Dynamic Analysis of HSDB System and Evaluation of Boundary Non-linearity through Experiments
Directory of Open Access Journals (Sweden)
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.
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.
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.
Solving Directly Two Point Non Linear Boundary Value Problems Using Direct Adams Moulton Method
Directory of Open Access Journals (Sweden)
Zanariah A. Majid
2011-01-01
Full Text Available Problem statement: In this study, a direct method of Adams Moulton type was developed for solving non linear two point Boundary Value Problems (BVPs directly. Most of the existence researches involving BVPs will reduced the problem to a system of first order Ordinary Differential Equations (ODEs. This approach is very well established but it obviously will enlarge the systems of first order equations. However, the direct method in this research will solved the second order BVPs directly without reducing it to first order ODEs. Approach: Lagrange interpolation polynomial was applied in the derivation of the proposed method. The method was implemented using constant step size via shooting technique in order to determine the approximated solutions. The shooting technique will employ the Newtons method for checking the convergent of the guessing values for the next iteration. Results: Numerical results confirmed that the direct method gave better accuracy and converged faster compared to the existing method. Conclusion: The proposed direct method is suitable for solving two point non linear boundary value problems.
General treatment of the non-linear Rsub(Xi) gauge condition
Energy Technology Data Exchange (ETDEWEB)
Girardi, G.; Malleville, C.; Sorba, P. (Grenoble-1 Univ., 74 - Annecy (France). Lab. de Physique des Particules)
1982-11-04
It is shown that the non-linear Rsub(xi) gauge condition already introduced for the standard SU(2)xU(1) model can be generalized for any gauge model with the same type of simplification, namely the suppression of any coupling of the form: (massless gauge boson)x(massive gauge boson)x(unphysical Higgs).
Non-linear imaging condition to image fractures as non-welded interfaces
Minato, S.; Ghose, R.
2014-01-01
Hydraulic properties of a fractured reservoir are often controlled by large fractures. In order to seismically detect and characterize them, a high-resolution imaging method is necessary. We apply a non-linear imaging condition to image fractures, considered as non-welded interfaces. We derive the i
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.
Annular pupil filter under shot-noise condition for linear and non linear microscopy.
Ronzitti, Emiliano; Vicidomini, Giuseppe; Caorsi, Valentina; Diaspro, Alberto
2009-04-13
The imaging performances of multiphoton excitation and confocal laser scanning microscopy are herby considered: in typical experimental imaging conditions, a small finite amount of photon reaches the detector giving shot-noise fluctuations which affects the signal acquired. A significant detriment in the high frequencies transmission capability is obtained. In order to partially recover the high frequencies information lost, the insertion of a pupil plane filter in the microscope illumination light pathway on the objective lens is proposed. We demonstrate high-frequency and resolution enhancement in the case of linear and non linear fluorescence microscope approach under shot-noise condition.
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
Monitoring Technical Conditions of Engineering Structures Using the Non-Linear Approach
Volkova, V. E.
2015-11-01
Conventional methods of monitoring technical condition are based on detection of damage in the structures of buildings or facilities during the entire period of their operation. In spite of considerable interest displayed to this issue and a significant number of publications, there is no unity of opinions. These methods differ from each other in the sets of values fixed for investigations, the techniques of their recording, transfer and further processing. Today's rules and regulations for structural designs expand the scope of application of the structures operating in the elastic-plastic stage. These damage-free structures originally display the nonlinear properties and can be adequately described only by the non-linear models. This paper presents a method for determining the type and level of non-linearity from the structural oscillations data for monitoring the change in the health of structures. It is shown that a plot of acceleration against the magnitude of the displacement represents the restoring force of a structure. If the structure is damaged during a new striking motion, the phase trajectories in plane “acceleration-displacement” will deviate from its healthy signature.
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.
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
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.
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.
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.
Peri-implantitis: a complex condition with non-linear characteristics
Papantonopoulos, G.H.; Gogos, C.; Housos, E.; Bountis, T.; Loos, B.G.
2015-01-01
Aim To cluster peri-implantitis patients and explore non-linear patterns in peri-implant bone levels. Materials and Methods Clinical and radiographic variables were retrieved from 94 implant-treated patients (340 implants, mean 7.1 ± 4.1 years in function). Kernel probability density estimations on
Peri-implantitis: a complex condition with non-linear characteristics
Papantonopoulos, G.H.; Gogos, C.; Housos, E.; Bountis, T.; Loos, B.G.
2015-01-01
Aim To cluster peri-implantitis patients and explore non-linear patterns in peri-implant bone levels. Materials and Methods Clinical and radiographic variables were retrieved from 94 implant-treated patients (340 implants, mean 7.1 ± 4.1 years in function). Kernel probability density estimations on
Gao, Q. D.; Budny, R. V.
2015-03-01
By using gyro-Landau fluid transport model (GLF23), time-dependent integrated modeling is carried out using TRANSP to explore the dynamic process of internal transport barrier (ITB) formation in the neutral beam heating discharges. When the current profile is controlled by LHCD (lower hybrid current drive), with appropriate neutral beam injection, the nonlinear interplay between the transport determined gradients in the plasma temperature (Ti,e) and toroidal velocity (Vϕ) and the E×B flow shear (including q-profile) produces transport bifurcations, generating spontaneously a stepwise growing ITB. In the discharge, the constraints imposed by the wave propagation condition causes interplay of the LH driven current distribution with the plasma configuration modification, which constitutes non-linearity in the LH wave deposition. The non-linear effects cause bifurcation in LHCD, generating two distinct quasi-stationary reversed magnetic shear configurations. The change of current profile during the transition period between the two quasi-stationary states results in increase of the E×B shearing flow arising from toroidal rotation. The turbulence transport suppression by sheared E×B flow during the ITB development is analysed, and the temporal evolution of some parameters characterized the plasma confinement is examined. Ample evidence shows that onset of the ITB development is correlated with the enhancement of E×B shearing rate caused by the bifurcation in LHCD. It is suggested that the ITB triggering is associated with the non-linear effects of the LH power deposition.
Non-linear Rsub(xi) gauge condition for the electroweak SU(2) x U(1) model
Energy Technology Data Exchange (ETDEWEB)
Gavela, M.B.; Girardi, G.; Malleville, C.; Sorba, P. (Grenoble-1 Univ., 74 - Annecy (France). Lab. de Physique des Particules)
1981-12-21
A non-linear Rsub(zeta) gauge condition is presented and explicitly developed in the framework of the SU(2) x U(1) gauge model. We give the corresponding Feynman rules, which are simpler than in Rsub(xi) gauges, because couplings involving unphysical Higgs and gauge bosons disappear or simplify. The Faddeev-Popov sector is more elegant, the ghosts coupling to neutral gauge bosons like in scalar electrodynamics. Finally, as a practical example, the transition Higgs ..-->.. ..gamma gamma.. is considered and compared with the usual calculation in linear gauges.
Energy Technology Data Exchange (ETDEWEB)
Gao, Q. D., E-mail: qgao@swip.ac.cn [Southwestern Institute of Physics, Chengdu 610041 (China); Budny, R. V. [Princeton Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543 (United States)
2015-03-15
By using gyro-Landau fluid transport model (GLF23), time-dependent integrated modeling is carried out using TRANSP to explore the dynamic process of internal transport barrier (ITB) formation in the neutral beam heating discharges. When the current profile is controlled by LHCD (lower hybrid current drive), with appropriate neutral beam injection, the nonlinear interplay between the transport determined gradients in the plasma temperature (T{sub i,e}) and toroidal velocity (V{sub ϕ}) and the E×B flow shear (including q-profile) produces transport bifurcations, generating spontaneously a stepwise growing ITB. In the discharge, the constraints imposed by the wave propagation condition causes interplay of the LH driven current distribution with the plasma configuration modification, which constitutes non-linearity in the LH wave deposition. The non-linear effects cause bifurcation in LHCD, generating two distinct quasi-stationary reversed magnetic shear configurations. The change of current profile during the transition period between the two quasi-stationary states results in increase of the E×B shearing flow arising from toroidal rotation. The turbulence transport suppression by sheared E×B flow during the ITB development is analysed, and the temporal evolution of some parameters characterized the plasma confinement is examined. Ample evidence shows that onset of the ITB development is correlated with the enhancement of E×B shearing rate caused by the bifurcation in LHCD. It is suggested that the ITB triggering is associated with the non-linear effects of the LH power deposition.
Initial conditions, Discreteness and non-linear structure formation in cosmology
Sylos-Labini, F; Gabrielli, A; Joyce, M; Labini, Francesco Sylos; Baertschiger, Thierry; Gabrielli, Andrea; Joyce, Michael
2002-01-01
In this lecture we address three different but related aspects of the initial continuous fluctuation field in standard cosmological models. Firstly we discuss the properties of the so-called Harrison-Zeldovich like spectra. This power spectrum is a fundamental feature of all current standard cosmological models. In a simple classification of all stationary stochastic processes into three categories, we highlight with the name ``super-homogeneous'' the properties of the class to which models like this, with $P(0)=0$, belong. In statistical physics language they are well described as glass-like. Secondly, the initial continuous density field with such small amplitude correlated Gaussian fluctuations must be discretised in order to set up the initial particle distribution used in gravitational N-body simulations. We discuss the main issues related to the effects of discretisation, particularly concerning the effect of particle induced fluctuations on the statistical properties of the initial conditions and on th...
