems.
Zou, Li; Liang, Songxin; Li, Yawei; Jeffrey, David J.
2017-03-01
Nonlinear boundary value problems arise frequently in physical and mechanical sciences. An effective analytic approach with two parameters is first proposed for solving nonlinear boundary value problems. It is demonstrated that solutions given by the two-parameter method are more accurate than solutions given by the Adomian decomposition method (ADM). It is further demonstrated that solutions given by the ADM can also be recovered from the solutions given by the two-parameter method. The effectiveness of this method is demonstrated by solving some nonlinear boundary value problems modeling beam-type nano-electromechanical systems.
Boundary regularity for some nonlinear elliptic degenerate equations. Technical summary report
Energy Technology Data Exchange (ETDEWEB)
Brezis, H.; Lions, P.
1979-08-01
Special solutions of the Yang-Mills field equations of theoretical physics may be obtained by solving a boundary value problem for a nonlinear elliptic equation in a two dimensional half space. This equation degenerates at the boundary of the region and this degeneracy makes it a delicate matter to study how the solutions behave near the boundary. In this work it is proved that the weak solutions previously known to exist are in fact smooth up to the boundary.
Direct approach for solving nonlinear evolution and two-point boundary value problems
Indian Academy of Sciences (India)
Jonu Lee; Rathinasamy Sakthivel
2013-12-01
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 including time-delayed nonlinear Burgers equation to illustrate the validity and the great potential of the differential transform method. Numerical experiments demonstrate the use and computational efﬁciency of the method. This method can easily be applied to many nonlinear problems and is capable of reducing the size of computational work.
Institute of Scientific and Technical Information of China (English)
唐登斌; 夏浩
2002-01-01
The nonlinear evolution problem in nonparallel boundary layer stability was studied. The relative parabolized stability equations of nonlinear nonparallel boundary layer were derived. The developed numerical method, which is very effective, was used to study the nonlinear evolution of T-S disturbance wave at finite amplitudes. Solving nonlinear equations of different modes by using predictor-corrector and iterative approach, which is uncoupled between modes, improving computational accuracy by using high order compact differential scheme, satisfying normalization condition, determining tables of nonlinear terms at different modes, and implementing stably the spatial marching, were included in this method. With different initial amplitudes, the nonlinear evolution of T-S wave was studied. The nonlinear nonparallel results of examples compare with data of direct numerical simulations (DNS) using full Navier- Stokes equations.
Fatigue crack damage detection using subharmonic component with nonlinear boundary condition
Energy Technology Data Exchange (ETDEWEB)
Wu, Weiliang, E-mail: wwl@whu.edu.cn; Qu, Wenzhong, E-mail: qwz@whu.edu.cn, E-mail: xiaoli6401@126.com; Xiao, Li, E-mail: qwz@whu.edu.cn, E-mail: xiaoli6401@126.com [Department of Engineering Mechanics, Wuhan University, Wuhan, Hubei (China); Shen, Yanfeng, E-mail: shen5@email.sc.edu; Giurgiutiu, Victor, E-mail: victorg@sc.edu [Department of Mechanical Engineering, University of South Carolina, Columbia, South Carolina (United States)
2015-03-31
In recent years, researchers have focused on structural health monitoring (SHM) and damage detection techniques using nonlinear vibration and nonlinear ultrasonic methods. Fatigue cracks may exhibit contact acoustic nonlinearity (CAN) with distinctive features such as superharmonics and subharmonics in the power spectrum of the sensing signals. However, challenges have been noticed in the practical applications of the harmonic methods. For instance, superharmonics can also be generated by the piezoelectric transducers and the electronic equipment; super/subharmonics may also stem from the nonlinear boundary conditions such as structural fixtures and joints. It is hard to tell whether the nonlinear features come from the structural damage or the intrinsic nonlinear boundary conditions. The objective of this paper is to demonstrate the application of nonlinear ultrasonic subharmonic method for detecting fatigue cracks with nonlinear boundary conditions. The fatigue crack was qualitatively modeled as a single-degree-of-freedom (SDOF) system with non-classical hysteretic nonlinear interface forces at both sides of the crack surfaces. The threshold of subharmonic generation was studied, and the influence of crack interface parameters on the subharmonic resonance condition was investigated. The different threshold behaviors between the nonlinear boundary condition and the fatigue crack was found, which can be used to distinguish the source of nonlinear subharmonic features. To evaluate the proposed method, experiments of an aluminum plate with a fatigue crack were conducted to quantitatively verify the subharmonic resonance range. Two surface-bonded piezoelectric transducers were used to generate and receive ultrasonic wave signals. The fatigue damage was characterized in terms of a subharmonic damage index. The experimental results demonstrated that the subharmonic component of the sensing signal can be used to detect the fatigue crack and further distinguish it from
Brahim Tellab; Kamel Haouam
2016-01-01
In this paper, we investigate the existence and uniqueness of solutions for second order nonlinear fractional differential equation with integral boundary conditions. Our result is an application of the Banach contraction principle and the Krasnoselskii fixed point theorem.
Eigenvalue Problem for Nonlinear Fractional Differential Equations with Integral Boundary Conditions
Directory of Open Access Journals (Sweden)
Guotao Wang
2014-01-01
Full Text Available By employing known Guo-Krasnoselskii fixed point theorem, we investigate the eigenvalue interval for the existence and nonexistence of at least one positive solution of nonlinear fractional differential equation with integral boundary conditions.
Institute of Scientific and Technical Information of China (English)
LiHongyu; SunJingxian
2005-01-01
By using topological method, we study a class of boundary value problem for a system of nonlinear ordinary differential equations. Under suitable conditions,we prove the existence of positive solution of the problem.
Black holes in nonlinear electrodynamics: quasi-normal spectra and parity splitting
Chaverra, Eliana; Moreno, Claudia; Sarbach, Olivier
2016-01-01
We discuss the quasi-normal oscillations of black holes which are sourced by a nonlinear electrodynamic field. While previous studies have focused on the computation of quasi-normal frequencies for the wave or higher spin equation on a fixed background geometry described by such black holes, here we compute for the first time the quasi-normal frequencies for the coupled electromagnetic-gravitational linear perturbations. To this purpose, we consider a parametrized family of Lagrangians for the electromagnetic field which contains the Maxwell Lagrangian as a special case. In the Maxwell case, the unique spherically symmetric black hole solutions are described by the Reissner-Nordstr\\"om family and in this case it is well-known that the quasi-normal spectra in the even- and odd-parity sectors are identical to each other. However, when moving away from the Maxwell case, we obtain deformed Reissner-Nordstr\\"om black holes, and we show that in this case there is a parity splitting in the quasi-normal mode spectra....
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.
Nonlinear solution for radiation boundary condition of heat transfer process in human eye.
Dehghani, A; Moradi, A; Dehghani, M; Ahani, A
2011-01-01
In this paper we propose a new method based on finite element method for solving radiation boundary condition of heat equation inside the human eye and other applications. Using this method, we can solve heat equation inside human eye without need to model radiation boundary condition to a robin boundary condition. Using finite element method we can obtain a nonlinear equation, and finally we use nonlinear algorithm to solve it. The human eye is modeled as a composition of several homogeneous regions. The Ritz method in the finite element method is used for solving heat differential equation. Applying the boundary conditions, the heat radiation condition and the robin condition on the cornea surface of the eye and on the outer part of sclera are used, respectively. Simulation results of solving nonlinear boundary condition show the accuracy of the proposed method.
Institute of Scientific and Technical Information of China (English)
Long Shuyao; Zhang Qin
2000-01-01
In this paper the dual reciprocity boundary element method is employed to solve nonlinear differential equation 2 u + u + εu3 = b. Results obtained in an example have a good agreement with those by FEM and show the applicability and simplicity of dual reciprocity method(DRM) in solving nonlinear dif ferential equations.
Energy Technology Data Exchange (ETDEWEB)
Zhang, H. [Univ. of Texas, Austin, TX (United States). Dept. of Mathematics
1994-10-01
In this paper the author considers a nonlinear evolution problem denoted in the paper as P. Problem (P) arises in the study of thermal evaporation of atoms and molecules from locally heated surface regions (spikes) invoked as one of several mechanisms of ion-bombardment-induced particle emission (sputtering). Then in the case of particle-induced evaporation, the Stefan-Boltzman law of heat loss by radiation is replaced by some activation law describing the loss of heat by evaporation. The equation in P is the so-called degenerate diffusion problem, which has been extensively studied in recent years. However, when dealing with the nonlinear flux boundary condition, {beta}({center_dot}) is usually assumed to be monotene. The purpose of this paper is to provide a general theory for problem P under a different assumption on {beta}({center_dot}), i.e., Lipschitz continuity instead of monotonicity. The main idea of the proof used here is to choose an appropriate test function from the corresponding linearized dual space of the solution. The similar idea has been used by many authors, e.g., Aronson, Crandall and Peletier, Bertsch and Hilhorst and Friedman. The author follows the proof of Bertsch and Hilhorst. The paper is organized as follows. They begin by stating the precise assumptions on the functions involved in P and by defining a weak solution. Then, in Section 2 they prove the existence of the solution by the method of parabolic regularization. The uniqueness is proved in Section 3. Finally, they study the large time behavior of the solution in Section 4.
A NONLOCAL NONLINEAR BOUNDARY VALUE PROBLEM FOR THE HEAT EQUATIONS
Institute of Scientific and Technical Information of China (English)
YANJINHAI
1996-01-01
The existenoe and limit hehaviour of the solution for a kind of nonloeal noulinear boundary value condition on a part of the boundary is studied for the heat equation, which physicallymeans that the potential is the function of the total flux. When this part of boundary shrinks to a point in a certain way, this condition either results in a Dirac measure or simply disappears in the corresponding problem.
A New Non-linear Technique for Measurement of Splitting Functions of Normal Modes of the Earth
Pachhai, S.; Masters, G.; Tkalcic, H.
2014-12-01
Normal modes are the vibrating patterns of the Earth in response to the large earthquakes. Normal mode spectra are split due to Earth's rotation, ellipticity, and heterogeneity. The normal mode splitting is visualized through splitting functions, which represent the local radial average of Earth's structure seen by a mode of vibration. The analysis of the splitting of normal modes can provide unique information about the lateral variation of the Earth's elastic properties that cannot be directly imaged in body wave tomographic images. The non-linear iterative spectral fitting of the observed complex spectra and autoregressive linear inversion have been widely utilized to compute the Earth's 3-D structure. However, the non-linear inversion requires a model of the earthquake source and the retrieved 3-D structure is sensitive to the initial constraints. In contrast, the autoregressive linear inversion does not require the source model. However, this method requires many events to achieve full convergence. In addition, significant disagreement exists between different studies because of the non-uniqueness of the problem and limitations of different methods. We thus apply the neighbourhood algorithm (NA) to measure splitting functions. The NA is an efficient model space search technique and works in two steps: In the first step, the algorithm finds all the models compatible with given data while the posterior probability density of the model parameters are obtained in the second step. The NA can address the problem of non-uniqueness by taking advantage of random sampling of the full model space. The parameter trade-offs are conveniently visualized using joint marginal distributions. In addition, structure coefficients uncertainties can be extracted from the posterior probability distribution. After demonstrating the feasibility of NA with synthetic examples, we compute the splitting functions for the mode 13S2 (sensitive to the inner core) from several large
Lie and Conditional Symmetries of a Class of Nonlinear (1 + 2-Dimensional Boundary Value Problems
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Roman Cherniha
2015-08-01
Full Text Available A new definition of conditional invariance for boundary value problems involving a wide range of boundary conditions (including initial value problems as a special case is proposed. It is shown that other definitions worked out in order to find Lie symmetries of boundary value problems with standard boundary conditions, followed as particular cases from our definition. Simple examples of direct applicability to the nonlinear problems arising in applications are demonstrated. Moreover, the successful application of the definition for the Lie and conditional symmetry classification of a class of (1 + 2-dimensional nonlinear boundary value problems governed by the nonlinear diffusion equation in a semi-infinite domain is realised. In particular, it is proven that there is a special exponent, k ≠ —2, for the power diffusivity uk when the problem in question with non-vanishing flux on the boundary admits additional Lie symmetry operators compared to the case k ≠ —2. In order to demonstrate the applicability of the symmetries derived, they are used for reducing the nonlinear problems with power diffusivity uk and a constant non-zero flux on the boundary (such problems are common in applications and describing a wide range of phenomena to (1 + 1-dimensional problems. The structure and properties of the problems obtained are briefly analysed. Finally, some results demonstrating how Lie invariance of the boundary value problem in question depends on the geometry of the domain are presented.
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
This paper is concerned with the existence of extreme solutions to three-point boundary value problems with nonlinear boundary conditions for a class of first order impulsive differential equations. We obtain suficient conditions for the existence of extreme solutions by the upper and lower solutions method coupled with a monotone iterative technique.
Existence of Solutions for Nonlinear Four-Point -Laplacian Boundary Value Problems on Time Scales
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Topal SGulsan
2009-01-01
Full Text Available We are concerned with proving the existence of positive solutions of a nonlinear second-order four-point boundary value problem with a -Laplacian operator on time scales. The proofs are based on the fixed point theorems concerning cones in a Banach space. Existence result for -Laplacian boundary value problem is also given by the monotone method.
Directory of Open Access Journals (Sweden)
Jianqiang Guo
2014-01-01
Full Text Available 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.
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Azizian Davood
2016-12-01
Full Text Available Regarding the importance of short circuit and inrush current simulations in the split-winding transformer, a novel nonlinear equivalent circuit is introduced in this paper for nonlinear simulation of this transformer. The equivalent circuit is extended using the nonlinear inductances. Employing a numerical method, leakage and magnetizing inductances in the split-winding transformer are extracted and the nonlinear model inductances are estimated using these inductances. The introduced model is validated and using this nonlinear model, inrush and short-circuit currents are calculated. It has been seen that the introduced model is valid and suitable for simulations of the split-winding transformer due to various loading conditions. Finally, the effects of nonlinearity of the model inductances are discussed in the following.
Institute of Scientific and Technical Information of China (English)
鲁世平
2003-01-01
By employing the theory of differential inequality and some analysis methods, a nonlinear boundary value problem subject to a general kind of second-order Volterra functional differential equation was considered first. Then, by constructing the right-side layer function and the outer solution, a nonlinear boundary value problem subject to a kind of second- order Volterra functional differential equation with a small parameter was studied further. By using the differential mean value theorem and the technique of upper and lower solution, a new result on the existence of the solutions to the boundary value problem is obtained, and a uniformly valid asymptotic expansions of the solution is given as well.
Multiple nested basin boundaries in nonlinear driven oscillators☆
Zhang, Yongxiang; Xie, Xiangpeng; Luo, Guanwei
2017-03-01
A special type of basins of attraction for high-period coexisting attractors is investigated, which basin boundaries possess multiple nested structures in a driven oscillator. We analyze the global organization of basins and discuss the mechanism for the appearance of layered structures. The unstable periodic orbits and unstable limit cycle are also detected in the oscillator. The basin organization is governed by the ordering of regular saddles and the regular saddle connections are the interrupted by the unstable limit cycle. Wada basin boundary with different Wada number is discovered. Wada basin boundaries for the hidden and rare attractors are also verified.
Institute of Scientific and Technical Information of China (English)
高永馨
2002-01-01
Studies the existence of solutions of nonlinear two point boundary value problems for nonlinear 4n-th-order differential equation y(4n)= f( t,y,y' ,y",… ,y(4n－1) ) (a) with the boundary conditions g2i(y(2i) (a) ,y(2i+1) (a)) = 0,h2i(y(2i) (c) ,y(2i+1) (c)) = 0, (I= 0,1,…,2n － 1 ) (b) where the functions f, gi and hi are continuous with certain monotone properties. For the boundary value problems of nonlinear nth order differential equation y(n) = f(t,y,y',y",… ,y(n－1)) many results have been given at the present time. But the existence of solutions of boundary value problem (a), (b) studied in this paper has not been covered by the above researches. Moreover, the corollary of the important theorem in this paper, I.e. Existence of solutions of the boundary value problem. Y(4n) = f(t,y,y',y",… ,y(4n－1) ) a2iy(2i) (at) + a2i+1y(2i+1) (a) = b2i ,c2iy(2O ( c ) + c2i+1y(2i+1) ( c ) = d2i, ( I = 0,1 ,…2n － 1) has not been dealt with in previous works.
Francés, Jorge; Bleda, Sergio; Bej, Subhajit; Tervo, Jani; Navarro-Fuster, Víctor; Fenoll, Sandra; Martínez-Gaurdiola, Francisco J.; Neipp, Cristian
2016-04-01
In this work the split-field finite-difference time-domain method (SF-FDTD) has been extended for the analysis of two-dimensionally periodic structures with third-order nonlinear media. The accuracy of the method is verified by comparisons with the nonlinear Fourier Modal Method (FMM). Once the formalism has been validated, examples of one- and two-dimensional nonlinear gratings are analysed. Regarding the 2D case, the shifting in resonant waveguides is corroborated. Here, not only the scalar Kerr effect is considered, the tensorial nature of the third-order nonlinear susceptibility is also included. The consideration of nonlinear materials in this kind of devices permits to design tunable devices such as variable band filters. However, the third-order nonlinear susceptibility is usually small and high intensities are needed in order to trigger the nonlinear effect. Here, a one-dimensional CBG is analysed in both linear and nonlinear regime and the shifting of the resonance peaks in both TE and TM are achieved numerically. The application of a numerical method based on the finite- difference time-domain method permits to analyse this issue from the time domain, thus bistability curves are also computed by means of the numerical method. These curves show how the nonlinear effect modifies the properties of the structure as a function of variable input pump field. When taking the nonlinear behaviour into account, the estimation of the electric field components becomes more challenging. In this paper, we present a set of acceleration strategies based on parallel software and hardware solutions.
A Reaction-diffusion System with Nonlinear Absorption Terms and Boundary Flux
Institute of Scientific and Technical Information of China (English)
2008-01-01
This paper deals with a reaction-diffusion system with nonlinear absorption terms and boundary flux. As results of interactions among the six nonlinear terms in the system, some sufficient conditions on global existence and finite time blow-up of the solutions are described via all the six nonlinear exponents appearing in the six nonlinear terms. In addition, we also show the influence of the coefficients of the absorption terms as well as the geometry of the domain to the global existence and finite time blow-up of the solutions for some cases. At last, some numerical results are given.
Subharmonic Route to Boundary-Layer Transition - Critical Layer Nonlinearity
Mankbadi, Reda R.
1991-01-01
The linear and nonlinear dynamics of a triad of initially linear stability waves comprising a single plane wave at fundamental frequency and two symmetric oblique waves with half the frequency and streamwise wave number of the plane wave are presented. Analysis is performed for the initial nonlinear development of the waves where the order of the oblique waves' amplitude is equal to or less than that of the plane wave. Results show that the fundamental basically follows the linear theory, while the subharmonic follows an exponential-of-an-exponential growth.
A Nonlinear Stability Theory for Plane Boundary-Layer Flows
1980-07-01
flows , Poiseuille flows and Couette flows . For example, 3 for plane Polseutlle flow with...published results for plane Poiseuille flow and the Orr-Sonunerfeld solutions for ~lasius flow and a numerical solution of Navier-Stokes flow along a flat...TWO-POINT BOUNDARY-VALUE PROBLEM .......... 21 4. NUMERICAL RESULTS ............................................. 44 4.1 Plane Poiseuille Flow
Nonlinear boundary value problem for biregular functions in Clifford analysis
Institute of Scientific and Technical Information of China (English)
黄沙
1996-01-01
The biregular function in Clifford analysis is discussed. Plemelj’s formula is obtained andnonlinear boundary value problem: is considered. Applying the methodof integral equations and Schauder fixed-point theorem, the existence of solution for the above problem is proved.
Attractor of Beam Equation with Structural Damping under Nonlinear Boundary Conditions
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Danxia Wang
2015-01-01
Full Text Available Simultaneously, considering the viscous effect of material, damping of medium, and rotational inertia, we study a kind of more general Kirchhoff-type extensible beam equation utt-uxxtt+uxxxx-σ(∫0l(ux2dxuxx-ϕ(∫0l(ux2dxuxxt=q(x, in [0,L]×R+ with the structural damping and the rotational inertia term. Little attention is paid to the longtime behavior of the beam equation under nonlinear boundary conditions. In this paper, under nonlinear boundary conditions, we prove not only the existence and uniqueness of global solutions by prior estimates combined with some inequality skills, but also the existence of a global attractor by the existence of an absorbing set and asymptotic compactness of corresponding solution semigroup. In addition, the same results also can be proved under the other nonlinear boundary conditions.
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.
On approximation of nonlinear boundary integral equations for the combined method
Energy Technology Data Exchange (ETDEWEB)
Gregus, M.; Khoromsky, B.N.; Mazurkevich, G.E.; Zhidkov, E.P.
1989-09-22
The nonlinear boundary integral equations that arise in research of nonlinear magnetostatic problems are investigated in combined formulation on an unbounded domain. Approximations of the derived operator equations are studied based on the Galerkin method. The investigated boundary operators are strongly monotone, Lipschitz-continuous, potential and have a symmetrical Gateaux derivative. The error estimates of the Galerkin's approximation in Sobolev spaces of fractional powers are obtained using the above-mentioned properties of the operators, too. The problem has been studied on surfaces in two and three-dimensional spaces. We answer also some questions on convergence connected with the discretized systems of equations. 21 refs.
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.
Freeform illumination design: a nonlinear boundary problem for the elliptic Monge-Ampére equation.
Wu, Rengmao; Xu, Liang; Liu, Peng; Zhang, Yaqin; Zheng, Zhenrong; Li, Haifeng; Liu, Xu
2013-01-15
We propose an approach to deal with the problem of freeform surface illumination design without assuming any symmetry based on the concept that this problem is similar to the problem of optimal mass transport. With this approach, the freeform design is converted into a nonlinear boundary problem for the elliptic Monge-Ampére equation. The theory and numerical method are given for solving this boundary problem. Experimental results show the feasibility of this approach in tackling this freeform design problem.
Nonlinear boundary value problems for first order impulsive integro-differential equations
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Xinzhi Liu
1989-01-01
Full Text Available In this paper, we investigate a class of first order impulsive integro-differential equations subject to certain nonlinear boundary conditions and prove, with the help of upper and lower solutions, that the problem has a solution lying between the upper and lower solutions. We also develop monotone iterative technique and show the existence of multiple solutions of a class of periodic boundary value problems.
Boundary layers for self-similar viscous approximations of nonlinear hyperbolic systems
Christoforou, Cleopatra
2011-01-01
We provide a precise description of the set of residual boundary conditions generated by the self-similar viscous approximation introduced by Dafermos et al. We then apply our results, valid for both conservative and non conservative systems, to the analysis of the boundary Riemann problem and we show that, under appropriate assumptions, the limits of the self-similar and the classical vanishing viscosity approximation coincide. We require neither genuinely nonlinearity nor linear degeneracy of the characteristic fields.
Boundary layer flow and heat transfer to Carreau fluid over a nonlinear stretching sheet
Masood Khan; Hashim
2015-01-01
This article studies the Carreau viscosity model (which is a generalized Newtonian model) and then use it to obtain a formulation for the boundary layer equations of the Carreau fluid. The boundary layer flow and heat transfer to a Carreau model over a nonlinear stretching surface is discussed. The Carreau model, adequate for many non-Newtonian fluids, is used to characterize the behavior of the fluids having shear thinning properties and fluids with shear thickening properties for numerical ...
Weakly nonlinear stability of vicsous vortices in three-dimensional boundary layers
Bassom, Andrew P.; Otto, S. R.
1993-01-01
Attention is given to the weakly nonlinear stability of essentially viscous vortices in 3D boundary layers. These modes are unstable in the absence of crossflow, but the imposition of small crossflow has a stabilizing effect. Bassom and Hall (1991) demonstrated the existence of neutrally stable vortices for certain crossflow/wave number combinations, and the weakly nonlinear stability properties of these disturbances are described. It is shown that the effect of crossflow is to stabilize the nonlinear modes, and the present calculations allow stable finite-amplitude vortices to be found. Predictions are made concerning the likelihood of observing some of these viscous modes within a practical setting.
Nonlinear vibrations of shallow shells with complex boundary: R-functions method and experiments
Kurpa, Lidia; Pilgun, Galina; Amabili, Marco
2007-10-01
Geometrically nonlinear vibrations of shallow circular cylindrical panels with complex shape of the boundary are considered. The R-functions theory and variational methods are used to study the problem. The R-functions method (RFM) allows constructing in analytical form the sequence of basis functions satisfying the given boundary conditions in case of complex shape of the boundary. The problem is reduced to a single second-order differential equation with quadratic and cubic nonlinear terms. The method developed has been initially applied to study free vibrations of shallow circular cylindrical panels with rectangular base for different boundary conditions: (i) clamped edges, (ii) in-plane immovable simply supported edges, (iii) classically simply supported edges, and (iv) in-plane free simply supported edges. Then, the same approach is applied to a shell with complex shape of the boundary. Experiments have been conducted on an aluminum panel with complex shape of the boundary in order to identify the nonlinear response of the fundamental mode; these experimental results have been compared to numerical results.
Institute of Scientific and Technical Information of China (English)
Jingsun Yao; Jiaqi Mo
2005-01-01
The nonlinear nonlocal singularly perturbed initial boundary value problems for reaction diffusion equations with a boundary perturbation is considered. Under suitable conditions, the outer solution of the original problem is obtained. Using the stretched variable, the composing expansion method and the expanding theory of power series the initial layer is constructed. And then using the theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems is studied. Finally the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation are discussed.
A smart nonstandard finite difference scheme for second order nonlinear boundary value problems
Erdogan, Utku; Ozis, Turgut
2011-01-01
A new kind of finite difference scheme is presented for special second order nonlinear two point boundary value problems. An artificial parameter is introduced in the scheme. Symbolic computation is proposed for the construction of the scheme. Local truncation error of the method is discussed. Numer
A smart nonstandard finite difference scheme for second order nonlinear boundary value problems
Erdogan, Utku; Ozis, Turgut
2011-01-01
A new kind of finite difference scheme is presented for special second order nonlinear two point boundary value problems. An artificial parameter is introduced in the scheme. Symbolic computation is proposed for the construction of the scheme. Local truncation error of the method is discussed.
Directory of Open Access Journals (Sweden)
Jiqiang Jiang
2012-01-01
Full Text Available We consider the existence of positive solutions for a class of nonlinear integral boundary value problems for fractional differential equations. By using some fixed point theorems, the existence and multiplicity results of positive solutions are obtained. The results obtained in this paper improve and generalize some well-known results.
Institute of Scientific and Technical Information of China (English)
Yepeng Xing; Qiong Wang; Valery G. Romanovski
2009-01-01
We prove several new comparison results and develop the monotone iterative tech-nique to show the existence of extremal solutions to a kind of periodic boundary value problem (PBVP) for nonlinear integro-differential equation of mixed type on time scales.
Positive Solutions of a Nonlinear Fourth-order Integral Boundary Value Problem
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Benaicha Slimane
2016-07-01
Full Text Available In this paper, the existence of positive solutions for a nonlinear fourth-order two-point boundary value problem with integral condition is investigated. By using Krasnoselskii’s fixed point theorem on cones, sufficient conditions for the existence of at least one positive solutions are obtained.
THE NONLINEAR BOUNDARY VALUE PROBLEM FOR A CLASS OF INTEGRO-DIFFERENTIAL SYSTEM
Institute of Scientific and Technical Information of China (English)
Rongrong Tang
2006-01-01
In this paper, using the theory of differential inequalities, we study the nonlinear boundary value problem for a class of integro-differential system. Under appropriate assumptions, the existence of solution is proved and the uniformly valid asymptotic expansions for arbitrary n-th order approximation and the estimation of remainder term are obtained simply and conveniently.
EXISTENCE AND UNIQUENESS RESULTS FOR NONLINEAR THIRD-ORDER BOUNDARY VALUE PROBLEM
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
In this paper,we investigate a nonlinear third-order three-point boundary value problem. By several well-known fixed point theorems,the existence of positive solutions is discussed. Besides,the uniqueness results are obtained by imposing growth restrictions on f.
Existence Theorems for Nonlinear Boundary Value Problems for Second Order Differential Inclusions
Kandilakis, Dimitrios A.; Papageorgiou, Nikolaos S.
1996-11-01
In this paper we consider a nonlinear two-point boundary value problem for second order differential inclusions. Using the Leray-Schauder principle and its multivalued analog due to Dugundji-Granas, we prove existence theorems for convex and nonconvex problems. Our results are quite general and incorporate as special cases several classes of problems which are of interest in the literature.
Institute of Scientific and Technical Information of China (English)
Yaohong LI; Xiaoyan ZHANG
2013-01-01
In this paper,we consider boundary value problems for systems of nonlinear thirdorder differential equations.By applying the fixed point theorems of cone expansion and compression of norm type and Leggett-Williams fixed point theorem,the existence of multiple positive solutions is obtained.As application,we give some examples to demonstrate our results.
Existence of three solutions for impulsive nonlinear fractional boundary value problems
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Shapour Heidarkhani
2017-01-01
Full Text Available In this work we present new criteria on the existence of three solutions for a class of impulsive nonlinear fractional boundary-value problems depending on two parameters. We use variational methods for smooth functionals defined on reflexive Banach spaces in order to achieve our results.
Existence of Two Solutions of Nonlinear m-Point Boundary Value Problems
Institute of Scientific and Technical Information of China (English)
任景莉; 葛渭高
2003-01-01
Sufficient conditions for the existence of at least two positive solutions of a nonlinear m-points boundary value problems are established. The results are obtained by using a new fixed point theorem in cones. An example is provided to illustrate the theory.
DEFF Research Database (Denmark)
Hansen, Kim Per; Petersson, A.; Folkenberg, Jakob Riis
2004-01-01
for transverse structural uniformity by adopting a simple effective-index approach in which the birefringence is calculated in a step-index fiber with an elliptical core. We find that to reduce the splitting to less than 1nm the birefringence should be less than 210 -5 , resulting in a transverse uniformity...
Roul, Pradip
2016-06-01
This paper presents a new iterative technique for solving nonlinear singular two-point boundary value problems with Neumann and Robin boundary conditions. The method is based on the homotopy perturbation method and the integral equation formalism in which a recursive scheme is established for the components of the approximate series solution. This method does not involve solution of a sequence of nonlinear algebraic or transcendental equations for the unknown coefficients as in some other iterative techniques developed for singular boundary value problems. The convergence result for the proposed method is established in the paper. The method is illustrated by four numerical examples, two of which have physical significance: The first problem is an application of the reaction-diffusion process in a porous spherical catalyst and the second problem arises in the study of steady-state oxygen-diffusion in a spherical cell with Michaelis-Menten uptake kinetics.
Nonlinear nonuniform torsional vibrations of bars by the boundary element method
Sapountzakis, E. J.; Tsipiras, V. J.
2010-05-01
In this paper a boundary element method is developed for the nonuniform torsional vibration problem of bars of arbitrary doubly symmetric constant cross-section taking into account the effect of geometrical nonlinearity. The bar is subjected to arbitrarily distributed or concentrated conservative dynamic twisting and warping moments along its length, while its edges are supported by the most general torsional boundary conditions. The transverse displacement components are expressed so as to be valid for large twisting rotations (finite displacement-small strain theory), thus the arising governing differential equations and boundary conditions are in general nonlinear. The resulting coupling effect between twisting and axial displacement components is considered and torsional vibration analysis is performed in both the torsional pre- or post-buckled state. A distributed mass model system is employed, taking into account the warping, rotatory and axial inertia, leading to the formulation of a coupled nonlinear initial boundary value problem with respect to the variable along the bar angle of twist and to an "average" axial displacement of the cross-section of the bar. The numerical solution of the aforementioned initial boundary value problem is performed using the analog equation method, a BEM based method, leading to a system of nonlinear differential-algebraic equations (DAE), which is solved using an efficient time discretization scheme. Additionally, for the free vibrations case, a nonlinear generalized eigenvalue problem is formulated with respect to the fundamental mode shape at the points of reversal of motion after ignoring the axial inertia to verify the accuracy of the proposed method. The problem is solved using the direct iteration technique (DIT), with a geometrically linear fundamental mode shape as a starting vector. The validity of negligible axial inertia assumption is examined for the problem at hand.
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.
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anjali devi
2015-01-01
Full Text Available The effects of nonlinear radiation on hydromagnetic boundary layer flow and heat transfer over a shrinking surface is investigated in the present work. Using suitable similarity transformations, the governing nonlinear partial differential equations are transformed into nonlinear ordinary differential equations. The resultant equations which are highly nonlinear are solved numerically using Nachtsheim Swigert shooting iteration scheme together with Fourth Order Runge Kutta method. Numerical solutions for velocity, skin friction coefficient and temperature are obtained for various values of physical parameters involved in the study namely Suction parameter, Magnetic parameter, Prandtl number, Radiation parameter and Temperature ratio parameter. Numerical values for dimensionless rate of heat transfer are also obtained for various physical parameters and are shown through tables. The analytical solution of the energy equation when the radiation term is taken in linear form is obtained using Confluent hypergeometric function.
Nonlinear Excitation of Inviscid Stationary Vortex in a Boundary-Layer Flow
Choudhari, Meelan; Duck, Peter W.
1996-01-01
We examine the excitation of inviscid stationary crossflow instabilities near an isolated surface hump (or indentation) underneath a three-dimensional boundary layer. As the hump height (or indentation depth) is increased from zero, the receptivity process becomes nonlinear even before the stability characteristics of the boundary layer are modified to a significant extent. This behavior contrasts sharply with earlier findings on the excitation of the lower branch Tollmien-Schlichting modes and is attributed to the inviscid nature of the crossflow modes, which leads to a decoupling between the regions of receptivity and stability. As a result of this decoupling, similarity transformations exist that allow the nonlinear receptivity of a general three-dimensional boundary layer to be studied with a set of canonical solutions to the viscous sublayer equations. The parametric study suggests that the receptivity is likely to become nonlinear even before the hump height becomes large enough for flow reversal to occur in the canonical solution. We also find that the receptivity to surface humps increases more rapidly as the hump height increases than is predicted by linear theory. On the other hand, receptivity near surface indentations is generally smaller in comparison with the linear approximation. Extension of the work to crossflow receptivity in compressible boundary layers and to Gortler vortex excitation is also discussed.
The nonlinear evolution of inviscid Goertler vortices in three-dimensional boundary layers
Blackaby, Nicholas; Dando, Andrew; Hall, Philip
1995-09-01
The nonlinear development of inviscid Gortler vortices in a three-dimensional boundary layer is considered. We do not follow the classical approach of weakly nonlinear stability problems and consider a mode which has just become unstable. Instead we extend the method of Blackaby, Dando, and Hall (1992), which considered the closely related nonlinear development of disturbances in stratified shear flows. The Gortler modes we consider are initially fast growing and we assume, following others, that boundary-layer spreading results in them evolving in a linear fashion until they reach a stage where their amplitudes are large enough and their growth rates have diminished sufficiently so that amplitude equations can be derived using weakly nonlinear and non-equilibrium critical-layer theories. From the work of Blackaby, Dando and Hall (1993) is apparent, given the range of parameters for the Gortler problem, that there are three possible nonlinear integro-differential evolution equations for the disturbance amplitude. These are a cubic due to viscous effects, a cubic which corresponds to the novel mechanism investigated in this previous paper, and a quintic. In this paper we shall concentrate on the two cubic integro-differential equations and in particular, on the one due to the novel mechanism as this will be the first to affect a disturbance. It is found that the consideration of a spatial evolution problem as opposed to temporal (as was considered in Blackaby, Dando, and Hall, 1992) causes a number of significant changes to the evolution equations.
Chen, Xiang-Jun; Lam, Wa Kun
2004-06-01
An inverse scattering transform for the derivative nonlinear Schrödinger equation with nonvanishing boundary conditions is derived by introducing an affine parameter to avoid constructing Riemann sheets. A one-soliton solution simpler than that in the literature is obtained, which is a breather and degenerates to a bright or dark soliton as the discrete eigenvalue becomes purely imaginary. The solution is mapped to that of the modified nonlinear Schrödinger equation by a gaugelike transformation, predicting some sub-picosecond solitons in optical fibers.
The Modified Adomian Decomposition Method for Nonlinear Fractional Boundary Value Problems
Institute of Scientific and Technical Information of China (English)
WANG Jie
2012-01-01
We use the modified Adomian decomposition method(ADM) for solving the nonlinear fractional boundary value problem Dα0+u(x)=f(x,u(x)), 0＜x＜1, 3＜α≤4u(0) =α0, u″(0) =α2 (1)u(1) =β0, u″(1) =β2where Dα0+u is Caputo fractional derivative and α0,α2,β0,β2 is not zero at all,and f:[0,1] x R → R is continuous.The calculated numerical results show reliability and efficiency of the algorithm given.The numerical procedure is tested on linear and nonlinear problems.
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Ying Wang
2015-03-01
Full Text Available In this article, we study the existence of multiple positive solutions for singular semipositone boundary-value problem (BVP with integral boundary conditions on infinite intervals. By using the properties of the Green's function and the Guo-Krasnosel'skii fixed point theorem, we obtain the existence of multiple positive solutions under conditions concerning the nonlinear functions. The method in this article can be used for a large number of problems. We illustrate the validity of our results with an example in the last section.
POSITIVE SOLUTIONS OF A NONLINEAR THREE-POINT EIGENVALUE PROBLEM WITH INTEGRAL BOUNDARY CONDITIONS
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FAOUZI HADDOUCHI
2015-11-01
Full Text Available In this paper, we study the existence of positive solutions of a three-point integral boundary value problem (BVP for the following second-order differential equation u''(t + \\lambda a(tf(u(t = 0; 0 0 is a parameter, 0 <\\eta < 1, 0 <\\alpha < 1/{\\eta}. . By using the properties of the Green's function and Krasnoselskii's fixed point theorem on cones, the eigenvalue intervals of the nonlinear boundary value problem are considered, some sufficient conditions for the existence of at least one positive solutions are established.
Verified solutions of two-point boundary value problems for nonlinear oscillators
Bünger, Florian
Using techniques introduced by Nakao [4], Oishi [5, 6] and applied by Takayasu, Oishi, Kubo [11, 12] to certain nonlinear two-point boundary value problems (see also Rump [7], Chapter 15), we provide a numerical method for verifying the existence of weak solutions of two-point boundary value problems of the form -u″ = a(x, u) + b(x, u)u‧, 0 b are functions that fulfill some regularity properties. The numerical approximation is done by cubic spline interpolation. Finally, the method is applied to the Duffing, the van der Pol and the Toda oscillator. The rigorous numerical computations were done with INTLAB [8].
Institute of Scientific and Technical Information of China (English)
张洪生; 洪广文; 丁平兴; 曹振轶
2001-01-01
In this paper, the characteristics of different forms of mild slope equations for non-linear wave are analyzed, and new non-linear theoretic models for wave propagation are presented, with non-linear terms added to the mild slope equations for non-stationary linear waves and dissipative effects considered. Numerical simulation models are developed of non-linear wave propagation for waters of mildly varying topography with complicated boundary, and the effects are studied of different non-linear corrections on calculation results of extended mild slope equations. Systematical numerical simulation tests show that the present models can effectively reflect non-linear effects.
Positive Solutions to Fractional Boundary Value Problems with Nonlinear Boundary Conditions
Directory of Open Access Journals (Sweden)
Nemat Nyamoradi
2013-01-01
Full Text Available We consider a system of boundary value problems for fractional differential equation given by D0+βϕp(D0+αu(t=λ1a1(tf1(u(t,v(t, t∈(0,1, D0+βϕp(D0+αv(t=λ2a2(tf2(u(t,v(t, t∈(0,1, where 1<α, β≤2, 2<α+β≤4, λ1, λ2 are eigenvalues, subject either to the boundary conditions D0+αu(0=D0+αu(1=0, u(0=0, D0+β1u(1-Σi=1m-2a1i D0+β1u(ξ1i=0, D0+αv(0=D0+αv(1=0, v(0=0, D0+β1v(1-Σi=1m-2a2i D0+β1v(ξ2i=0 or D0+αu(0=D0+αu(1=0, u(0=0, D0+β1u(1-Σi=1m-2a1i D0+β1u(ξ1i=ψ1(u, D0+αv(0=D0+αv(1=0, v(0=0, D0+β1v(1-Σi=1m-2a2i D0+β1v(ξ2i=ψ2(v, where 0<β1<1, α-β1-1≥0 and ψ1, ψ2:C([0,1]→[0, ∞ are continuous functions. The Krasnoselskiis fixed point theorem is applied to prove the existence of at least one positive solution for both fractional boundary value problems. As an application, an example is given to demonstrate some of main results.
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.
Nonlinear stability of non-stationary cross-flow vortices in compressible boundary layers
Gajjar, J. S. B.
1995-01-01
The nonlinear evolution of long wavelength non-stationary cross-flow vortices in a compressible boundary layer is investigated and the work extends that of Gajjar (1994) to flows involving multiple critical layers. The basic flow profile considered in this paper is that appropriate for a fully three-dimensional boundary layer with O(1) Mach number and with wall heating or cooling. The governing equations for the evolution of the cross-flow vortex are obtained and some special cases are discussed. One special case includes linear theory where exact analytic expressions for the growth rate of the vortices are obtained. Another special case is a generalization of the Bassom & Gajjar (1988) results for neutral waves to compressible flows. The viscous correction to the growth rate is derived and it is shown how the unsteady nonlinear critical layer structure merges with that for a Haberman type of viscous critical layer.
Blow-up in p-Laplacian heat equations with nonlinear boundary conditions
Ding, Juntang; Shen, Xuhui
2016-10-01
In this paper, we investigate the blow-up of solutions to the following p-Laplacian heat equations with nonlinear boundary conditions: {l@{quad}l}(h(u))_t =nabla\\cdot(|nabla u|pnabla u)+k(t)f(u) &{in } Ω×(0,t^{*}), |nabla u|ppartial u/partial n=g(u) &on partialΩ×(0,t^{*}), u(x,0)=u0(x) ≥ 0 & {in } overline{Ω},. where {p ≥ 0} and {Ω} is a bounded convex domain in {RN}, {N ≥ 2} with smooth boundary {partialΩ}. By constructing suitable auxiliary functions and using a first-order differential inequality technique, we establish the conditions on the nonlinearities and data to ensure that the solution u( x, t) blows up at some finite time. Moreover, the upper and lower bounds for the blow-up time, when blow-up does occur, are obtained.
Waveguides with Absorbing Boundaries: Nonlinearity Controlled by an Exceptional Point and Solitons
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.
EXISTENCE OF SOLUTIONS OF A FAMILY OF NONLINEAR BOUNDARY VALUE PROBLEMS IN L2-SPACES
Institute of Scientific and Technical Information of China (English)
WeiLi; ZhouHaiyun
2005-01-01
By using the perturbation results of sums of ranges of accretive mappings of Calvert and Gupta (1978),the abstract results on the existence of solutions of a family of nonlinear boundary value problems in L2 (Ω) are studied. The equation discussed in this paper and the methods used here are extension and complement to the corresponding results of Wei Li and He Zhen's previous papers. Especially,some new techniques are used in this paper.
A two-phase free boundary problem for a nonlinear diffusion-convection equation
Energy Technology Data Exchange (ETDEWEB)
De Lillo, S; Lupo, G [Dipartimento di Matematica e Informatica, Universita degli Studi di Perugia, Via Vanvitelli 1, 06123 Perugia (Italy)], E-mail: silvana.delillo@pg.infn.it
2008-04-11
A two-phase free boundary problem associated with a diffusion-convection equation is considered. The problem is reduced to a system of nonlinear integral equations, which admits a unique solution for small times. The system admits an explicit two-component solution corresponding to a two-component shock wave of the Burgers equation. The stability of such a solution is also discussed.
On the Stability of Nonlinear Viscous Vortices in Three-Dimensional Boundary Layers
1992-04-01
wave disturbances in stable and unsta- ble parallel flows , Part 2. The development of a solution for plane Poiseuille and plane Couette flow . J. Fluid...unstable parallel flows , Part 1. The basic behaviour in plane Poiseuille flow . J. Fluid Mech. 9, 353-370. Watson, J. 1960 On the nonlinear mechanics of...vortices which a particular boundary layer may support. According to a linearised theory vortices within a high G6rtler number flow can take one of
Solvability of a three-point nonlinear boundary-value problem
Directory of Open Access Journals (Sweden)
Assia Guezane-Lakoud
2010-09-01
Full Text Available Using the Leray Schauder nonlinear alternative, we prove the existence of a nontrivial solution for the three-point boundary-value problem $$displaylines{ u''+f(t,u= 0,quad 0
Positive solutions for a nonlinear periodic boundary-value problem with a parameter
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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, $$ lim_{lambdao +infty}|x_{lambda}|=+infty,quadhbox{or}quad lim_{lambdao+infty}|x_{lambda}|=0. $$
Kounadis, A. N.
1992-05-01
An efficient and easily applicable, approximate analytic technique for the solution of nonlinear initial and boundary-value problems associated with nonlinear ordinary differential equations (O.D.E.) of any order and variable coefficients, is presented. Convergence, uniqueness and upper bound error estimates of solutions, obtained by the successive approximations scheme of the proposed technique, are thoroughly established. Important conclusions regarding the improvement of convergence for large time and large displacement solutions in case of nonlinear initial-value problems are also assessed. The proposed technique is much more efficient than the perturbations schemes for establishing the large postbuckling response of structural systems. The efficiency, simplicity and reliability of the proposed technique is demonstrated by two illustrative examples for which available numerical results exist.
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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.
Wittig, A; Di Lizia, P.; Armellin, R.; Zazzera, FB; Makino, K; Berzş, M
2014-01-01
Current approaches to uncertainty propagation in astrodynamics mainly refer to linearized models or Monte Carlo simulations. Naive linear methods fail in nonlinear dynamics, whereas Monte Carlo simulations tend to be computationally intensive. Differential algebra has already proven to be an efficient compromise by replacing thousands of pointwise integrations of Monte Carlo runs with the fast evaluation of the arbitrary order Taylor expansion of the flow of the dynamics. However, the current...
A fully nonlinear iterative solution method for self-similar potential flows with a free boundary
Iafrati, Alessandro
2013-01-01
An iterative solution method for fully nonlinear boundary value problems governing self-similar flows with a free boundary is presented. Specifically, the method is developed for application to water entry problems, which can be studied under the assumptions of an ideal and incompressible fluid with negligible gravity and surface tension effects. The approach is based on a pseudo time stepping procedure, which uses a boundary integral equation method for the solution of the Laplace problem governing the velocity potential at each iteration. In order to demonstrate the flexibility and the capabilities of the approach, several applications are presented: the classical wedge entry problem, which is also used for a validation of the approach, the block sliding along an inclined sea bed, the vertical water entry of a flat plate and the ditching of an inclined plate. The solution procedure is also applied to cases in which the body surface is either porous or perforated. Comparisons with numerical or experimental d...
Modeling Charge-Sign Asymmetric Solvation Free Energies With Nonlinear Boundary Conditions
Bardhan, Jaydeep P
2014-01-01
We show that charge-sign-dependent asymmetric hydration can be modeled accurately using linear Poisson theory but 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 [J. Phys. Chem. B, v. 112:2408, 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.
Mawhin, Jean; Ure??a, Antonio J.
2002-01-01
A generalization of the well-known Hartman-Nagumo inequality to the case of the vector ordinary p-Laplacian and classical degree theory provide existence results for some associated 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.
Institute of Scientific and Technical Information of China (English)
CHEN Xiang-Jun; HOU Li-Jie; LAM Wa Kun
2005-01-01
@@ Conservation laws for the derivative nonlinear Schr(o)dinger equation with non-vanishing boundary conditions are derived, based on the recently developed inverse scattering transform using the affine parameter technique.
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Gilles Carbou
2015-02-01
Full Text Available We study the Landau-Lifshitz system associated with Maxwell equations in a bilayered ferromagnetic body when super-exchange and surface anisotropy interactions are present in the spacer in-between the layers. In the presence of these surface energies, the Neumann boundary condition becomes nonlinear. We prove, in three dimensions, the existence of global weak solutions to the Landau-Lifshitz-Maxwell system with nonlinear Neumann boundary conditions.
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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.
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Allaberen Ashyralyev
2012-01-01
Full Text Available In the present study, the nonlocal and integral boundary value problems for the system of nonlinear fractional differential equations involving the Caputo fractional derivative are investigated. Theorems on existence and uniqueness of a solution are established under some sufficient conditions on nonlinear terms. A simple example of application of the main result of this paper is presented.
Institute of Scientific and Technical Information of China (English)
Wu Xuesong; Gao Wenjie; Cao Jianwen
2011-01-01
In this paper, the authors discuss the global existence and blow-up of the solution to an evolution ρ-Laplace system with nonlinear sources and nonlinear boundary condition. The authors first establish the local existence of solutions, then give a necessary and sufficient condition on the global existence of the positive solution.
Institute of Scientific and Technical Information of China (English)
无
2012-01-01
The iterative technique of sign-changing solution is studied for a nonlinear third-order two-point boundary value problem, where the nonlinear term has the time sin-gularity. By applying the monotonically iterative technique, an existence theorem is established and two useful iterative schemes are obtained.
Nonlinear optimal control of bypass transition in a boundary layer flow
Xiao, Dandan; Papadakis, George
2016-11-01
Bypass transition is observed in a flat-plate boundary-layer flow when high levels of free stream turbulence are present. This scenario is characterized by the formation of streamwise elongated streaks inside the boundary layer, their break down into turbulent spots and eventually fully turbulent flow. In the current work, we perform DNS simulations of control of bypass transition in a zero-pressure-gradient boundary layer. A non-linear optimal control algorithm is developed that employs the direct-adjoint approach to minimise a quadratic cost function based on the deviation from the Blasius velocity profile. Using the Lagrange variational approach, the distribution of the blowing/suction control velocity is found by solving iteratively the non-linear Navier-Stokes and its adjoint equations in a forward/backward loop. The optimisation is performed over a finite time horizon during which the Lagrange functional is to be minimised. Large values of optimisation horizon result in instability of the adjoint equations. The results show that the controller is able to reduce the turbulent kinetic energy of the flow in the region where the objective function is defined and the velocity profile is seen to approach the Blasius solution. Significant drag reduction is also achieved.
Dynamic Analysis of HSDB System and Evaluation of Boundary Non-linearity through Experiments
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K. Chandrakar
2016-04-01
Full Text Available This paper deals with mechanical design and development of high speed digital board (HSDB system which consists of printed circuit board (PCB with all electronic components packaged inside the cavity for military application. The military environment poses a variety of extreme dynamic loading conditions, namely, quasi static, vibration, shock and acoustic loads that can seriously degrade or even cause failure of electronics. The vibrational requirement for the HSDB system is that the natural frequency should be more than 200 Hz and sustain power spectrum density of 14.8 Grms in the overall spectrum. Structural integrity of HSDB is studied in detail using finite element analysis (FEA tool against the dynamic loads and configured the system. Experimental vibration tests are conducted on HSDB with the help of vibration shaker and validated the FE results. The natural frequency and maximum acceleration response computed from vibration tests for the configured design were found. The finite element results show a good correlation with the experiment results for the same boundary conditions. In case of fitment scenario of HSDB system, it is observed that the influence of boundary non-linearity during experiments. This influence of boundary non-linearity is evaluated to obtain the closeout of random vibration simulation results.
Boundary layer flow and heat transfer to Carreau fluid over a nonlinear stretching sheet
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Masood Khan
2015-10-01
Full Text Available This article studies the Carreau viscosity model (which is a generalized Newtonian model and then use it to obtain a formulation for the boundary layer equations of the Carreau fluid. The boundary layer flow and heat transfer to a Carreau model over a nonlinear stretching surface is discussed. The Carreau model, adequate for many non-Newtonian fluids, is used to characterize the behavior of the fluids having shear thinning properties and fluids with shear thickening properties for numerical values of the power law exponent n. The modeled boundary layer conservation equations are converted to non-linear coupled ordinary differential equations by a suitable transformation. Numerical solution of the resulting equations are obtained by using the Runge-Kutta Fehlberg method along with shooting technique. This analysis reveals many important physical aspects of flow and heat transfer. Computations are performed for different values of the stretching parameter (m, the Weissenberg number (We and the Prandtl number (Pr. The obtained results show that for shear thinning fluid the fluid velocity is depressed by the Weissenberg number while opposite behavior for the shear thickening fluid is observed. A comparison with previously published data in limiting cases is performed and they are in excellent agreement.
奇摄动非线性边值问题%THE SINGULARLY PERTURBED NONLINEAR BOUNDARY VALUE PROBLEMS
Institute of Scientific and Technical Information of China (English)
莫嘉琪
2000-01-01
The singularly perturbed nonlinear boundary value problems are considered.Using the stretched variable and the method of boundary layer correction,the formal asymptotic expansion of solution is obtained.And then the uniform validity of solution is proved by using the differential inequalities.
Homotopy deform method for reproducing kernel space for nonlinear boundary value problems
Indian Academy of Sciences (India)
MIN-QIANG XU; YING-ZHEN LIN
2016-10-01
In this paper, the combination of homotopy deform method (HDM) and simplified reproducing kernel method (SRKM) is introduced for solving the boundary value problems (BVPs) of nonlinear differential equations. The solution methodology is based on Adomian decomposition and reproducing kernel method (RKM). By the HDM, the nonlinear equations can be converted into a series of linear BVPs. After that, the simplified reproducing kernel method, which not only facilitates the reproducing kernel but also avoids the time-consuming Schmidt orthogonalization process, is proposed to solve linear equations. Some numerical test problems including ordinary differential equations and partial differential equations are analysed to illustrate the procedure and confirm the performance of the proposed method. The results faithfully reveal that our algorithm is considerably accurate and effective as expected.
Modeling Granular Materials as Compressible Non-Linear Fluids: Heat Transfer Boundary Value Problems
Energy Technology Data Exchange (ETDEWEB)
Massoudi, M.C.; Tran, P.X.
2006-01-01
We discuss three boundary value problems in the flow and heat transfer analysis in flowing granular materials: (i) the flow down an inclined plane with radiation effects at the free surface; (ii) the natural convection flow between two heated vertical walls; (iii) the shearing motion between two horizontal flat plates with heat conduction. It is assumed that the material behaves like a continuum, similar to a compressible nonlinear fluid where the effects of density gradients are incorporated in the stress tensor. For a fully developed flow the equations are simplified to a system of three nonlinear ordinary differential equations. The equations are made dimensionless and a parametric study is performed where the effects of various dimensionless numbers representing the effects of heat conduction, viscous dissipation, radiation, and so forth are presented.
Existence of positive solutions to a Laplace equation with nonlinear boundary condition
Kim, C.-G.; Liang, Z.-P.; Shi, J.-P.
2015-12-01
The positive solutions of a Laplace equation with a superlinear nonlinear boundary condition on a bounded domain are studied. For higher-dimensional domains, it is shown that non-constant positive solutions bifurcate from a branch of trivial solutions at a sequence of bifurcation points, and under additional conditions on nonlinearity, the existence of a non-constant positive solution for any sufficiently large parameter value is proved by using variational approach. It is also proved that for one-dimensional domain, there is only one bifurcation point, all non-constant positive solutions lie on the bifurcating curve, and for large parameter values, there exist at least two non-constant positive solutions. For a special case, there are exactly two non-constant positive solutions.
Murio, Diego A.
1991-01-01
An explicit and unconditionally stable finite difference method for the solution of the transient inverse heat conduction problem in a semi-infinite or finite slab mediums subject to nonlinear radiation boundary conditions is presented. After measuring two interior temperature histories, the mollification method is used to determine the surface transient heat source if the energy radiation law is known. Alternatively, if the active surface is heated by a source at a rate proportional to a given function, the nonlinear surface radiation law is then recovered as a function of the interface temperature when the problem is feasible. Two typical examples corresponding to Newton cooling law and Stefan-Boltzmann radiation law respectively are illustrated. In all cases, the method predicts the surface conditions with an accuracy suitable for many practical purposes.
Attractors for strongly damped wave equations with nonlinear hyperbolic dynamic boundary conditions
Jameson Graber, P.; Shomberg, Joseph L.
2016-04-01
We establish the well-posedness of a strongly damped semilinear wave equation equipped with nonlinear hyperbolic dynamic boundary conditions. Results are carried out with the presence of a parameter distinguishing whether the underlying operator is analytic, α >0 , or only of Gevrey class, α =0 . We establish the existence of a global attractor for each α \\in ≤ft[0,1\\right], and we show that the family of global attractors is upper-semicontinuous as α \\to 0. Furthermore, for each α \\in ≤ft[0,1\\right] , we show the existence of a weak exponential attractor. A weak exponential attractor is a finite dimensional compact set in the weak topology of the phase space. This result ensures the corresponding global attractor also possesses finite fractal dimension in the weak topology; moreover, the dimension is independent of the perturbation parameter α. In both settings, attractors are found under minimal assumptions on the nonlinear terms.
Institute of Scientific and Technical Information of China (English)
Chien-Yu Lin; Rameez Asif; Michael Holtmannspoetter; Bernhard Schmauss
2012-01-01
Non-uniform step-size distribution is implemented for split-step based nonlinear compensation in single-channel 112-Gb/s 16 quadrature amplitude modulation (QAM) transmission. Numerical simulations of the system including a 20x80 km uncompensated link are performed using logarithmic step size distribution to compensate signal distortions. 50% of reduction in number of steps with respect to using constant step sizes is observed. The performance is further improved by optimizing nonlinear calculating position (NLCP) in case of using constant step sizes while NLCP optimization becomes unnecessary when using logarithmic step sizes, which reduces the computational effort due to uniformly distributed nonlinear phase for all successive steps.%Non-uniform step-size distribution is implemented for split-step based nonlinear compensation in singlechannel 112-Gb/s 16 quadrature amplitude modulation (QAM) transmission.Numerical simulations of the system including a 20×80 km uncompensated link are performed using logarithmic step size distribution to compensate signal distortions.50％ of reduction in number of steps with respect to using constant step sizes is observed.The performance is further improved by optimizing nonlinear calculating position (NLCP) in case of using constant step sizes while NLCP optimization becomes unnecessary when using logarithmic step sizes,which reduces the computational effort due to uniformly distributed nonlinear phase for all successive steps.
Babinski, A.; Ortner, G.; Raymond, S.; Potemski, M.; Bayer, M.; Hawrylak, P.; Forchel, A.; Wasilewski, Z.; Fafard,S.
2005-01-01
We report on the magnetic field dispersion of the exciton spin-splitting and diamagnetic shift in single InAs/GaAs quantum dots (QDs) and dot molecules (QDMs) up to $B$ = 28 T. Only for systems with strong geometric confinement, the dispersions can be well described by simple field dependencies, while for dots with weaker confinement considerable deviations are observed: most importantly, in the high field limit the spin-splitting shows a non-linear dependence on $B$, clearly indicating light...
Solutions and Multiple Solutions for p(x)-Laplacian Equations with Nonlinear Boundary Condition
Institute of Scientific and Technical Information of China (English)
Zifei SHEN; Chenyin QIAN
2009-01-01
The authors study the p(x)-Laplacian equations with nonlinear boundary condition.By using the variational method,under appropriate assumptions on the perturbation terms f1(x,u),f2(x,u) and h1(x),h2(x),such that the associated functional satisfies the "mountain pass lemma" and "fountain theorem" respectively,the existence and multiplicity of solutions are obtained.The discussion is based on the theory of variable exponent Lebesgue and Sobolev spaces.
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Nicolae Tarfulea
2009-10-01
Full Text Available We investigate the existence of weak solutions to a class of quasilinear elliptic equations with nonlinear Neumann boundary conditions in exterior domains. Problems of this kind arise in various areas of science and technology. An important model case related to the initial data problem in general relativity is presented. As an application of our main result, we deduce the existence of the conformal factor for the Hamiltonian constraint in general relativity in the presence of multiple black holes. We also give a proof for uniqueness in this case.
SOME BOUNDARY VALUE PROBLEMS FOR NONLINEAR DEGENERATE ELLIPTIC EQUATIONS OF SECOND ORDER
Institute of Scientific and Technical Information of China (English)
Wen Guochun
2007-01-01
The present article deals with some boundary value problems for nonlinear elliptic equations with degenerate rank 0 including the oblique derivative problem. Firstly the formulation and estimates of solutions of the oblique derivative problem are given, and then by the above estimates and the method of parameter extension, the existence of solutions of the above problem is proved. In this article, the complex analytic method is used, namely the corresponding problem for degenerate elliptic complex equations of first order is firstly discussed, afterwards the above problem for the degenerate elliptic equations of second order is solved.
Nonlinear systems of differential inequalities and solvability of certain boundary value problems
Directory of Open Access Journals (Sweden)
Tvrdý Milan
2001-01-01
Full Text Available In the paper we present some new existence results for nonlinear second order generalized periodic boundary value problems of the form These results are based on the method of lower and upper functions defined as solutions of the system of differential inequalities associated with the problem and their relation to the Leray–Schauder topological degree of the corresponding operator. Our main goal consists in a fairly general definition of these functions as couples from . Some conditions ensuring their existence are indicated, as well.
Possible management of near shore nonlinear surging waves through bottom boundary conditions
Mukherjee, Abhik; Janaki, M. S.; Kundu, Anjan
2017-03-01
We propose an alternative way for managing near shore surging waves, including extreme waves like tsunamis, going beyond the conventional passive measures like the warning system. We study theoretically the possibility of influencing the nonlinear surface waves through a leakage boundary effect at the bottom. It has been found through analytic result, that the controlled leakage at the bottom might regulate the amplitude of the surface solitary waves. This could lead to a possible decay of the surging waves to reduce its hazardous effects near the shore. Our theoretical results are estimated by applying it to a real coastal bathymetry of the Bay of Bengal in India.
Institute of Scientific and Technical Information of China (English)
SONG Li-mei; WENG Pei-xuan
2012-01-01
In this paper,we study a Dirichlet-type boundary value problem(BVP) of nonlinear fractional differential equation with an order α ∈ (3,4],where the fractional derivative D0α+ is the standard Riemann-Liouville fractional derivative.By constructing the Green function and investigating its properties,we obtain some criteria for the existence of one positive solution and two positive solutions for the above BVP.The Krasnosel'skii fixedpoint theorem in cones is used here.We also give an example to illustrate the applicability of our results.
A (k, n-k) Conjugate Boundary Value Problem with Semip ositone Nonlinearity
Institute of Scientific and Technical Information of China (English)
Yao Qing-liu; Shi Shao-yun
2015-01-01
The existence of positive solution is proved for a (k, n−k) conjugate boundary value problem in which the nonlinearity may make negative values and may be singular with respect to the time variable. The main results of Agarwal et al. (Agarwal R P, Grace S R, O’Regan D. Semipositive higher-order differential equa-tions. Appl. Math. Letters, 2004, 14: 201–207) are extended. The basic tools are the Hammerstein integral equation and the Krasnosel’skii’s cone expansion-compression technique.
Mertiri, Alket; Hong, M K; Mehta, P; Mertz, J; Ziegler, L D; Erramilli, Shyamsunder
2013-01-01
We report on the mid-infrared nonlinear photothermal spectrum of the neat liquid crystal 4-Octyl-4'-Cyanobiphenyl (8CB) using a tunable Quantum Cascade Laser (QCL). The nonequilibrium steady state characterized by the nonlinear photothermal infrared response undergoes a supercritical pitchfork bifurcation. The bifurcation, observed in heterodyne two-color pump-probe detection, leads to ultrasharp nonlinear infrared spectra similar to those reported in the visible region. A systematic study of the peak splitting as function of absorbed infrared power shows the bifurcation has a critical exponent of 0.5. The surprising observation of an apparently universal critical exponent in a nonequilibrium state is explained using a simple model reminiscent of mean field theory. Apart from the intrinsic interest for nonequilibrium studies, nonlinear photothermal methods lead to a dramatic narrowing of spectral lines, giving rise to a potential new contrast mechanism for the rapidly emerging new field of mid-infrared micros...
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 effects on western boundary current structure and separation: a laboratory study
Pierini, S.; Falco, P.; Zambardino, G.; McClimans, T. A.; Ellingsen, I.
2009-04-01
The role played by nonlinear effects in shaping the structure of barotropic western boundary currents (WBCs) and in determining WBC separation from the coast has been investigated through laboratory simulations by means of the 5-m-diameter Coriolis rotating basin at SINTEF (Trondheim, Norway) in the framework of the HYDRALAB-III project. The laboratory setup consists of two parallel rectangular channels separated by an island and linked by two curved connections: in the first channel, a piston is forced at a constant speed U ranging from 0.05 to 3 cm/s over a distance of 2.5 m, producing a virtually unsheared current at the entrance of the second channel. In the latter, a linear reduction of the water depth provides the topographic beta-effect that produces the westward intensification. Nearly steady currents are obtained and measured photogrammetrically over a region of about 1 m2. The broad range of piston speeds permitted by the mechanical apparatus has allowed us to achieve an unprecedented coverage of the range of nonlinearity for WBCs in terms of experimental data, so that the cross-stream WBC profile could be analyzed from the nearly linear Munk-type case (e.g., for U=0.1 cm/s with T=30 s, where T is the rotation period of the basin) up to the more realistic highly nonlinear limit (particularly significant is the case U=1 cm/s and T=30 s, which is close to be dynamically similar to the Gulf Stream). Thanks to the large size of the rotating basin, cross-stream widths of the simulated WBC as large as 80 cm could be obtained. Moreover, in order to analyze the process of WBC separation, coastal variations have been introduced along the western boundary in the form of wedge-shaped continents with different coastline orientations, whose northern limit corresponds to an idealized Cape Hatteras. While weak WBCs follow the coast also past the cape, for sufficiently strong nonlinear effects the current detaches from the coast as a consequence of flow deceleration
Jeong, Hyunjo; Zhang, Shuzeng; Li, Xiongbing
2017-02-01
In this work, we employ a focused beam theory to modify the phase reversal at the stress-free boundary, and consequently enhance the second harmonic generation during its back-propagation toward the initial source position. We first confirmed this concept through experiment by using a spherically focused beam at the water-air interface, and measuring the reflected second harmonic and comparing with a planar wave reflected from the same stress-free or a rigid boundary. In order to test the feasibility of this idea for measuring the nonlinearity parameter of solids in a reflection mode, a focused nonlinear ultrasonic beam is modeled for focusing at and reflection from a stress-free boundary. A nonlinearity parameter expression is then defined together with diffraction and attenuation corrections.
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Liaqat Ali
2016-09-01
Full Text Available In this research work a new version of Optimal Homotopy Asymptotic Method is applied to solve nonlinear boundary value problems (BVPs in finite and infinite intervals. It comprises of initial guess, auxiliary functions (containing unknown convergence controlling parameters and a homotopy. The said method is applied to solve nonlinear Riccati equations and nonlinear BVP of order two for thin film flow of a third grade fluid on a moving belt. It is also used to solve nonlinear BVP of order three achieved by Mostafa et al. for Hydro-magnetic boundary layer and micro-polar fluid flow over a stretching surface embedded in a non-Darcian porous medium with radiation. The obtained results are compared with the existing results of Runge-Kutta (RK-4 and Optimal Homotopy Asymptotic Method (OHAM-1. The outcomes achieved by this method are in excellent concurrence with the exact solution and hence it is proved that this method is easy and effective.