Directory of Open Access Journals (Sweden)
Chi-Chang Wang
2013-09-01
Full Text Available This paper seeks to use the proposed residual correction method in coordination with the monotone iterative technique to obtain upper and lower approximate solutions of singularly perturbed non-linear boundary value problems. First, the monotonicity of a non-linear differential equation is reinforced using the monotone iterative technique, then the cubic-spline method is applied to discretize and convert the differential equation into the mathematical programming problems of an inequation, and finally based on the residual correction concept, complex constraint solution problems are transformed into simpler questions of equational iteration. As verified by the four examples given in this paper, the method proposed hereof can be utilized to fast obtain the upper and lower solutions of questions of this kind, and to easily identify the error range between mean approximate solutions and exact solutions.
Directory of Open Access Journals (Sweden)
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.
Normal transmitting boundary conditions
Institute of Scientific and Technical Information of China (English)
廖振鹏
1996-01-01
The multi-transmitting formula (MTF) governed by a single artificial speed is analytically developed into a generalized MTF governed by a few artificial speeds to improve its capacity in simultaneous simulation of several one-way waves propagating at different speeds.The generalized MTF is then discretized and further generalized using the space extrapolation to improve its accuracies in numerical simulation of transient waves at large angles of incidence.The above two successive generalizitions of MTF based on the notion of normal transmission lead to a compact formula of local non-reflecting boundary condition.The formula not only provides a general representation of the major schemes of existing local boundary conditions but can be used to generate new schemes,which combine advantages of different schemes.
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.
Directory of Open Access Journals (Sweden)
Xudong Yin
2014-02-01
Full Text Available The authors propose to implement conditional non-linear optimal perturbation related to model parameters (CNOP-P through an ensemble-based approach. The approach was first used in our earlier study and is improved to be suitable for calculating CNOP-P. Idealised experiments using the Lorenz-63 model are conducted to evaluate the performance of the improved ensemble-based approach. The results show that the maximum prediction error after optimisation has been multiplied manifold compared with the initial-guess prediction error, and is extremely close to, or greater than, the maximum value of the exhaustive attack method (a million random samples. The calculation of CNOP-P by the ensemble-based approach is capable of maintaining a high accuracy over a long prediction time under different constraints and initial conditions. Further, the CNOP-P obtained by the approach is applied to sensitivity analysis of the Lorenz-63 model. The sensitivity analysis indicates that when the prediction time is set to 0.2 time units, the Lorenz-63 model becomes extremely insensitive to one parameter, which leaves the other two parameters to affect the uncertainty of the model. Finally, a serial of parameter estimation experiments are performed to verify sensitivity analysis. It is found that when the three parameters are estimated simultaneously, the insensitive parameter is estimated much worse, but the Lorenz-63 model can still generate a very good simulation thanks to the relatively accurate values of the other two parameters. When only two sensitive parameters are estimated simultaneously and the insensitive parameter is left to be non-optimised, the outcome is better than the case when the three parameters are estimated simultaneously. With the increase of prediction time and observation, however, the model sensitivity to the insensitive parameter increases accordingly and the insensitive parameter can also be estimated successfully.
Reproducing Kernel Particle Method for Non-Linear Fracture Analysis
Institute of Scientific and Technical Information of China (English)
Cao Zhongqing; Zhou Benkuan; Chen Dapeng
2006-01-01
To study the non-linear fracture, a non-linear constitutive model for piezoelectric ceramics was proposed, in which the polarization switching and saturation were taken into account. Based on the model, the non-linear fracture analysis was implemented using reproducing kernel particle method (RKPM). Using local J-integral as a fracture criterion, a relation curve of fracture loads against electric fields was obtained. Qualitatively, the curve is in agreement with the experimental observations reported in literature. The reproducing equation, the shape function of RKPM, and the transformation method to impose essential boundary conditions for meshless methods were also introduced. The computation was implemented using object-oriented programming method.
Reweighting twisted boundary conditions
Bussone, Andrea; Hansen, Martin; Pica, Claudio
2015-01-01
Imposing twisted boundary conditions on the fermionic fields is a procedure extensively used when evaluating, for example, form factors on the lattice. Twisting is usually performed for one flavour and only in the valence, and this causes a breaking of unitarity. In this work we explore the possibility of restoring unitarity through the reweighting method. We first study some properties of the approach at tree level and then we stochastically evaluate ratios of fermionic determinants for different boundary conditions in order to include them in the gauge averages, avoiding in this way the expensive generation of new configurations for each choice of the twisting angle, $\\theta$. As expected the effect of reweighting is negligible in the case of large volumes but it is important when the volumes are small and the twisting angles are large. In particular we find a measurable effect for the plaquette and the pion correlation function in the case of $\\theta=\\pi/2$ in a volume $16\\times 8^3$, and we observe a syst...
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.
Echeikh, Hamdi; Trabelsi, Ramzi; Iqbal, Atif; Bianchi, Nicola; Mimouni, Mohamed Fouizi
2016-11-01
In this paper non-linear backstepping control (BSC) is employed for high performance five-phase induction motor drive for low speed operation. The traditional control approaches such as direct torque control and indirect rotor field oriented control introduces stability problem at low speed. The proposed BSC is shown to offer stable operation in the sense of Lyapunov and high dynamics at low speed. Experimental results are provided to present the proprieties of the proposed approach at low speed in terms of stability, torque ripple, desired control performance, achievable dynamics and complexity of implementation etc. Copyright © 2016. Published by Elsevier Ltd.
Efficient Non Linear Loudspeakers
DEFF Research Database (Denmark)
Petersen, Bo R.; Agerkvist, Finn T.
2006-01-01
Loudspeakers have traditionally been designed to be as linear as possible. However, as techniques for compensating non linearities are emerging, it becomes possible to use other design criteria. This paper present and examines a new idea for improving the efficiency of loudspeakers at high levels...... by changing the voice coil layout. This deliberate non-linear design has the benefit that a smaller amplifier can be used, which has the benefit of reducing system cost as well as reducing power consumption....
Efficient Non Linear Loudspeakers
DEFF Research Database (Denmark)
Petersen, Bo R.; Agerkvist, Finn T.
2006-01-01
Loudspeakers have traditionally been designed to be as linear as possible. However, as techniques for compensating non linearities are emerging, it becomes possible to use other design criteria. This paper present and examines a new idea for improving the efficiency of loudspeakers at high levels...... by changing the voice coil layout. This deliberate non-linear design has the benefit that a smaller amplifier can be used, which has the benefit of reducing system cost as well as reducing power consumption.......Loudspeakers have traditionally been designed to be as linear as possible. However, as techniques for compensating non linearities are emerging, it becomes possible to use other design criteria. This paper present and examines a new idea for improving the efficiency of loudspeakers at high levels...
Boundary Conditions of Weyl Semimetals
Hashimoto, Koji; Wu, Xi
2016-01-01
We find that generic boundary conditions of Weyl semimetal is dictated by only a single real parameter, in the continuum limit. We determine how the energy dispersions (the Fermi arcs) and the wave functions of edge states depend on this parameter. Lattice models are found to be consistent with our generic observation. Furthermore, the enhanced parameter space of the boundary condition is shown to support a novel topological number.
Boundary condition may change chaos
Energy Technology Data Exchange (ETDEWEB)
Itoh, Sanae-I.; Yagi, Masatoshi [Kyushu Univ., RIAM, Kasuga, Fukuoka (Japan); Kawai, Yoshinobu [Kyushu Univ., Interdisciplinary Graduate School of Engineering Sciences, Kasuga, Fukuoka (Japan)
2001-07-01
Role of boundary condition for the appearance of chaos is examined. Imposition of the boundary condition is interpreted as the reduction of the system size L. For a demonstration, Rayleigh-Benard instability is considered and the shell model analysis is applied. It is shown that the reduction of L reduces the number of positive Lyapunov exponent of the system, hence opens the route from the turbulence, to the chaos and to the limit cycle/fixed point. (author)
Entropy Stable Wall Boundary Conditions for the Compressible Navier-Stokes Equations
Parsani, Matteo; Carpenter, Mark H.; Nielsen, Eric J.
2014-01-01
Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the compressible Navier-Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although discontinuous spectral collocation operators are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite volume, finite difference, discontinuous Galerkin, and flux reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary conditions.
Parsani, Matteo; Carpenter, Mark H.; Nielsen, Eric J.
2015-01-01
Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the three-dimensional compressible Navier-Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although discontinuous spectral collocation operators on unstructured grids are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite difference, finite volume, discontinuous Galerkin, and flux reconstruction/correction procedure via reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary conditions.
NON-STATIONARY STOKES FLOWS UNDER LEAK BOUNDARY CONDITIONS OF FRICTION TYPE
Institute of Scientific and Technical Information of China (English)
Hiroshi Fujita
2001-01-01
This paper is concerned with the initial value problem for non-stationary Stokes flows,under a certain non-linear boundary condition which can be called the leak boundarycondition of friction type. Theoretically, our main purpose is to show the strong solvability(i.e.,the unique existence of the L2-strong solution) of this initial value problem by meansof the non-linear semi-group theory originated with Y. Komura. The method of analysiscan be applied to other boundary or interface conditions of friction type. It should benoted that the result yields a sound basis of simulation methods for evolution problemsinvolving these conditions.