Renormalization-group symmetries for solutions of nonlinear boundary value problems
Kovalev, V F
2008-01-01
Approximately 10 years ago, the method of renormalization-group symmetries entered the field of boundary value problems of classical mathematical physics, stemming from the concepts of functional self-similarity and of the Bogoliubov renormalization group treated as a Lie group of continuous transformations. Overwhelmingly dominating practical quantum field theory calculations, the renormalization-group method formed the basis for the discovery of the asymptotic freedom of strong nuclear interactions and underlies the Grand Unification scenario. This paper describes the logical framework of a new algorithm based on the modern theory of transformation groups and presents the most interesting results of application of the method to differential and/or integral equation problems and to problems that involve linear functionals of solutions. Examples from nonlinear optics, kinetic theory, and plasma dynamics are given, where new analytical solutions obtained with this algorithm have allowed describing the singular...
An efficient numerical technique for the solution of nonlinear singular boundary value problems
Singh, Randhir; Kumar, Jitendra
2014-04-01
In this work, a new technique based on Green's function and the Adomian decomposition method (ADM) for solving nonlinear singular boundary value problems (SBVPs) is proposed. The technique relies on constructing Green's function before establishing the recursive scheme for the solution components. In contrast to the existing recursive schemes based on the ADM, the proposed technique avoids solving a sequence of transcendental equations for the undetermined coefficients. It approximates the solution in the form of a series with easily computable components. Additionally, the convergence analysis and the error estimate of the proposed method are supplemented. The reliability and efficiency of the proposed method are demonstrated by several numerical examples. The numerical results reveal that the proposed method is very efficient and accurate.
Institute of Scientific and Technical Information of China (English)
李仁贵; 刘立山
2001-01-01
New existence results are presented for the singular second-order nonlinear boundary value problems u" + g(t)f(u) = 0, 0 ＜ t ＜ 1, au(0) - βu′(0) = 0,γu(1) +δu'(l) = 0 under the conditions 0 ≤ fn+ ＜ M1, m1 ＜ f∞-≤∞ or 0 ≤ f∞+＜M1, m1 ＜ f 0-≤ ∞, where f +0＝ limu→of(u)/u, f∞-＝ limu-→∞(u)/u, f0-＝limu-→of(u)/u, f+∞＝ limu→=f(u)/u, g may be singular att ＝ 0 and/ort ＝ 1 . Theproof uses a fixed point theorem in cone theory.
Modelling of hydrogen thermal desorption spectrum in nonlinear dynamical boundary-value problem
Kostikova, E. K.; Zaika, Yu V.
2016-11-01
One of the technological challenges for hydrogen materials science (including the ITER project) is the currently active search for structural materials with various potential applications that will have predetermined limits of hydrogen permeability. One of the experimental methods is thermal desorption spectrometry (TDS). A hydrogen-saturated sample is degassed under vacuum and monotone heating. The desorption flux is measured by mass spectrometer to determine the character of interactions of hydrogen isotopes with the solid. We are interested in such transfer parameters as the coefficients of diffusion, dissolution, desorption. The paper presents a distributed boundary-value problem of thermal desorption and a numerical method for TDS spectrum simulation, where only integration of a nonlinear system of low order (compared with, e.g., the method of lines) ordinary differential equations (ODE) is required. This work is supported by the Russian Foundation for Basic Research (project 15-01-00744).
SOLUTION WITH SHOCK-BOUNDARY LAYER AND SHOCK-INTERIOR LAYER TO A CLASS OF NONLINEAR PROBLEMS
Institute of Scientific and Technical Information of China (English)
无
2012-01-01
In this paper,the shock behaviors of solution to a class of nonlinear singularly perturbed problems are considered.Under some appropriate conditions,the outer and interior solutions to the original problem are constructed.Using the special limit and matching theory,the expressions of solutions with the shock behavior near the boundary and some interior points are given and the domain for boundary values is obtained.
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Alsaedi Ahmed
2009-01-01
Full Text Available A generalized quasilinearization technique is developed to obtain a sequence of approximate solutions converging monotonically and quadratically to a unique solution of a boundary value problem involving Duffing type nonlinear integro-differential equation with integral boundary conditions. The convergence of order for the sequence of iterates is also established. It is found that the work presented in this paper not only produces new results but also yields several old results in certain limits.
Solov'ev, M. B.
2010-10-01
Based on finite-difference approximations in time and a bilinear finite-element approximation in spatial variables, numerical implementations of a new iterative method with boundary condition splitting are constructed for solving the Dirichlet initial-boundary value problem for the nonstationary Stokes system. The problem is considered in a strip with a periodicity condition along it. At each iteration step of the method, the original problem splits into two much simpler boundary value problems that can be stably numerically approximated. As a result, this approach can be used to construct new effective and stable numerical methods for solving the nonstationary Stokes problem. The velocity and pressure are approximated by identical bilinear finite elements, and there is no need to satisfy the well-known difficult-to-verify Ladyzhenskaya-Brezzi-Babuska condition, as is usually required when the problem is discretized as a whole. Numerical iterative methods are constructed that are first- and second-order accurate in time and second-order accurate in space in the max norm for both velocity and pressure. The numerical methods have fairly high convergence rates corresponding to those of the original iterative method at the differential level (the error decreases approximately 7 times per iteration step). Numerical results are presented that illustrate the capabilities of the methods developed.
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.
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. 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. PMID:24949738
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.
Nonlinear optimal control of bypass transition in a boundary layer flow
Xiao, Dandan; Papadakis, George
2017-05-01
The central aim of the paper is to apply and assess a nonlinear optimal control strategy to suppress bypass transition, due to bimodal interactions [T. A. Zaki and P. A. Durbin, "Mode interaction and the bypass route to transition," J. Fluid Mech. 531, 85 (2005)] in a zero-pressure-gradient boundary layer. To this end, a Lagrange variational formulation is employed that results in a set of adjoint equations. The optimal wall actuation (blowing and suction from a control slot) is found by solving iteratively the nonlinear Navier-Stokes and the adjoint equations in a forward/backward loop using direct numerical simulation. The optimization is performed in a finite time horizon. Large values of optimization horizon result in the instability of the adjoint equations. The control slot is located exactly in the region of transition. The results show that the control is able to significantly reduce the objective function, which is defined as the spatial and temporal integral of the quadratic deviation from the Blasius profile plus a term that quantifies the control cost. The physical mechanism with which the actuation interacts with the flow field is investigated and analysed in relation to the objective function employed. Examination of the joint probability density function shows that the control velocity is correlated with the streamwise velocity in the near wall region but this correlation is reduced as time elapses. The spanwise averaged velocity is distorted by the control action, resulting in a significant reduction of the skin friction coefficient. Results are presented with and without zero-net mass flow constraint of the actuation velocity. The skin friction coefficient drops below the laminar value if there is no mass constraint; it remains however larger than laminar when this constraint is imposed. Results are also compared with uniform blowing using the same time-average velocity obtained from the nonlinear optimal algorithm.
Initial-Boundary Value Problem Solution of the Nonlinear Shallow-water Wave Equations
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
Andrieux, Stéphane; Baranger, Thouraya N.
2016-12-01
The paper is devoted to the derivation of a numerical method for expanding available mechanical fields (stress vector and displacements) on a part of the boundary of a solid into its interior and up to unreachable parts of its boundary (with possibly internal surfaces). This expansion enables various identification or inverse problems to be solved in mechanics. The method is based on the solution of a nonlinear elliptic Cauchy problem because the mechanical behavior of the solid is considered as nonlinear (hyperelastic or elastoplastic medium). Advantage is taken of the assumption of convexity of the potentials used for modeling the constitutive equation, encompassing previous work by the authors for linear elastic solids, in order to derive an appropriate error functional. Two illustrations are given in order to evaluate the overall efficiency of the proposed method within the framework of small strains and isothermal transformation.
Institute of Scientific and Technical Information of China (English)
Sun Fuqin; Wang Mingxin
2004-01-01
In this paper, we study the non-negative solutions to a degenerate parabolic system with nonlinear boundary conditions in the multi-dimensional case.By the upper and lower solutions method, we give the conditions on the existence and non-existence of global solutions.
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Peiguo Zhang
2013-01-01
Full Text Available By using the cone theory and the Banach contraction mapping principle, the existence and uniqueness results are established for nonlinear higher-order differential equation boundary value problems with sign-changing Green’s function. The theorems obtained are very general and complement previous known results.
Peter E. Zhidkov
2001-01-01
We find sufficient conditions for systems of functions to be Riesz bases in $L_2(0,1)$. Then we improve a theorem presented in [13] by showing that a ``standard'' system of solutions of a nonlinear boundary-value problem, normalized to 1, is a Riesz basis in $L_2(0,1)$. The proofs in this article use Bari's theorem.
Solov'ev, M. B.
2010-11-01
Numerical implementations of a new fast-converging iterative method with boundary condition splitting are constructed for solving the Dirichlet initial-boundary value problem for the nonstationary Stokes system in the gap between two coaxial cylinders. The problem is assumed to be axially symmetric and periodic along the cylinders. The construction is based on finite-difference approximations in time and bilinear finite-element approximations in a cylindrical coordinate system. A numerical study has revealed that the iterative methods constructed have fairly high convergence rates that do not degrade with decreasing viscosity (the error is reduced by approximately 7 times per iteration step). Moreover, the methods are second-order accurate with respect to the mesh size in the max norm for both velocity and pressure.
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A. Belmiloudi
2014-01-01
Full Text Available The paper investigates boundary optimal controls and parameter estimates to the well-posedness nonlinear model of dehydration of thermic problems. We summarize the general formulations for the boundary control for initial-boundary value problem for nonlinear partial differential equations modeling the heat transfer and derive necessary optimality conditions, including the adjoint equation, for the optimal set of parameters minimizing objective functions J. Numerical simulations illustrate several numerical optimization methods, examples, and realistic cases, in which several interesting phenomena are observed. A large amount of computational effort is required to solve the coupled state equation and the adjoint equation (which is backwards in time, and the algebraic gradient equation (which implements the coupling between the adjoint and control variables. The state and adjoint equations are solved using the finite element method.
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A. Malvandi
2014-01-01
Full Text Available Steady two-dimensional boundary layer flow of a nanofluid past a nonlinear stretching sheet is investigated analytically using the Homotopy Analysis Method (HAM. The employed model for nanofluid includes twocomponent four-equation non-homogeneous equilibrium model that incorporates the effects of Brownian motion ( Nb , thermophoresis ( Nt and Lewis number ( Le simultaneously. The basic partial boundary layer equations have been reduced to a two-point boundary value problem via the similarity variables. Analytical results are in best agreements with those existing in the literatures. The outcomes signify the decreasing trend of heat transfer rate with thermophoresis, Brownian motion and Lewis number. However, concentration rate has a sensitive behavior with parameters, especially the Brownian motion and thermophoresis parameters. Also, the weak points of numerical methods in such problems have been mentioned and the efficiency of HAM, as an alternative approach, in solving these kinds of nonlinear coupled problems has been shown.
Caplan, R M
2011-01-01
An easy to implement modulus-squared Dirichlet (MSD) boundary condition is formulated for numerical simulations of time-dependent complex partial differential equations in multidimensional settings. The MSD boundary condition approximates a constant modulus-square value of the solution at the boundaries. Application of the MSD boundary condition to the nonlinear Schr\\"odinger equation is shown, and numerical simulations are performed to demonstrate its usefulness and advantages over other simple boundary conditions.
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.
leMesurier, Brenton John; Christiansen, Peter Leth; Gaididei, Yuri B; Rasmussen, Jens Juul
2004-10-01
The effect of attractive linear potentials on self-focusing in-waves modeled by a nonlinear Schrödinger equation is considered. It is shown that the attractive potential can prevent both singular collapse and dispersion that are generic in the cubic Schrödinger equation in the critical dimension 2 and can lead to a stable oscillating beam. This is observed to involve a splitting of the beam into an inner part that is oscillatory and of subcritical power and an outer dispersing part. An analysis is given in terms of the rate competition between the linear and nonlinear focusing effects, radiation losses, and known stable periodic behavior of certain solutions in the presence of attractive potentials.
Blow up and quenching for a problem with nonlinear boundary conditions
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Nuri Ozalp
2015-07-01
Full Text Available In this article, we study the blow up behavior of the heat equation $ u_t=u_{xx}$ with $u_x(0,t=u^{p}(0,t$, $u_x(a,t=u^q(a,t$. We also study the quenching behavior of the nonlinear parabolic equation $v_t=v_{xx}+2v_x^{2}/(1-v$ with $v_x(0,t=(1-v(0,t^{-p+2}$, $ v_x(a,t=(1-v(a,t^{-q+2}$. In the blow up problem, if $u_0$ is a lower solution then we get the blow up occurs in a finite time at the boundary $x=a$ and using positive steady state we give criteria for blow up and non-blow up. In the quenching problem, we show that the only quenching point is $x=a$ and $v_t$ blows up at the quenching time, under certain conditions and using positive steady state we give criteria for quenching and non-quenching. These analysis is based on the equivalence between the blow up and the quenching for these two equations.
Nonlinear Dynamics of Two Western Boundary Currents Colliding at a Gap
Wang, Z.; Yuan, D.
2012-04-01
Dynamics and hysteresis of two western boundary currents of Munk thickness LM encounter near a gap is studied using a 1.5 layer reduced-gravity quasi-geostrophic ocean model. When the gap (of width 2a) is narrow, γ≤7.3 (where γ= (a/LM), neither of the flow can penetrate into the western basin due to the viscous force. When 7.39.6, there is no choke state, and multiple states and hysteresis exist between penetrating states and periodic eddy-shedding states. A Hopf bifurcation emerges when the two flows transit from steady penetrating or choke state to periodic eddy-shedding state, and is found to be sensitive to the magnitude of γ and the baroclinic deformation radius. It occurs at lower Reynolds numbers for larger γ or deformation radius. Multiple steady states and hysteresis exist between some certain range parameters. Through vorticity term analysis, we found the time-dependent relative vorticity term varies remarkably and triggers the WBCs to alternately shed eddy into the western basin. The hysteresis is derived from the difference magnitude of the nonlinear inertial between the two different initial states.
Energy Technology Data Exchange (ETDEWEB)
Mabood, F., E-mail: mabood1971@yahoo.com [School of Mathematical Sciences, Universiti Sains Malaysia, Penang 11800 (Malaysia); Khan, W.A., E-mail: wkhan_2000@yahoo.com [Department of Mechanical Engineering, University of Waterloo, Waterloo, ON, Canada N2L 3G1 (Canada); Ismail, A.I.M., E-mail: izani@cs.usm.my [School of Mathematical Sciences, Universiti Sains Malaysia, Penang 11800 (Malaysia)
2015-01-15
The MHD laminar boundary layer flow with heat and mass transfer of an electrically conducting water-based nanofluid over a nonlinear stretching sheet with viscous dissipation effect is investigated numerically. This is the extension of the previous study on flow and heat transfer of a nanofluid over nonlinear stretching sheet (Rana and Bhargava, Commun. Nonlinear Sci. Numer. Simul. 17 (2012) 212–226). The governing equations are reduced to nonlinear ordinary differential equations using suitable similarity transformation. The effects of the governing parameters on dimensionless quantities like velocity, temperature, nanoparticle concentration, friction factor, local Nusselt, and Sherwood numbers are explored. It is found that the dimensionless velocity decreases and temperature increases with magnetic parameter, and the thermal boundary layer thickness increases with Brownian motion and thermophoresis parameters. - Highlights: • MHD flow of nanofluid and heat transfer over a nonlinear stretching sheet has not been studied yet. • Numerical solutions are computed with Runge–Kutta Fehlberg fourth–fifth order method. • Previous published results can be obtained from present study. • Reduced Nusselt and Sherwood numbers decrease with magnetic parameter.
Institute of Scientific and Technical Information of China (English)
WEI Li; ZHOU Haiyun
2005-01-01
By using the perturbation theories on sums of ranges of nonlinear accretive mappings of Calvert and Gupta, we study the abstract results on the existence of a solution u ∈ Ls (Ω) of nonlinear boundary value problems involving the p-Laplacian operator, where2 ≤ s ＜ +∞, and 2N/N+1 ＜ p ≤ 2 for N(≥ 1) which denotes the dimension of RN. To obtain the result, some new techniques are used in this paper. The equation discussed in this paper and our methods here are extension and complement to the corresponding results of L. Wei and Z. He.
Institute of Scientific and Technical Information of China (English)
Xiu Hui YANG; Fu Cai LI; Chun Hong XIE
2005-01-01
In this paper, we investigate the positive solutions of strongly coupled nonlinear parabolic systems with nonlinear boundary conditions:({ut-α(u,v)△u=g(u,v),vt-b(u,v)△v=h(u,v),(e)u/(e)(g)=d(u,v),(e)u/(e)(g)=f(u,v),)Under appropriate hypotheses on the functions a, b, g, h, d and f, we obtain that the solutions may exist globally or blow up in finite time by utilizing upper and lower solution techniques.
Institute of Scientific and Technical Information of China (English)
LI Huiling; WANG Mingxin
2005-01-01
This paper deals with the blow-up properties of the solution to a semilinear parabolic system with localized nonlinear reaction terms, subject to the null Dirichlet boundary condition. We first give sufficient conditions for that the classical solution blows up in the finite time, secondly give necessary conditions and a sufficient condition for that two components blow up simultaneously, and then obtain the uniform blow-up profiles in the interior. Finally we describe the asymptotic behavior of the blow-up solution in the boundary layer.
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A. Sakabekov
2016-01-01
Full Text Available We prove existence and uniqueness of the solution of the problem with initial and Maxwell-Auzhan boundary conditions for nonstationary nonlinear one-dimensional Boltzmann’s six-moment system equations in space of functions continuous in time and summable in square by a spatial variable. In order to obtain a priori estimation of the initial and boundary value problem for nonstationary nonlinear one-dimensional Boltzmann’s six-moment system equations we get the integral equality and then use the spherical representation of vector. Then we obtain the initial value problem for Riccati equation. We have managed to obtain a particular solution of this equation in an explicit form.
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Peter E. Zhidkov
2001-12-01
Full Text Available We find sufficient conditions for systems of functions to be Riesz bases in $L_2(0,1$. Then we improve a theorem presented in [13] by showing that a ``standard'' system of solutions of a nonlinear boundary-value problem, normalized to 1, is a Riesz basis in $L_2(0,1$. The proofs in this article use Bari's theorem.
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
In this paper, we consider a singular nth order three-point boundary value problem with sign changing nonlinearity. By the method of lower solution and topology degree theorem, we investigate the existence of positive solutions to the above problem. Moreover, the associated Green’s function for the above problem is also given. The results of this paper are new and extend the previous known results.
Institute of Scientific and Technical Information of China (English)
Guogang LIU; Yi ZHAO
2004-01-01
The one-dimensional linear wave equation with a van der Pol nonlinear boundary condition is one of the simplest models that may cause isotropic or nonisotropic chaotic vibrations.It characterizes the nonisotropic chaotic vibration by means of the total variation theory.Some results are derived on the exponential growth of total variation of the snapshots on the spatial interval in the long-time horizon when the map and the initial condition satisfy some conditions.
Liang Yue; Yang He
2011-01-01
Abstract The paper deals with the existence of positive solutions for Neumann boundary value problems of nonlinear second-order integro-differential equations - u ″ ( t ) + M u ( t ) = f ( t , u ( t ) , ( S u ) ( t ) ) , 0 < t < 1 , u ′ ( 0 ) = u ′ ( 1 ) = θ and u ″ ( t ) + M u ( t ) = f ( t , u ( t ) , ( S u ) ( t ) ) , 0 < t < 1 , u ′ ( 0 ) ...
Solvability of Third-order Three-point Boundary Value Problems with Carathéodory Nonlinearity
Institute of Scientific and Technical Information of China (English)
YAO QING-LIU; Shi Shao-yun
2012-01-01
A class of third-order three-point boundary value problems is considered,where the nonlinear term is a Carathéodory function.By introducing a height function and considering the integration of this height function,an existence theorem of solution is proved when the limit growth function exists.The main tools are the Lebesgue dominated convergence theorem and the Schauder fixed point theorem.
RamReddy, Ch.; Pradeepa, T.
2016-09-01
The significance of nonlinear temperaturedependent density relation and convective boundary condition on natural convection flow of an incompressible micropolar fluid with homogeneous-heterogeneous reactions is analyzed. In spite of the complicated nonlinear structure of the present setup and to allow all the essential features, the representation of similarity transformations for the system of non-dimensional fluid flow equations is attained through Lie group transformations and hence the governing similarity equations are worked out by a numerical approach known as spectral quasi-linearization method. It is noticed that in the presence of the nonlinear convection parameter enhance the velocity, species concentration, heat transfer rate, skin friction, but decreases the temperature and wall couple stress.
Blackman, Karin; Perret, Laurent
2016-09-01
In the present work, a boundary layer developing over a rough-wall consisting of staggered cubes with a plan area packing density, λp = 25%, is studied within a wind tunnel using combined particle image velocimetry and hot-wire anemometry to investigate the non-linear interactions between large-scale momentum regions and small-scale structures induced by the presence of the roughness. Due to the highly turbulent nature of the roughness sub-layer and measurement equipment limitations, temporally resolved flow measurements are not feasible, making the conventional filtering methods used for triple decomposition unsuitable for the present work. Thus, multi-time delay linear stochastic estimation is used to decompose the flow into large-scales and small-scales. Analysis of the scale-decomposed skewness of the turbulent velocity (u') shows a significant contribution of the non-linear term uL ' uS ' 2 ¯ , which represents the influence of the large-scales ( uL ' ) onto the small-scales ( uS ' ). It is shown that this non-linear influence of the large-scale momentum regions occurs with all three components of velocity in a similar manner. Finally, through two-point spatio-temporal correlation analysis, it is shown quantitatively that large-scale momentum regions influence small-scale structures throughout the boundary layer through a non-linear top-down mechanism.
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.
Payette, G. S.; Reddy, J. N.
2011-05-01
In this paper we examine the roles of minimization and linearization in the least-squares finite element formulations of nonlinear boundary-values problems. The least-squares principle is based upon the minimization of the least-squares functional constructed via the sum of the squares of appropriate norms of the residuals of the partial differential equations (in the present case we consider L2 norms). Since the least-squares method is independent of the discretization procedure and the solution scheme, the least-squares principle suggests that minimization should be performed prior to linearization, where linearization is employed in the context of either the Picard or Newton iterative solution procedures. However, in the least-squares finite element analysis of nonlinear boundary-value problems, it has become common practice in the literature to exchange the sequence of application of the minimization and linearization operations. The main purpose of this study is to provide a detailed assessment on how the finite element solution is affected when the order of application of these operators is interchanged. The assessment is performed mathematically, through an examination of the variational setting for the least-squares formulation of an abstract nonlinear boundary-value problem, and also computationally, through the numerical simulation of the least-squares finite element solutions of both a nonlinear form of the Poisson equation and also the incompressible Navier-Stokes equations. The assessment suggests that although the least-squares principle indicates that minimization should be performed prior to linearization, such an approach is often impractical and not necessary.
DEFF Research Database (Denmark)
leMesurier, B.J.; Christiansen, Peter Leth; Gaididei, Yuri Borisovich
2004-01-01
The effect of attractive linear potentials on self-focusing in-waves modeled by a nonlinear Schrodinger equation is considered. It is shown that the attractive potential can prevent both singular collapse and dispersion that are generic in the cubic Schrodinger equation in the critical dimension 2...
Lorenz, HW; Nusse, HE
Goodwin's nonlinear accelerator model with periodic investment outlays is reconsidered and used as an economic example of the emergence of complex motion in nonlinear dynamical systems. In addition to chaotic attractors, the model can possess coexisting attracting periodic orbits or simple
Energy Technology Data Exchange (ETDEWEB)
Kong Dexing [Department of Mathematics, Zhejiang University, Hangzhou 310027 (China); Sun Qingyou, E-mail: qysun@cms.zju.edu.cn [Center of Mathematical Sciences, Zhejiang University, Hangzhou 310027 (China)
2011-04-01
All articles must In this paper we introduce some new concepts for second-order hyperbolic equations: two-point boundary value problem, global exact controllability and exact controllability. For several kinds of important linear and nonlinear wave equations arising from physics and geometry, we prove the existence of smooth solutions of the two-point boundary value problems and show the global exact controllability of these wave equations. In particular, we investigate the two-point boundary value problem for one-dimensional wave equation defined on a closed curve and prove the existence of smooth solution which implies the exact controllability of this kind of wave equation. Furthermore, based on this, we study the two-point boundary value problems for the wave equation defined on a strip with Dirichlet or Neumann boundary conditions and show that the equation still possesses the exact controllability in these cases. Finally, as an application, we introduce the hyperbolic curvature flow and obtain a result analogous to the well-known theorem of Gage and Hamilton for the curvature flow of plane curves.
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.
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S.K. Parida
2015-12-01
Full Text Available This work considers the two-dimensional steady MHD boundary layer flow of heat and mass transfer over a flat plate with partial slip at the surface subjected to the convective heat flux. The particular attraction lies in searching the effects of variable viscosity and variable thermal diffusivity on the behavior of the flow. In addition, non-linear thermal radiation effects and thermophoresis are taken into account. The governing nonlinear partial differential equations for the flow, heat and mass transfer are transformed into a set of coupled nonlinear ordinary differential equations by using similarity variable, which are solved numerically by applying Runge–Kutta fourth–fifth order integration scheme in association with quasilinear shooting technique. The novel results for the dimensionless velocity, temperature, concentration and ambient Prandtl number within the boundary layer are displayed graphically for various parameters that characterize the flow. The local skin friction, Nusselt number and Sherwood number are shown graphically. The numerical results obtained for the particular case are fairly in good agreement with the result of Rahman [6].
A free boundary problem of a diffusive SIRS model with nonlinear incidence
Cao, Jia-Feng; Li, Wan-Tong; Wang, Jie; Yang, Fei-Ying
2017-04-01
This paper is concerned with the spreading (persistence) and vanishing (extinction) of a disease which is characterized by a diffusive SIRS model with a bilinear incidence rate and free boundary. Through discussing the dynamics of a free boundary problem of an SIRS model, the spreading of a disease is described. We get the sufficient conditions which ensure the disease spreading or vanishing. In addition, the estimate of the expanding speed is also given when the free boundaries extend to the whole R.
Dattoli, Giuseppe
2005-01-01
The coherent synchrotron radiation (CSR) is one of the main problems limiting the performance of high intensity electron accelerators. A code devoted to the analysis of this type of problems should be fast and reliable: conditions that are usually hardly achieved at the same time. In the past, codes based on Lie algebraic techniques have been very efficient to treat transport problem in accelerators. The extension of these method to the non-linear case is ideally suited to treat CSR instability problems. We report on the development of a numerical code, based on the solution of the Vlasov equation, with the inclusion of non-linear contribution due to wake field effects. The proposed solution method exploits an algebraic technique, using exponential operators implemented numerically in C++. We show that the integration procedure is capable of reproducing the onset of an instability and effects associated with bunching mechanisms leading to the growth of the instability itself. In addition, parametric studies a...
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...
Energy Technology Data Exchange (ETDEWEB)
Siewe, M. Siewe [Laboratoire de Mecanique, Departement de Physique, Faculte des sciences, Universite de Yaounde I, B.P. 812 Yaounde (Cameroon); Cao, Hongjun [Department of Mathematics, School of Science, Beijing Jiaotong University, Beijing 100044 (China); Nonlinear Dynamics and Chaos Group, Departamento de Fisica, Universidad Rey Juan Carlos, Tulipan s/n, 28933 Mostoles, Madrid (Spain); Sanjuan, Miguel A.F. [Nonlinear Dynamics and Chaos Group, Departamento de Fisica, Universidad Rey Juan Carlos, Tulipan s/n, 28933 Mostoles, Madrid (Spain)], E-mail: miguel.sanjuan@urjc.es
2009-02-15
The Rayleigh oscillator is one canonical example of self-excited systems. However, simple generalizations of such systems, such as the Rayleigh-Duffing oscillator, have not received much attention. The presence of a cubic term makes the Rayleigh-Duffing oscillator a more complex and interesting case to analyze. In this work, we use analytical techniques such as the Melnikov theory, to obtain the threshold condition for the occurrence of Smale-horseshoe type chaos in the Rayleigh-Duffing oscillator. Moreover, we examine carefully the phase space of initial conditions in order to analyze the effect of the nonlinear damping, and in particular how the basin boundaries become fractalized.
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Le Xuan Truong
2016-07-01
Full Text Available This work concerns the multi-point nonlinear Neumann boundary-value problem involving a p-Laplacian-like operator $$\\displaylines{ (\\phi( u'' = f(t, u, u',\\quad t\\in (0,1, \\cr u'(0 = u'(\\eta, \\quad \\phi(u'(1 = \\sum_{i=1}^m{\\alpha_i \\phi(u'(\\xi_i}, }$$ where $\\phi:\\mathbb{R} \\to \\mathbb{R}$ is an odd increasing homeomorphism with $\\phi(\\pm \\infty = \\pm \\infty$ such that $$ 00. $$ By using an extension of Mawhin's continuation theorem, we establish sufficient conditions for the existence of at least one solution.
Timergaliev, S. N.
2009-06-01
This paper deals with the proof of the existence of solutions of a geometrically and physically nonlinear boundary value problem for shallow Timoshenko shells with the transverse shear strains taken into account. The shell edge is assumed to be partly fixed. It is proposed to study the problem by a variational method based on searching the points of minimum of the total energy functional for the shell-load system in the space of generalized displacements. We show that there exists a generalized solution of the problemon which the total energy functional attains its minimum on a weakly closed subset of the space of generalized displacements.
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Cristian Enache
2006-06-01
Full Text Available For a class of nonlinear elliptic boundary value problems in divergence form, we construct some general elliptic inequalities for appropriate combinations of u(x and |Ã¢ÂˆÂ‡u|2, where u(x are the solutions of our problems. From these inequalities, we derive, using Hopf's maximum principles, some maximum principles for the appropriate combinations of u(x and |Ã¢ÂˆÂ‡u|2, and we list a few examples of problems to which these maximum principles may be applied.
Institute of Scientific and Technical Information of China (English)
Cheng Xiaoliang; Ying Weiting
2005-01-01
In this paper, we discuss the existence of solution of a nonlinear two-point boundary value problem with a positive parameter Q arising in the study of surfacetension-induced flows of a liquid metal or semiconductor. By applying the Schauder's fixed-point theorem, we prove that the problem admits a solution for 0 ≤ Q ≤ 14.306.It improves the result of 0 ≤ Q ＜ 1 in [2] and 0 ≤ Q ≤ 13.213 in [3].
Institute of Scientific and Technical Information of China (English)
WANG Rouhuai
2006-01-01
The main aim of this paper is to discuss the problem concerning the analyticity of the solutions of analytic non-linear elliptic boundary value problems.It is proved that if the corresponding first variation is regular in Lopatinski(i) sense,then the solution is analytic up to the boundary.The method of proof really covers the case that the corresponding first variation is regularly elliptic in the sense of Douglis-Nirenberg-Volevich,and hence completely generalize the previous result of C.B.Morrey.The author also discusses linear elliptic boundary value problems for systems of ellip tic partial differential equations where the boundary operators are allowed to have singular integral operators as their coefficients.Combining the standard Fourier transform technique with analytic continuation argument,the author constructs the Poisson and Green's kernel matrices related to the problems discussed and hence obtain some representation formulae to the solutions.Some a priori estimates of Schauder type and Lp type are obtained.
Lin, Zhi; Zhang, Qinghai
2017-09-01
We propose high-order finite-volume schemes for numerically solving the steady-state advection-diffusion equation with nonlinear Robin boundary conditions. Although the original motivation comes from a mathematical model of blood clotting, the nonlinear boundary conditions may also apply to other scientific problems. The main contribution of this work is a generic algorithm for generating third-order, fourth-order, and even higher-order explicit ghost-filling formulas to enforce nonlinear Robin boundary conditions in multiple dimensions. Under the framework of finite volume methods, this appears to be the first algorithm of its kind. Numerical experiments on boundary value problems show that the proposed fourth-order formula can be much more accurate and efficient than a simple second-order formula. Furthermore, the proposed ghost-filling formulas may also be useful for solving other partial differential equations.
Afeyan, Bedros; Crouseilles, Nicolas; Dodhy, Adila; Faou, Erwan; Mehrenberger, Michel; Sonnendrücker, Eric
2014-01-01
KEEN waves are nonlinear, non-stationary, self-organized asymptotic states in Vlasov plasmas outside the scope or purview of linear theory constructs such as electron plasma waves or ion acoustic waves. Nonlinear stationary mode theories such as those leading to BGK modes also do not apply. The range in velocity that is strongly perturbed by KEEN waves depends on the amplitude and duration of the ponderomotive force used to drive them. Smaller amplitude drives create highly localized structures attempting to coalesce into KEEN waves. These cases have much more chaotic and intricate time histories than strongly driven ones. The narrow range in which one must maintain adequate velocity resolution in the weakly driven cases challenges xed grid numerical schemes. What is missing there is the capability of resolving locally in velocity while maintaining a coarse grid outside the highly perturbed region of phase space. We here report on a new Semi-Lagrangian Vlasov-Poisson solver based on conservative non-uniform c...
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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.
Institute of Scientific and Technical Information of China (English)
Jia-qi Mo; Wan-tao Lin
2006-01-01
In this paper the singularly perturbed initial boundary value problems for the nonlocal reaction diffusion system are considered. Using the iteration method and the comparison theorem, the existence and its asymptotic behavior of the solution for the problem are studied.