Entropy stable wall boundary conditions for the compressible Navier-Stokes equations
Parsani, Matteo; Nielsen, Eric J
2014-01-01
Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the compressible Navier-Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although discontinuous spectral collocation operators are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite volume, finite difference, discontinuous Galerkin, and flux reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary...
Higgsless Deconstruction Without Boundary Condition
He, H J
2004-01-01
Deconstruction is a powerful means to explore the rich dynamics of gauge theories in four and higher dimensions. We demonstrate that gauge symmetry breaking in a compactified higher dimensional theory can be formulated via deconstructed 4D moose theory with {\\it spontaneous symmetry breaking} and {\\it without boundary condition.} The proper higher-D boundary conditions are automatically induced in the continuum limit rather than being imposed. We identify and analyze the moose theories which exhibit {\\it delayed unitarity violation} (effective unitarity) as a {\\it collective effect} of many gauge groups, without resorting to any known 5D geometry. Relevant phenomenological constraints are also addressed.
Incoherent boundary conditions and metastates
Enter, Aernout C.D. van; Netočný, Karel; Schaap, Hendrikjan G.
2006-01-01
In this contribution we discuss the role which incoherent boundary conditions can play in the study of phase transitions. This is a question of particular relevance for the analysis of disordered systems, and in particular of spin glasses. For the moment our mathematical results only apply to ferrom
Gowdy waves as a test-bed for constraint-preserving boundary conditions
Bona, C
2010-01-01
Gowdy waves, one of the standard 'apples with apples' tests, is proposed as a test-bed for constraint-preserving boundary conditions in the non-linear regime. As an illustration, energy-constraint preservation is separately tested in the Z4 framework. Both algebraic conditions, derived from energy estimates, and derivative conditions, deduced from the constraint-propagation system, are considered. The numerical errors at the boundary are of the same order than those at the interior points.
Topological expansion and boundary conditions
Eynard, Bertrand
2008-01-01
In this article, we compute the topological expansion of all possible mixed-traces in a hermitian two matrix model. In other words we give a recipe to compute the number of discrete surfaces of given genus, carrying an Ising model, and with all possible given boundary conditions. The method is recursive, and amounts to recursively cutting surfaces along interfaces. The result is best represented in a diagrammatic way, and is thus rather simple to use.
Some analytical solutions for flows of Casson fluid with slip boundary conditions
Directory of Open Access Journals (Sweden)
K. Ramesh
2015-09-01
Full Text Available In the present paper, we have studied three fundamental flows namely Couette, Poiseuille and generalized Couette flows of an incompressible Casson fluid between parallel plates using slip boundary conditions. The equations governing the flow of Casson fluid are non-linear in nature. Analytical solutions of the non-linear governing equations with non-linear boundary conditions are obtained for each case. The effect of the various parameters on the velocity and volume flow rate for each problem is studied and the results are presented through graphs. It is observed that, the presence of Casson number decreases the velocity and volume flow rate of the fluid. Increasing of slip parameter increases the velocity and volume flow rate in both Poiseuille and generalized Couette flows.
Quantum "violation" of Dirichlet boundary condition
Park, I. Y.
2017-02-01
Dirichlet boundary conditions have been widely used in general relativity. They seem at odds with the holographic property of gravity simply because a boundary configuration can be varying and dynamic instead of dying out as required by the conditions. In this work we report what should be a tension between the Dirichlet boundary conditions and quantum gravitational effects, and show that a quantum-corrected black hole solution of the 1PI action no longer obeys, in the naive manner one may expect, the Dirichlet boundary conditions imposed at the classical level. We attribute the 'violation' of the Dirichlet boundary conditions to a certain mechanism of the information storage on the boundary.
Quantum violation of Dirichlet boundary condition
Park, I Y
2016-01-01
Dirichlet boundary conditions have been widely used in general relativity. They seem at odds with the holographic property of gravity simply because a boundary configuration can be varying and dynamic instead of dying out as required by the conditions. In this work we report what should be a clash between the Dirichlet boundary conditions and quantum gravitational effects, and show that a quantum corrected solution of the 1PI action no longer obeys the Dirichlet boundary conditions imposed at the classical level. We attribute the violation of the Dirichlet boundary conditions to a certain mechanism of the information storage on the boundary.
Probability of boundary conditions in quantum cosmology
Suenobu, Hiroshi; Nambu, Yasusada
2017-02-01
One of the main interest in quantum cosmology is to determine boundary conditions for the wave function of the universe which can predict observational data of our universe. For this purpose, we solve the Wheeler-DeWitt equation for a closed universe with a scalar field numerically and evaluate probabilities for boundary conditions of the wave function of the universe. To impose boundary conditions of the wave function, we use exact solutions of the Wheeler-DeWitt equation with a constant scalar field potential. These exact solutions include wave functions with well known boundary condition proposals, the no-boundary proposal and the tunneling proposal. We specify the exact solutions by introducing two real parameters to discriminate boundary conditions, and obtain the probability for these parameters under the requirement of sufficient e-foldings of the inflation. The probability distribution of boundary conditions prefers the tunneling boundary condition to the no-boundary boundary condition. Furthermore, for large values of a model parameter related to the inflaton mass and the cosmological constant, the probability of boundary conditions selects an unique boundary condition different from the tunneling type.
Absorbing Boundary Conditions for Hyperbolic Systems
Institute of Scientific and Technical Information of China (English)
Matthias Ehrhardt
2010-01-01
This paper deals with absorbing boundary conditions for hyperbolic systems in one and two space dimensions. We prove the strict well-posedness of the resulting initial boundary value problem in 1D. Afterwards we establish the GKS-stability of the corresponding Lax-Wendroff-type finite difference scheme. Hereby, we have to extend the classical proofs, since the (discretized) absorbing boundary conditions do not fit the standard form of boundary conditions for hyperbolic systems.
Compact difference approximation with consistent boundary condition
Institute of Scientific and Technical Information of China (English)
FU Dexun; MA Yanwen; LI Xinliang; LIU Mingyu
2003-01-01
For simulating multi-scale complex flow fields it should be noted that all the physical quantities we are interested in must be simulated well. With limitation of the computer resources it is preferred to use high order accurate difference schemes. Because of their high accuracy and small stencil of grid points computational fluid dynamics (CFD) workers pay more attention to compact schemes recently. For simulating the complex flow fields the treatment of boundary conditions at the far field boundary points and near far field boundary points is very important. According to authors' experience and published results some aspects of boundary condition treatment for far field boundary are presented, and the emphasis is on treatment of boundary conditions for the upwind compact schemes. The consistent treatment of boundary conditions at the near boundary points is also discussed. At the end of the paper are given some numerical examples. The computed results with presented method are satisfactory.
Probability of boundary conditions in quantum cosmology
Nambu, Yasusada; Suenobu, Hiroshi
2017-08-01
One of the main interest in quantum cosmology is to determine boundary conditions for the wave function of the universe which can predict observational data of our universe. For this purpose, we solve the Wheeler-DeWitt equation for a closed universe with a scalar field numerically and evaluate probabilities for boundary conditions of the wave function of the universe. To impose boundary conditions of the wave function, we use exact solutions of the Wheeler-DeWitt equation with a constant scalar field potential. We specify the exact solutions by introducing two real parameters to discriminate boundary conditions, and obtain the probability for these parameters under the requirement of sufficient e-foldings of the inflation. The probability distribution of boundary conditions prefers the tunneling boundary condition to the no-boundary boundary condition. Furthermore, for large values of a model parameter related to the inflaton mass and the cosmological constant, the probability of boundary conditions selects an unique boundary condition different from the tunneling type.
Boundary conditions of methamphetamine craving.
Lopez, Richard B; Onyemekwu, Chukwudi; Hart, Carl L; Ochsner, Kevin N; Kober, Hedy
2015-12-01
Methamphetamine use has increased significantly and become a global health concern. Craving is known to predict methamphetamine use and relapse following abstinence. Some have suggested that cravings are automatic, generalized, and uncontrollable, but experimental work addressing these claims is lacking. In 2 exploratory studies, we tested the boundary conditions of methamphetamine craving by asking: (a) is craving specific to users' preferred route of administration?, and (b) can craving be regulated by cognitive strategies? Two groups of methamphetamine users were recruited. In Study 1, participants were grouped by their preferred route of administration (intranasal vs. smoking), and rated their craving in response to photographs and movies depicting methamphetamine use (via the intranasal vs. smoking route). In Study 2, methamphetamine smokers implemented cognitive regulation strategies while viewing photographs depicting methamphetamine smoking. Strategies involved either focusing on the positive aspects of smoking methamphetamine or the negative consequences of doing so-the latter strategy based on treatment protocols for addiction. In Study 1, we found a significant interaction between group and route of administration, such that participants who preferred to smoke methamphetamine reported significantly stronger craving for smoking stimuli, whereas those who preferred the intranasal route reported stronger craving for intranasal stimuli. In Study 2, participants reported significantly lower craving when focusing on the negative consequences associated with methamphetamine use. Taken together, these findings suggest that strength of craving for methamphetamine is moderated by users' route of administration and can be reduced by cognitive strategies. This has important theoretical, methodological, and clinical implications. (PsycINFO Database Record (c) 2015 APA, all rights reserved).
The femur as a musculo-skeletal construct: a free boundary condition modelling approach.
Phillips, A T M
2009-07-01
Previous finite element studies of the femur have made simplifications to varying extents with regard to the boundary conditions used during analysis. Fixed boundary conditions are generally applied to the distal femur when examining the proximal behaviour at the hip joint, while the same can be said for the proximal femur when examining the distal behaviour at the knee joint. While fixed boundary condition analyses have been validated against in vitro experiments it remains a matter of debate as to whether the numerical and experimental models are indicative of the in vivo situation. This study presents a finite element model in which the femur is treated as a complete musculo-skeletal construct, spanning between the hip and knee joints. Linear and non-linear implementations of a free boundary condition modelling approach are applied to the bone through the explicit inclusion of muscles and ligaments spanning both the hip joint and the knee joint. A non-linear force regulated, muscle strain based activation strategy was found to result in lower observed principal strains in the cortex of the femur, compared to a linear activation strategy. The non-linear implementation of the model in particular, was found to produce hip and knee joint reaction forces consistent with in vivo data from instrumented implants.
Asymptotic theory for weakly non-linear wave equations in semi-infinite domains
Directory of Open Access Journals (Sweden)
Chirakkal V. Easwaran
2004-01-01
Full Text Available We prove the existence and uniqueness of solutions of a class of weakly non-linear wave equations in a semi-infinite region $0le x$, $t< L/sqrt{|epsilon|}$ under arbitrary initial and boundary conditions. We also establish the asymptotic validity of formal perturbation approximations of the solutions in this region.
Controller reconfiguration for non-linear systems
Kanev, S.; Verhaegen, M.
2000-01-01
This paper outlines an algorithm for controller reconfiguration for non-linear systems, based on a combination of a multiple model estimator and a generalized predictive controller. A set of models is constructed, each corresponding to a different operating condition of the system. The interacting m
Boundary conditions for viscous vortex methods
Energy Technology Data Exchange (ETDEWEB)
Koumoutsakos, P.; Leonard, A.; Pepin, F. (California Institute of Technology, Pasadena, CA (United States))
1994-07-01
This paper presents a Neumann-type vorticity boundary condition for the vorticity formulation of the Navier-Stokes equations. The vorticity creation process at the boundary, due to the no-slip condition, is expressed in terms of a vorticity flux. The scheme is incorporated then into a Lagrangian vortex blob method that uses a particle strength exchange algorithm for viscous diffusion. The no-slip condition is not enforced by the generation of new vortices at the boundary but instead by modifying the strength of the vortices in the vicinity of the boundary. 19 refs., 5 figs.
Born series for the Robin boundary condition
Machida, Manabu; Nakamura, Gen
2017-01-01
We solve the diffusion equation by constructing the Born series for the Robin boundary condition. We develop a general theory for arbitrary domains with smooth enough boundaries and explore the convergence. The proposed Born series is validated by numerical calculation in the three-dimensional half space. We show that in this case the Born series converges regardless the value of the impedance term in the Robin boundary condition. We point out that the solution from the so-called extrapolated...
Absorption boundary conditions for geomertical acoustics
DEFF Research Database (Denmark)
Jeong, Cheol-Ho
2012-01-01
Defining accurate acoustical boundary conditions is of crucial importance for room acoustic simulations. In predicting sound fields using phased geometrical acoustics methods, the absorption coefficients or surface impedances of the boundary surfaces can be used, but no guideline has been developed...... solutions. Two rectangular rooms with uniform and non-uniform absorption distributions are tested. It is concluded that the impedance and random incidence absorption boundary conditions produce reasonable results with some exceptions at low frequencies for acoustically soft materials....
Boundary conditions: The path integral approach
Energy Technology Data Exchange (ETDEWEB)
Asorey, M [Departamento de Fisica Teorica, Universidad de Zaragoza 50009 Zaragoza (Spain); Clemente-Gallardo, J [BIFI, Universidad de Zaragoza, 50009 Zaragoza (Spain); Munoz-Castaneda, J M [Departamento de Fisica Teorica, Universidad de Zaragoza 50009 Zaragoza (Spain)
2007-11-15
The path integral approach to quantum mechanics requires a substantial generalisation to describe the dynamics of systems confined to bounded domains. Nonlocal boundary conditions can be introduced in Feynman's approach by means of boundary amplitude distributions and complex phases to describe the quantum dynamics in terms of the classical trajectories. The different prescriptions involve only trajectories reaching the boundary and correspond to different choices of boundary conditions of selfadjoint extensions of the Hamiltonian. One dimensional particle dynamics is analysed in detail.
On filter boundary conditions in topology optimization
DEFF Research Database (Denmark)
Clausen, Anders; Andreassen, Erik
2017-01-01
we define three requirements that boundary conditions must fulfill in order to eliminate boundary effects. Previously suggested approaches are briefly reviewed in the light of these requirements. A new approach referred to as the “domain extension approach” is suggested. It effectively eliminates......Most research papers on topology optimization involve filters for regularization. Typically, boundary effects from the filters are ignored. Despite significant drawbacks the inappropriate homogeneous Neumann boundary conditions are used, probably because they are trivial to implement. In this paper...
Probability of Boundary Conditions in Quantum Cosmology
Suenobu, Hiroshi
2016-01-01
One of the main interest in quantum cosmology is to determine which type of boundary conditions for the wave function of the universe can predict observational data of our universe. For this purpose, we solve the Wheeler-DeWitt equation numerically and evaluate probabilities for an observable representing evolution of the classical universe, especially, the number of e-foldings of the inflation. To express boundary conditions of the wave function, we use exact solutions of the Wheeler-DeWitt equation with constant scalar field potential. These exact solutions include wave functions with well known boundary condition proposals, the no-boundary proposal and the tunneling proposal. We specify them introducing two real parameters which discriminate boundary conditions and estimate values of these parameters resulting in observationally preferable predictions. We obtain the probability for these parameters under the requirement of the sufficient e-foldings of the inflation.
Logarithmic Minimal Models with Robin Boundary Conditions
Bourgine, Jean-Emile; Tartaglia, Elena
2016-01-01
We consider general logarithmic minimal models ${\\cal LM}(p,p')$, with $p,p'$ coprime, on a strip of $N$ columns with the $(r,s)$ Robin boundary conditions introduced by Pearce, Rasmussen and Tipunin. The associated conformal boundary conditions are labelled by the Kac labels $r\\in{\\Bbb Z}$ and $s\\in{\\Bbb N}$. The Robin vacuum boundary condition, labelled by $(r,s\\!-\\!\\frac{1}{2})=(0,\\mbox{$\\textstyle \\frac{1}{2}$})$, is given as a linear combination of Neumann and Dirichlet boundary conditions. The general $(r,s)$ Robin boundary conditions are constructed, using fusion, by acting on the Robin vacuum boundary with an $(r,s)$-type seam consisting of an $r$-type seam of width $w$ columns and an $s$-type seam of width $d=s-1$ columns. The $r$-type seam admits an arbitrary boundary field which we fix to the special value $\\xi=-\\tfrac{\\lambda}{2}$ where $\\lambda=\\frac{(p'-p)\\pi}{2p'}$ is the crossing parameter. The $s$-type boundary introduces $d$ defects into the bulk. We consider the associated quantum Hamiltoni...
Non-linear canonical correlation
van der Burg, Eeke; de Leeuw, Jan
1983-01-01
Non-linear canonical correlation analysis is a method for canonical correlation analysis with optimal scaling features. The method fits many kinds of discrete data. The different parameters are solved for in an alternating least squares way and the corresponding program is called CANALS. An
DEFF Research Database (Denmark)
Andersen, Steffen; Harrison, Glenn W.; Hole, Arne Risa
2012-01-01
We develop an extension of the familiar linear mixed logit model to allow for the direct estimation of parametric non-linear functions defined over structural parameters. Classic applications include the estimation of coefficients of utility functions to characterize risk attitudes and discountin...
Numerical implementation of isolated horizon boundary conditions
Jaramillo, J L; Limousin, F
2006-01-01
We study the numerical implementation of a set of boundary conditions derived from the isolated horizon formalism, and which characterize a black hole whose horizon is in quasi-equilibrium. More precisely, we enforce these geometrical prescriptions as inner boundary conditions on an excised sphere, in the numerical resolution of the Conformal Thin Sandwich equations. As main results, we firstly establish the consistency of including in the set of boundary conditions a "constant surface gravity" prescription, interpretable as a lapse boundary condition, and secondly we assess how the prescriptions presented recently by Dain et al. for guaranteeing the well-posedness of the Conformal Transverse Traceless equations with quasi-equilibrium horizon conditions extend to the Conformal Thin Sandwich elliptic system. As a consequence of the latter analysis, we discuss the freedom of prescribing the expansion associated with the ingoing null normal at the horizon.
Modelling classroom conditions with different boundary conditions
DEFF Research Database (Denmark)
Marbjerg, Gerd Høy; Jeong, Cheol-Ho; Brunskog, Jonas
2014-01-01
both specular and diffuse reflections with complex-valued acoustical descriptions of the surfaces. In this paper the PARISM model is used to simulate a rectangular room with most of the absorption located in the ceiling. This room configuration is typical for classroom conditions. The simulations...... measures which are important for evaluation of the acoustics in classrooms....