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Chen Yi
2011-01-01
Full Text Available We study a boundary value problem to Langevin equation involving two fractional orders. The Banach fixed point theorem and Krasnoselskii's fixed point theorem are applied to establish the existence results.
Institute of Scientific and Technical Information of China (English)
Liu YANG; Zongmin QIAO
2012-01-01
In this paper,the existence and multiplicity of positive solutions for Robin type boundary value problem of differential equation involving the Riemann-Liouville fractional order derivative are established.
On the Boundary between Nonlinear Jump Phenomenon and Linear Response of Hypoid Gear Dynamics
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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.
An iterative HAM approach for nonlinear boundary value problems in a semi-infinite domain
Zhao, Yinlong; Lin, Zhiliang; Liao, Shijun
2013-09-01
In this paper, we propose an iterative approach to increase the computation efficiency of the homotopy analysis method (HAM), a analytic technique for highly nonlinear problems. By means of the Schmidt-Gram process (Arfken et al., 1985) [15], we approximate the right-hand side terms of high-order linear sub-equations by a finite set of orthonormal bases. Based on this truncation technique, we introduce the Mth-order iterative HAM by using each Mth-order approximation as a new initial guess. It is found that the iterative HAM is much more efficient than the standard HAM without truncation, as illustrated by three nonlinear differential equations defined in an infinite domain as examples. This work might greatly improve the computational efficiency of the HAM and also the Mathematica package BVPh for nonlinear BVPs.
The effects of oppositely sloping boundaries with Ekman dissipation in a nonlinear baroclinic system
Weng, H.-Y.
1990-01-01
The present analytical and numerical examination of the effect of the slope Delta with dissipation delta on baroclinic flows in linear and nonlinear systems uses a modified Eady channel model with oppositely sloping top and bottom Ekman layers, and truncates the spectral wave solution up to six components. Comparisons are made wherever possible with results from beta-plane dissipative systems. In the linear system, the combined effect of Delta and delta strongly stabilizes long waves. In a nonlinear system without wave-wave interaction, Delta stabilizes the flow even for small delta and reduces the domain of vacillation while enlarging the domain of single-wave steady state.
Gajjar, J. S. B.
1995-01-01
We consider the nonlinear stability of a fully three-dimensional boundary layer flow in an incompressible fluid and derive an equation governing the nonlinear development of a stationary cross-flow vortex. The amplitude equation is a novel integro-differential equation which has spatial derivatives of the amplitude occurring in the kernal function. It is shown that the evolution of the cross-flow vortex is strongly coupled to the properties of an unsteady wall layer which is in fact driven by an unknown slip velocity, proportional to the amplitude of the cross-flow vortex. The work is extended to obtain the corresponding equation for rotating disk flow. A number of special cases are examined and the numerical solution for one of cases, and further analysis, demonstrates the existence of finite-distance as well as focussing type singularities. The numerical solutions also indicate the presence of a new type of nonlinear wave solution for a certain set of parameter values.
Experimental study of nonlinear processes in a swept-wing boundary layer at the mach number M=2
Yermolaev, Yu. G.; Kosinov, A. D.; Semionov, N. V.
2014-09-01
Results of experiments aimed at studying the linear and nonlinear stages of the development of natural disturbances in the boundary layer on a swept wing at supersonic velocities are presented. The experiments are performed on a swept wing model with a lens-shaped airfoil, leading-edge sweep angle of 45°, and relative thickness of 3%. The disturbances in the flow are recorded by a constant-temperature hot-wire anemometer. For determining the nonlinear interaction of disturbances, the kurtosis and skewness are estimated for experimentally obtained distributions of the oscillating signal over the streamwise coordinate or along the normal to the surface. The disturbances are found to increase in the frequency range from 8 to 35 kHz in the region of their linear development, whereas enhancement of high-frequency disturbances is observed in the region of their nonlinear evolution. It is demonstrated that the growth of disturbances in the high-frequency spectral range ( f > 35 kHz) is caused by the secondary instability.
Van Dijk, N.P.
2012-01-01
This thesis aims at understanding and improving topology optimization techniques focusing on density-based level-set methods and geometrical nonlinearities. Central in this work are the numerical modeling of the mechanical response of a design and the consistency of the optimization process itself.
Multipoint Singular Boundary-Value Problem for Systems of Nonlinear Differential Equations
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Zdeněk Šmarda
2009-01-01
Full Text Available A singular Cauchy-Nicoletti problem for a system of nonlinear ordinary differential equations is considered. With the aid of combination of Ważewski's topological method and Schauder's principle, the theorem concerning the existence of a solution of this problem (having the graph in a prescribed domain is proved.
NONLINEAR DYNAMICAL ANALYSIS OF BIFURCATION AND CONFLUENCE OF THE PACIFIC WESTERN BOUNDARY CURRENTS
Institute of Scientific and Technical Information of China (English)
NI Guo-xi; JIANG Song; JU Qiang-chang; KONG Ling-hai
2012-01-01
In this paper,we analyze the bifurcation and the confluence of the Pacific western boundary currents by an analytical approach.Applying the conservation law,the geostrophie balance relation and the Bernoulli integral to a reduced gravity model,we get a quantitative relation for the outflow and the inflow,and establish the related formulae for the width and the veering angle of offshore currents under the inflow condition.Furthermore,a comparison between the volume transport based on the observation data and the analytical value for the Pacific western boundary currents is presented,which validates the theoretical analysis.
Biondini, Gino; Fagerstrom, Emily; Prinari, Barbara
2016-10-01
We formulate the inverse scattering transform (IST) for the defocusing nonlinear Schrödinger (NLS) equation with fully asymmetric non-zero boundary conditions (i.e., when the limiting values of the solution at space infinities have different non-zero moduli). The theory is formulated without making use of Riemann surfaces, and instead by dealing explicitly with the branched nature of the eigenvalues of the associated scattering problem. For the direct problem, we give explicit single-valued definitions of the Jost eigenfunctions and scattering coefficients over the whole complex plane, and we characterize their discontinuous behavior across the branch cut arising from the square root behavior of the corresponding eigenvalues. We pose the inverse problem as a Riemann-Hilbert Problem on an open contour, and we reduce the problem to a standard set of linear integral equations. Finally, for comparison purposes, we present the single-sheet, branch cut formulation of the inverse scattering transform for the initial value problem with symmetric (equimodular) non-zero boundary conditions, as well as for the initial value problem with one-sided non-zero boundary conditions, and we also briefly describe the formulation of the inverse scattering transform when a different choice is made for the location of the branch cuts.
PIV measurements of the bottom boundary layer under nonlinear surface waves
Henriquez, M.; Reniers, A. J H M; Ruessink, B. G.; Stive, M. J F
2014-01-01
Sediment in the nearshore is largely mobilized in the wave bottom boundary layer (wbbl) hereby emphasizing the importance of this relatively thin layer to nearshore morphology. This paper presents a laboratory experiment where hydrodynamic properties of the wbbl were quantified by measuring flow vel
He, Cong
2011-01-01
In this paper, we are concerned with the Cauchy problem on the one-dimensional Landau equation with $\\gamma\\geq -2$\\ with specular boundary condition and the time asymptotic behavior toward to a given local Maxwellian under some initial conditions. A time decay rate is also obtained. The method include energy method, micro-macro decomposition and the properties of Burnett functions.
EXISTENCE OF SOLUTIONS TO A CLASS OF NONLINEAR n-DIMENSIONAL DISCRETE BOUNDARY VALUE PROBLEMS
Institute of Scientific and Technical Information of China (English)
无
2012-01-01
In this paper,using the critical point theory,we obtain a new result on the existence of the solutions to a class of n-dimensional discrete boundary value problems.Results obtained extend or improve the existing ones.
Institute of Scientific and Technical Information of China (English)
Shanying Zhu
2009-01-01
This paper deals with the existence of positive solutions to the singular second-order periodic boundary value problem, We obtain the existence results of positive solutions by the fixed point index theory. The results obtained extend and complement some known results.
Zarepour, Misagh; Amirhosein Hosseini, Seyed
2016-08-01
This study presents an examination of nonlinear free vibration of a nanobeam under electro-thermo-mechanical loading with elastic medium and various boundary conditions, especially the elastic boundary condition. The nanobeam is modeled as an Euler-Bernoulli beam. The von Kármán strain-displacement relationship together with Hamilton’s principle and Eringen’s theory are employed to derive equations of motion. The nonlinear free vibration frequency is obtained for simply supported (S-S) and elastic supported (E-E) boundary conditions. E-E boundary condition is a general and actual form of boundary conditions and it is chosen because of more realistic behavior. By applying the differential transform method (DTM), the nanobeam’s natural frequencies can be easily obtained for the two different boundary conditions mentioned above. Performing a precise study led to investigation of the influences of nonlocal parameter, temperature change, spring constants (either for elastic medium or boundary condition) and imposed electric potential on the nonlinear free vibration characteristics of nanobeam. The results for S-S and E-E nanobeams are compared with each other. In order to validate the results, some comparisons are presented between DTM results and open literature to show the accuracy of this new approach. It has been discovered that DTM solves the equations with minimum calculation cost.
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M. G. Crandall
1999-07-01
Full Text Available We study existence of continuous weak (viscosity solutions of Dirichlet and Cauchy-Dirichlet problems for fully nonlinear uniformly elliptic and parabolic equations. Two types of results are obtained in contexts where uniqueness of solutions fails or is unknown. For equations with merely measurable coefficients we prove solvability of the problem, while in the continuous case we construct maximal and minimal solutions. Necessary barriers on external cones are also constructed.
On a Mixed Nonlinear One Point Boundary Value Problem for an Integrodifferential Equation
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Said Mesloub
2008-03-01
Full Text Available This paper is devoted to the study of a mixed problem for a nonlinear parabolic integro-differential equation which mainly arise from a one dimensional quasistatic contact problem. We prove the existence and uniqueness of solutions in a weighted Sobolev space. Proofs are based on some a priori estimates and on the Schauder fixed point theorem. we also give a result which helps to establish the regularity of a solution.
On a Mixed Nonlinear One Point Boundary Value Problem for an Integrodifferential Equation
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Mesloub Said
2008-01-01
Full Text Available This paper is devoted to the study of a mixed problem for a nonlinear parabolic integro-differential equation which mainly arise from a one dimensional quasistatic contact problem. We prove the existence and uniqueness of solutions in a weighted Sobolev space. Proofs are based on some a priori estimates and on the Schauder fixed point theorem. we also give a result which helps to establish the regularity of a solution.
Institute of Scientific and Technical Information of China (English)
徐云滨; 郑连存
2008-01-01
A class of singular nonlinear boundary value problems arising in the boundary layer behind expansion wave are studied. Sufficient conditions for the existence and uniqueness of positive solutions to the problems are established by utilizing the monotonic approaching technique. And a theoretical estimate formula for skin friction coefficient is presented. The numerical solution is presented by using the shoot method. The reliability and efficiency of the theoretical prediction are verified by numerical results.
Computation of Nonlinear Gravity Waves by a Desingularized Boundary Integral Method
1991-10-01
and Whitham 1974). The I perturbation method has also been used in numerical calculations by researchers, for 3 example, Nakos & Sclavounos (1990) in...pulsating sources using fundamental solutions I satisfying a linear free surface boundary condition. Nakos and Sclavounos (1990) calculated the time...231-254. [561 Nakos , D.E. and Sclavounos, P.D. 1990 Ship motions by a three- dimensional Rankine panel method. Proc. 18th symp. on Naval Hydro
Denison, Marie F. C.
The reduction of drag and aerodynamic heating caused by boundary layer transition is of central interest for the development of hypersonic vehicles. Receptivity to flow perturbation in the form of Tollmien-Schlichting (TS) wave growth often determines the first stage of the transition process, which can be delayed by depositing specific excitations into the boundary layer. Weakly ionized Dielectric Barrier Discharge (DBD) actuators are being investigated as possible sources of such excitations, but little is known today about their interaction with high-speed flows. In this framework, the first part of the thesis is dedicated to a receptivity study of laminar compressible boundary layers over a flat plate by linear stability analysis following an adjoint operator formulation, under DBD representative excitations assumed independent of flow conditions. The second part of the work concentrates on the development of a coupled plasma-Navier and Stokes solver targeted at the study of supersonic flow and compressibility effects on DBD forcing and non-parallel receptivity. The linear receptivity study of quasi-parallel compressible flows reveals several interesting features such as a significant shift of the region of maximum receptivity deeper into the flow at high Mach number and strong wave amplitude reduction compared to incompressible flows. The response to DBD relevant excitation distributions and to variations of the base flow conditions and system length scales follows these trends. Observed absolute amplitude changes and relative sensitivity modifications between source types are related to the evolution of the offset between forcing peak profile and relevant adjoint mode maximum. The analysis highlights the crucial importance of designing and placing the actuator in a way that matches its force field to the position of maximum boundary layer receptivity for the specific flow conditions of interest. In order to address the broad time and length scale spectrum
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.
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I. J. Cabrera
2012-01-01
Full Text Available We are concerned with the existence and uniqueness of a positive and nondecreasing solution for the following nonlinear fractional m-point boundary value problem: D0+αu(t+f(t,u(t=0, 0
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R. Garra
2015-01-01
Full Text Available The evolution of strong transients of temperature and pressure in two adjacent fluid-saturated porous rocks is described by a Burgers equation in an early model of Natale and Salusti (1996. We here consider the effect of a realistic intermediate region between the two media and infer how transient processes can also happen, such as chemical reactions, diffusion of fine particles, and filter cake formations. This suggests enlarging our analysis and taking into account not only punctual quantities but also “time averaged” quantities. These boundary effects are here analyzed by using a “memory formalism”; that is, we replace the ordinary punctual time-derivatives with Caputo fractional time-derivatives. We therefore obtain a nonlinear fractional model, whose explicit solution is shown, and finally discuss its geological importance.
Caixia Guo; Jianmin Guo; Ying Gao; Shugui Kang
2016-01-01
This paper is concerned with the two-point boundary value problems of nonlinear finite discrete fractional differential equations. On one hand, we discuss some new properties of the Green function. On the other hand, by using the main properties of Green function and the Krasnoselskii fixed point theorem on cones, some sufficient conditions for the existence of at least one or two positive solutions for the boundary value problem are established.
Fully Nonlinear Edge Gyrokinetic Simulations of Kinetic Geodesic-Acoustic Modes and Boundary Flows
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Xu, X Q; Belli, E; Bodi, K; Candy, J; Chang, C S; Cohen, B I; Cohen, R H; Colella, P; Dimits, A M; Dorr, M R; Gao, Z; Hittinger, J A; Ko, S; Krasheninnikov, S; McKee, G R; Nevins, W M; Rognlien, T D; Snyder, P B; Suh, J; Umansky, M V
2008-09-18
We present edge gyrokinetic neoclassical simulations of tokamak plasmas using the fully nonlinear (full-f) continuum code TEMPEST. A nonlinear Boltzmann model is used for the electrons. The electric field is obtained by solving the 2D gyrokinetic Poisson Equation. We demonstrate the following: (1) High harmonic resonances (n > 2) significantly enhance geodesic-acoustic mode (GAM) damping at high-q (tokamak safety factor), and are necessary to explain both the damping observed in our TEMPEST q-scans and experimental measurements of the scaling of the GAM amplitude with edge q{sub 95} in the absence of obvious evidence that there is a strong q dependence of the turbulent drive and damping of the GAM. (2) The kinetic GAM exists in the edge for steep density and temperature gradients in the form of outgoing waves, its radial scale is set by the ion temperature profile, and ion temperature inhomogeneity is necessary for GAM radial propagation. (3) The development of the neoclassical electric field evolves through different phases of relaxation, including GAMs, their radial propagation, and their long-time collisional decay. (4) Natural consequences of orbits in the pedestal and scrape-off layer region in divertor geometry are substantial non-Maxwellian ion distributions and flow characteristics qualitatively like those observed in experiments.
Mittal, R. C.; Jain, R. K.
2012-12-01
In this paper, a numerical method is proposed to approximate the solution of the nonlinear parabolic partial differential equation with Neumann's boundary conditions. The method is based on collocation of cubic B-splines over finite elements so that we have continuity of the dependent variable and its first two derivatives throughout the solution range. We apply cubic B-splines for spatial variable and its derivatives, which produce a system of first order ordinary differential equations. We solve this system by using SSP-RK3 scheme. The numerical approximate solutions to the nonlinear parabolic partial differential equations have been computed without transforming the equation and without using the linearization. Four illustrative examples are included to demonstrate the validity and applicability of the technique. In numerical test problems, the performance of this method is shown by computing L∞andL2error norms for different time levels. Results shown by this method are found to be in good agreement with the known exact solutions.
Fixed set theorems for discrete dynamics and nonlinear boundary-value problems
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Robert Brooks
2011-05-01
Full Text Available We consider self-mappings of Hausdorff topological spaces which map compact sets to compact sets and establish the existence of invariant (fixed sets. The fixed set results are used to provide fixed set analogues of well-known fixed point theorems. An algorithm is employed to compute the existence of fixed sets which are self-similar in a generalized sense. Some numerical examples are given. The utility of the abstract result is further illustrated via the study of a boundary value problem for a system of differential equations
Zhai, Chengbo; Hao, Mengru
2014-01-01
By using Krasnoselskii's fixed point theorem, we study the existence of at least one or two positive solutions to a system of fractional boundary value problems given by -D(0+)(ν1)y1(t) = λ1a1(t)f(y1(t), y2(t)), - D(0+)(ν2)y2(t) = λ2a2(t)g(y1(t), y2(t)), where D(0+)(ν) is the standard Riemann-Liouville fractional derivative, ν1, ν2 ∈ (n - 1, n] for n > 3 and n ∈ N, subject to the boundary conditions y1((i))(0) = 0 = y ((i))(0), for 0 ≤ i ≤ n - 2, and [D(0+)(α)y1(t)] t=1 = 0 = [D(0+ (α)y2(t)] t=1, for 1 ≤ α ≤ n - 2, or y1((i))(0) = 0 = y ((i))(0), for 0 ≤ i ≤ n - 2, and [D(0+)(α)y1(t)] t=1 = ϕ1(y1), [D(0+)(α)y2(t)] t=1 = ϕ2(y2), for 1 ≤ α ≤ n - 2, ϕ1, ϕ2 ∈ C([0,1], R). Our results are new and complement previously known results. As an application, we also give an example to demonstrate our result.
Clarelli, Fabrizio; Inglese, Gabriele
2016-11-01
Heat exchange between a conducting plate and the environment is described here by means of an unknown nonlinear function F of the temperature u. In this paper we construct a method for recovering F by means of polynomial expansion, perturbation theory and the toolbox of thermal inverse problems. We test our method on two examples: In the first one, we heat the plate (initially at 20 ^\\circ {{C}}) from one side, read the temperature on the same side and identify the heat exchange law on the opposite side (active thermography); in the second example we measure the temperature of one side of the plate (initially at 1500 ^\\circ {{C}}) and study the heat exchange while cooling (passive thermography).
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.
Non-linear aspects of Görtler instability in boundary layers with pressure gradient
Rogenski, J. K.; de Souza, L. F.; Floryan, J. M.
2016-12-01
The laminar flow over a concave surface may undergo transition to a turbulent state driven by secondary instabilities initiated by the longitudinal vortices known as Görtler vortices. These vortices distort the boundary layer structure by modifying the streamwise velocity component in both spanwise and wall-normal directions. Numerical simulations have been conducted to identify the role of the external pressure gradients in the development and saturation of the vortices. The results show that flows with adverse pressure gradients reach saturation upstream from the saturation location for neutral and favorable pressure gradients. In the transition region, the mean spanwise shear stress is about three times larger than in the flow without the vortices.
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Bashir Ahmad
2010-01-01
Full Text Available We study a Dirichlet boundary value problem for Langevin equation involving two fractional orders. Langevin equation has been widely used to describe the evolution of physical phenomena in fluctuating environments. However, ordinary Langevin equation does not provide the correct description of the dynamics for systems in complex media. In order to overcome this problem and describe dynamical processes in a fractal medium, numerous generalizations of Langevin equation have been proposed. One such generalization replaces the ordinary derivative by a fractional derivative in the Langevin equation. This gives rise to the fractional Langevin equation with a single index. Recently, a new type of Langevin equation with two different fractional orders has been introduced which provides a more flexible model for fractal processes as compared with the usual one characterized by a single index. The contraction mapping principle and Krasnoselskii's fixed point theorem are applied to prove the existence of solutions of the problem in a Banach space.
Zhidkov, P E
2001-01-01
We establish examples of systems of functions being Riesz bases in L_{2}(0,1). We then apply this result to improve a theorem presented in [9] showing that an arbitrary "standard" system of solutions of a nonlinear boundary value problem, normalized to 1 in the same space, is a Riesz basis in this space. The proofs in this work are quite elementary.
Kawai, Yusuke; Yamada, Yoshio
2016-07-01
This paper deals with a free boundary problem for diffusion equation with a certain class of bistable nonlinearity which allows two positive stable equilibrium states as an ODE model. This problem models the invasion of a biological species and the free boundary represents the spreading front of its habitat. Our main interest is to study large-time behaviors of solutions for the free boundary problem. We will completely classify asymptotic behaviors of solutions and, in particular, observe two different types of spreading phenomena corresponding to two positive stable equilibrium states. Moreover, it will be proved that, if the free boundary expands to infinity, an asymptotic speed of the moving free boundary for large time can be uniquely determined from the related semi-wave problem.
Quinzler, R; Haefeli, W E
2006-06-01
The splitting of scored tablets provides many advantages. One benefit is to achieve dose flexibility to account for the huge interindividual differences in dose requirements for instance in paediatric and geriatric patients, which are often not covered by the available strengths in the market. Moreover, large-sized tablets can easier be swallowed if broken before swallowing and medication costs can often be reduced by splitting brands with higher strength. But not all tablets, mostly unscored tablets, are suitable for splitting. Splitting of extended release formulations can result in an overdose by uncontrolled release of the active component and degradation of the compound can occur if an enteric coating is destroyed by the splitting process. Whether tablets are suitable for splitting depends on the properties of the active component (e.g. light sensitivity), the galenics, the shape of the tablet, and the shape of the scoreline. Moreover, not all patients are informed, able, or willing to split tablets and the majority of the elderly population is not capable to break tablets. When split tablets are prescribed it is therefore important to view the shape of the tablet, to assess the patients ability and willingness to break tablets, to properly inform the patient about the appropriate way of splitting, and if necessary to suggest (and instruct) the use of a tablet splitting device.
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Nguyen Thanh Long
2005-12-01
Full Text Available In this paper we consider the nonlinear wave equation problem $$displaylines{ u_{tt}-Big(|u|_0^2,|u_{r}|_0^2ig(u_{rr}+frac{1}{r}u_{r} =f(r,t,u,u_{r},quad 0less than r less than 1,; 0 less than t less than T, ig|lim_{ro 0^+}sqrt{r}u_{r}(r,tig| less than infty, u_{r}(1,t+hu(1,t=0, u(r,0=widetilde{u}_0(r, u_{t}(r,0=widetilde{u}_1(r. }$$ To this problem, we associate a linear recursive scheme for which the existence of a local and unique weak solution is proved, in weighted Sobolev using standard compactness arguments. In the latter part, we give sufficient conditions for quadratic convergence to the solution of the original problem, for an autonomous right-hand side independent on $u_{r}$ and a coefficient function $B$ of the form $B=B(|u|_0^2=b_0+|u|_0^2$ with $b_0$ greater than 0.
Valero, C.; Javierre, E.; García-Aznar, J. M.; Gómez-Benito, M. J.
2015-01-01
SUMMARY Wound healing is a process driven by biochemical and mechanical variables in which new tissue is synthesised to recover original tissue functionality. Wound morphology plays a crucial role in this process, as the skin behaviour is not uniform along different directions. In this work we simulate the contraction of surgical wounds, which can be characterised as elongated and deep wounds. Due to the regularity of this morphology, we approximate the evolution of the wound through its cross-section, adopting a plane strain hypothesis. This simplification reduces the complexity of the computational problem while maintaining allows for a thorough analysis of the role of wound depth in the healing process, an aspect of medical and computational relevance that has not yet been addressed. To reproduce wound contraction we consider the role of fibroblasts, myofibroblasts, collagen and a generic growth factor. The contraction phenomenon is driven by cell-generated forces. We postulate that these forces are adjusted to the mechanical environment of the tissue where cells are embedded through a mechanosensing and mechanotransduction mechanism. To solve the non-linear problem we use the Finite Element Method and an updated Lagrangian approach to represent the change in the geometry. To elucidate the role of wound depth and width on the contraction pattern and evolution of the involved species, we analyse different wound geometries with the same wound area. We find that deeper wounds contract less and reach a maximum contraction rate earlier than superficial wounds. PMID:24443355
Valero, C; Javierre, E; García-Aznar, J M; Gómez-Benito, M J
2014-06-01
Wound healing is a process driven by biochemical and mechanical variables in which a new tissue is synthesised to recover original tissue functionality. Wound morphology plays a crucial role in this process, as the skin behaviour is not uniform along different directions. In this work, we simulate the contraction of surgical wounds, which can be characterised as elongated and deep wounds. Because of the regularity of this morphology, we approximate the evolution of the wound through its cross section, adopting a plane strain hypothesis. This simplification reduces the complexity of the computational problem; while allows for a thorough analysis of the role of wound depth in the healing process, an aspect of medical and computational relevance that has not yet been addressed. To reproduce wound contraction, we consider the role of fibroblasts, myofibroblasts, collagen and a generic growth factor. The contraction phenomenon is driven by cell-generated forces. We postulate that these forces are adjusted to the mechanical environment of the tissue where cells are embedded through a mechanosensing and mechanotransduction mechanism. To solve the nonlinear problem, we use the finite element method (FEM) and an updated Lagrangian approach to represent the change in the geometry. To elucidate the role of wound depth and width on the contraction pattern and evolution of the involved species, we analyse different wound geometries with the same wound area. We find that deeper wounds contract less and reach a maximum contraction rate earlier than superficial wounds. Copyright © 2014 John Wiley & Sons, Ltd.
Salusti, E; Garra, R
2016-01-01
We here analyze the propagation of transients of fluid-rock temperature and pressure through a thin boundary layer, where a steady trend is present, between two adjacent homogeneous rocks. We focus on the effect of convection on transients crossing such thin layer. In comparison with early models where this boundary was assumed a sharp mathematical plane separating the two rocks, here we show a realistic analysis of such boundary layer that implies a novel nonlinear model. Its solutions describe large amplitude, quick and sharp transients characterized by a novel drift and variations of the signal amplitude, leading to a nonlinear wave propagation. Possible applications are in volcanic, hydrologic, hydrothermal systems as well as for deep oil drilling. In addition, this formalism could easily be generalized for the case of a signal arriving in a rock characterized by a steady trend of pressure and/or temperature. These effects, being proportional to the initial conditions, can also give velocity variations no...
Dietrich, David E.; Mehra, Avichal; Haney, Robert L.; Bowman, Malcolm J.; Tseng, Yu-Heng
2003-01-01
Gulf Stream (GS) separation near its observed Cape Hatteras (CH) separation location, and its ensuing path and dynamics, is a challenging ocean modeling problem. If a model GS separates much farther north than CH, then northward GS meanders, which pinch off warm core eddies (rings), are not possible or are strongly constrained by the Grand Banks shelfbreak. Cold core rings pinch off the southward GS meanders. The rings are often re-absorbed by the GS. The important warm core rings enhance heat exchange and, especially, affect the northern GS branch after GS bifurcation near the New England Seamount Chain. This northern branch gains heat by contact with the southern branch water upstream of bifurcation, and warms the Arctic Ocean and northern seas, thus playing a major role in ice dynamics, thermohaline circulation and possible global climate warming. These rings transport heat northward between the separated GS and shelf slope/Deep Western Boundary Current system (DWBC). This region has nearly level time mean isopycnals. The eddy heat transport convergence/divergence enhances the shelfbreak and GS front intensities and thus also increases watermass transformation. The fronts are maintained by warm advection by the Florida Current and cool advection by the DWBC. Thus, the GS interaction with the DWBC through the intermediate eddy field is climatologically important.
Positive Solutions for Nonlinear nth-Order Singular Nonlocal Boundary Value Problems
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Xin'an Hao
2007-04-01
Full Text Available We study the existence and multiplicity of positive solutions for a class of nth-order singular nonlocal boundary value problemsu(n(t+a(tf(t,u=0, tÃ¢ÂˆÂˆ(0,1, u(0=0, u'(0=0, Ã¢Â€Â¦,u(nÃ¢ÂˆÂ’2(0=0, ÃŽÂ±u(ÃŽÂ·=u(1, where 0<ÃŽÂ·<1,Ã¢Â€Â‰Ã¢Â€Â‰0<ÃŽÂ±ÃŽÂ·nÃ¢ÂˆÂ’1Ã¢Â€Â‰<1. The singularity may appear at t=0 and/or t=1. The Krasnosel'skii-Guo theorem on cone expansion and compression is used in this study. The main results improve and generalize the existing results.
Uniqueness of positive solutions of a class of ODE with nonlinear boundary conditions
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Yulian An
2005-11-01
Full Text Available We study the uniqueness of positive solutions of the boundary value problem uÃ¢Â€Â³+a(tuÃ¢Â€Â²+f(u=0, tÃ¢ÂˆÂˆ(0,b, B1(u(0Ã¢ÂˆÂ’uÃ¢Â€Â²(0=0, B2(u(b+uÃ¢Â€Â²(b=0, where 0
Wedin, Håkan; Cherubini, Stefania
2016-12-01
The asymptotic suction boundary layer (ASBL) is used for studying two permeability models, namely the Darcy and the Forchheimer model, the latter being more physically correct according to the literature. The term that defines the two apart is a function of the non-Darcian wall permeability {\\hat{K}}2 and of the wall suction {\\hat{V}}0, whereas the Darcian wall permeability {\\hat{K}}1 is common to the two models. The underlying interest of the study lies in the field of transition to turbulence where focus is put on two-dimensional nonlinear traveling waves (TWs) and their three-dimensional linear stability. Following a previous study by Wedin et al (2015 Phys. Rev. E 92 013022), where only the Darcy model was considered, the present work aims at comparing the two models, assessing where in the parameter space they cease to produce the same results. For low values of {\\hat{K}}1 both models produce almost identical TW solutions. However, when both increasing the suction {\\hat{V}}0 to sufficiently high amplitudes (i.e. lowering the Reynolds number Re, based on the displacement thickness) and using large values of the wall porosity, differences are observed. In terms of the non-dimensional Darcian wall permeability parameter, a, strong differences in the overall shape of the bifurcation curves are observed for a≳ 0.70, with the emergence of a new family of solutions at Re lower than 100. For these large values of a, a Forchheimer number {{Fo}}\\max ≳ 0.5 is found, where Fo expresses the ratio between the kinetic and viscous forces acting on the porous wall. Moreover, the minimum Reynolds number, {{Re}}g, for which the Navier-Stokes equations allow for nonlinear solutions, decreases for increasing values of a. Fixing the streamwise wavenumber to α = 0.154, as used in the study by Wedin et al referenced above, we find that {{Re}}g is lowered from Re ≈ 3000 for zero permeability, to below 50 for a = 0.80 for both permeability models. Finally, the stability of
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Hammad Khalil
2016-06-01
Full Text Available In this paper, we have proposed a new formulation for the solution of a general class of fractional differential equations (linear and nonlinear under $\\hat{m}$-point boundary conditions. We derive some new operational matrices and based on these operational matrices we develop scheme to approximate solution of the problem. The scheme convert the boundary value problem to a system of easily solvable algebraic equations. We show the applicability of the scheme by solving some test problems. The scheme is computer oriented.
Mustafa, Meraj; Mushtaq, Ammar; Hayat, Tasawar; Ahmad, Bashir
2014-01-01
The problem of natural convective boundary layer flow of nanofluid past a vertical plate is discussed in the presence of nonlinear radiative heat flux. The effects of magnetic field, Joule heating and viscous dissipation are also taken into consideration. The governing partial differential equations are transformed into a system of coupled nonlinear ordinary differential equations via similarity transformations and then solved numerically using the Runge-Kutta fourth-fifth order method with shooting technique. The results reveal an existence of point of inflection for the temperature distribution for sufficiently large wall to ambient temperature ratio. Temperature and thermal boundary layer thickness increase as Brownian motion and thermophoretic effects intensify. Moreover temperature increases and heat transfer from the plate decreases with an increase in the radiation parameter.
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Meraj Mustafa
Full Text Available The problem of natural convective boundary layer flow of nanofluid past a vertical plate is discussed in the presence of nonlinear radiative heat flux. The effects of magnetic field, Joule heating and viscous dissipation are also taken into consideration. The governing partial differential equations are transformed into a system of coupled nonlinear ordinary differential equations via similarity transformations and then solved numerically using the Runge-Kutta fourth-fifth order method with shooting technique. The results reveal an existence of point of inflection for the temperature distribution for sufficiently large wall to ambient temperature ratio. Temperature and thermal boundary layer thickness increase as Brownian motion and thermophoretic effects intensify. Moreover temperature increases and heat transfer from the plate decreases with an increase in the radiation parameter.
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
In this paper,Fucik spectrum,ordinary differential equation theory of Banach spaces and Morse theory are used to study semilinear elliptic boundary value problems with jumping nonlinearities at zero or infinity,and some new results on the existence of nontrivial solutions,multiple solutions and sign-changing solutions are obtained.In one case seven nontrivial solutions are got.The techniques have independent interest.
Tan, Heping; Yu, Qizheng; Zhang, Jizhou
In this paper, the transient combined heat transfer in the silicon glass porthole of Space Shuttle is studied by control volume method, ray tracing method and spectral band model. The temperature field in the silicon glass and heat flux entering the space cabin are given under the 3rd kind nonlinear boundary condition. The computational results show, if the radiation in the silicon glass is omitted, the errors for temperature fields are not too evident, but for heat flux are quite large.