Modelling classroom conditions with different boundary conditions
DEFF Research Database (Denmark)
Marbjerg, Gerd Høy; Jeong, Cheol-Ho; Brunskog, Jonas
2014-01-01
both specular and diffuse reflections with complex-valued acoustical descriptions of the surfaces. In this paper the PARISM model is used to simulate a rectangular room with most of the absorption located in the ceiling. This room configuration is typical for classroom conditions. The simulations...
Student difficulties with Boundary Conditions in electrodynamics
Ryan, Qing X; Wilcox, Bethany R
2015-01-01
Boundary conditions (BCs) are considered as an important topic that advanced physics under- graduates are expected to understand and apply. We report findings from an investigation of student difficulties using boundary conditions (BCs) in electrodynamics. Our data sources include student responses to traditional exam questions, conceptual survey questions, and think-aloud interviews. The analysis was guided by an analytical framework that characterizes how students activate, con- struct, execute, and reflect on boundary conditions. Common student difficulties include: activating boundary conditions in appropriate contexts; constructing a complex expression for the E&M waves; mathematically simplifying complex exponentials and checking if the reflection and transmission co- efficient are physical. We also present potential pedagogical implications based on our observations.
Optimal Boundary Conditions for ORCA-2 Model
Kazantsev, Eugene
2012-01-01
A 4D-Var data assimilation technique is applied to a ORCA-2 configuration of the NEMO in order to identify the optimal parametrization of the boundary conditions on the lateral boundaries as well as on the bottom and on the surface of the ocean. The influence of the boundary conditions on the solution is analyzed as in the assimilation window and beyond the window. It is shown that optimal conditions for vertical operators allows to get stronger and finer jet streams (Gulf Stream, Kuroshio) in the solution. Analyzing the reasons of the jets reinforcement, we see that the major impact of the data assimilation is made on the parametrization of the bottom boundary conditions for lateral velocities u and v. Automatic generation of the tangent and adjoint codes is also discussed. Tapenade software is shown to be able to produce the adjoint code that can be used after a memory usage optimization.
Multireflection boundary conditions for lattice Boltzmann models.
Ginzburg, Irina; d'Humières, Dominique
2003-12-01
We present a general framework for several previously introduced boundary conditions for lattice Boltzmann models, such as the bounce-back rule and the linear and quadratic interpolations. The objectives are twofold: first to give theoretical tools to study the existing link-type boundary conditions and their corresponding accuracy; second to design boundary conditions for general flows which are third-order kinetic accurate. Using these new boundary conditions, Couette and Poiseuille flows are exact solutions of the lattice Boltzmann models for a Reynolds number Re=0 (Stokes limit) for arbitrary inclination with the lattice directions. Numerical comparisons are given for Stokes flows in periodic arrays of spheres and cylinders, linear periodic array of cylinders between moving plates, and for Navier-Stokes flows in periodic arrays of cylinders for Re<200. These results show a significant improvement of the overall accuracy when using the linear interpolations instead of the bounce-back reflection (up to an order of magnitude on the hydrodynamics fields). Further improvement is achieved with the new multireflection boundary conditions, reaching a level of accuracy close to the quasianalytical reference solutions, even for rather modest grid resolutions and few points in the narrowest channels. More important, the pressure and velocity fields in the vicinity of the obstacles are much smoother with multireflection than with the other boundary conditions. Finally the good stability of these schemes is highlighted by some simulations of moving obstacles: a cylinder between flat walls and a sphere in a cylinder.
Twisted Boundary Conditions in Lattice Simulations
Sachrajda, Christopher T C
2004-01-01
By imposing twisted boundary conditions on quark fields it is possible to access components of momenta other than integer multiples of 2pi/L on a lattice with spatial volume L^3. We use Chiral Perturbation Theory to study finite-volume effects with twisted boundary conditions for quantities without final-state interactions, such as meson masses, decay constants and semileptonic form factors, and confirm that they remain exponentially small with the volume. We show that this is also the case for "partially twisted" boundary conditions, in which (some of) the valence quarks satisfy twisted boundary conditions but the sea quarks satisfy periodic boundary conditions. This observation implies that it is not necessary to generate new gluon configurations for every choice of the twist angle, making the method much more practicable. For K->pipi decays we show that the breaking of isospin symmetry by the twisted boundary conditions implies that the amplitudes cannot be determined in general (on this point we disagree ...
DEFF Research Database (Denmark)
Du, Yigang
without iteration steps. The ASA is implemented in combination with Field II and extended to simulate the pulsed ultrasound fields. The simulated results from a linear array transducer are made by the ASA based on Field II, and by a released non-linear simulation program- Abersim, respectively....... The calculation speed of the ASA is increased approximately by a factor of 140. For the second harmonic point spread function the error of the full width is 1.5% at -6 dB and 6.4% at -12 dB compared to Abersim. To further investigate the linear and non-linear ultrasound fields, hydrophone measurements.......3% relative to the measurement from a 1 inch diameter transducer. A preliminary study for harmonic imaging using synthetic aperture sequential beamforming (SASB) has been demonstrated. A wire phantom underwater measurement is made by an experimental synthetic aperture real-time ultrasound scanner (SARUS...
Reconstruction of boundary conditions from internal conditions using viability theory
Hofleitner, Aude
2012-06-01
This article presents a method for reconstructing downstream boundary conditions to a HamiltonJacobi partial differential equation for which initial and upstream boundary conditions are prescribed as piecewise affine functions and an internal condition is prescribed as an affine function. Based on viability theory, we reconstruct the downstream boundary condition such that the solution of the Hamilton-Jacobi equation with the prescribed initial and upstream conditions and reconstructed downstream boundary condition satisfies the internal value condition. This work has important applications for estimation in flow networks with unknown capacity reductions. It is applied to urban traffic, to reconstruct signal timings and temporary capacity reductions at intersections, using Lagrangian sensing such as GPS devices onboard vehicles.
Future Boundary Conditions in De Sitter Space
Anninos, Dionysios; Strominger, Andrew
2011-01-01
We consider asymptotically future de Sitter spacetimes endowed with an eternal observatory. In the conventional descriptions, the conformal metric at the future boundary I^+ is deformed by the flux of gravitational radiation. We however impose an unconventional future "Dirichlet" boundary condition requiring that the conformal metric is flat everywhere except at the conformal point where the observatory arrives at I^+. This boundary condition violates conventional causality, but we argue the causality violations cannot be detected by any experiment in the observatory. We show that the bulk-to-bulk two-point functions obeying this future boundary condition are not realizable as operator correlation functions in any de Sitter invariant vacuum, but they do agree with those obtained by double analytic continuation from anti-de Sitter space.
Boundary conditions for the gravitational field
Winicour, Jeffrey
2012-06-01
A review of the treatment of boundaries in general relativity is presented with the emphasis on application to the formulations of Einstein's equations used in numerical relativity. At present, it is known how to treat boundaries in the harmonic formulation of Einstein's equations and a tetrad formulation of the Einstein-Bianchi system. However, a universal approach valid for other formulations is not in hand. In particular, there is no satisfactory boundary theory for the 3+1 formulations which have been highly successful in binary black hole simulation. I discuss the underlying problems that make the initial-boundary-value problem much more complicated than the Cauchy problem. I review the progress that has been made and the important open questions that remain. Science is a differential equation. Religion is a boundary condition. (Alan Turing, quoted in J D Barrow, ‘Theories of Everything’)
Transmitting boundary and radiation conditions at infinity
Institute of Scientific and Technical Information of China (English)
廖振鹏
2001-01-01
Relationship between the radiation conditions at infinity and the transmitting boundary for numerical simulation of the near-field wave motion has been studied in this paper. The conclusion is that the transmitting boundary is approximately equivalent to the radiation conditions at infinity for a large class of infinite media. And the errors of the approximation are of the same order of magnitude as those of the finite elements or finite differences in numerical simulation of wave motion. This result provides a sound theoretical basis for the transmitting boundary used in the numerical simulation of the near-field wave motion and gives a complete explanation for the major experiences accumulated in applications of the transmitting boundary to the numerical simulation.
Generalized additional boundary conditions for wire media
Energy Technology Data Exchange (ETDEWEB)
Maslovski, Stanislav I; Morgado, Tiago A; Silveirinha, Mario G [Departamento de Engenharia Electrotecnica, Instituto de Telecomunicacoes, Universidade de Coimbra, Polo II, 3030-290 Coimbra (Portugal); Kaipa, Chandra S R; Yakovlev, Alexander B, E-mail: stas@co.it.p [Department of Electrical Engineering, University of Mississippi, University, MS 38677-1848 (United States)
2010-11-15
We generalize additional boundary conditions (ABCs) for wire media by including arbitrary wire junctions with impedance loading. Special attention is given to the conditions at the interface of two uniaxial wire media with metallic patches at the junction. The derived ABCs are validated against full-wave numerical simulations.
Modelling Loudspeaker Non-Linearities
DEFF Research Database (Denmark)
Agerkvist, Finn T.
2007-01-01
This paper investigates different techniques for modelling the non-linear parameters of the electrodynamic loudspeaker. The methods are tested not only for their accuracy within the range of original data, but also for the ability to work reasonable outside that range, and it is demonstrated...... that polynomial expansions are rather poor at this, whereas an inverse polynomial expansion or localized fitting functions such as the gaussian are better suited for modelling the Bl-factor and compliance. For the inductance the sigmoid function is shown to give very good results. Finally the time varying...
Anchored boundary conditions for locally isostatic networks
Theran, Louis; Nixon, Anthony; Ross, Elissa; Sadjadi, Mahdi; Servatius, Brigitte; Thorpe, M. F.
2015-11-01
Finite pieces of locally isostatic networks have a large number of floppy modes because of missing constraints at the surface. Here we show that by imposing suitable boundary conditions at the surface the network can be rendered effectively isostatic. We refer to these as anchored boundary conditions. An important example is formed by a two-dimensional network of corner sharing triangles, which is the focus of this paper. Another way of rendering such networks isostatic is by adding an external wire along which all unpinned vertices can slide (sliding boundary conditions). This approach also allows for the incorporation of boundaries associated with internal holes and complex sample geometries, which are illustrated with examples. The recent synthesis of bilayers of vitreous silica has provided impetus for this work. Experimental results from the imaging of finite pieces at the atomic level need such boundary conditions, if the observed structure is to be computer refined so that the interior atoms have the perception of being in an infinite isostatic environment.
Constructing parametric triangular patches with boundary conditions
Institute of Scientific and Technical Information of China (English)
Hui Liu; Jun Ma; Fuhua Cheng
2008-01-01
The problem of constructing a parametric triangular patch to smoothly connect three surface patches is studied. Usually, these surface patches are defined on different parameter spaces. Therefore, it is necessary to define interpolation conditions, with values from the given surface patches, on the boundary of the triangular patch that can ensure smooth transition between different parameter spaces. In this paper we present a new method to define boundary conditions. Boundary conditions defined by the new method have the same parameter space if the three given surface patches can be converted into the same form through affine transformation. Consequently, any of the classic methods for constructing functional triangular patches can be used directly to construct a parametric triangular patch to connect given surface patches with G continuity. The resulting parametric triangular patch preserves precision of the applied classic method.
ADHMN boundary conditions from removing monopoles
Chen, X; Chen, Xingang; Weinberg, Erick J.
2003-01-01
Boundary conditions play an important role in the ADHMN construction of BPS monopole solutions. In this paper we show how different types of boundary conditions can be related to each other by removing monopoles to spatial infinity. In particular, we use this method to show how the jumping data naturally emerge. The results can be interpreted in the D-brane picture and provide a better understanding of the derivation of the ADHMN construction from D-branes. We comment briefly on the cases with non-Abelian unbroken symmetry and massless monopoles.
Mixed boundary conditions for piezoelectric plates
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
For plate bending and stretching problems in piezoelectric materials,the reciprocal theorem and the general solution of piezoelasticity are applied in a novel way to obtain the appropriate mixed boundary conditions accurate to all order.A decay analysis technique is used to establish necessary conditions that the prescribed data on the edge of the plate must satisfy in order that it should generate a decaying state within the plate.For the case of axisymmetric bending and stretching of a circular plate,these decaying state conditions are obtained explicitly for the first time when the mixed conditions are imposed on the plate edge.They are then used for the correct formulation of boundary conditions for the interior solution.
Casimir pistons with general boundary conditions
Directory of Open Access Journals (Sweden)
Guglielmo Fucci
2015-02-01
Full Text Available In this work we analyze the Casimir energy and force for a scalar field endowed with general self-adjoint boundary conditions propagating in a higher dimensional piston configuration. The piston is constructed as a direct product I×N, with I=[0,L]⊂R and N a smooth, compact Riemannian manifold with or without boundary. The study of the Casimir energy and force for this configuration is performed by employing the spectral zeta function regularization technique. The obtained analytic results depend explicitly on the spectral zeta function associated with the manifold N and the parameters describing the general boundary conditions imposed. These results are then specialized to the case in which the manifold N is a d-dimensional sphere.
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.
Boundary Conditions at Infinity for Physical Theories
Trautman, Andrzej
2016-01-01
The Sommerfeld boundary conditions, imposed on hyperbolic differential equations to obtain solutions in the form of outgoing waves, are formulated here so as to make explicit the role of an appropriate null vector field. When applied to the scalar and Maxwell equations, they lead to the asymptotic form of the energy-momentum tensor representing radiation as a null, perfect dust.
An h-principle with boundary condition
DEFF Research Database (Denmark)
Dotto, Emanuele
2010-01-01
We prove an h-principle with boundary condition for a certain class of topological spaces valued sheaves. The techniques used in the proof come from the study of the homotopy type of the cobordism categories, and they are of simplicial and categorical nature. Applying the main result of this paper...
Abstract wave equations with acoustic boundary conditions
Mugnolo, Delio
2010-01-01
We define an abstract setting to treat wave equations equipped with time-dependent acoustic boundary conditions on bounded domains of ${\\bf R}^n$. We prove a well-posedness result and develop a spectral theory which also allows to prove a conjecture proposed in (Gal-Goldstein-Goldstein, J. Evol. Equations 3 (2004), 623-636). Concrete problems are also discussed.
Energy Technology Data Exchange (ETDEWEB)
Rauf, A., E-mail: raufamar@ciitsahiwal.edu.pk [Department of Mathematics, Comsats Institute of Information Technology, Sahiwal 57000 (Pakistan); Siddiq, M.K. [Centre for Advanced Studies in Pure and Applied Mathematics, Department of Mathematics, Bahauddin Zakariya University, Multan 63000 (Pakistan); Abbasi, F.M. [Department of Mathematics, Comsats Institute of Information Technology, Islamabad 44000 (Pakistan); Meraj, M.A. [Department of Mathematics, Comsats Institute of Information Technology, Sahiwal 57000 (Pakistan); Ashraf, M. [Centre for Advanced Studies in Pure and Applied Mathematics, Department of Mathematics, Bahauddin Zakariya University, Multan 63000 (Pakistan); Shehzad, S.A. [Department of Mathematics, Comsats Institute of Information Technology, Sahiwal 57000 (Pakistan)
2016-10-15
The present work deals with the steady laminar three-dimensional mixed convective magnetohydrodynamic (MHD) boundary layer flow of Casson nanofluid over a bidirectional stretching surface. A uniform magnetic field is applied normal to the flow direction. Similarity variables are implemented to convert the non-linear partial differential equations into ordinary ones. Convective boundary conditions are utilized at surface of the sheet. A numerical technique of Runge–Kutta–Fehlberg (RFK45) is used to obtain the results of velocity, temperature and concentration fields. The physical dimensionless parameters are discussed through tables and graphs. - Highlights: • Mixed convective boundary layer flow of Casson nanofluid is taken into account. • Impact of magnetic field is examined. • Convective heat and mass conditions are imposed. • Numerical solutions are presented and discussed.
Radiation (absorbing) boundary conditions for electromagnetic fields
Bevensee, R. M.; Pennock, S. T.
1987-01-01
An important problem in finite difference or finite element computation of the electromagnetic field obeying the space-time Maxwell equations with self-consistent sources is that of truncating the outer numerical boundaries properly to avoid spurious numerical reflection. Methods for extrapolating properly the fields just beyond a numerical boundary in free space have been treated by a number of workers. This report avoids plane wave assumptions and derives boundary conditions more directly related to the source distribution within the region. The Panofsky-Phillips' relations, which enable one to extrapolate conveniently the vector field components parallel and perpendicular to a radial from the coordinate origin chosen near the center of the charge-current distribution are used to describe the space-time fields.
de Jong, Roelof
2005-07-01
This program incorporates a number of tests to analyse the count rate dependent non-linearity seen in NICMOS spectro-photometric observations. In visit 1 we will observe a few fields with stars of a range in luminosity in NGC1850 with NICMOS in NIC1 in F090M, F110W and F160W and NIC2 F110W, F160W, and F180W. We will repeat the observations with flatfield lamp on, creating artificially high count-rates, allowing tests of NICMOS linearity as function of count rate. To access the effect of charge trapping and persistence, we first take darks {so there is not too much charge already trapped}, than take exposures with the lamp off, exposures with the lamp on, and repeat at the end with lamp off. Finally, we continue with taking darks during occultation. In visit 2 we will observe spectro-photometric standard P041C using the G096 and G141 grisms in NIC3, and repeat the lamp off/on/off test to artificially create a high background. In visits 3&4 we repeat photometry measurements of faint standard stars SNAP-2 and WD1657+343, on which the NICMOS non-linearity was originally discovered using grism observations. These measurements are repeated, because previous photometry was obtained with too short exposure times, hence substantially affected by charge trapping non-linearity. Measurements will be made with NIC1: Visit 5 forms the persistence test of the program. The bright star GL-390 {used in a previous persistence test} will iluminate the 3 NICMOS detectors in turn for a fixed time, saturating the center many times, after which a series of darks will be taken to measure the persistence {i.e. trapped electrons and the decay time of the traps}. To determine the wavelength dependence of the trap chance, exposures of the bright star in different filters will be taken, as well as one in the G096 grism with NIC3. Most exposures will be 128s long, but two exposures in the 3rd orbit will be 3x longer, to seperate the effects of count rate versus total counts of the trap
Javili, A.; Saeb, S.; Steinmann, P.