Developing High-Order Weighted Compact Nonlinear Schemes
Deng, Xiaogang; Zhang, Hanxin
2000-11-01
The weighted technique is introduced in the compact high-order nonlinear schemes (CNS) and three fourth- and fifth-order weighted compact nonlinear schemes (WCNS) are developed in this paper. By Fourier analysis, the dissipative and dispersive features of WCNS are discussed. In view of the modified wave number, the WCNS are equivalent to fifth-order upwind biased explicit schemes in smooth regions and the interpolations at cell-edges dominate the properties of WCNS. Both flux difference splitting and flux vector splitting methods can be applied in WCNS, though they are finite difference schemes. Boundary and near boundary schemes are developed and the asymptotic stability of WCNS is analyzed. Several numerical results are given which show the good performances of WCNS for discontinuity capture high accuracy for boundary layer calculation, and good convergent rate. We also compare WCNS with MUSCL scheme and spectral solutions. WCNS are more accurate than MUSCL, as expected, especially for heat transfer calculations.
Feng, Zhaosheng
Many physical phenomena can be described by nonlinear models. The last few decades have seen an enormous growth of the applicability of nonlinear models and of the development of related nonlinear concepts. This has been driven by modern computer power as well as by the discovery of new mathematical techniques, which include two contrasting themes: (i) the theory of dynamical systems, most popularly associated with the study of chaos, and (ii) the theory of integrable systems associated, among other things, with the study of solitons. In this dissertation, we study two nonlinear models. One is the 1-dimensional vibrating string satisfying wtt - wxx = 0 with van der Pol boundary conditions. We formulate the problem into an equivalent first order Hyperbolic system, and use the method of characteristics to derive a nonlinear reflection relation caused by the nonlinear boundary conditions. Thus, the problem is reduced to the discrete iteration problem of the type un+1 = F( un). Periodic solutions are investigated, an invariant interval for the Abel equation is studied, and numerical simulations and visualizations with different coefficients are illustrated. The other model is the Korteweg-de Vries-Burgers (KdVB) equation. In this dissertation, we proposed two new approaches: One is what we currently call First Integral Method, which is based on the ring theory of commutative algebra. Applying the Hilbert-Nullstellensatz, we reduce the KdVB equation to a first-order integrable ordinary differential equation. The other approach is called the Coordinate Transformation Method, which involves a series of variable transformations. Some new results on the traveling wave solution are established by using these two methods, which not only are more general than the existing ones in the previous literature, but also indicate that some corresponding solutions presented in the literature contain errors. We clarify the errors and instead give a refined result.
Institute of Scientific and Technical Information of China (English)
LU Chang-gen; CAO Wei-dong; QIAN Jian-hua
2006-01-01
A new method for direct numerical simulation of incompressible Navier-Stokes equations is studied in the paper. The compact finite difference and the non-linear terms upwind compact finite difference schemes on non-uniform meshes in x and y directions are developed respectively. With the Fourier spectral expansion in the spanwise direction, three-dimensional N-S equation are converted to a system of two-dimensional equations. The third-order mixed explicit-implicit scheme is employed for time integration. The treatment of the three-dimensional non-reflecting outflow boundary conditions is presented, which is important for the numerical simulations of the problem of transition in boundary layers, jets, and mixing layer. The numerical results indicate that high accuracy, stabilization and efficiency are achieved by the proposed numerical method. In addition, a theory model for the coherent structure in a laminar boundary layer is also proposed, based on which the numerical method is implemented to the non-linear evolution of coherent structure. It is found that the numerical results of the distribution of Reynolds stress, the formation of high shear layer, and the event of ejection and sweeping, match well with the observed characteristics of the coherent structures in a turbulence boundary layer.
Institute of Scientific and Technical Information of China (English)
李志龙
2008-01-01
In this paper, we study the nonlinear second-order boundary value problem of delay differential equation. Without the assumption of the nonnegativity of f, we still obtain the existence of the positive solution.
Institute of Scientific and Technical Information of China (English)
杨茂; 陈建军
1999-01-01
In this paper,combining Riemann's method with the fixed point theory effectively,we proved that the migration equation of the moisture in soil with nonlinear initial boundary value problem has unique classical solution.
Institute of Scientific and Technical Information of China (English)
LI; Shujie
2001-01-01
［1］Martin Schecher,The Fucik spectrum,Indiana University Mathematics Journal,1994,43(4):1139-1157.［2］Dancer,E.N.,Remarks on jumping nonlinearities,in Topics in Nonlinear Analysis (eds.Escher,Simonett),Basel:Birkhauser,1999,101-116.［3］Dancer,E.N.,Du Yihong,Existence of changing sign solutions for semilinear problems with jumping nonlinearities at zero,Proceedings of the Royal Society of Edinburgh,1994,124A:1165-1176.［4］Dancer,E.N.,Du Yihong,Multiple solutions of some semilinear elliptic equations via generalized conley index,Journal of Mathematical Analysis and Applications,1995,189:848-871.［5］Li Shujie,Zhang Zhitao,Sign-changing solutions and multiple solutions theorems for semilinear elliptic boundary value problems with jumping nonlinearities,Acta Mathematica Sinica,2000,16(1):113-122.［6］Chang Kung-ching,Li Shujie,Liu Jiaquan,Remarks on multiple solutions for asymptotically linear elliptic boundary value problems.Topological methods for Nonlinear Analysis,Journal of the Juliusz Schauder Center,1994,3:179-187.［7］Alfonso Castro,Jorge Cossio,Multiple solutions for a nonlinear Dirichlet problem,SIAM J.Math.Anal.,1994,25(6):1554-1561.［8］Alfonso Castro,Jorge Cossio,John M.Neuberger,A sign-changing solution for a superlinear Dirichlet problem,Rocky Mountain J.M.,1997,27:1041-1053.［9］Alfonso Castro,Jorge Cossio,John M.Neuberger,A minimax principle,index of the critical point,and existence of sign-changing solutions to Elliptic boundary value problems,E.J.Diff.Eqn.,1998 (2):1-18.［10］Thomas Bartsch,Wang Zhiqiang,On the existence of sign-changing solutions for semilinear Dirichlet problems,Topological Methods in Nonlinear Analysis,Journal of the Juliusz Schauder Center,1996,(7):115-131.［11］Li Shujie,Zhang Zhitao,Multiple solutions theorems for semilinear elliptic boundary value problems with resonance at infinity,Discrete and Continuous Dynamical System,1999,5(3):489-493.［12］Mawhin,J.,Willem,M.,Critical Point Theory and
Krishnamurthy, M. R.; Gireesha, B. J.; Prasannakumara, B. C.; Gorla, Rama Subba Reddy
2016-09-01
A theoretically investigation has been performed to study the effects of thermal radiation and chemical reaction on MHD velocity slip boundary layer flow and melting heat transfer of nanofluid induced by a nonlinear stretching sheet. The Brownian motion and thermophoresis effects are incorporated in the present nanofluid model. A set of proper similarity variables is used to reduce the governing equations into a system of nonlinear ordinary differential equations. An efficient numerical method like Runge-Kutta-Fehlberg-45 order is used to solve the resultant equations for velocity, temperature and volume fraction of the nanoparticle. The effects of different flow parameters on flow fields are elucidated through graphs and tables. The present results have been compared with existing one for some limiting case and found excellent validation.
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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.
Institute of Scientific and Technical Information of China (English)
Muhaimin; R. Kandasamy; Azme B. Khamis
2008-01-01
This work is concerned with Magnetohydrodynamic viscous flow due to a shrinking sheet in the presence of suction. The cases of two dimensional and axisymmetric shrinking are discussed. The governing boundary layer equations are written into a dimensionless form by similarity transformations. The transformed coupled nonlinear ordinary differential equations are numerically solved by using an advanced numeric technique. Favorability comparisons with previously published work are presented. Numerical results for the dimensionless velocity, temperature and concentration profiles as well as for the skin friction, heat and mass transfer and deposition rate are obtained and displayed graphically for pertinent parameters to show interesting aspects of the solution.
Mahabaleshwar, U. S.; Nagaraju, K. R.; Vinay Kumar, P. N.; Baleanu, Dumitru; Lorenzini, Giulio
2017-03-01
In this paper, we investigate the theoretical analysis for the unsteady magnetohydrodynamic laminar boundary layer flow due to impulsively stretching sheet. The third-order highly nonlinear partial differential equation modeling the unsteady boundary layer flow brought on by an impulsively stretching flat sheet was solved by applying Adomian decomposition method and Pade approximants. The exact analytical solution so obtained is in terms of rapidly converging power series and each of the variants are easily computable. Variations in parameters such as mass transfer (suction/injection) and Chandrasekhar number on the velocity are observed by plotting the graphs. This particular problem is technically sound and has got applications in expulsion process and related process in fluid dynamics problems.
Gordon, Peter V
2012-01-01
This paper deals with the long-time behavior of solutions of nonlinear reaction-diffusion equations describing formation of morphogen gradients, the concentration fields of molecules acting as spatial regulators of cell differentiation in developing tissues. For the considered class of models, we establish existence of a new type of ultra-singular self-similar solutions. These solutions arise as limits of the solutions of the initial value problem with zero initial data and infinitely strong source at the boundary. We prove existence and uniqueness of such solutions in the suitable weighted energy spaces. Moreover, we prove that the obtained self-similar solutions are the long-time limits of the solutions of the initial value problem with zero initial data and a time-independent boundary source.
Mahabaleshwar, U. S.; Nagaraju, K. R.; Vinay Kumar, P. N.; Baleanu, Dumitru; Lorenzini, Giulio
2016-12-01
In this paper, we investigate the theoretical analysis for the unsteady magnetohydrodynamic laminar boundary layer flow due to impulsively stretching sheet. The third-order highly nonlinear partial differential equation modeling the unsteady boundary layer flow brought on by an impulsively stretching flat sheet was solved by applying Adomian decomposition method and Pade approximants. The exact analytical solution so obtained is in terms of rapidly converging power series and each of the variants are easily computable. Variations in parameters such as mass transfer (suction/injection) and Chandrasekhar number on the velocity are observed by plotting the graphs. This particular problem is technically sound and has got applications in expulsion process and related process in fluid dynamics problems.
DEFF Research Database (Denmark)
Schilhab, Theresa
2007-01-01
Kognition og Pædagogik vol. 48:10-18. 2003 Short description : The cognitivistic paradigm and Descartes' view of embodied knowledge. Abstract: That the philosopher Descartes separated the mind from the body is hardly news: He did it so effectively that his name is forever tied to that division....... But what exactly is Descartes' point? How does the Kartesian split hold up to recent biologically based learning theories?...
Tabrizi, Amirhossein Molavi; Bardhan, Jaydeep P
2016-01-01
In this paper we extend the familiar continuum electrostatic model with a perturbation to the usual macroscopic boundary condition. The perturbation is based on the mean spherical approximation (MSA), to derive a multiscale hydration-shell boundary condition (HSBC). We show that the HSBC/MSA model reproduces MSA predictions for Born ions in a variety of polar solvents, including both protic and aprotic solvents. Importantly, the HSBC/MSA model predicts not only solvation free energies accurately but also solvation entropies, which standard continuum electrostatic models fail to predict. The HSBC/MSA model depends only on the normal electric field at the dielectric boundary, similar to our recent development of an HSBC model for charge-sign hydration asymmetry, and the reformulation of the MSA as a boundary condition enables its straightforward application to complex molecules such as proteins.
Lenci, Stefano; Rega, Giuseppe
2016-06-01
The nonlinear free oscillations of a straight planar Timoshenko beam are investigated analytically by means of the asymptotic development method. Attention is focused for the first time, to the best of our knowledge, on the nonlinear coupling between the axial and the transversal oscillations of the beam, which are decoupled in the linear regime. The existence of coupled and uncoupled motion is discussed. Furthermore, the softening versus hardening nature of the backbone curves is investigated in depth. The results are summarized by means of behaviour charts that illustrate the different possible classes of motion in the parameter space. New, and partially unexpected, phenomena, such as the changing of the nonlinear behaviour from softening to hardening by adding/removing the axial vibrations, are highlighted.
Directory of Open Access Journals (Sweden)
Nguyen Anh Dao
2016-11-01
Full Text Available We prove the existence and uniqueness of singular solutions (fundamental solution, very singular solution, and large solution of quasilinear parabolic equations with absorption for Dirichlet boundary condition. We also show the short time behavior of singular solutions as t tends to 0.
Directory of Open Access Journals (Sweden)
Lv Xuezhe
2010-01-01
Full Text Available Abstract The existence and uniqueness of positive solution is obtained for the singular second-order -point boundary value problem for , , , where , , are constants, and can have singularities for and/or and for . The main tool is the perturbation technique and Schauder fixed point theorem.
Energy Technology Data Exchange (ETDEWEB)
Geniet, F; Leon, J [Physique Mathematique et Theorique, CNRS-UMR 5825, 34095 Montpellier (France)
2003-05-07
A nonlinear system possessing a natural forbidden band gap can transmit energy of a signal with a frequency in the gap, as recently shown for a nonlinear chain of coupled pendulums (Geniet and Leon 2002 Phys. Rev. Lett. 89 134102). This process of nonlinear supratransmission, occurring at a threshold that is exactly predictable in many cases, is shown to have a simple experimental realization with a mechanical chain of pendulums coupled by a coil spring. It is then analysed in more detail. First we go to different (nonintegrable) systems which do sustain nonlinear supratransmission. Then a Josephson transmission line (a one-dimensional array of short Josephson junctions coupled through superconducting wires) is shown to also sustain nonlinear supratransmission, though being related to a different class of boundary conditions, and despite the presence of damping, finiteness, and discreteness. Finally, the mechanism at the origin of nonlinear supratransmission is found to be a nonlinear instability, and this is briefly discussed here.
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.
Do, K. D.
2017-02-01
Equations of motion of extensible and shearable slender beams with large translational and rotational motions under external loads in three-dimensional space are first derived in a vector form. Boundary feedback controllers are then designed to ensure that the beams are practically K∞-exponentially stable at the equilibrium. The control design, well-posedness, and stability analysis are based on two Lyapunov-type theorems developed for a class of evolution systems in Hilbert space. Numerical simulations on a slender beam immersed in sea water are included to illustrate the effectiveness of the proposed control design.
Directory of Open Access Journals (Sweden)
Baoqiang Yan
2008-10-01
Full Text Available Using the fixed point theorem in cones, this paper shows the existence of multiple positive solutions for the singular $m$-point boundary-value problem $$displaylines{ x''(t+a(tf(t,x(t,x'(t=0,quad 0
Thermally induced photon splitting
Elmfors, P; Elmfors, Per; Skagerstam, Bo-Sture
1998-01-01
We calculate thermal corrections to the non-linear QED effective action for low-energy photon interactions in a background electromagnetic field. The high-temperature expansion shows that at $T \\gg m$ the vacuum contribution is exactly cancelled to all orders in the external field except for a non-trivial two-point function contribution. The high-temperature expansion derived reveals a remarkable cancellation of infrared sensitive contributions. As a result photon-splitting in the presence of a magnetic field is suppressed in the presence of an electron-positron QED-plasma at very high temperatures. In a cold and dense plasma a similar suppression takes place. At the same time Compton scattering dominates for weak fields and the suppression is rarely important in physical situations.
Generalized Supersymetric Boundary State
1999-01-01
Following our previous paper (hep-th/9909027), we generalize a supersymmetric boundary state so that arbitrary configuration of the gauge field coupled to the boundary of the worldsheet is incorpolated. This generalized boundary state is BRST invariant and satisfy the non-linear boundary conditions with non-constant gauge field strength. This boundary state contains divergence which is identical with the loop divergence in a superstring sigma model. Hence vanishing of the beta function in the...
Institute of Scientific and Technical Information of China (English)
莫嘉琪
2006-01-01
A class of nonlinear nonlocal singularly perturbed Robin initial boundary value problems for reaction diffusion equations with boundary perturbation is considered. Under suitable conditions, firstly, the outer solution of the original problem is obtained; secondly, by using the stretched variable, the composing expansion method and the expanding theory of power series, the initial layer is constructed; and finally,by using the theory of differential inequalities the asymptotic behavior of solutions for initial boundary value problems is studied, and including some relational inequalities the existence and uniqueness of solutions for the original problem and the uniformly valid asymptotic estimation are discussed.
Institute of Scientific and Technical Information of China (English)
徐龙封
2004-01-01
In this paper the nonnegative classical solutions of a parabolic system with nonlinear boundary conditions are discussed. The existence and uniqueness of a nonnegative classical solution are proved. And some sufficient conditions to ensure the global existence and nonexistence of nonnegative classical solution to this problem are given.
2n阶非线性微分方程的第二边值问题%Second Boundary Value Problems for 2n-th Order Nonlinear Differential Equations
Institute of Scientific and Technical Information of China (English)
吕显瑞; 徐庆; 高广学
2002-01-01
Sufficient conditions for the existence and uniqueness of second boundary value problems of two kinds of even order nonlinear differential equations are obtained. The proofs are based on the lemma on bilinear form, developed by A.C.Lazer, Schauder fixed point theorem and the Leray-Schauder degree theory, respectively.
Institute of Scientific and Technical Information of China (English)
彭丽
2002-01-01
The finite element solution of two points boundary value problem for nonlinear ordinary differential equation is studied by using the collocation-Galerkin method.The Jacobi points are introduced to establish high orders of accuracy for the approximate solution.Numerical results are presented for a sample problem.
Numerical solution of the nonlinear Schrödinger equation with wave operator on unbounded domains.
Li, Hongwei; Wu, Xiaonan; Zhang, Jiwei
2014-09-01
In this paper, we generalize the unified approach proposed in Zhang et al. [J. Zhang, Z. Xu, and X. Wu, Phys. Rev. E 78, 026709 (2008)] to design the nonlinear local absorbing boundary conditions (LABCs) for the nonlinear Schrödinger equation with wave operator on unbounded domains. In fact, based on the methodology underlying the unified approach, we first split the original equation into two parts-the linear equation and the nonlinear equation-then achieve a one-way operator to approximate the linear equation to make the wave outgoing, and finally combine the one-way operator with the nonlinear equation to achieve the nonlinear LABCs. The stability of the equation with the nonlinear LABCs is also analyzed by introducing some auxiliary variables, and some numerical examples are presented to verify the accuracy and effectiveness of our proposed method.
Control and Detection of Discrete Spectral Amplitudes in Nonlinear Fourier Spectrum
Aref, Vahid
2016-01-01
Nonlinear Fourier division Multiplexing (NFDM) can be realized from modulating the discrete nonlinear spectrum of an $N$-solitary waveform. To generate an $N$-solitary waveform from desired discrete spectrum (eigenvalue and discrete spectral amplitudes), we use the Darboux Transform. We explain how to the norming factors must be set in order to have the desired discrete spectrum. To derive these norming factors, we study the evolution of nonlinear spectrum by adding a new eigenvalue and its spectral amplitude. We further simplify the Darboux transform algorithm. We propose a novel algorithm (to the best of our knowledge) to numerically compute the nonlinear Fourier Transform (NFT) of a given pulse. The NFT algorithm, called forward-backward method, is based on splitting the signal into two parts and computing the nonlinear spectrum of each part from boundary ($\\pm\\infty$) inward. The nonlinear spectrum (discrete and continuous) derived from efficiently combining both parts has a promising numerical precision....
Directory of Open Access Journals (Sweden)
E. Amata
2006-01-01
Full Text Available We study plasma transport at a thin magnetopause (MP, described hereafter as a thin current sheet (TCS, observed by Cluster at the southern cusp on 13 February 2001 around 20:01 UT. The Cluster observations generally agree with the predictions of the Gas Dynamic Convection Field (GDCF model in the magnetosheath (MSH up to the MSH boundary layer, where significant differences are seen. We find for the MP a normal roughly along the GSE x-axis, which implies a clear departure from the local average MP normal, a ~90 km thickness and an outward speed of 35 km/s. Two populations are identified in the MSH boundary layer: the first one roughly perpendicular to the MSH magnetic field, which we interpret as the "incident" MSH plasma, the second one mostly parallel to B. Just after the MP crossing a velocity jet is observed with a peak speed of 240 km/s, perpendicular to B, with MA=3 and β>10 (peak value 23. The magnetic field clock angle rotates by 70° across the MP. Ex is the main electric field component on both sides of the MP, displaying a bipolar signature, positive on the MSH side and negative on the opposite side, corresponding to a ~300 V electric potential jump across the TCS. The E×B velocity generally coincides with the perpendicular velocity measured by CIS; however, in the speed jet a difference between the two is observed, which suggests the need for an extra flow source. We propose that the MP TCS can act locally as an obstacle for low-energy ions (<350 eV, being transparent for ions with larger gyroradius. As a result, the penetration of plasma by finite gyroradius is considered as a possible source for the jet. The role of reconnection is briefly discussed. The electrodynamics of the TCS along with mass and momentum transfer across it are further discussed in the companion paper by Savin et al. (2006.
Operator Splitting Method for Simulation of Dynamic Flows in Natural Gas Pipeline Networks
Dyachenko, Sergey A; Chertkov, Michael
2016-01-01
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.
Multi-dimensional upwind fluctuation splitting scheme with mesh adaption for hypersonic viscous flow
Wood, William Alfred, III
production is shown relative to DMFDSFV. Remarkably the fluctuation splitting scheme shows grid converged skin friction coefficients with only five points in the boundary layer for this case. A viscous Mach 17.6 (perfect gas) cylinder case demonstrates solution monotonicity and heat transfer capability with the fluctuation splitting scheme. While fluctuation splitting is recommended over DMFDSFV, the difference in performance between the schemes is not so great as to obsolete DMFDSFV. The second half of the dissertation develops a local, compact, anisotropic unstructured mesh adaption scheme in conjunction with the multi-dimensional upwind solver, exhibiting a characteristic alignment behavior for scalar problems. This alignment behavior stands in contrast to the curvature clustering nature of the local, anisotropic unstructured adaption strategy based upon a posteriori error estimation that is used for comparison. The characteristic alignment is most pronounced for linear advection, with reduced improvement seen for the more complex non-linear advection and advection-diffusion cases. The adaption strategy is extended to the two-dimensional and axisymmetric Navier-Stokes equations of motion through the concept of fluctuation minimization. The system test case for the adaption strategy is a sting mounted capsule at Mach-10 wind tunnel conditions, considered in both two-dimensional and axisymmetric configurations. For this complex flowfield the adaption results are disappointing since feature alignment does not emerge from the local operations. Aggressive adaption is shown to result in a loss of robustness for the solver, particularly in the bow shock/stagnation point interaction region. Reducing the adaption strength maintains solution robustness but fails to produce significant improvement in the surface heat transfer predictions.
Splitting methods in communication, imaging, science, and engineering
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. .
THE NAVIER-STOKES EQUATIONS IN STREAM LAYER AND ON STREAM SURFACE AND A DIMENSION SPLIT METHODS
Institute of Scientific and Technical Information of China (English)
李开泰; 黄艾香
2002-01-01
In this paper,we proposal stream surface and stream layer. By using classical tensor calculus, we derive 3-D Navier-Stokes Equations(NSE) in the stream layer under semigeodesic coordinate system, Navier-Stokes equation on the stream surface and 2-D Navier-Stokes equations on a two dimensional manifold. After introducing stream function on the stream surface, a nonlinear initial-boundary value problem satisfies by stream function is obtained, existence and uniqueness of its solution are proven. Based this theory we proposal a new method called "dimension split method" to solve 3D NSE.
Nonlinear magnetic metamaterials.
Shadrivov, Ilya V; Kozyrev, Alexander B; van der Weide, Daniel W; Kivshar, Yuri S
2008-12-08
We study experimentally nonlinear tunable magnetic metamaterials operating at microwave frequencies. We fabricate the nonlinear metamaterial composed of double split-ring resonators where a varactor diode is introduced into each resonator so that the magnetic resonance can be tuned dynamically by varying the input power. We demonstrate that at higher powers the transmission of the metamaterial becomes power-dependent and, as a result, such metamaterial can demonstrate various nonlinear properties. In particular, we study experimentally the power-dependent shift of the transmission band and demonstrate nonlinearity-induced enhancement (or suppression) of wave transmission. (c) 2008 Optical Society of America
Institute of Scientific and Technical Information of China (English)
杜宁
2001-01-01
Mixed finite element method is used to treat a kind of second-order nonlinear hyperbolic equations with absorbing boundary conditions. explicit-intime procedures are formulated and analyzed. Optimal L2-in-space error estimates are derived.
Yersiz, H; Cameron, A M; Carmody, I; Zimmerman, M A; Kelly, B S; Ghobrial, R M; Farmer, D G; Busuttil, R W
2006-03-01
Seventy-five thousand Americans develop organ failure each year. Fifteen percent of those on the list for transplantation die while waiting. Several possible mechanisms to expand the organ pool are being pursued including the use of extended criteria donors, living donation, and split deceased donor transplants. Cadaveric organ splitting results from improved understanding of the surgical anatomy of the liver derived from Couinaud. Early efforts focused on reduced-liver transplantation (RLT) reported by both Bismuth and Broelsch in the mid-1980s. These techniques were soon modified to create both a left lateral segment graft appropriate for a pediatric recipient and a right trisegment for an appropriately sized adult. Techniques of split liver transplantation (SLT) were also modified to create living donor liver transplantation. Pichlmayr and Bismuth reported successful split liver transplantation in 1989 and Emond reported a larger series of nine split procedures in 1990. Broelsch and Busuttil described a technical modification in which the split was performed in situ at the donor institution with surgical division completed in the heart beating cadaveric donor. In situ splitting reduces cold ischemia, simplifies identification of biliary and vascular structures, and reduces reperfusion hemorrhage. However, in situ splits require specialized skills, prolonged operating room time, and increased logistical coordination at the donor institution. At UCLA over 120 in situ splits have been performed and this technique is the default when an optimal donor is available. Split liver transplantation now accounts for 10% of adult transplantations at UCLA and 40% of pediatric transplantations.
Santillana, Mauricio; Zhang, Lin; Yantosca, Robert
2016-01-01
We present upper bounds for the numerical errors introduced when using operator splitting methods to integrate transport and non-linear chemistry processes in global chemical transport models (CTM). We show that (a) operator splitting strategies that evaluate the stiff non-linear chemistry operator at the end of the time step are more accurate, and (b) the results of numerical simulations that use different operator splitting strategies differ by at most 10%, in a prototype one-dimensional non-linear chemistry-transport model. We find similar upper bounds in operator splitting numerical errors in global CTM simulations.
Prasannakumara, B. C.; Shashikumar, N. S.; Venkatesh, P.
2017-09-01
An analysis has been carried out to study the effect of nonlinear thermal radiation on slip flow and heat transfer of fluid particle suspension with nanoparticles over a nonlinear stretching sheet immersed in a porous medium. Water is considered as a base fluid with dust particles along with suspended Aluminum Oxide (Al2O3) nanoparticles. Using appropriate similarity transformations, the coupled nonlinear partial differential equations are reduced into a set of coupled nonlinear ordinary differential equations. The reduced equations are then solved numerically using Runge-Kutta-Fehlberg45 order method with the help of shooting technique to investigate the impact of various pertinent parameters for the velocity and temperature fields. The obtained results are presented in tabular form as well as graphically and discussed in detail. Effect of different parameters on skin friction coefficient and Nusselt number are also discussed.
Directory of Open Access Journals (Sweden)
Yurdal Gezercan
2015-06-01
Full Text Available Split cord malformations are rare form of occult spinal dysraphism in children. Split cord malformations are characterized by septum that cleaves the spinal canal in sagittal plane within the single or duplicated thecal sac. Although their precise incidence is unknown, split cord malformations are exceedingly rare and represent %3.8-5 of all congenital spinal anomalies. Characteristic neurological, urological, orthopedic clinical manifestations are variable and asymptomatic course is possible. Earlier diagnosis and surgical intervention for split cord malformations is associated with better long-term fuctional outcome. For this reason, diagnostic imaging is indicated for children with associated cutaneous and orthopedic signs. Additional congenital anomalies usually to accompany the split cord malformations. Earlier diagnosis, meticuolus surgical therapy and interdisciplinary careful evaluation and follow-up should be made for good prognosis. [Cukurova Med J 2015; 40(2.000: 199-207
McDevitt, J T; Gurst, A H; Chen, Y
1998-01-01
We attempted to determine the accuracy of manually splitting hydrochlorothiazide tablets. Ninety-four healthy volunteers each split ten 25-mg hydrochlorothiazide tablets, which were then weighed using an analytical balance. Demographics, grip and pinch strength, digit circumference, and tablet-splitting experience were documented. Subjects were also surveyed regarding their willingness to pay a premium for commercially available, lower-dose tablets. Of 1752 manually split tablet portions, 41.3% deviated from ideal weight by more than 10% and 12.4% deviated by more than 20%. Gender, age, education, and tablet-splitting experience were not predictive of variability. Most subjects (96.8%) stated a preference for commercially produced, lower-dose tablets, and 77.2% were willing to pay more for them. For drugs with steep dose-response curves or narrow therapeutic windows, the differences we recorded could be clinically relevant.
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...... as possible. Evaluations show that the proposed protocol provides considerable gains over the standard tree splitting protocol applying SIC. The improvement comes at the expense of an increased feedback and receiver complexity....
Institute of Scientific and Technical Information of China (English)
姜朝欣
2007-01-01
This paper deals with blow-up criterion for a doubly degenerate parabolic equation of the form (un)t = (|ux|m-1ux)x + up in (0, 1) × (0, T) subject to nonlinear boundary source (|ux|m-1ux)(1,t) = uq(1,t), (|ux|m-1ux)(0,t) = 0, and positive initial data u(x,0) = uo(x), where the parameters m, n, p, q ＞ 0.It is proved that the problem possesses global solutions if and only if p ≤ n and q≤min{n, m(n+1)/ m+1}.
Institute of Scientific and Technical Information of China (English)
李小龙
2012-01-01
The existence of positive solutions for nonlinear Robin boundary value problem in an ordered Banach spaces was discussed. An existence result of positive solutions was obtained by employing a new estimate of noncompactness measure and the fixed point index theory of condensing mapping.%讨论有序Banach空间E中的非线性Robin边值问题正解的存在性,通过非紧性测度的估计技巧与凝聚映射的不动点指数理论获得该问题正解的存在性结果.
Multi-component Cahn-Hilliard system with different boundary conditions in complex domains
Li, Yibao; Choi, Jung-Il; Kim, Junseok
2016-10-01
We propose an efficient phase-field model for multi-component Cahn-Hilliard (CH) systems in complex domains. The original multi-component Cahn-Hilliard system with a fixed phase is modified in order to make it suitable for complex domains in the Cartesian grid, along with contact angle or no mass flow boundary conditions on the complex boundaries. The proposed method uses a practically unconditionally gradient stable nonlinear splitting numerical scheme. Further, a nonlinear full approximation storage multigrid algorithm is used for solving semi-implicit formulations of the multi-component CH system, incorporated with an adaptive mesh refinement technique. The robustness of the proposed method is validated through various numerical simulations including multi-phase separations via spinodal decomposition, equilibrium contact angle problems, and multi-phase flows with a background velocity field in complex domains.
Reduced order of the local error of splitting for parabolic problems
Auzinger, Winfried; Hofstätter, Harald; Koch, Othmar; Thalhammer, Mechthild
2017-07-01
We give a theoretical analysis of the local error of splitting methods applied to parabolic initial-boundary value problems under homogeneous Dirichlet or Neumann boundary conditions. For the Lie-Trotter splitting, we provide a theoretical local error analysis that rigorously explains the order reduction observed in numerical experiments.
Institute of Scientific and Technical Information of China (English)
万洪林; 于海涛; 杨济民
2014-01-01
边界定位是非理想虹膜识别的关键问题之一。非理想虹膜由于经常存在纹理过强、睫毛和眼睑遮挡、虹膜巩膜对比度较差、瞳孔位置偏移等问题，这使其边界尤其是外边界定位容易出现偏差。针对上述问题，笔者提出了一种基于非线性图像增强的非理想虹膜边界定位方法。在内边界定位中，该方法首先使用混合高斯模型得到瞳孔粗略位置，然后使用弦长均衡策略搜索虹膜内边界及其中心；在外边界定位中，首先对虹膜图像进行非线性灰度变换，再利用边缘检测和改进的 Hough 变换定位虹膜外边界。实验结果表明：本算法与经典方法相比可大大提高非理想虹膜分割的准确率。%Iris boundary localization is one of the key issues of an iris recognition system.For non -ideal iris images,frequently -occurred strong texture,eyelashes or eyelids occlusion,low contrast between iris and sclera, and pupil deviation,etc,will lead inaccuracy localization of iris boundaries,particularly the outer one.We investigate this issue and propose the boundaries localization for non -ideal iris images based on the nonlinear image enhancement.In the process of inner localization,we firstly employ EM algorithm to segment pupil approximately,then use the string -equilibrium technique to search iris center and the inner boundary.In outer boundary localization,we transform nonlinearly the iris intensity,and adopt edge detector and improved Hough transform to find outer boundary.The experimental results depict that our algorithm improves the non -ideal iris localization accuracy compared to the classical algorithms.
Timergaliev, S. N.; Kharasova, L. S.
2016-11-01
Solvability of one system of nonlinear second order partial differential equations with given initial conditions is considered in an arbitrary field. Reduction of the initial system of equations to one nonlinear operator equation is used to study the problem. The solvability is established with the use of the principle of contracting mappings. The method used in these studies is based on the integral representations for the displacements. These representations are constructed with the use of general solutions to the inhomogeneous Cauchy-Riemann equation.
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.