2016-10-01
In the past decades computational homogenization has proven to be a powerful strategy to compute the overall response of continua. Central to computational homogenization is the Hill-Mandel condition. The Hill-Mandel condition is fulfilled via imposing displacement boundary conditions (DBC), periodic boundary conditions (PBC) or traction boundary conditions (TBC) collectively referred to as canonical boundary conditions. While DBC and PBC are widely implemented, TBC remains poorly understood, with a few exceptions. The main issue with TBC is the singularity of the stiffness matrix due to rigid body motions. The objective of this manuscript is to propose a generic strategy to implement TBC in the context of computational homogenization at finite strains. To eliminate rigid body motions, we introduce the concept of semi-Dirichlet boundary conditions. Semi-Dirichlet boundary conditions are non-homogeneous Dirichlet-type constraints that simultaneously satisfy the Neumann-type conditions. A key feature of the proposed methodology is its applicability for both strain-driven as well as stress-driven homogenization. The performance of the proposed scheme is demonstrated via a series of numerical examples.
Javili, A.; Saeb, S.; Steinmann, P.
2017-01-01
In the past decades computational homogenization has proven to be a powerful strategy to compute the overall response of continua. Central to computational homogenization is the Hill-Mandel condition. The Hill-Mandel condition is fulfilled via imposing displacement boundary conditions (DBC), periodic boundary conditions (PBC) or traction boundary conditions (TBC) collectively referred to as canonical boundary conditions. While DBC and PBC are widely implemented, TBC remains poorly understood, with a few exceptions. The main issue with TBC is the singularity of the stiffness matrix due to rigid body motions. The objective of this manuscript is to propose a generic strategy to implement TBC in the context of computational homogenization at finite strains. To eliminate rigid body motions, we introduce the concept of semi-Dirichlet boundary conditions. Semi-Dirichlet boundary conditions are non-homogeneous Dirichlet-type constraints that simultaneously satisfy the Neumann-type conditions. A key feature of the proposed methodology is its applicability for both strain-driven as well as stress-driven homogenization. The performance of the proposed scheme is demonstrated via a series of numerical examples.
Non-linear elastic deformations
Ogden, R W
1997-01-01
Classic in the field covers application of theory of finite elasticity to solution of boundary-value problems, analysis of mechanical properties of solid materials capable of large elastic deformations. Problems. References.
Restructuring surface tessellation with irregular boundary conditions
Directory of Open Access Journals (Sweden)
Tsung-Hsien Wang
2014-12-01
Full Text Available In this paper, the surface tessellation problem is explored, in particular, the task of meshing a surface with the added consideration of incorporating constructible building components. When a surface is tessellated into discrete counterparts, certain unexpected conditions usually occur at the boundary of the surface, in particular, when the surface is being trimmed. For example, irregularly shaped panels form at the trimmed edges. To reduce the number of irregular panels that may form during the tessellation process, this paper presents an algorithmic approach to restructuring the surface tessellation by investigating irregular boundary conditions. The objective of this approach is to provide an alternative way for freeform surface manifestation from a well-structured discrete model of the given surface.
Boundary conditions in conformal and integrable theories
Petkova, V B
2000-01-01
The study of boundary conditions in rational conformal field theories is not only physically important. It also reveals a lot on the structure of the theory ``in the bulk''. The same graphs classify both the torus and the cylinder partition functions and provide data on their hidden ``quantum symmetry''. The Ocneanu triangular cells -- the 3j-symbols of these symmetries, admit various interpretations and make a link between different problems.
Semi-implicit Image Denoising Algorithm for Different Boundary Conditions
Directory of Open Access Journals (Sweden)
Yuying Shi
2013-04-01
Full Text Available In this paper, the Crank-Nicolson semi-implicit difference scheme in matrix form is applied to discrete the Rudin-Osher-Fatemi model. We also consider different boundary conditions: Dirichlet boundary conditions, periodic boundary conditions, Neumann boundary conditions, antireflective boundary conditions and mean boundary conditions. By comparing the experimental results of Crank-Nicolson semi-implicit scheme and explicit scheme with the proposed boundary conditions, we can get that the semi-implicit scheme can overcome the instability and the number of iterations of the shortcomings that the explicit discrete scheme has, and its recovery effects are better than the explicit discrete scheme. In addition, the antireflective boundary conditions and Neumann boundary conditions can better maintain the continuity of the boundary in image denoising.
Non-Linear Dynamics of Saturn's Rings
Esposito, L. W.
2015-12-01
Non-linear processes can explain why Saturn's rings are so active and dynamic. Some of this non-linearity is captured in a simple Predator-Prey Model: Periodic forcing from the moon causes streamline crowding; This damps the relative velocity, and allows aggregates to grow. About a quarter phase later, the aggregates stir the system to higher relative velocity and the limit cycle repeats each orbit, with relative velocity ranging from nearly zero to a multiple of the orbit average: 2-10x is possible. Summary of Halo Results: A predator-prey model for ring dynamics produces transient structures like 'straw' that can explain the halo structure and spectroscopy: Cyclic velocity changes cause perturbed regions to reach higher collision speeds at some orbital phases, which preferentially removes small regolith particles; Surrounding particles diffuse back too slowly to erase the effect: this gives the halo morphology; This requires energetic collisions (v ≈ 10m/sec, with throw distances about 200km, implying objects of scale R ≈ 20km); We propose 'straw', as observed ny Cassini cameras. Transform to Duffing Eqn : With the coordinate transformation, z = M2/3, the Predator-Prey equations can be combined to form a single second-order differential equation with harmonic resonance forcing. Ring dynamics and history implications: Moon-triggered clumping at perturbed regions in Saturn's rings creates both high velocity dispersion and large aggregates at these distances, explaining both small and large particles observed there. This confirms the triple architecture of ring particles: a broad size distribution of particles; these aggregate into temporary rubble piles; coated by a regolith of dust. We calculate the stationary size distribution using a cell-to-cell mapping procedure that converts the phase-plane trajectories to a Markov chain. Approximating the Markov chain as an asymmetric random walk with reflecting boundaries allows us to determine the power law index from
Directory of Open Access Journals (Sweden)
Azeem SHAHZAD
2013-02-01
Full Text Available In this article, we study the power law model of steady state, viscous, incompressible MHD flow over a vertically stretching sheet. Furthermore, heat transfer is also addressed by using the convective boundary conditions. The coupled partial differential equations are transformed into ordinary differential equations (ODEs using similarity transformations. The transformed highly non-linear ODEs are solved by using the Homotopy Analysis Method (HAM. The influence of different parameters on the velocity and temperature fields are analyzed and discussed.
Open Boundary Conditions for Dissipative MHD
Energy Technology Data Exchange (ETDEWEB)
Meier, E T
2011-11-10
In modeling magnetic confinement, astrophysics, and plasma propulsion, representing the entire physical domain is often difficult or impossible, and artificial, or 'open' boundaries are appropriate. A novel open boundary condition (BC) for dissipative MHD, called Lacuna-based open BC (LOBC), is presented. LOBC, based on the idea of lacuna-based truncation originally presented by V.S. Ryaben'kii and S.V. Tsynkov, provide truncation with low numerical noise and minimal reflections. For hyperbolic systems, characteristic-based BC (CBC) exist for separating the solution into outgoing and incoming parts. In the hyperbolic-parabolic dissipative MHD system, such separation is not possible, and CBC are numerically unstable. LOBC are applied in dissipative MHD test problems including a translating FRC, and coaxial-electrode plasma acceleration. Solution quality is compared to solutions using CBC and zero-normal derivative BC. LOBC are a promising new open BC option for dissipative MHD.
Asymptotic Stability of Interconnected Passive Non-Linear Systems
Isidori, A.; Joshi, S. M.; Kelkar, A. G.
1999-01-01
This paper addresses the problem of stabilization of a class of internally passive non-linear time-invariant dynamic systems. A class of non-linear marginally strictly passive (MSP) systems is defined, which is less restrictive than input-strictly passive systems. It is shown that the interconnection of a non-linear passive system and a non-linear MSP system is globally asymptotically stable. The result generalizes and weakens the conditions of the passivity theorem, which requires one of the systems to be input-strictly passive. In the case of linear time-invariant systems, it is shown that the MSP property is equivalent to the marginally strictly positive real (MSPR) property, which is much simpler to check.
NON-LINEAR FORCED VIBRATION OF AXIALLY MOVING VISCOELASTIC BEAMS
Institute of Scientific and Technical Information of China (English)
Yang Xiaodong; Chen Li-Qun
2006-01-01
The non-linear forced vibration of axially moving viscoelastic beams excited by the vibration of the supporting foundation is investigated. A non-linear partial-differential equation governing the transverse motion is derived from the dynamical, constitutive equations and geometrical relations. By referring to the quasi-static stretch assumption, the partial-differential non-linearity is reduced to an integro-partial-differential one. The method of multiple scales is directly applied to the governing equations with the two types of non-linearity, respectively. The amplitude of near- and exact-resonant steady state is analyzed by use of the solvability condition of eliminating secular terms. Numerical results are presented to show the contributions of foundation vibration amplitude, viscoelastic damping, and nonlinearity to the response amplitude for the first and the second mode.