Transverse momentum dependent splitting functions at work: quark-to-gluon splitting
Hentschinski, M; Kutak, K
2016-01-01
Using the recently obtained Pgq splitting function we extend the low x evolution equation for gluons to account for contributions originating from quark-to-gluon splitting. In order to write down a consistent equation we resum virtual corrections coming from the gluon channel and demonstrate that this implies a suitable regularization of the Pgq singularity, corresponding to a soft emitted quark. We also note that the obtained equation is in a straightforward manner generalized to a nonlinear evolution equation which takes into account effects due to the presence of high gluon densities.
An Explicit High Resolution Scheme for Nonlinear Shallow Water Equations
Institute of Scientific and Technical Information of China (English)
FANG Ke-zhao; ZOU Zhi-li; WANG Yan
2005-01-01
The present study develops a numerical model of the two-dimensional fully nonlinear shallow water equations (NSWE) for the wave run-up on a beach. The finite volume method (FVM) is used to solve the equations, and a second-order explicit scheme is developed to improve the computation efficiency. The numerical fluxes are obtained by the two dimensional Roe's flux function to overcome the errors caused by the use of one dimensional fluxes in dimension splitting methods. The high-resolution Godunov-type TVD upwind scheme is employed and a second-order accuracy is achieved based on monotonic upstream schemes for conservation laws (MUSCL) variable extrapolation; a nonlinear limiter is applied to prevent unwanted spurious oscillation. A simple but efficient technique is adopted to deal with the moving shoreline boundary. The verification of the solution technique is carried out by comparing the model output with documented results and it shows that the solution technique is robust.
Polarized Antenna Splitting Functions
Energy Technology Data Exchange (ETDEWEB)
Larkoski, Andrew J.; Peskin, Michael E.; /SLAC
2009-10-17
We consider parton showers based on radiation from QCD dipoles or 'antennae'. These showers are built from 2 {yields} 3 parton splitting processes. The question then arises of what functions replace the Altarelli-Parisi splitting functions in this approach. We give a detailed answer to this question, applicable to antenna showers in which partons carry definite helicity, and to both initial- and final-state emissions.
Boundary Value Problems and Approximate Solutions
African Journals Online (AJOL)
Tadesse
boundary value problems suggested by nonlinear diffusion process. .... According to VIM, a correction functional could be written as follows: (5.4) ... The Variational Iteration Method is remarkably effective for solving boundary value problems.
Energy Technology Data Exchange (ETDEWEB)
Mahanthesh, B., E-mail: bmanths@gmail.com [Department of Mathematics, AIMS Institutes, Peenya, 560058 Bangalore (India); Department of Studies and Research in Mathematics, Kuvempu University, Shankaraghatta, 577451 Shimoga, Karnataka (India); Gireesha, B.J., E-mail: bjgireesu@rediffmail.com [Department of Studies and Research in Mathematics, Kuvempu University, Shankaraghatta, 577451 Shimoga, Karnataka (India); Department of Mechanical Engineering, Cleveland State University, Cleveland, OH (United States); Gorla, R.S. Reddy, E-mail: r.gorla@csuohio.edu [Department of Mechanical Engineering, Cleveland State University, Cleveland, OH (United States); Abbasi, F.M., E-mail: abbasisarkar@gmail.com [Department of Mathematics, Comsats Institute of Information Technology, Islamabad 44000 (Pakistan); Shehzad, S.A., E-mail: ali_qau70@yahoo.com [Department of Mathematics, Comsats Institute of Information Technology, Sahiwal 57000 (Pakistan)
2016-11-01
Numerical solutions of three-dimensional flow over a non-linear stretching surface are developed in this article. An electrically conducting flow of viscous nanoliquid is considered. Heat transfer phenomenon is accounted under thermal radiation, Joule heating and viscous dissipation effects. We considered the variable heat flux condition at the surface of sheet. The governing mathematical equations are reduced to nonlinear ordinary differential systems through suitable dimensionless variables. A well-known shooting technique is implemented to obtain the results of dimensionless velocities and temperature. The obtained results are plotted for multiple values of pertinent parameters to discuss the salient features of these parameters on fluid velocity and temperature. The expressions of skin-friction coefficient and Nusselt number are computed and analyzed comprehensively through numerical values. A comparison of present results with the previous results in absence of nanoparticle volume fraction, mixed convection and magnetic field is computed and an excellent agreement noticed. We also computed the results for both linear and non-linear stretching sheet cases. - Highlights: • Hydromagnetic flow of nanofluid over a bidirectional non-linear stretching surface is examined. • Cu, Al{sub 2}O3 and TiO{sub 2} types nanoparticles are taken into account. • Numerical solutions have been computed and addressed. • The values of skin-friction and Nusselt number are presented.
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....
Macías-Díaz, J E; 10.1002/zamm.200700172
2011-01-01
In this work, we present a conditionally stable finite-difference scheme that consistently approximates the solution of a general class of (3+1)-dimensional nonlinear equations that generalizes in various ways the quantitative model governing discrete arrays consisting of coupled harmonic oscillators. Associated with this method, there exists a discrete scheme of energy that consistently approximates its continuous counterpart. The method has the properties that the associated rate of change of the discrete energy consistently approximates its continuous counterpart, and it approximates both a fully continuous medium and a spatially discretized system. Conditional stability of the numerical technique is established, and applications are provided to the existence of the process of nonlinear supratransmission in generalized Klein-Gordon systems and the propagation of binary signals in semi-unbounded, three-dimensional arrays of harmonic oscillators coupled through springs and perturbed harmonically at the bound...
Mahanthesh, B.; Gireesha, B. J.; Gorla, R. S. Reddy; Abbasi, F. M.; Shehzad, S. A.
2016-11-01
Numerical solutions of three-dimensional flow over a non-linear stretching surface are developed in this article. An electrically conducting flow of viscous nanoliquid is considered. Heat transfer phenomenon is accounted under thermal radiation, Joule heating and viscous dissipation effects. We considered the variable heat flux condition at the surface of sheet. The governing mathematical equations are reduced to nonlinear ordinary differential systems through suitable dimensionless variables. A well-known shooting technique is implemented to obtain the results of dimensionless velocities and temperature. The obtained results are plotted for multiple values of pertinent parameters to discuss the salient features of these parameters on fluid velocity and temperature. The expressions of skin-friction coefficient and Nusselt number are computed and analyzed comprehensively through numerical values. A comparison of present results with the previous results in absence of nanoparticle volume fraction, mixed convection and magnetic field is computed and an excellent agreement noticed. We also computed the results for both linear and non-linear stretching sheet cases.
Numerical modeling of nonlinear acoustic waves in a tube with an array of Helmholtz resonators
Lombard, Bruno
2013-01-01
Wave propagation in a 1-D guide with an array of Helmholtz resonators is studied numerically, considering large amplitude waves and viscous boundary layers. The model consists in two coupled equations: a nonlinear PDE of nonlinear acoustics, and a linear ODE describing the oscillations in the Helmholtz resonators. The dissipative effects in the tube and in the throats of the resonators are modeled by fractional derivatives. Based on a diffusive representation, the convolution kernels are replaced by a finite number of memory variables that satisfy local ordinary differential equations. An optimization procedure provides an efficient diffusive representation. A splitting strategy is then applied to the evolution equations: the propagative part is solved by a standard TVD scheme for hyperbolic equations, whereas the diffusive part is solved exactly. This approach is validated by comparisons with exact solutions. The properties of the full nonlinear solutions are investigated numerically. In particular, existenc...
Benakli, Karim; Goodsell, Mark
2015-01-01
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, 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 the supersymmetry scale, which we derive. On the other hand, we show that renormalisation group running of soft masses above the supersymmetry scale 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, ...
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.)
Indian Academy of Sciences (India)
Antonio J Calderón Martín; Manuel Forero Piulestán; José M Sánchez Delgado
2012-05-01
We study the structure of split Malcev algebras of arbitrary dimension over an algebraically closed field of characteristic zero. We show that any such algebras is of the form $M=\\mathcal{U}+\\sum_jI_j$ with $\\mathcal{U}$ a subspace of the abelian Malcev subalgebra and any $I_j$ a well described ideal of satisfying $[I_j, I_k]=0$ if ≠ . Under certain conditions, the simplicity of is characterized and it is shown that is the direct sum of a semisimple split Lie algebra and a direct sum of simple non-Lie Malcev algebras.
BOUNDARY STABILIZATION OF TIMOSHENKO BEAM
Institute of Scientific and Technical Information of China (English)
YAN Qingxu
2000-01-01
In this paper, the stabilization problem of Timoshenko beam by some nonlinear boundary feedback controls is considered. By virtue of nonlinear semigroup theory and energy-perturbed method, it is shown that the vibration of the beam under the proposed control action decays exponentially or in negative power of time t as t → ∞.
Institute of Scientific and Technical Information of China (English)
陆海霞
2013-01-01
首先研究通过椭圆型偏微分方程歧点的连通分支的性质,然后得到椭圆型偏微分方程边值问题至少有一个正解存在结果.主要研究方法是全局分歧理论.%In this paper,the properties of the connected component containing the bifurcation points of a nonlinear elliptic partial differential equation is firstly studied.Then the existence of at least one positive solution for the boundary value problems of the equation is proved.The method to show our main results is the global bifurcation theol.
Institute of Scientific and Technical Information of China (English)
高永馨; 谢燕华
2009-01-01
利用上下解的方法研究了非线性2n阶常微分方程Y~((2n))=f(t,y,y',…,y~((2n-1))满足如下边界条件条件g_0(y(a),y'(a))=0,g_1(y'(a),y"(a),…,y~((2n-3))(a))=0,g_2(y~((2n-2))(a),y~((2n-1))(a))=0,h_0(y(c),y'(c),y"(c))=0,h_i(y~((i))(c),Y(i+1)(c))=0(i=3,4,…,2n-2).的非线性两点边值问题解的存在性.%By using the method of upper-lower solutions,the sufficient conditions are given for the existence of solutions to nonlinear two point boundary value problems for nonlinear 2nth-order differential equation y~((2n))=f(t,y,y',...,y~((2n-1))) with the boundary conditions g_0(y(a),y'(a)) =0,g_1(y'(a),y"(a),...,y~((2n-3))(a)) =0,g_2(y~((2n-2))(a),y~((2n-1))(a)) =0,h_0(y(c),y'(c),y"(c))=0,h_i(y~((i))(c),y~((i+1))(c))=0(i=3,4,...,2n-2).
Wilkins, Jesse L. M.; Norton, Anderson
2011-01-01
Teaching experiments have generated several hypotheses concerning the construction of fraction schemes and operations and relationships among them. In particular, researchers have hypothesized that children's construction of splitting operations is crucial to their construction of more advanced fractions concepts (Steffe, 2002). The authors…
Gallavotti, G; Mastropietro, V
1997-01-01
An exact expression for the determinant of the splitting matrix is derived: it allows us to analyze the asympotic behaviour needed to amend the large angles theorem proposed in Ann. Inst. H. Poincaré, B-60, 1, 1994. The asymptotic validity of Melnokov's formulae is proved for the class of models considered, which include polynomial perturbations.
Solitary waves of the splitted RLW equation
Zaki, S. I.
2001-07-01
A combination of the splitting method and the cubic B-spline finite elements is used to solve the non-linear regularized long wave (RLW) equation. This approach involves a Bubnov-Galerkin method with cubic B-spline finite elements so that there is continuity of the dependent variable and its first derivative throughout the solution region. Time integration of the resulting systems is effected using a Crank-Nicholson approximation. In simulations of the migration of a single solitary wave this algorithm is shown to have higher accuracy and better conservation than a recent splitting difference scheme based on cubic spline interpolation functions, for different amplitudes ranging from a very small ( ⩾0.03) to a considerably high amplitudes ( ⩽0.3). The development of an undular bore is modeled.
Nonlinear magnetoinductive transmission lines
Lazarides, Nikos; Tsironis, G P
2011-01-01
Power transmission in one-dimensional nonlinear magnetic metamaterials driven at one end is investigated numerically and analytically in a wide frequency range. The nonlinear magnetic metamaterials are composed of varactor-loaded split-ring resonators which are coupled magnetically through their mutual inductances, forming thus a magnetoiductive transmission line. In the linear limit, significant power transmission along the array only appears for frequencies inside the linear magnetoinductive wave band. We present analytical, closed form solutions for the magnetoinductive waves transmitting the power in this regime, and their discrete frequency dispersion. When nonlinearity is important, more frequency bands with significant power transmission along the array may appear. In the equivalent circuit picture, the nonlinear magnetoiductive transmission line driven at one end by a relatively weak electromotive force, can be modeled by coupled resistive-inductive-capacitive (RLC) circuits with voltage-dependent cap...
Effects of Higher Order Dispersion Terms in the Nonlinear Schrodinger Equation
Directory of Open Access Journals (Sweden)
Robert Beech
2005-01-01
Full Text Available This study presents a concise graphical analysis of solitonic solutions to a nonlinear Schrodinger equation (NLSE. A sequence of code using the standard NDSolve function has been developed in Mathematica to investigate the acceptable accuracy of the NLSE in relatively small ranges of the dispersive parameter space. An operator splitting approach was used in the numerical solutions to expand the boundaries and reduce the artifacts for a reliable solution. These numerical routines were implemented through the use with Mathematica and the results give a very clear view of this interesting and important practical phenomenon.
Boundary monotonicity formulae and applications to free boundary problems I: The elliptic case
Directory of Open Access Journals (Sweden)
Georg S. Weiss
2004-03-01
Full Text Available We derive a monotonicity formula at boundary points for a class of nonlinear elliptic partial differential equations, including the obstacle problem case, quenching, a free boundary problem with Bernoulli-type free boundary condition as well as the blow-up case. As application model we prove - for Dirichlet boundary data satisfying certain assumptions - the global existence of a classical solution of the free boundary problem with Bernoulli-type free boundary condition in two and three dimensions.
Boundary fluxes for nonlocal diffusion
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.
Fee splitting in ophthalmology.
Levin, Alex V; Ganesh, Anuradha; Al-Busaidi, Ahmed
2011-02-01
Fee splitting and co-management are common practices in ophthalmology. These arrangements may conflict with the ethical principles governing the doctor-patient relationship, may constitute professional misconduct, and at times, may be illegal. Implications and perceptions of these practices may vary between different cultures. Full disclosure to the patient may minimize the adverse effects of conflicts of interest that arise from these practices, and may thereby allow these practices to be deemed acceptable by some cultural morays, professional guidelines, or by law. Disclosure does not necessarily relieve the physician from a potential ethical compromise. This review examines the practice of fee splitting in ophthalmology, its legal implications, the policies or guidelines governing such arrangements, and the possible ethical ramifications. A comparative view between 3 countries, Canada, the United States, and Oman, was conducted; illustrating that even in disparate cultures, there may be some universality to the application of ethical principles.
Generalized Supersymetric Boundary State
Hashimoto, K
2000-01-01
Following our previous paper (hep-th/9909027), we generalize a supersymmetric boundary state so that arbitrary configuration of the gauge field coupled to the boundary of the worldsheet is incorpolated. This generalized boundary state is BRST invariant and satisfy the non-linear boundary conditions with non-constant gauge field strength. This boundary state contains divergence which is identical with the loop divergence in a superstring sigma model. Hence vanishing of the beta function in the superstring sigma model corresponds to a well-defined boundary state with no divergence. The coupling of a single closed superstring massless mode with multiple open string massless modes is encoded in the boundary state, and we confirm that derivative correction to the D-brane action in this sector vanishes up to the first non-trivial order O(alpha'(derivative)^2). Combining T-dualities, we incorpolate also general configurations of the scalar fields on the D-brane, and construct boundary states representing branes stuc...
Dosen, K
2009-01-01
A split preorder is a preordering relation on the disjoint union of two sets, which function as source and target when one composes split preorders. The paper presents by generators and equations the category SplPre, whose arrows are the split preorders on the disjoint union of two finite ordinals. The same is done for the subcategory Gen of SplPre, whose arrows are equivalence relations, and for the category Rel, whose arrows are the binary relations between finite ordinals, and which has an isomorphic image within SplPre by a map that preserves composition, but not identity arrows. It was shown previously that SplPre and Gen have an isomorphic representation in Rel in the style of Brauer. The syntactical presentation of Gen and Rel in this paper exhibits the particular Frobenius algebra structure of Gen and the particular bialgebraic structure of Rel, the latter structure being built upon the former structure in SplPre. This points towards algebraic modelling of various categories motivated by logic, and re...
Directory of Open Access Journals (Sweden)
Muhammad Naseer
2014-09-01
Full Text Available The present problem is the steady boundary layer flow and heat transfer of a hyperbolic tangent fluid flowing over a vertical exponentially stretching cylinder in its axial direction. After applying usual boundary layer with a suitable similarity transformation to the given partial differential equations and the boundary conditions, a system of coupled nonlinear ordinary differential equations is obtained. This system of ordinary differential equations subject to the boundary conditions is solved with the help of Runge–Kutta–Fehlberg method. The effects of the involved parameters such as Reynolds numbers, Prandtl numbers, Weissenberg numbers and the natural convection parameter are presented through the graphs. The associated physical properties on the flow and heat transfer characteristics that is the skin friction coefficient and Nusselt numbers are presented for different parameters.
Institute of Scientific and Technical Information of China (English)
张银; 毕勤胜
2011-01-01
本文分析了具有多分界面的非线性电路在不同时间尺度下的快慢动力学行为．在一定的参数条件下，系统的周期解为簇发解，表现出明显的快慢效应．根据状态变量变化的快慢，把全系统划分为快子系统和慢子系统两组．根据快慢分析法将慢变量看作快子系统的控制参数，分析了快子系统的平衡点在向量场不同区域内的稳定性．非光滑系统的分岔与向量场的分界面密切相关，对于具有快慢效应的两时间尺度非光滑系统，快子系统的分岔则取决于分界面两侧平衡点的性质．通过在临界面引入广义Jacobi矩阵，讨论了快子系统非光滑分岔的类型，即多次穿越分岔（mul%The fast-slow dynamics of a nonlinear electrical circuit with muhiple switching boundaries is investigated in this paper. For suitable parameters, periodic bursting phenomenon can be observed. The full system can be divided into slow and fast subsystems because of the difference between variational speeds of state variables. According to the slow-fast analysis, the slow variable, which modulates the behavior of the system, can be treated as a quasi-static bifurcation parameter for the fast subsystem to analyze the stabilities of equilibrium points in different areas of vector field. The bifurcation is dependent on the switching boundary in the vector field. In particular, for the two-time scale non-smooth system with fast-slow effect, the bifurcation of fast subsystem is determined by the characteristics of equilibrium points on both sides of the switching boundary. Furthermore, the generalized Jacobian matrix at the non-smooth boundary is introduced to explore the type of non-smooth bifurcation （i. e. , multiple crossing bifurcation） in the fast subsystem, which can also be used to explain the mechanism for symmetric bursting phenomenon of the full system.
State vector splitting for the Euler equations of gasdynamics
Öksüzoglu, H.
2001-01-01
A new upwind scheme is introduced for the Euler equations of gasdynamics in multi- dimensions. Its relation to Steger-Warming Flux Vector Splitting is discussed. Imple- mentation of the conservative boundary condi- tions on solid walls is also given. The method is intuitive, easy to implement and do
Institute of Scientific and Technical Information of China (English)
侯祥林; 刘铁林; 翟中海
2011-01-01
针对椭圆类非线性偏微分方程边值问题,以差分法和动态设计变量优化算法为基础,以离散网格点未知函数值为设计变量,以离散网格点的差分方程组构建为复杂程式化形式的目标函数.提出一种求解离散网格点处未知函数值的优化算法.编制了求解未知离散点函数值的通用程序.求解了具体算例.通过与解析解对比,表明了本文提出求解算法的有效性和精确性,将为更复杂工程问题分析提供良好的解决方法.%For elliptic nonlinear partial differential equations with boundary value problem, based on difference method and dynamic design variable optimization method, by taking unknown function value on discrete net point as design variables, difference equation of all the discrete net points is constructed as an objective function. A kind of optimization algorithm about solving unknown function value on discrete net point is proposed. Universal computing program is designed. Practical example is analyzed. By comparing the computing result with the analytical solution, effectiveness and feasibility are verified. Thus complicated nonlinear mathematical physics equations can be solved by the numerical calculation method.
Bazeia, D.; Losano, L.; Marques, M. A.; Menezes, R.
2017-02-01
We investigate the presence of non-topological solutions of the Q-ball type in (1 , 1) spacetime dimensions. The model engenders the global U (1) symmetry and is of the k-field type, since it contains a new term, of the fourth-order power in the derivative of the complex scalar field. It supports analytical solution of the Q-ball type which is stable quantum mechanically. The new solution engenders an interesting behavior, with the charge and energy densities unveiling a splitting profile.
Operator splitting for well-posed active scalar equations
Holden, Helge; Karper, Trygve K
2012-01-01
We analyze operator splitting methods applied to scalar equations with a nonlinear advection operator, and a linear (local or nonlocal) diffusion operator or a linear dispersion operator. The advection velocity is determined from the scalar unknown itself and hence the equations are so-called active scalar equations. Examples are provided by the surface quasi-geostrophic and aggregation equations. In addition, Burgers-type equations with fractional diffusion as well as the KdV and Kawahara equations are covered. Our main result is that the Godunov and Strang splitting methods converge with the expected rates provided the initial data is sufficiently regular.
Nonlinear Elliptic Differential Equations with Multivalued Nonlinearities
Indian Academy of Sciences (India)
Antonella Fiacca; Nikolaos Matzakos; Nikolaos S Papageorgiou; Raffaella Servadei
2001-11-01
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 $\\mathbb{R}$. Assuming the existence of an upper and of a lower solution, we prove the existence of a solution between them. Also for a special version of the problem, we prove the existence of extremal solutions in the order interval formed by the upper and lower solutions. Then we drop the requirement that the monotone nonlinearity is defined on all of $\\mathbb{R}$. This case is important because it covers variational inequalities. Using the theory of operators of monotone type we show that the problem has a solution. Finally in the last part we consider an eigenvalue problem with a nonmonotone multivalued nonlinearity. Using the critical point theory for nonsmooth locally Lipschitz functionals we prove the existence of at least two nontrivial solutions (multiplicity theorem).
Solar water splitting: efficiency discussion
Juodkazyte, Jurga; Seniutinas, Gediminas; Sebeka, Benjaminas; Savickaja, Irena; Malinauskas, Tadas; Badokas, Kazimieras; Juodkazis, Kestutis; Juodkazis, Saulius
2016-01-01
The current state of the art in direct water splitting in photo-electrochemical cells (PECs) is presented together with: (i) a case study of water splitting using a simple solar cell with the most efficient water splitting electrodes and (ii) a detailed mechanism analysis. Detailed analysis of the energy balance and efficiency of solar hydrogen production are presented. The role of hydrogen peroxide formation as an intermediate in oxygen evolution reaction is newly revealed and explains why a...
Split Quasi-adequate Semigroups
Institute of Scientific and Technical Information of China (English)
Xiao Jiang GUO; Ting Ting PENG
2012-01-01
The so-called split IC quasi-adequate semigroups are in the class of idempotent-connected quasi-adequate semigroups.It is proved that an IC quasi-adequate semigroup is split if and only if it has an adequate transversal.The structure of such semigroup whose band of idempotents is regular will be particularly investigated.Our obtained results enrich those results given by McAlister and Blyth on split orthodox semigroups.
2001-05-01
Third Nucleus Observed with the VLT Summary New images from the VLT show that one of the two nuclei of Comet LINEAR (C/2001 A2), now about 100 million km from the Earth, has just split into at least two pieces . The three fragments are now moving through space in nearly parallel orbits while they slowly drift apart. This comet will pass through its perihelion (nearest point to the Sun) on May 25, 2001, at a distance of about 116 million kilometres. It has brightened considerably due to the splitting of its "dirty snowball" nucleus and can now be seen with the unaided eye by observers in the southern hemisphere as a faint object in the southern constellation of Lepus (The Hare). PR Photo 18a/01 : Three nuclei of Comet LINEAR . PR Photo 18b/01 : The break-up of Comet LINEAR (false-colour). Comet LINEAR splits and brightens ESO PR Photo 18a/01 ESO PR Photo 18a/01 [Preview - JPEG: 400 x 438 pix - 55k] [Normal - JPEG: 800 x 875 pix - 136k] ESO PR Photo 18b/01 ESO PR Photo 18b/01 [Preview - JPEG: 367 x 400 pix - 112k] [Normal - JPEG: 734 x 800 pix - 272k] Caption : ESO PR Photo 18a/01 shows the three nuclei of Comet LINEAR (C/2001 A2). It is a reproduction of a 1-min exposure in red light, obtained in the early evening of May 16, 2001, with the 8.2-m VLT YEPUN (UT4) telescope at Paranal. ESO PR Photo 18b/01 shows the same image, but in a false-colour rendering for more clarity. The cometary fragment "B" (right) has split into "B1" and "B2" (separation about 1 arcsec, or 500 km) while fragment "A" (upper left) is considerably fainter. Technical information about these photos is available below. Comet LINEAR was discovered on January 3, 2001, and designated by the International Astronomical Union (IAU) as C/2001 A2 (see IAU Circular 7564 [1]). Six weeks ago, it was suddenly observed to brighten (IAUC 7605 [1]). Amateurs all over the world saw the comparatively faint comet reaching naked-eye magnitude and soon thereafter, observations with professional telescopes indicated
Bambusi, Dario; Grebert, Benoit
2012-01-01
In this paper we study the long time behavior of a discrete approximation in time and space of the cubic nonlinear Schr\\"odinger equation on the real line. More precisely, we consider a symplectic time splitting integrator applied to a discrete nonlinear Schr\\"odinger equation with additional Dirichlet boundary conditions on a large interval. We give conditions ensuring the existence of a numerical soliton which is close in energy norm to the continuous soliton. Such result is valid under a CFL condition between the time and space stepsizes. Furthermore we prove that if the initial datum is symmetric and close to the continuous soliton, then the associated numerical solution remains close to the orbit of the continuous soliton for very long times.
Nonlinear unsteady supersonic flow analysis for slender bodies of revolution: Theory
Directory of Open Access Journals (Sweden)
D. E. Panayotounakos
1997-01-01
Full Text Available We construct analytical solutions for the problem of nonlinear supersonic flow past slender bodies of revolution due to small amplitude oscillations. The method employed is based on the splitting of the time dependent small perturbation equation to a nonlinear time independent partial differential equation (P.D.E. concerning the steady flow, and a linear time dependent one, concerning the unsteady flow. Solutions in the form of three parameters family of surfaces for the first equation are constructed, while solutions including one arbitrary function for the second equation are extracted. As an application the evaluation of the small perturbation velocity resultants for a flow past a right circular cone is obtained making use of convenient boundary and initial conditions in accordance with the physical problem.
Nonlinear feedback control of Timoshenko beam
Institute of Scientific and Technical Information of China (English)
冯德兴; 张维弢
1995-01-01
This note is concerned with nonlinear boundary feedback control of a Timoshenko beam. Under some nonlinear boundary feedback control, first the nonlinear semigroup theory is used to show the existence and uniqueness of solution for the corresponding closed loop system. Then by using the Lyapunov method, it is proved that the vibration of the beam under the proposed control action decays in a negative power of time t as t→.
Development of A Fully Nonlinear Numerical Wave Tank
Institute of Scientific and Technical Information of China (English)
陈永平; 李志伟; 张长宽
2004-01-01
A fully nonlinear numerical wave tank (NWT) based on the solution of the σ-transformed Navier-Stokes equation is developed in this study. The numerical wave is generated from the inflow boundary, where the surface elevation and/or velocity are specified by use of the analytical solution or the laboratory data. The Sommerfeld/Orlanski radiation condition in conjunction with an artificial damping zone is applied to reduce wave reflection from the outflow boundary. The whole numerical solution procedures are split into three steps, i.e., advection, diffusion and propagation, and a new method,the Lagrange-Euler Method, instead of the MAC or VOF method, is introduced to solve the free surface elevation at the new time step. Several typical wave cases, including solitary waves, regular waves and irregular waves, are simulated in the wave tank. The robustness and accuracy of the NWT are verified by the good agreement between the numerical results and the linear or nonlinear analytical solutions. This research will be further developed by study of wave-wave, wave-current, wave-structure or wave-jet interaction in the future.
Leptogenesis from split fermions
Energy Technology Data Exchange (ETDEWEB)
Nagatani, Yukinori; Perez, Gilad
2004-01-11
We present a new type of leptogenesis mechanism based on a two-scalar split-fermions framework. At high temperatures the bulk scalar vacuum expectation values (VEVs) vanish and lepton number is strongly violated. Below some temperature, T{sub c}, the scalars develop extra dimension dependent VEVs. This transition is assumed to proceed via a first order phase transition. In the broken phase the fermions are localized and lepton number violation is negligible. The lepton-bulk scalar Yukawa couplings contain sizable CP phases which induce lepton production near the interface between the two phases. We provide a qualitative estimation of the resultant baryon asymmetry which agrees with current observation. The neutrino flavor parameters are accounted for by the above model with an additional approximate U(1) symmetry.
Analysis of Nonlinear Electromagnetic Metamaterials
Poutrina, Ekaterina; Smith, David R
2010-01-01
We analyze the properties of a nonlinear metamaterial formed by integrating nonlinear components or materials into the capacitive regions of metamaterial elements. A straightforward homogenization procedure leads to general expressions for the nonlinear susceptibilities of the composite metamaterial medium. The expressions are convenient, as they enable inhomogeneous system of scattering elements to be described as a continuous medium using the standard notation of nonlinear optics. We illustrate the validity and accuracy of our theoretical framework by performing measurements on a fabricated metamaterial sample composed of an array of split ring resonators (SRRs) with packaged varactors embedded in the capacitive gaps in a manner similar to that of Wang et al. [Opt. Express 16, 16058 (2008)]. Because the SRRs exhibit a predominant magnetic response to electromagnetic fields, the varactor-loaded SRR composite can be described as a magnetic material with nonlinear terms in its effective magnetic susceptibility...
Stabilizing and destabilizing Heegaard splittings of sufficiently complicated 3-manifolds
Bachman, David
2012-01-01
Let M_1 and M_2 be compact, orientable 3-manifolds with incompressible boundary, and M the manifold obtained by gluing with a homeomorphism $\\phi:\\bdy M_1 \\to \\bdy M_2$. We analyze the relationship between the sets of low genus Heegaard splittings of M_1, M_2, and M, assuming the map \\phi is "sufficiently complicated." This analysis yields counter-examples to the Stabilization Conjecture, a resolution of the higher genus analogue of a conjecture of Gordon, and a result about the uniqueness of expressions of Heegaard splittings as amalgamations.
A splitting approach for the Kadomtsev--Petviashvili equation
Einkemmer, Lukas
2014-01-01
We consider a splitting approach for the Kadomtsev--Petviashvili equation with periodic boundary conditions and show that the necessary interpolation procedure can be efficiently implemented. The error made by this numerical scheme is compared to exponential integrators which have been shown in Klein and Roidot (SIAM J. Sci. Comput., 2011) to perform best for stiff solutions of the Kadomtsev--Petviashvili equation. Since splitting methods are limited to order two in this case, we propose a stable extrapolation method in order to construct a numerical scheme of order four. In addition, the conservation properties of the numerical schemes under consideration are investigated.
Savin, Sergey; Büchner, Jörg; Zelenyi, Lev; Kronberg, Elena; Klimov, Stanislav; Kozak, Lyudmila; Blecki, Jan; Budaev, Viacheslav; Nemecek, Zdenek; Safrankova, Jana; Skalsky, Alexander; Amata, Ermanno
The identification of the role of the Supersonic Plasma Streams (SPS) interactions with the Earth magnetosphere should be interesting in the context of the planetary and astrophysical magnetospheres and of that of laboratory plasmas. The interactions can be inherently non-local and non-equilibrium, and even explosive due to both solar wind (SW) induced and self-generated coherent structures in the multiscale system with the scales ranging from the micro to global scales. We study the main fundamental processes arising from the SPS cascading and interactions with surface and cavity resonances in the Earth’s magnetosphere, using multi-spacecraft data (SPECTR-R, DOUBLE STAR, CLUSTER, GEOTAIL, ACE, WIND etc.). We will address the following key problems to advance our understanding of anomalous transport and boundary dynamics: - the BS disturbances role in the SPS production; it requires to base on the relevant databases from the CLUSTER/ DOUBLE STAR/ GEOTAIL/SPECTR-R/ ACE/ WIND spacecraft, which will be used for a statistical analysis targeting the SPS statistical features as extreme events. - analysis of the SPS generation mechanisms, e.g., by bow shock (BS) surface or magnetosheath (MSH) cavity resonances, triggering by interplanetary shocks, solar wind (SW) dynamic pressure jumps, foreshock nonlinear structures, etc. - pumping of substantial part of the SW kinetic energy into the BS membrane and MSH cavity modes and initiate further cascades towards higher frequencies. Accordingly we present the multipoint studies of the SPS and of related nonlinear discrete cascades (carried generally by the SPS), along with the transformation of discrete cascades of the dynamic pressure into turbulent cascades. - explorations of spectral and bi-spectral cross-correlations in SW, foreshock, MSH and in vicinity of BS and magnetopause (MP) would demonstrate that both inflow and outflow into/ from magnetosphere can be modulated by the SPS and by the related outer magnetospheric
High Order Three Part Split Symplectic Integration Schemes
Gerlach, Enrico; Skokos, Charalampos; Bodyfelt, Joshua D; Papamikos, Georgios
2013-01-01
Symplectic integration methods based on operator splitting are well established in many branches of science. For Hamiltonian systems which split in more than two parts, symplectic methods of higher order have been studied in detail only for a few special cases. In this work, we present and compare different ways to construct high order symplectic schemes for general Hamiltonian systems that can be split in three integrable parts. We use these techniques to numerically solve the equations of motion for a simple toy model, as well as the disordered discrete nonlinear Schr\\"odinger equation. We thereby compare the efficiency of symplectic and non-symplectic integration methods. Our results show that the new symplectic schemes are superior to the other tested methods, with respect to both long term energy conservation and computational time requirements.
LOCAL EXACT BOUNDARY CONTROLLABILITY FOR A CLASS OFQUASILINEAR HYPERBOLIC SYSTEMS
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
For a class of mixed initial-boundary value problem for general quasilinear hyperbolic systems, this paper establishes the local exact boundary controllability with boundary controls only acting on one end. As an application, the authors show the local exact boundary controllability for a kind of nonlinear vibrating string problem.
Kuznetsov, Arseniy I; Fu, Yuan Hsing; Viswanathan, Vignesh; Rahmani, Mohsen; Valuckas, Vytautas; Kivshar, Yuri; Pickard, Daniel S; Lukiyanchuk, Boris
2014-01-01
We introduce a new concept of split-ball resonator and demonstrate a strong omnidirectional magnetic dipole response for both gold and silver spherical plasmonic nanoparticles with nanometer-scale cuts. Tunability of the magnetic dipole resonance throughout the visible spectral range is demonstrated by a change of the depth and width of the nanoscale cut. We realize this novel concept experimentally by employing the laser-induced transfer method to produce near-perfect spheres and helium ion beam milling to make cuts with the nanometer resolution. Due to high quality of the spherical particle shape, governed by strong surface tension forces during the laser transfer process, and the clean, straight side walls of the cut made by helium ion milling, magnetic resonance is observed at 600 nm in gold and at 565 nm in silver nanoparticles. Structuring arbitrary features on the surface of ideal spherical resonators with nanoscale dimensions provides new ways of engineering hybrid resonant modes and ultra-high near-f...
A note on the Lie symmetries of complex partial differential equations and their split real systems
Indian Academy of Sciences (India)
F M Mahomed; Rehana Naz
2011-09-01
Folklore suggests that the split Lie-like operators of a complex partial differential equation are symmetries of the split system of real partial differential equations. However, this is not the case generally. We illustrate this by using the complex heat equation, wave equation with dissipation, the nonlinear Burgers equation and nonlinear KdV equations. We split the Lie symmetries of a complex partial differential equation in the real domain and obtain real Lie-like operators. Further, the complex partial differential equation is split into two coupled or uncoupled real partial differential equations which constitute a system of two equations for two real functions of two real variables. The Lie symmetries of this system are constructed by the classical Lie approach. We compare these Lie symmetries with the split Lie-like operators of the given complex partial differential equation for the examples considered. We conclude that the split Lie-like operators of complex partial differential equations are not in general symmetries of the split system of real partial differential equations. We prove a proposition that gives the criteria when the Lie-like operators are symmetries of the split system.
Simulation of non-linear ultrasound fields
DEFF Research Database (Denmark)
Jensen, Jørgen Arendt; Fox, Paul D.; Wilhjelm, Jens E.
2002-01-01
An approach for simulating non-linear ultrasound imaging using Field II has been implemented using the operator splitting approach, where diffraction, attenuation, and non-linear propagation can be handled individually. The method uses the Earnshaw/Poisson solution to Burgcrs' equation for the non......-linear ultrasound imaging in 3D using filters or pulse inversion for any kind of transducer, focusing, apodization, pulse emission and scattering phantom. This is done by first simulating the non-linear emitted field and assuming that the scattered field is weak and linear. The received signal is then the spatial...
Boundary Value Problems With Integral Conditions
Karandzhulov, L. I.; Sirakova, N. D.
2011-12-01
The weakly perturbed nonlinear boundary value problems (BVP) for almost linear systems of ordinary differential equations (ODE) are considered. We assume that the nonlinear part contain an additional function, which defines the perturbation as singular. Then the Poincare method is not applicable. The problem of existence, uniqueness and construction of a solution of the posed BVP with integral condition is studied.
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.
Semantic Parameters of Split Intransitivity.
Van Valin, Jr., Robert D.
1990-01-01
This paper argues that split-intransitive phenomena are better explained in semantic terms. A semantic analysis is carried out in Role and Reference Grammar, which assumes the theory of verb classification proposed in Dowty 1979. (49 references) (JL)
1975-01-01
The experimental apparatus used at intersection 4 around the Split-Field Magnet by the CERN-Bologna Collaboration (experiment R406). The plastic scintillator telescopes are used for precise pulse-height and time-of-flight measurements.
On the exact controllability of a nonlinear stochastic heat equation
Directory of Open Access Journals (Sweden)
Bui An Ton
2006-01-01
Full Text Available The exact controllability of a nonlinear stochastic heat equation with null Dirichlet boundary conditions, nonzero initial and target values, and an interior control is established.
Split NMSSM with electroweak baryogenesis
Demidov, S.; Gorbunov, D; Kirpichnikov, D.
2016-01-01
In light of the Higgs boson discovery and other results of the LHC we re-consider generation of the baryon asymmetry in the split Supersymmetry model with an additional singlet superfield in the Higgs sector (non-minimal split SUSY). We find that successful baryogenesis during the first order electroweak phase transition is possible within a phenomenologically viable part of the model parameter space. We discuss several phenomenological consequences of this scenario, namely, predictions for t...
Wave envelopes method for description of nonlinear acoustic wave propagation.
Wójcik, J; Nowicki, A; Lewin, P A; Bloomfield, P E; Kujawska, T; Filipczyński, L
2006-07-01
A novel, free from paraxial approximation and computationally efficient numerical algorithm capable of predicting 4D acoustic fields in lossy and nonlinear media from arbitrary shaped sources (relevant to probes used in medical ultrasonic imaging and therapeutic systems) is described. The new WE (wave envelopes) approach to nonlinear propagation modeling is based on the solution of the second order nonlinear differential wave equation reported in [J. Wójcik, J. Acoust. Soc. Am. 104 (1998) 2654-2663; V.P. Kuznetsov, Akust. Zh. 16 (1970) 548-553]. An incremental stepping scheme allows for forward wave propagation. The operator-splitting method accounts independently for the effects of full diffraction, absorption and nonlinear interactions of harmonics. The WE method represents the propagating pulsed acoustic wave as a superposition of wavelet-like sinusoidal pulses with carrier frequencies being the harmonics of the boundary tone burst disturbance. The model is valid for lossy media, arbitrarily shaped plane and focused sources, accounts for the effects of diffraction and can be applied to continuous as well as to pulsed waves. Depending on the source geometry, level of nonlinearity and frequency bandwidth, in comparison with the conventional approach the Time-Averaged Wave Envelopes (TAWE) method shortens computational time of the full 4D nonlinear field calculation by at least an order of magnitude; thus, predictions of nonlinear beam propagation from complex sources (such as phased arrays) can be available within 30-60 min using only a standard PC. The approximate ratio between the computational time costs obtained by using the TAWE method and the conventional approach in calculations of the nonlinear interactions is proportional to 1/N2, and in memory consumption to 1/N where N is the average bandwidth of the individual wavelets. Numerical computations comparing the spatial field distributions obtained by using both the TAWE method and the conventional approach
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.
Tunable polarization beam splitting based on a symmetrical metal-cladding waveguide structure.
Wang, Yi; Cao, Zhuangqi; Li, Honggen; Shen, Qishun; Yuan, Wen; Xiao, Pingping
2009-08-03
Electrical tuning of polarization beam splitting is demonstrated in the structure of symmetrical metal-cladding waveguide by introducing optically nonlinear material into both the coupling prism and the guiding layer. Due to the anisotropy of the coupling material, different excitation conditions for TE and TM modes are obtained, which results in polarization-dependent reflections and transmissions. And the splitting effect of the two orthogonally polarized beams can be manipulated through an electrical modulation of the guiding layer properties.
Gilardoni, S S; Martini, M; Métral, E; Steerenberg, R; Müller, A-S
2006-01-01
Recently, a novel technique to perform multi-turn 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.
Hilbert complexes of nonlinear elasticity
Angoshtari, Arzhang; Yavari, Arash
2016-12-01
We introduce some Hilbert complexes involving second-order tensors on flat compact manifolds with boundary that describe the kinematics and the kinetics of motion in nonlinear elasticity. We then use the general framework of Hilbert complexes to write Hodge-type and Helmholtz-type orthogonal decompositions for second-order tensors. As some applications of these decompositions in nonlinear elasticity, we study the strain compatibility equations of linear and nonlinear elasticity in the presence of Dirichlet boundary conditions and the existence of stress functions on non-contractible bodies. As an application of these Hilbert complexes in computational mechanics, we briefly discuss the derivation of a new class of mixed finite element methods for nonlinear elasticity.
Field-Split Preconditioned Inexact Newton Algorithms
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.
Mode matching for optimal plasmonic nonlinear generation
O'Brien, Kevin; Suchowski, Haim; Rho, Jun Suk; Kante, Boubacar; Yin, Xiaobo; Zhang, Xiang
2013-03-01
Nanostructures and metamaterials have attracted interest in the nonlinear optics community due to the possibility of engineering their nonlinear responses; however, the underlying physics to describe nonlinear light generation in nanostructures and the design rules to maximize the emission are still under debate. We study the geometry dependence of the second harmonic and third harmonic emission from gold nanostructures, by designing arrays of nanostructures whose geometry varies from bars to split ring resonators. We fix the length (and volume) of the nanostructure on one axis, and change the morphology from a split ring resonator on the other axis. We observed that the optimal second harmonic generation does not occur at the morphology indicated by a nonlinear oscillator model with parameters derived from the far field transmission and is not maximized by a spectral overlap of the plasmonic modes; however, we find a near field overlap integral and mode matching considerations accurately predict the optimal geometry.
An almost symmetric Strang splitting scheme for the construction of high order composition methods.
Einkemmer, Lukas; Ostermann, Alexander
2014-12-01
In this paper we consider splitting methods for nonlinear ordinary differential equations in which one of the (partial) flows that results from the splitting procedure cannot be computed exactly. Instead, we insert a well-chosen state [Formula: see text] into the corresponding nonlinearity [Formula: see text], which results in a linear term [Formula: see text] whose exact flow can be determined efficiently. Therefore, in the spirit of splitting methods, it is still possible for the numerical simulation to satisfy certain properties of the exact flow. However, Strang splitting is no longer symmetric (even though it is still a second order method) and thus high order composition methods are not easily attainable. We will show that an iterated Strang splitting scheme can be constructed which yields a method that is symmetric up to a given order. This method can then be used to attain high order composition schemes. We will illustrate our theoretical results, up to order six, by conducting numerical experiments for a charged particle in an inhomogeneous electric field, a post-Newtonian computation in celestial mechanics, and a nonlinear population model and show that the methods constructed yield superior efficiency as compared to Strang splitting. For the first example we also perform a comparison with the standard fourth order Runge-Kutta methods and find significant gains in efficiency as well better conservation properties.
Institute of Scientific and Technical Information of China (English)
Jie－MinZHAN; Yao－SongCHEN
1996-01-01
An operator splitting method combining finite difference method and finite element method is proposed in this paper by using boundary-fitted coordinate system.The governing equation is split into advection and diffusion equations and solved by finit difference method using boundary-fitted coordinate system and finite element method respectively.An example for which analytic solution is available is used to verified the proposed methods and the agreement is very good.Numerical results show that it is very efficient.
DEFF Research Database (Denmark)
Løvschal, Mette
2014-01-01
This article proposes a processual ontology for the emergence of man-made, linear boundaries across northwestern Europe, particularly in the first millennium BC. Over a significant period of time, these boundaries became new ways of organizing the landscape and settlements—a phenomenon that has...... of this phenomenon emerged along equivalent trajectories. At the same time, variation in the regional incorporation of these linear phenomena points toward situation-specific applications and independent development....
DEFF Research Database (Denmark)
Zølner, Mette
The paper explores how locals span boundaries between corporate and local levels. The aim is to better comprehend potentialities and challenges when MNCs draws on locals’ culture specific knowledge. The study is based on an in-depth, interpretive case study of boundary spanning by local actors in...... approach with pattern matching is a way to shed light on the tacit local knowledge that organizational actors cannot articulate and that an exclusively inductive research is not likely to unveil....
Flux vector splitting of the inviscid equations with application to finite difference methods
Steger, J. L.; Warming, R. F.
1979-01-01
The conservation-law form of the inviscid gasdynamic equations has the remarkable property that the nonlinear flux vectors are homogeneous functions of degree one. This property readily permits the splitting of flux vectors into subvectors by similarity transformations so that each subvector has associated with it a specified eigenvalue spectrum. As a consequence of flux vector splitting, new explicit and implicit dissipative finite-difference schemes are developed for first-order hyperbolic systems of equations. Appropriate one-sided spatial differences for each split flux vector are used throughout the computational field even if the flow is locally subsonic. The results of some preliminary numerical computations are included.
Steger, J. L.; Warming, R. F.
1981-01-01
The conservation-law form of the inviscid gasdynamic equations has the remarkable property that the nonlinear flux vectors are homogeneous functions of degree one. This property readily permits the splitting of flux vectors into subvectors by similarity transformations so that each subvector has associated with it a specified eigenvalue spectrum. As a consequence of flux vector splitting, new explicit and implicit dissipative finite-difference schemes are developed for first-order hyperbolic systems of equations. Appropriate one-sided spatial differences for each split flux vector are used throughout the computational field even if the flow is locally subsonic. The results of some preliminary numerical computations are included.
Observations of Autler-Townes spatial splitting of four-wave mixing image
Huang, Gaoping; Sun, Jia; Feng, Weikang; Yuan, Jiamin; Wu, Zhenkun; Qin, Mengzhe; Zhang, Yiqi; Zhang, Yanpeng
2013-08-01
We report the self- and external-dressed Autler-Townes (A-T) splittings of the images of the generated four-wave mixing signal (FWM) and electromagnetically induced transparency (EIT) of probe images in cascade three-level atomic system. Such spatial properties of probe and FWM signals are induced by the enhanced cross-Kerr nonlinearity. We demonstrate the controlled electromagnetically induced spatial dispersion (EISD), splitting and focusing of probe and FWM signals images by adjusting self- and external-dressing fields. Studies on such controllable A-T spatial splitting and spatial EIT effect can be very useful in applications of spatial signal processing and optical communication.
Bloembergen, Nicolaas
1996-01-01
Nicolaas Bloembergen, recipient of the Nobel Prize for Physics (1981), wrote Nonlinear Optics in 1964, when the field of nonlinear optics was only three years old. The available literature has since grown by at least three orders of magnitude.The vitality of Nonlinear Optics is evident from the still-growing number of scientists and engineers engaged in the study of new nonlinear phenomena and in the development of new nonlinear devices in the field of opto-electronics. This monograph should be helpful in providing a historical introduction and a general background of basic ideas both for expe
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.
Boundary energy of the open XXX chain with a non-diagonal boundary term
Nepomechie, Rafael I.; Wang, Chunguang
2014-01-01
We analyze the ground state of the open spin-1/2 isotropic quantum spin chain with a non-diagonal boundary term using a recently proposed Bethe ansatz solution. As the coefficient of the non-diagonal boundary term tends to zero, the Bethe roots split evenly into two sets: those that remain finite, and those that become infinite. We argue that the former satisfy conventional Bethe equations, while the latter satisfy a generalization of the Richardson-Gaudin equations. We derive an expression for the leading correction to the boundary energy in terms of the boundary parameters.
Boundary energy of the open XXX chain with a non-diagonal boundary term
Nepomechie, Rafael I
2013-01-01
We analyze the ground state of the open spin-1/2 isotropic quantum spin chain with a non-diagonal boundary term using a recently proposed Bethe ansatz solution. As the coefficient of the non-diagonal boundary term tends to zero, the Bethe roots split evenly into two sets: those that remain finite, and those that become infinite. We argue that the former satisfy conventional Bethe equations, while the latter satisfy a generalization of the Richardson-Gaudin equations. We derive an expression for the leading correction to the boundary energy in terms of the boundary parameters.
Optimal boundary control and boundary stabilization of hyperbolic systems
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.
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...
Solar water splitting: efficiency discussion
Juodkazyte, Jurga; Sebeka, Benjaminas; Savickaja, Irena; Malinauskas, Tadas; Badokas, Kazimieras; Juodkazis, Kestutis; Juodkazis, Saulius
2016-01-01
The current state of the art in direct water splitting in photo-electrochemical cells (PECs) is presented together with: (i) a case study of water splitting using a simple solar cell with the most efficient water splitting electrodes and (ii) a detailed mechanism analysis. Detailed analysis of the energy balance and efficiency of solar hydrogen production are presented. The role of hydrogen peroxide formation as an intermediate in oxygen evolution reaction is newly revealed and explains why an oxygen evolution is not taking place at the thermodynamically expected 1.23 V potential. Solar hydrogen production with electrical-to-hydrogen conversion efficiency of 52% is demonstrated using a simple ~0.7%-efficient n-Si/Ni Schottky solar cell connected to a water electrolysis cell. This case study shows that separation of the processes of solar harvesting and electrolysis avoids photo-electrode corrosion and utilizes optimal electrodes for hydrogen and oxygen evolution reactions and achieves ~10% efficiency in light...
Lattice splitting under intermittent flows
Schläpfer, Markus
2010-01-01
We study the splitting of regular square lattices subject to stochastic intermittent flows. By extensive Monte Carlo simulations we reveal how the time span until the occurence of a splitting depends on various flow patterns imposed on the lattices. Increasing the flow fluctuation frequencies shortens this time span which reaches a minimum before rising again due to inertia effects incorporated in the model. The size of the largest connected component after the splitting is rather independent of the flow fluctuations but sligthly decreases with the link capacities. Our results are relevant for assessing the robustness of real-life systems, such as electric power grids with a large share of renewable energy sources including wind turbines and photovoltaic systems.
Indian Academy of Sciences (India)
Antonio J Calderón Martín
2009-04-01
We begin the study of arbitrary split Lie triple systems by focussing on those with a coherent 0-root space. We show that any such triple systems with a symmetric root system is of the form $T=\\mathcal{U}+\\sum_j I_j$ with $\\mathcal{U}$ a subspace of the 0-root space $T_0$ and any $I_j$ a well described ideal of , satisfying $[I_j,T,I_k]=0$ if $j≠ k$. Under certain conditions, it is shown that is the direct sum of the family of its minimal ideals, each one being a simple split Lie triple system, and the simplicity of is characterized. The key tool in this job is the notion of connection of roots in the framework of split Lie triple systems.
Split supersymmetry in brane models
Indian Academy of Sciences (India)
Ignatios Antoniadis
2006-11-01
Type-I string theory in the presence of internal magnetic fields provides a concrete realization of split supersymmetry. To lowest order, gauginos are massless while squarks and sleptons are superheavy. For weak magnetic fields, the correct Standard Model spectrum guarantees gauge coupling unification with sin2 W = 3/8 at the com-pactification scale of GUT ≃ 2 × 1016 GeV. I discuss mechanisms for generating gaugino and higgsino masses at the TeV scale, as well as generalizations to models with split extended supersymmetry in the gauge sector.
Split NMSSM with electroweak baryogenesis
Demidov, S. V.; Gorbunov, D. S.; Kirpichnikov, D. V.
2016-11-01
In light of the Higgs boson discovery and other results of the LHC we re-consider generation of the baryon asymmetry in the split Supersymmetry model with an additional singlet superfield in the Higgs sector (non-minimal split SUSY). We find that successful baryogenesis during the first order electroweak phase transition is possible within a phenomenologically viable part of the model parameter space. We discuss several phenomenological consequences of this scenario, namely, predictions for the electric dipole moments of electron and neutron and collider signatures of light charginos and neutralinos.
Splitting strings on integrable backgrounds
Energy Technology Data Exchange (ETDEWEB)
Vicedo, Benoit
2011-05-15
We use integrability to construct the general classical splitting string solution on R x S{sup 3}. Namely, given any incoming string solution satisfying a necessary self-intersection property at some given instant in time, we use the integrability of the worldsheet {sigma}-model to construct the pair of outgoing strings resulting from a split. The solution for each outgoing string is expressed recursively through a sequence of dressing transformations, the parameters of which are determined by the solutions to Birkhoff factorization problems in an appropriate real form of the loop group of SL{sub 2}(C). (orig.)
Split Supersymmetry in String Theory
Antoniadis, Ignatios
2006-01-01
Type I string theory in the presence of internal magnetic fields provides a concrete realization of split supersymmetry. To lowest order, gauginos are massless while squarks and sleptons are superheavy. For weak magnetic fields, the correct Standard Model spectrum guarantees gauge coupling unification with \\sin^2{\\theta_W}=3/8 at the compactification scale of M_{\\rm GUT}\\simeq 2 \\times 10^{16} GeV. I discuss mechanisms for generating gaugino and higgsino masses at the TeV scale, as well as generalizations to models with split extended supersymmetry in the gauge sector.
TWO APPROACHES TO CALCULATION OF SPLIT PHASE DANCING OF OVERHEAD ELECTRICAL TRANSMISSION LINE
Directory of Open Access Journals (Sweden)
I. I. Sergey
2005-01-01
Full Text Available The paper shows two approaches to mathematical modeling of split phase dancing of overhead electrical transmission line. The first approach is based on calculative method when a phase is in the shape of flexible elastic thread connected with rigid rods. The phase is represented with equivalent wire in the second approach. Principle of mechanics relations has been used to set combined boundary problem of split phase dynamics. Two packets of computer programs for calculation of split phase dancing of overhead (electric power line have been set up and tested.
DEFF Research Database (Denmark)
Neergaard, Ulla; Nielsen, Ruth
2010-01-01
; and 3) Services of general interest. In the Blurring Boundaries project, three aspects of the European Social Model have been particularly highlighted: the constitutionalisation of the European Social Model, its multi-level legal character, and the clash between market access justice at EU level...... of welfare functions into EU law both from an internal market law and a constitutional law perspective. The main problem areas covered by the Blurring Boundaries project were studied in sub-projects on: 1) Internal market law and welfare services; 2) Fundamental rights and non-discrimination law aspects...... and distributive justice at national level....
DEFF Research Database (Denmark)
Neergaard, Ulla; Nielsen, Ruth
2010-01-01
; and 3) Services of general interest. In the Blurring Boundaries project, three aspects of the European Social Model have been particularly highlighted: the constitutionalisation of the European Social Model, its multi-level legal character, and the clash between market access justice at EU level...... of welfare functions into EU law both from an internal market law and a constitutional law perspective. The main problem areas covered by the Blurring Boundaries project were studied in sub-projects on: 1) Internal market law and welfare services; 2) Fundamental rights and non-discrimination law aspects...... and distributive justice at national level....
2016-07-01
Advanced Research Projects Agency (DARPA) Dynamics-Enabled Frequency Sources (DEFYS) program is focused on the convergence of nonlinear dynamics and...Early work in this program has shown that nonlinear dynamics can provide performance advantages. However, the pathway from initial results to...dependent nonlinear stiffness observed in these devices. This work is ongoing, and will continue through the final period of this program . Reference 9
Institute of Scientific and Technical Information of China (English)
沈建和; 周哲彦; 余赞平
2009-01-01
In this paper,existence of solutions of third-order differential equationy (t) = f(t,y(t),y'(t),y"(t))with nonlinear three-point boundary condition g(y(a),y'(a),y"(a)) = 0,h(y(b),y'(b))=0,I(y(c),y'(c),y"(c)) = 0is obtained by embedding Leray-Schauder degree theory in upper and lower solutions method,where a,b,c ∈ R,a < b< c; f:[a,c] × R3a → R,g:R3 → R,h:R2→R and I:R3 → Rare continuous functions.The existence result is obtained by defining the suitable upper and lower solutions and introducing an appropriate auxiliary boundary value problem.As an application,an example with an explicit solution is given to demonstrate the validity of the results in this paper.
On some nonlinear potential problems
Directory of Open Access Journals (Sweden)
M. A. Efendiev
1999-05-01
Full Text Available The degree theory of mappings is applied to a two-dimensional semilinear elliptic problem with the Laplacian as principal part subject to a nonlinear boundary condition of Robin type. Under some growth conditions we obtain existence. The analysis is based on an equivalent coupled system of domain--boundary variational equations whose principal parts are the Dirichlet bilinear form in the domain and the single layer potential bilinear form on the boundary, respectively. This system consists of a monotone and a compact part. Additional monotonicity implies convergence of an appropriate Richardson iteration.
Nayfeh, Ali Hasan
1995-01-01
Nonlinear Oscillations is a self-contained and thorough treatment of the vigorous research that has occurred in nonlinear mechanics since 1970. The book begins with fundamental concepts and techniques of analysis and progresses through recent developments and provides an overview that abstracts and introduces main nonlinear phenomena. It treats systems having a single degree of freedom, introducing basic concepts and analytical methods, and extends concepts and methods to systems having degrees of freedom. Most of this material cannot be found in any other text. Nonlinear Oscillations uses sim
Yoshida, Zensho
2010-01-01
This book gives a general, basic understanding of the mathematical structure "nonlinearity" that lies in the depths of complex systems. Analyzing the heterogeneity that the prefix "non" represents with respect to notions such as the linear space, integrability and scale hierarchy, "nonlinear science" is explained as a challenge of deconstruction of the modern sciences. This book is not a technical guide to teach mathematical tools of nonlinear analysis, nor a zoology of so-called nonlinear phenomena. By critically analyzing the structure of linear theories, and cl
Nanda, Sudarsan
2013-01-01
"Nonlinear analysis" presents recent developments in calculus in Banach space, convex sets, convex functions, best approximation, fixed point theorems, nonlinear operators, variational inequality, complementary problem and semi-inner-product spaces. Nonlinear Analysis has become important and useful in the present days because many real world problems are nonlinear, nonconvex and nonsmooth in nature. Although basic concepts have been presented here but many results presented have not appeared in any book till now. The book could be used as a text for graduate students and also it will be useful for researchers working in this field.
Discrete dissipative localized modes in nonlinear magnetic metamaterials.
Rosanov, Nikolay N; Vysotina, Nina V; Shatsev, Anatoly N; Shadrivov, Ilya V; Powell, David A; Kivshar, Yuri S
2011-12-19
We analyze the existence, stability, and propagation of dissipative discrete localized modes in one- and two-dimensional nonlinear lattices composed of weakly coupled split-ring resonators (SRRs) excited by an external electromagnetic field. We employ the near-field interaction approach for describing quasi-static electric and magnetic interaction between the resonators, and demonstrate the crucial importance of the electric coupling, which can completely reverse the sign of the overall interaction between the resonators. We derive the effective nonlinear model and analyze the properties of nonlinear localized modes excited in one-and two-dimensional lattices. In particular, we study nonlinear magnetic domain walls (the so-called switching waves) separating two different states of nonlinear magnetization, and reveal the bistable dependence of the domain wall velocity on the external field. Then, we study two-dimensional localized modes in nonlinear lattices of SRRs and demonstrate that larger domains may experience modulational instability and splitting.
Shin, Jaemin; Lee, Hyun Geun; Lee, June-Yub
2016-12-01
The phase-field crystal equation derived from the Swift-Hohenberg energy functional is a sixth order nonlinear equation. We propose numerical methods based on a new convex splitting for the phase-field crystal equation. The first order convex splitting method based on the proposed splitting is unconditionally gradient stable, which means that the discrete energy is non-increasing for any time step. The second order scheme is unconditionally weakly energy stable, which means that the discrete energy is bounded by its initial value for any time step. We prove mass conservation, unique solvability, energy stability, and the order of truncation error for the proposed methods. Numerical experiments are presented to show the accuracy and stability of the proposed splitting methods compared to the existing other splitting methods. Numerical tests indicate that the proposed convex splitting is a good choice for numerical methods of the phase-field crystal equation.
Beam splitting on weak illumination.
Snyder, A W; Buryak, A V; Mitchell, D J
1998-01-01
We demonstrate, in both two and three dimensions, how a self-guided beam in a non-Kerr medium is split into two beams on weak illumination. We also provide an elegant physical explanation that predicts the universal character of the observed phenomenon. Possible applications of our findings to guiding light with light are also discussed.
Kish, J.
1991-01-01
Geared drive train transmits torque from input shaft in equal parts along two paths in parallel, then combines torques in single output shaft. Scheme reduces load on teeth of meshing gears while furnishing redundancy to protect against failures. Such splitting and recombination of torques common in design of turbine engines.
Water splitting by cooperative catalysis
D.G.H. Hetterscheid; J.I. van der Vlugt; B. de Bruin; J.N.H. Reek
2009-01-01
A mononuclear Ru complex is shown to efficiently split water into H2 and O2 in consecutive steps through a heat- and light-driven process (see picture). Thermally driven H2 formation involves the aid of a non-innocent ligand scaffold, while dioxygen is generated by initial photochemically induced re
DEFF Research Database (Denmark)
Neergaard, Ulla; Nielsen, Ruth
2010-01-01
This article builds on the results obtained in the so-called Blurring Boundaries project which was undertaken at the Law Department, Copenhagen Business School, in the period from 2007 to 2009. It looks at the sustainability of the Danish welfare state in an EU law context and on the integration ...
DEFF Research Database (Denmark)
Aarhus, Rikke; Ballegaard, Stinne Aaløkke
2010-01-01
To move treatment successfully from the hospital to that of technology assisted self-care at home, it is vital in the design of such technologies to understand the setting in which the health IT should be used. Based on qualitative studies we find that people engage in elaborate boundary work to ...
Solving Fluid Structure Interaction Problems with an Immersed Boundary Method
Barad, Michael F.; Brehm, Christoph; Kiris, Cetin C.
2016-01-01
An immersed boundary method for the compressible Navier-Stokes equations can be used for moving boundary problems as well as fully coupled fluid-structure interaction is presented. The underlying Cartesian immersed boundary method of the Launch Ascent and Vehicle Aerodynamics (LAVA) framework, based on the locally stabilized immersed boundary method previously presented by the authors, is extended to account for unsteady boundary motion and coupled to linear and geometrically nonlinear structural finite element solvers. The approach is validated for moving boundary problems with prescribed body motion and fully coupled fluid structure interaction problems. Keywords: Immersed Boundary Method, Higher-Order Finite Difference Method, Fluid Structure Interaction.
Wright, Marvin N; Dankowski, Theresa; Ziegler, Andreas
2017-04-15
The most popular approach for analyzing survival data is the Cox regression model. The Cox model may, however, be misspecified, and its proportionality assumption may not always be fulfilled. An alternative approach for survival prediction is random forests for survival outcomes. The standard split criterion for random survival forests is the log-rank test statistic, which favors splitting variables with many possible split points. Conditional inference forests avoid this split variable selection bias. However, linear rank statistics are utilized by default in conditional inference forests to select the optimal splitting variable, which cannot detect non-linear effects in the independent variables. An alternative is to use maximally selected rank statistics for the split point selection. As in conditional inference forests, splitting variables are compared on the p-value scale. However, instead of the conditional Monte-Carlo approach used in conditional inference forests, p-value approximations are employed. We describe several p-value approximations and the implementation of the proposed random forest approach. A simulation study demonstrates that unbiased split variable selection is possible. However, there is a trade-off between unbiased split variable selection and runtime. In benchmark studies of prediction performance on simulated and real datasets, the new method performs better than random survival forests if informative dichotomous variables are combined with uninformative variables with more categories and better than conditional inference forests if non-linear covariate effects are included. In a runtime comparison, the method proves to be computationally faster than both alternatives, if a simple p-value approximation is used. Copyright © 2017 John Wiley & Sons, Ltd.
Directory of Open Access Journals (Sweden)
D. Diederen
2015-06-01
Full Text Available We present a new equation describing the hydrodynamics in infinitely long tidal channels (i.e., no reflection under the influence of oceanic forcing. The proposed equation is a simple relationship between partial derivatives of water level and velocity. It is formally derived for a progressive wave in a frictionless, prismatic, tidal channel with a horizontal bed. Assessment of a large number of numerical simulations, where an open boundary condition is posed at a certain distance landward, suggests that it can also be considered accurate in the more natural case of converging estuaries with nonlinear friction and a bed slope. The equation follows from the open boundary condition and is therefore a part of the problem formulation for an infinite tidal channel. This finding provides a practical tool for evaluating tidal wave dynamics, by reconstructing the temporal variation of the velocity based on local observations of the water level, providing a fully local open boundary condition and allowing for local friction calibration.
Quasiclassical Theory of Twin Boundaries in High-Tc Superconductors
Belzig, Wolfgang; Bruder, Christoph; Sigrist, Manfred
1998-01-01
We investigate the electronic structure of twin boundaries in orthorhombically distorted high-T$_c$ materials using the quasiclassical theory of superconductivity. At low temperatures we find a local instability to a time-reversal symmetry breaking state at the twin boundary. This state yields spontaneous currents along the twin boundary that are microscopically explained by the structure of the quasiparticle bound states. We calculate the local density of states and find a splitting in the z...
2011-12-09
... Bureau of Land Management Notice of Administrative Boundary Change for Bureau of Land Management Offices in Montana To Eliminate the County Split of Lewis and Clark County AGENCY: Bureau of Land Management... changed. The administrative boundary change will realign Lewis and Clark County, currently a split...
Transistor-based metamaterials with dynamically tunable nonlinear susceptibility
Barrett, John P.; Katko, Alexander R.; Cummer, Steven A.
2016-08-01
We present the design, analysis, and experimental demonstration of an electromagnetic metamaterial with a dynamically tunable effective nonlinear susceptibility. Split-ring resonators loaded with transistors are shown theoretically and experimentally to act as metamaterials with a second-order nonlinear susceptibility that can be adjusted through the use of a bias voltage. Measurements confirm that this allows for the design of a nonlinear metamaterial with adjustable mixing efficiency.
Development of new flux splitting schemes. [computational fluid dynamics algorithms
Liou, Meng-Sing; Steffen, Christopher J., Jr.
1992-01-01
Maximizing both accuracy and efficiency has been the primary objective in designing a numerical algorithm for computational fluid dynamics (CFD). This is especially important for solutions of complex three dimensional systems of Navier-Stokes equations which often include turbulence modeling and chemistry effects. Recently, upwind schemes have been well received for their capability in resolving discontinuities. With this in mind, presented are two new flux splitting techniques for upwind differencing. The first method is based on High-Order Polynomial Expansions (HOPE) of the mass flux vector. The second new flux splitting is based on the Advection Upwind Splitting Method (AUSM). The calculation of the hypersonic conical flow demonstrates the accuracy of the splitting in resolving the flow in the presence of strong gradients. A second series of tests involving the two dimensional inviscid flow over a NACA 0012 airfoil demonstrates the ability of the AUSM to resolve the shock discontinuity at transonic speed. A third case calculates a series of supersonic flows over a circular cylinder. Finally, the fourth case deals with tests of a two dimensional shock wave/boundary layer interaction.
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.
Nonlinear second order elliptic equations involving measures
Marcus, Moshe
2013-01-01
This book presents a comprehensive study of boundary value problems for linear and semilinear second order elliptic equations with measure data,especially semilinear equations with absorption. The interactions between the diffusion operator and the absorption term give rise to a large class of nonlinear phenomena in the study of which singularities and boundary trace play a central role.
Shear wave splitting and subcontinental mantle deformation
Silver, Paul G.; Chan, W. Winston
1991-09-01
We have made measurements of shear wave splitting in the phases SKS and SKKS at 21 broadband stations in North America, South America, Europe, Asia, and Africa. Measurements are made using a retrieval scheme that yields the azimuth of the fast polarization direction ϕ and delay time δt of the split shear wave plus uncertainties. Detectable anisotropy was found at most stations, suggesting that it is a general feature of the subcontinental mantle. Delay times range from 0.65 s to 1.70 s and average about 1 s. Somewhat surprisingly, the largest delay time is found in the 2.7 b.y.-old Western Superior Province of the Canadian Shield. The splitting observations are interpreted in terms of the strain-induced lattice preferred orientation of mantle minerals, especially olivine. We consider three hypotheses concerning the origin of the continental anisotropy: (1) strain associated with absolute plate motion, as in the oceanic upper mantle, (2) crustal stress, and (3) the past and present internal deformation of the subcontinental upper mantle by tectonic episodes. It is found that the last hypothesis is the most successful, namely that the most recent significant episode of internal deformation appears to be the best predictor of ϕ. For stable continental regions, this is interpreted as "fossil" anisotropy, whereas for presently active regions, such as Alaska, the anisotropy reflects present-day tectonic activity. In the stable portion of North America there is a good correlation between delay time and lithospheric thickness; this is consistent with the anisotropy being localized in the subcontinental lithosphere and suggests that intrinsic anisotropy is approximately constant. The acceptance of this hypothesis has several implications for subcontinental mantle deformation. First, it argues for coherent deformation of the continental lithosphere (crust and mantle) during orogenies. This implies that the anisotropic portion of the lithosphere was present since the
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.
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...
Small-amplitude excitations in a deformable discrete nonlinear Schrödinger equation
Konotop, V V
1996-01-01
A detailed analysis of the small-amplitude solutions of a deformed discrete nonlinear Schrödinger equation is performed. For generic deformations the system possesses "singular" points which split the infinite chain in a number of independent segments. We show that small-amplitude dark solitons in the vicinity of the singular points are described by the Toda-lattice equation while away from the singular points are described by the Korteweg-de Vries equation. Depending on the value of the deformation parameter and of the background level several kinds of solutions are possible. In particular we delimit the regions in the parameter space in which dark solitons are stable in contrast with regions in which bright pulses on nonzero background are possible. On the boundaries of these regions we find that shock waves and rapidly spreading solutions may exist.
Nonlinear mechanics of thin-walled structures asymptotics, direct approach and numerical analysis
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...
Conformal structure-preserving method for damped nonlinear Schrödinger equation
Fu, Hao; Zhou, Wei-En; Qian, Xu; Song, Song-He; Zhang, Li-Ying
2016-11-01
In this paper, we propose a conformal momentum-preserving method to solve a damped nonlinear Schrödinger (DNLS) equation. Based on its damped multi-symplectic formulation, the DNLS system can be split into a Hamiltonian part and a dissipative part. For the Hamiltonian part, the average vector field (AVF) method and implicit midpoint method are employed in spatial and temporal discretizations, respectively. For the dissipative part, we can solve it exactly. The proposed method conserves the conformal momentum conservation law in any local time-space region. With periodic boundary conditions, this method also preserves the total conformal momentum and the dissipation rate of momentum exactly. Numerical experiments are presented to demonstrate the conservative properties of the proposed method. Project supported by the National Natural Science Foundation of China (Grant Nos. 11571366, 11501570, and 11601514) and the Open Foundation of State Key Laboratory of High Performance Computing of China (Grant No. JC15-02-02).
A Cauchy problem in nonlinear heat conduction
Energy Technology Data Exchange (ETDEWEB)
De Lillo, S [Istituto Nazionale di Fisica Nucleare, Sezione di Perugia, Perugia (Italy); Lupo, G [Dipartimento di Matematica e Informatica, Universita degli Studi di Perugia, Via Vanvitelli, 1, 06123 Perugia (Italy); Sanchini, G [Istituto Nazionale di Fisica Nucleare, Sezione di Perugia, Perugia (Italy)
2006-06-09
A Cauchy problem on the semiline for a nonlinear diffusion equation is considered, with a boundary condition corresponding to a prescribed thermal conductivity at the origin. The problem is mapped into a moving boundary problem for the linear heat equation with a Robin-type boundary condition. Such a problem is then reduced to a linear integral Volterra equation of II type which admits a unique solution.
DEFF Research Database (Denmark)
Brodkin, Evelyn; Larsen, Flemming
2013-01-01
In recent decades, workfare-style policies have become part of the institutional architecture of welfare and labor market arrangements around the world. In this article, we offer a comparative, historical view of workfare´s advance. Our analysis recognizes the complexity and diversity of what we...... call the “policies of workfare” and highlights the different paths through which these policies have developed in the U.S. and parts of Europe. We argue that it is necessary to look beyond familiar policy labels and language in order to consider workfare-style policies as part of a broader political...... project that is altering the boundary between the democratic welfare state and the market economy. We see workfare policies as boundary-changing with potentially profound implications both for individuals disadvantaged by market arrangements and for societies seeking to grapple with the increasing...
Dirac and Maxwell equations in Split Octonions
Beradze, Revaz
2016-01-01
The split octonionic form of Dirac and Maxwell equations are found. In contrast with the previous attempts these equations are derived from the octonionic analyticity condition and also we use different basis of the 8-dimensional space of split octonions.
Interpretation and inverse analysis of the wedge splitting test
DEFF Research Database (Denmark)
Østergaard, Lennart; Stang, Henrik
2002-01-01
Determination of the stress-crack opening relationship, s(w) a material parameter in the fictitious crack model by Hillerborg has proven to be problematic and is still not a simple task to perform. However, this paper demonstrates that the cracked non-linear hinge model by Olesen may be applied...... to the wedge splitting test and that it is well suited for the interpretation of test results in terms of s(w). A fine agreement between the hinge and FEM-models has been found. It has also been found that the test and the hinge model form a solid basis for inverse analysis. The paper also discusses possible...
Combined algorithms in nonlinear problems of magnetostatics
Energy Technology Data Exchange (ETDEWEB)
Gregus, M.; Khoromsky, B.N.; Mazurkevich, G.E.; Zhidkov, E.P.
1988-05-09
To solve boundary problems of magnetostatics in unbounded two- or 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 in nonlinear magnetostatic problems without the preliminary discretization of equations and give some results on the convergence of iterative processes that arise in nonlinear 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.
Institute of Scientific and Technical Information of China (English)
Zhen Zhen LI; Xiao Jiang GUO; Zhi Qing FU
2012-01-01
A left GC-lpp semigroup S is called split if the natural homomorphism γb of S onto S/γ induced by γ is split.It is proved that a left GC-lpp semigroup is split if and only if it has a left adequate transversal.In particular,a construction theorem for split left GC-lpp semigroups is established.
ON THE EXISTENCE AND UNIQUENESS OFSOLUTIONS FOR 2nTH-ORDER BOUNDARY VALUE PROBLEMS
Institute of Scientific and Technical Information of China (English)
PeiMinghe; SungKagChang
2005-01-01
In this paper, by using the Leray-Schauder continuation theorem, we establish the existence and uniqueness theorems of solutions of two-point boundary value problems for 2nth-order nonlinear differential equations with nonlinear growth.
2010-01-01
... 7 Agriculture 2 2010-01-01 2010-01-01 false Split shell. 51.2002 Section 51.2002 Agriculture... Standards for Grades of Filberts in the Shell 1 Definitions § 51.2002 Split shell. Split shell means a shell... of the shell, measured in the direction of the crack....
Split NMSSM with electroweak baryogenesis
Demidov, S V; Kirpichnikov, D V
2016-01-01
In light of the Higgs boson discovery we reconsider generation of the baryon asymmetry in the non-minimal split Supersymmetry model with an additional singlet superfield in the Higgs sector. We find that successful baryogenesis during the first order electroweak phase transition is possible within phenomenologically viable part of the model parameter space. We discuss several phenomenological consequences of this scenario, namely, predictions for the electric dipole moments of electron and neutron and collider signatures of light charginos and neutralinos.
The Split Variational Inequality Problem
Censor, Yair; Reich, Simeon
2010-01-01
We propose a new variational problem which we call the Split Variational Inequality Problem (SVIP). It entails finding a solution of one Variational Inequality Problem (VIP), the image of which under a given bounded linear transformation is a solution of another VIP. We construct iterative algorithms that solve such problems, under reasonable conditions, in Hilbert space and then discuss special cases, some of which are new even in Euclidean space.
Torsional Split Hopkinson Bar Optimization
2012-04-10
pillow blocks used to mount the incident and transmitter bars are cast iron based- mounted Babbitt -lined bearing split, for 1 in. shaft diameter...Total 1 McMaster-CARR 5911k16 1" Dia, 6" long anodized aluminum shaft $15.38 8 $123.04 2 McMaster-CARR 6359k37 Cast iron base-mounted babbitt
On the Splitting Algorithm Based on Multi-target Model for Image Segmentation
Yuezhongyi Sun
2014-01-01
Against to the different regions of membership functions indicated image in the traditional image segmentation variational model, resulting segmentation is not clear, de-noising effect is not obvious problems, this paper proposes multi-target model for image segmentation and the splitting algorithm. The model uses a sparse regularization method to maintain the boundaries of segmented regions, to overcome the disadvantages of segmentation fuzzy boundaries resulting from total variation regular...
Zhu, Hong-Ming; Pen, Ue-Li; Chen, Xuelei; Yu, Hao-Ran
2016-01-01
We present a direct approach to non-parametrically reconstruct the linear density field from an observed non-linear map. We solve for the unique displacement potential consistent with the non-linear density and positive definite coordinate transformation using a multigrid algorithm. We show that we recover the linear initial conditions up to $k\\sim 1\\ h/\\mathrm{Mpc}$ with minimal computational cost. This reconstruction approach generalizes the linear displacement theory to fully non-linear fields, potentially substantially expanding the BAO and RSD information content of dense large scale structure surveys, including for example SDSS main sample and 21cm intensity mapping.
Boyd, Robert W
2013-01-01
Nonlinear Optics is an advanced textbook for courses dealing with nonlinear optics, quantum electronics, laser physics, contemporary and quantum optics, and electrooptics. Its pedagogical emphasis is on fundamentals rather than particular, transitory applications. As a result, this textbook will have lasting appeal to a wide audience of electrical engineering, physics, and optics students, as well as those in related fields such as materials science and chemistry.Key Features* The origin of optical nonlinearities, including dependence on the polarization of light* A detailed treatment of the q
Group invariance in engineering boundary value problems
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...
Geometrical Applications of Split Octonions
Directory of Open Access Journals (Sweden)
Merab Gogberashvili
2015-01-01
Full Text Available It is shown that physical signals and space-time intervals modeled on split-octonion geometry naturally exhibit properties from conventional (3 + 1-theory (e.g., number of dimensions, existence of maximal velocities, Heisenberg uncertainty, and particle generations. This paper demonstrates these properties using an explicit representation of the automorphisms on split-octonions, the noncompact form of the exceptional Lie group G2. This group generates specific rotations of (3 + 4-vector parts of split octonions with three extra time-like coordinates and in infinitesimal limit imitates standard Poincare transformations. In this picture translations are represented by noncompact Lorentz-type rotations towards the extra time-like coordinates. It is shown how the G2 algebra’s chirality yields an intrinsic left-right asymmetry of a certain 3-vector (spin, as well as a parity violating effect on light emitted by a moving quantum system. Elementary particles are connected with the special elements of the algebra which nullify octonionic intervals. Then the zero-norm conditions lead to free particle Lagrangians, which allow virtual trajectories also and exhibit the appearance of spatial horizons governing by mass parameters.
Testing split supersymmetry with inflation
Craig, Nathaniel; Green, Daniel
2014-07-01
Split supersymmetry (SUSY) — in which SUSY is relevant to our universe but largely inaccessible at current accelerators — has become increasingly plausible given the absence of new physics at the LHC, the success of gauge coupling unification, and the observed Higgs mass. Indirect probes of split SUSY such as electric dipole moments (EDMs) and flavor violation offer hope for further evidence but are ultimately limited in their reach. Inflation offers an alternate window into SUSY through the direct production of superpartners during inflation. These particles are capable of leaving imprints in future cosmological probes of primordial non-gaussianity. Given the recent observations of BICEP2, the scale of inflation is likely high enough to probe the full range of split SUSY scenarios and therefore offers a unique advantage over low energy probes. The key observable for future experiments is equilateral non-gaussianity, which will be probed by both cosmic microwave background (CMB) and large scale structure (LSS) surveys. In the event of a detection, we forecast our ability to find evidence for superpartners through the scaling behavior in the squeezed limit of the bispectrum.
Directory of Open Access Journals (Sweden)
DJAIRO G. DEFIGUEIREDO
2000-12-01
Full Text Available In this paper we treat the question of the existence of solutions of boundary value problems for systems of nonlinear elliptic equations of the form - deltau = f (x, u, v,Ñu,Ñv, - deltav = g(x, u, v, Ñu, Ñv, in omega, We discuss several classes of such systems using both variational and topological methods. The notion of criticality takes into consideration the coupling, which plays important roles in both a priori estimates for the solutions and Palais-Smale conditions for the associated functional in the variational case.
Device Applications of Nonlinear Dynamics
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.
Townsend, Alan R.; Porder, Stephen
2011-03-01
What is our point of no return? Caesar proclaimed 'the die is cast' while crossing the Rubicon, but rarely does modern society find so visible a threshold in our continued degradation of ecosystems and the services they provide. Humans have always used their surroundings to make a living— sometimes successfully, sometimes not (Diamond 2005)—and we intuitively know that there are boundaries to our exploitation. But defining these boundaries has been a challenge since Malthus first prophesied that nature would limit the human population (Malthus 1798). In 2009, Rockström and colleagues tried to quantify what the 6.8 billion (and counting) of us could continue to get away with, and what we couldn't (Rockström et al 2009). In selecting ten 'planetary boundaries', the authors contend that a sustainable human enterprise requires treating a number of environmental thresholds as points of no return. They suggest we breach these Rubicons at our own peril, and that we've already crossed three: biodiversity loss, atmospheric CO2, and disruption of the global nitrogen (N) cycle. As they clearly hoped, the very act of setting targets has provoked scientific inquiry about their accuracy, and about the value of hard targets in the first place (Schlesinger 2009). Such debate is a good thing. Despite recent emphasis on the science of human-ecosystem interactions, understanding of our planetary boundaries is still in its infancy, and controversy can speed scientific progress (Engelhardt and Caplan 1987). A few weeks ago in this journal, Carpenter and Bennett (2011) took aim at one of the more controversial boundaries in the Rockström analysis: that for human alteration of the global phosphorus (P) cycle. Rockström's group chose riverine P export as the key indicator, suggesting that humans should not exceed a value that could trigger widespread marine anoxic events—and asserting that we have not yet crossed this threshold. There are defensible reasons for a marine
Directory of Open Access Journals (Sweden)
Mehmet Camurdan
1998-01-01
are coupled by appropriate trace operators. This overall model differs from those previously studied in the literature in that the elastic chamber floor is here more realistically modeled by a hyperbolic Kirchoff equation, rather than by a parabolic Euler-Bernoulli equation with Kelvin-Voight structural damping, as in past literature. Thus, the hyperbolic/parabolic coupled system of past literature is replaced here by a hyperbolic/hyperbolic coupled model. The main result of this paper is a uniform stabilization of the coupled PDE system by a (physically appealing boundary dissipation.
Ruszczynski, Andrzej
2011-01-01
Optimization is one of the most important areas of modern applied mathematics, with applications in fields from engineering and economics to finance, statistics, management science, and medicine. While many books have addressed its various aspects, Nonlinear Optimization is the first comprehensive treatment that will allow graduate students and researchers to understand its modern ideas, principles, and methods within a reasonable time, but without sacrificing mathematical precision. Andrzej Ruszczynski, a leading expert in the optimization of nonlinear stochastic systems, integrates t
Alternating tip splitting in directional solidification.
Utter, B; Ragnarsson, R; Bodenschatz, E
2001-05-14
We report experimental results on the tip splitting dynamics of seaweed growth in directional solidification of succinonitrile alloys. Despite the random appearance of the growth, a tip splitting morphology was observed in which the tip alternately splits to the left and to the right. The tip splitting frequency f was found to be related to the growth velocity V as a power law f~V1.5. This finding is consistent with the predictions of a tip splitting model that is also presented. Small anisotropies are shown to lead to different kinds of seaweed morphologies.
Lanser, D.; Verwer, J.G.
1998-01-01
Operator or time splitting is often used in the numerical solution of initial boundary value problems for differential equations. It is, for example, standard practice in computational air pollution modelling where we encounter systems of three-dimensional, time-dependent partial differential equati
Nonlinear terahertz metamaterials with active electrical control
Keiser, G. R.; Karl, N.; Liu, P. Q.; Tulloss, C.; Chen, H.-T.; Taylor, A. J.; Brener, I.; Reno, J. L.; Mittleman, D. M.
2017-09-01
We present a study of an electrically modulated nonlinear metamaterial consisting of an array of split-ring resonators fabricated on n-type gallium arsenide. The resonant metamaterial nonlinearity appears as an intensity-dependent transmission minimum at terahertz frequencies and arises from the interaction between local electric fields in the split-ring resonator (SRR) capacitive gaps and charge carriers in the n-type substrate. We investigate the active tuning range of the metamaterial device as the incident terahertz field intensity is increased and conversely the effect of an applied DC bias on the terahertz field-induced nonlinear modulation of the metamaterial response. Applying a DC bias to the metamaterial sample alters the nonlinear response and reduces the net nonlinear modulation. Similarly, increasing the incident terahertz field intensity decreases the net modulation induced by an applied DC bias. We interpret these results in terms of DC and terahertz-field-assisted carrier acceleration, scattering, and multiplication processes, highlighting the unique nature of this DC-field modulated terahertz nonlinearity.
Planetary boundaries: Governing emerging risks and opportunities
2016-01-01
The climate, ecosystems and species, ozone layer, acidity of the oceans, the flow of energy and elements through nature, landscape change, freshwater systems, aerosols, and toxins—these constitute the planetary boundaries within which humanity must find a safe way to live and prosper. These are thresholds that, if we cross them, we run the risk of rapid, non-linear, and irreversible changes to the environment, with severe consequences for human wellbeing. The concept of planetary boundaries, ...
All passive photonic power divider with arbitrary split ratio
Xu, Ke; Wen, Xiang; Sun, Wenzhao; Zhang, Nan; Yi, Ningbo; Sun, Shang; Xiao, Shumin; Song, Qinghai
2016-01-01
Integrated optical power splitter is one of the fundamental building blocks in photonic integrated circuits (PIC). Conventional multimode interferometer based power splitter is widely used as it has reasonable footprint and is easy to fabricate. However, it is challenging to realize arbitrary split ratio especially for multi-outputs. In this work, an ultra-compact power splitter with a QR code-like nanostructure is designed by a nonlinear fast search method (FSM). The highly functional structure is composed of a number of freely designed square pixels with the size of 120nm x 120nm which could be either dielectric or air. The lightwaves are scattered by a number of etched squares with optimized locations and the scattered waves superimpose at the outputs with the desired power ratio. We demonstrate 1x2 splitters with 1:1, 1:2, 1:3 split ratios and a 1x3 splitter with the ratio of 1:2:1. The footprint for all the devices is only 3.6umx3.6 um. Well-controlled split ratios are measured for all the cases. The mea...
Spontaneous symmetry breaking in a split potential box
Shamriz, Elad; Malomed, Boris A
2016-01-01
We report results of the analysis of the spontaneous symmetry breaking (SSB) in the basic (actually, simplest) model which is capable to produce the SSB phenomenology in the one-dimensional setting. It is based on the Gross-Pitaevskii - nonlinear Schroedinger equation with the cubic self-attractive term and a double-well-potential built as an infinitely deep potential box split by a narrow (delta-functional) barrier. The barrier's strength, epsilon, is the single free parameter of the scaled form of the model. It may be implemented in atomic Bose-Einstein condensates and nonlinear optics. The SSB bifurcation of the symmetric ground state (GS) is predicted analytically in two limit cases, viz., for deep or weak splitting of the potential box by the barrier. For the generic case, a variational approximation (VA) is elaborated. The analytical findings are presented along with systematic numerical results. Stability of stationary states is studied through the calculation of eigenvalues for small perturbations, an...
Energy Technology Data Exchange (ETDEWEB)
Campbell, L.M. [EnCana Corp., Calgary, AB (Canada); Laurin, W.
2006-07-01
Coalbed methane (CBM) coal underlies most of central and southern Alberta. This article discussed disputes surrounding CBM ownership and split-titles. Historically, ownership of lands in Alberta implied possession and rights of all under- and overground substances. Surface estates are now typically separated from the subsurface estate, and subsurface estates are further divided either on the basis of substances or stratigraphically to create a split-title. Mineral severances are used to separate respective mineral rights among owners. While there is a relative certainty that under provincial Crown tenure CBM is included in natural gas tenure, there is currently no Canadian jurisprudence in respect of CBM entitlement on split-title private lands. Where compressed natural gas (CNG) and coal are separately held, and CBM ownership is not specifically addressed in the mineral severance, there is no Canadian law respecting CBM ownership. Resolution of ownership issues has proceeded on a case by case basis. Coal owners argue that there is a distinct interrelationship between CBM and its host coal strata. Gas owners argue that the chemical composition of CBM is identical to CNG, and that the recovery method is similar to that of CNG. Courts have historically applied the vernacular test to resolve mineral substance ownership disputes, which considers the meanings of the word coal and coalbed methane as defined by industry. The most recent and relevant application of the vernacular test were the Borys/Anderson, which effectively implemented a gas-oil interface ownership determination, which if applied to a coal grant or reservation, may lead to the conclusion that the coal strata includes CBM. It was concluded that there are 26,000 individual mineral owners in Alberta that may become involved in CBM litigation. and could become parties to litigation. refs., tabs., figs.
Partitions of generalized split graphs
Shklarsky, Oren
2012-01-01
We discuss matrix partition problems for graphs that admit a partition into k independent sets and ` cliques. We show that when k + ` 6 2, any matrix M has finitely many (k; `) minimal obstructions and hence all of these problems are polynomial time solvable. We provide upper bounds for the size of any (k; `) minimal obstruction when k = ` = 1 (split graphs), when k = 2; ` = 0 (bipartite graphs), and when k = 0; ` = 2 (co-bipartite graphs). When k = ` = 1, we construct an exponential size spl...
Generalized Forward-Backward Splitting
2011-01-01
International audience; This paper introduces a generalized forward-backward splitting algorithm for finding a zero of a sum of maximal monotone operators $B + \\sum_{i=1}^{n} A_i$, where $B$ is cocoercive. It involves the computation of $B$ in an explicit (forward) step and of the parallel computation of the resolvents of the $A_i$'s in a subsequent implicit (backward) step. We prove its convergence in infinite dimension, and robustness to summable errors on the computed operators in the expl...
Positive solutions of some nonlocal boundary value problems
Directory of Open Access Journals (Sweden)
Gennaro Infante
2003-01-01
employed. In particular, we do not require all the parameters occurring in the boundary conditions to be positive. Our results allow more general behaviour for the nonlinear term than being either sub- or superlinear.
BOUNDARY VALUE PROBLEM TO DYNAMIC EQUATION ON TIME SCALE
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
In this paper we consider a nonlinear first-order boundary value problem on a time scale. The existence results of three positive solutions are obtained using fixed point theorems. Finally,examples are presented to illustrate the main results.
Boundary value problems for partial differential equations with exponential dichotomies
Laederich, Stephane
We are extending the notion of exponential dichotomies to partial differential evolution equations on the n-torus. This allows us to give some simple geometric criteria for the existence of solutions to certain nonlinear Dirichlet boundary value problems.
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.
In, Visarath; Longhini, Patrick; Kho, Andy; Neff, Joseph D.; Leung, Daniel; Liu, Norman; Meadows, Brian K.; Gordon, Frank; Bulsara, Adi R.; Palacios, Antonio
2012-12-01
The nonlinear channelizer is an integrated circuit made up of large parallel arrays of analog nonlinear oscillators, which, collectively, serve as a broad-spectrum analyzer with the ability to receive complex signals containing multiple frequencies and instantaneously lock-on or respond to a received signal in a few oscillation cycles. The concept is based on the generation of internal oscillations in coupled nonlinear systems that do not normally oscillate in the absence of coupling. In particular, the system consists of unidirectionally coupled bistable nonlinear elements, where the frequency and other dynamical characteristics of the emergent oscillations depend on the system's internal parameters and the received signal. These properties and characteristics are being employed to develop a system capable of locking onto any arbitrary input radio frequency signal. The system is efficient by eliminating the need for high-speed, high-accuracy analog-to-digital converters, and compact by making use of nonlinear coupled systems to act as a channelizer (frequency binning and channeling), a low noise amplifier, and a frequency down-converter in a single step which, in turn, will reduce the size, weight, power, and cost of the entire communication system. This paper covers the theory, numerical simulations, and some engineering details that validate the concept at the frequency band of 1-4 GHz.
The Efficiency of Split Panel Designs in an Analysis of Variance Model
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
Directory of Open Access Journals (Sweden)
S. Zahertar
2015-11-01
Full Text Available In this work, transmission characteristics of rectangular split-ring resonators with single-split and two-splits are analyzed at microwave frequencies. The resonators are coupled with monopole antennas for excitation. The scattering parameters of the devices are investigated under different polarizations of E and H fields. The magnetic resonances induced by E and H fields are identified and the differences in the behavior of the resonators due to orientations of the fields are explained based on simulation and experimental results. The addition of the second split of the device is investigated considering different configurations of the excitation vectors. It is demonstrated that the single-split and the two-splits resonators exhibit identical transmission characteristics for a certain excitation configuration as verified with simulations and experiments. The presented resonators can effectively function as frequency selective media for varying excitation conditions.
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The authors consider the existence of singular limit solutions for a family of nonlinear elliptic problems with exponentially dominated nonlinearity and Dirichlet boundary condition and generalize the results of [3].
Nonlinear Ekman Layer Theories and Their Applications
Institute of Scientific and Technical Information of China (English)
TAN Zhemin; FANG Juan; WU Rongsheng
2006-01-01
Based on the classical Ekman theory, a series of intermediate boundary layer models, which retain the nonlinear advective process while discard embellishments, have been proposed with the intention to understand the complex nonlinear features of the atmospheric boundary layer and its interaction with the free atmosphere. In this paper, the recent advances in the intermediate boundary-layer dynamic models are reviewed. Several intermediate models such as the boundary-layer models incorporating geostrophic momentum approximation, Ekman momentum approximation, and the weak nonlinear Ekman-layer model are a major theme.With inspection of the theoretical frameworks, the physical meaning and the limitations of each intermediate model are discussed. It is found that the qualitative descriptions of the nonlinear nature in Ekman layer made by the intermediate models are fairly consistent though the details may be different. As the application of the intermediate models is concerned, the application of the intermediate models to the study of the topographic boundary layer, frontogenesis, low-level frontal structure, and low-level jet are especially summarized in this paper. It is shown that the intermediate boundary-layer models have great potential in illustrating the low-level structures of the weather and climate systems as they are coupled with the free atmospheric models.In addition, the important remaining scientific challenges and a prospectus for future research on the intermediate model are also discussed.
Energy Technology Data Exchange (ETDEWEB)
Turchetti, G. (Bologna Univ. (Italy). Dipt. di Fisica)
1989-01-01
Research in nonlinear dynamics is rapidly expanding and its range of applications is extending beyond the traditional areas of science where it was first developed. Indeed while linear analysis and modelling, which has been very successful in mathematical physics and engineering, has become a mature science, many elementary phenomena of intrinsic nonlinear nature were recently experimentally detected and investigated, suggesting new theoretical work. Complex systems, as turbulent fluids, were known to be governed by intrinsically nonlinear laws since a long time ago, but received purely phenomenological descriptions. The pioneering works of Boltzmann and Poincare, probably because of their intrinsic difficulty, did not have a revolutionary impact at their time; it is only very recently that their message is reaching a significant number of mathematicians and physicists. Certainly the development of computers and computer graphics played an important role in developing geometric intuition of complex phenomena through simple numerical experiments, while a new mathematical framework to understand them was being developed.
Generalized Forward-Backward Splitting
Raguet, Hugo; Peyré, Gabriel
2011-01-01
This paper introduces the generalized forward-backward splitting algorithm for minimizing convex functions of the form $F + \\sum_{i=1}^n G_i$, where $F$ has a Lipschitz-continuous gradient and the $G_i$'s are simple in the sense that their Moreau proximity operators are easy to compute. While the forward-backward algorithm cannot deal with more than $n = 1$ non-smooth function, our method generalizes it to the case of arbitrary $n$. Our method makes an explicit use of the regularity of $F$ in the forward step, and the proximity operators of the $G_i$'s are applied in parallel in the backward step. This allows the generalized forward backward to efficiently address an important class of convex problems. We prove its convergence in infinite dimension, and its robustness to errors on the computation of the proximity operators and of the gradient of $F$. Examples on inverse problems in imaging demonstrate the advantage of the proposed methods in comparison to other splitting algorithms.
Institute of Scientific and Technical Information of China (English)
Chen Daohan; Liu Linzhong; Alan Gilmore
2000-01-01
In combination with the authors previous obsewation about the splitting of Comet Halley in March 1986, the events involving the sharp, straight feature in the antisolar direction observed in the head of Comet Halley in 1910 (such as those occurring on May 14, 25 and 31, and June 2) are rediscussed The analysis leads to the following scenario: When Comet Halley explodes and splits, a fragment jettisoned or thrown off from the nucleus will, after moving in the direction of its tail, develop into a mini-comet. Although not well developed or permanent, it has its own plasma tail and, sometimes, a dust tail. If Bobrovnikoffs definition of a secondary nucleus is assumed, then the fragment should be considered as a real secondary nucleus. It seems that the current idea of a tailward jet suggested by Sekanina and Larson is a wrong explanation for the plasma tail of a mini-comet and hence the rotation period of 52-53h for Comet Halley is doubtful
Institute of Scientific and Technical Information of China (English)
陈道汉; 刘麟仲; Alan Gilmore
1995-01-01
In combination with the authors’ previous observation about the splitting of Comet Halley in March 1986, the events involving the sharp, straight feature in the antisolar direction observed in the bead of Comet Halley in 1910 (such as those occurring on May 14, 25 and 31, and June 2) are rediscussed. The analysis leads to the following scenario: When Comet Halley explodes and splits, a fragment jettisoned or thrown off from the nucleus will, after moving in the direction of its tail, develop into a mini-comet. Although not well developed or permanent, it has its own plasma tail and, sometimes, a dust tail. If Bobrovnikoff’s definition of a secondary nucleus is assumed, then the fragment should be considered as a real secondary nucleus. It seems that the current idea of a tailward jet suggested by Sekanina and Larson is a wrong explanation for the plasma tail of a mini-comet and hence the rotation period of 52- 53 h for Comet Halley is doubtful.
Institute of Scientific and Technical Information of China (English)
杜增吉; 林晓洁; 葛渭高
2005-01-01
This paper is concerned with the following second-order vector boundary value problem:x″=f(t,Sx,x,x′),0＜t＜1,x(0)=A,g(x(1),x′(1))=B,where x,f,g,A and B are n-vectors.Under appropriate assumptions,existence and uniqueness of solutions are obtained by using upper and lower solutions method.
DEFF Research Database (Denmark)
Rasmussen, Christian Jørgen
2001-01-01
Presents a simple and fast method for determination of the step size that exactly leads to a prescribed accuracy when signal propagation through nonlinear optical fibres is computed using the split-step Fourier method.......Presents a simple and fast method for determination of the step size that exactly leads to a prescribed accuracy when signal propagation through nonlinear optical fibres is computed using the split-step Fourier method....
Energy Technology Data Exchange (ETDEWEB)
Jiang, Tongsong, E-mail: jiangtongsong@sina.com [Department of Mathematics, Linyi University, Linyi, Shandong 276005 (China); Department of Mathematics, Heze University, Heze, Shandong 274015 (China); Jiang, Ziwu; Zhang, Zhaozhong [Department of Mathematics, Linyi University, Linyi, Shandong 276005 (China)
2015-08-15
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.