AMABILI, M.; PELLICANO, F.; PAÏDOUSSIS, M. P.
1999-08-01
The study presented is an investigation of the non-linear dynamics and stability of simply supported, circular cylindrical shells containing inviscid incompressible fluid flow. Non-linearities due to large-amplitude shell motion are considered by using the non-linear Donnell's shallow shell theory, with account taken of the effect of viscous structural damping. Linear potential flow theory is applied to describe the fluid-structure interaction. The system is discretiszd by Galerkin's method, and is investigated by using a model involving seven degrees of freedom, allowing for travelling wave response of the shell and shell axisymmetric contraction. Two different boundary conditions are applied to the fluid flow beyond the shell, corresponding to: (i) infinite baffles (rigid extensions of the shell), and (ii) connection with a flexible wall of infinite extent in the longitudinal direction, permitting solution by separation of variables; they give two different kinds of dynamical behaviour of the system, as a consequence of the fact that axisymmetric contraction, responsible for the softening non-linear dynamical behaviour of shells, is not allowed if the fluid flow beyond the shell is constrained by rigid baffles. Results show that the system loses stability by divergence.
Canonical group quantization and boundary conditions
Energy Technology Data Exchange (ETDEWEB)
Jung, Florian
2012-07-16
In the present thesis, we study quantization of classical systems with non-trivial phase spaces using the group-theoretical quantization technique proposed by Isham. Our main goal is a better understanding of global and topological aspects of quantum theory. In practice, the group-theoretical approach enables direct quantization of systems subject to constraints and boundary conditions in a natural and physically transparent manner -- cases for which the canonical quantization method of Dirac fails. First, we provide a clarification of the quantization formalism. In contrast to prior treatments, we introduce a sharp distinction between the two group structures that are involved and explain their physical meaning. The benefit is a consistent and conceptually much clearer construction of the Canonical Group. In particular, we shed light upon the 'pathological' case for which the Canonical Group must be defined via a central Lie algebra extension and emphasise the role of the central extension in general. In addition, we study direct quantization of a particle restricted to a half-line with 'hard wall' boundary condition. Despite the apparent simplicity of this example, we show that a naive quantization attempt based on the cotangent bundle over the half-line as classical phase space leads to an incomplete quantum theory; the reflection which is a characteristic aspect of the 'hard wall' is not reproduced. Instead, we propose a different phase space that realises the necessary boundary condition as a topological feature and demonstrate that quantization yields a suitable quantum theory for the half-line model. The insights gained in the present special case improve our understanding of the relation between classical and quantum theory and illustrate how contact interactions may be incorporated.
An H-Principle With Boundary Condition
Dotto, Emanuele
2010-01-01
We prove an h-principle with boundary condition for a certain class of topological spaces valued sheaves. The techniques used in the proof come from the study of the homotopy type of the cobordism categories, and they are of simplicial and categorical nature. Applying the main result of this paper to a certain sheaf we find another proof of the homotopy equivalence between the classifying space of a cobordism category and a loop space of the Thom space of the complement of the tautological bundle over the Grassmannians.
An h-principle with boundary condition
DEFF Research Database (Denmark)
Dotto, Emanuele
2010-01-01
We prove an h-principle with boundary condition for a certain class of topological spaces valued sheaves. The techniques used in the proof come from the study of the homotopy type of the cobordism categories, and they are of simplicial and categorical nature. Applying the main result of this paper...... to a certain sheaf we find another proof of the homotopy equivalence between the classifying space of a cobordism category and a loop space of the Thom space of the complement of the tautological bundle over the Grassmannians....
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...
Non-linear modal analysis of structural components subjected to unilateral constraints
Attar, M.; Karrech, A.; Regenauer-Lieb, K.
2017-02-01
In this paper, we present a detailed numerical study of the non-linear dynamics in structural components under unilateral contact constraints. Here, the unilateral term characterises the constitutive law of the restoring force in the constraints as they only sustain elastic reactions in one direction, either compressive or tensile. Thus, the non-differentiability of the contact law at the discontinuity point is the only source of non-linearity. In our approach, the discrete lattice method (DLM) is used to treat the continuous system as a piecewise linear model. Thus, the trajectory of each node in the discrete model would be a sequence of smooth solutions with the switching times between them. The application of the one-step integration scheme allows us to detect the occurrence of contact (i.e. the instants that the lattice nodes cross the discontinuity boundary) and consequently update the active constraints. We also consider embedding the bisection algorithm into the time integration procedure to localise the instants at which the nodes cross the boundary and minimise the accumulative error. Subsequently, the resulting unconditionally stable integration scheme is utilised as the modelling tool in combination with the shooting technique to perform a novel non-smooth modal analysis. In analogy with the smooth non-linear systems, the evolution of non-smooth periodic motions is presented in the frequency-stiffness plots. We apply our method to obtain non-linear normal modes (NNMs) for a number of representative problems, including a bar-obstacle system, a beam-substrate system and a granular chain with tensionless interactions. These numerical examples demonstrate the efficiency of the solution procedure to trace the family of energy-independent non-linear modes across the range of contact stiffnesses. Moreover, the stability analysis of the modes on the plot backbone reveal that they may become unstable due to the interaction with the higher modes or bifurcation of
Thermal field theories and shifted boundary conditions
Giusti, Leonardo
2013-01-01
The analytic continuation to an imaginary velocity of the canonical partition function of a thermal system expressed in a moving frame has a natural implementation in the Euclidean path-integral formulation in terms of shifted boundary conditions. The Poincare' invariance underlying a relativistic theory implies a dependence of the free-energy on the compact length L_0 and the shift xi only through the combination beta=L_0(1+xi^2)^(1/2). This in turn implies that the energy and the momentum distributions of the thermal theory are related, a fact which is encoded in a set of Ward identities among the correlators of the energy-momentum tensor. The latter have interesting applications in lattice field theory: they offer novel ways to compute thermodynamic potentials, and a set of identities to renormalize non-perturbatively the energy-momentum tensor. At fixed bare parameters the shifted boundary conditions also provide a simple method to vary the temperature in much smaller steps than with the standard procedur...
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...
Effective Hydrodynamic Boundary Conditions for Corrugated Surfaces
Mongruel, Anne; Asmolov, Evgeny S; Vinogradova, Olga I
2012-01-01
We report measurements of the hydrodynamic drag force acting on a smooth sphere falling down under gravity to a plane decorated with microscopic periodic grooves. Both surfaces are lyophilic, so that a liquid (silicone oil) invades the surface texture being in the Wenzel state. A significant decrease in the hydrodynamic resistance force as compared with that predicted for two smooth surfaces is observed. To quantify the effect of roughness we use the effective no-slip boundary condition, which is applied at the imaginary smooth homogeneous isotropic surface located at an intermediate position between top and bottom of grooves. Such an effective condition fully characterizes the force reduction measured with the real surface, and the location of this effective plane is related to geometric parameters of the texture by a simple analytical formula.
Processing Approach of Non-linear Adjustment Models in the Space of Non-linear Models
Institute of Scientific and Technical Information of China (English)
LI Chaokui; ZHU Qing; SONG Chengfang
2003-01-01
This paper investigates the mathematic features of non-linear models and discusses the processing way of non-linear factors which contributes to the non-linearity of a nonlinear model. On the basis of the error definition, this paper puts forward a new adjustment criterion, SGPE.Last, this paper investigates the solution of a non-linear regression model in the non-linear model space and makes the comparison between the estimated values in non-linear model space and those in linear model space.
Non-Linear Approximation of Bayesian Update
Litvinenko, Alexander
2016-06-23
We develop a non-linear approximation of expensive Bayesian formula. This non-linear approximation is applied directly to Polynomial Chaos Coefficients. In this way, we avoid Monte Carlo sampling and sampling error. We can show that the famous Kalman Update formula is a particular case of this update.
Non-linear finite element modeling
DEFF Research Database (Denmark)
Mikkelsen, Lars Pilgaard
The note is written for courses in "Non-linear finite element method". The note has been used by the author teaching non-linear finite element modeling at Civil Engineering at Aalborg University, Computational Mechanics at Aalborg University Esbjerg, Structural Engineering at the University...... on the governing equations and methods of implementing....
Neural Networks for Non-linear Control
DEFF Research Database (Denmark)
Sørensen, O.
1994-01-01
This paper describes how a neural network, structured as a Multi Layer Perceptron, is trained to predict, simulate and control a non-linear process.......This paper describes how a neural network, structured as a Multi Layer Perceptron, is trained to predict, simulate and control a non-linear process....
Neural Networks for Non-linear Control
DEFF Research Database (Denmark)
Sørensen, O.
1994-01-01
This paper describes how a neural network, structured as a Multi Layer Perceptron, is trained to predict, simulate and control a non-linear process.......This paper describes how a neural network, structured as a Multi Layer Perceptron, is trained to predict, simulate and control a non-linear process....
Surface Tension of Acid Solutions: Fluctuations beyond the Non-linear Poisson-Boltzmann Theory
Markovich, Tomer; Podgornik, Rudi
2016-01-01
We extend our previous study of surface tension of ionic solutions and apply it to the case of acids (and salts) with strong ion-surface interactions. These ion-surface interactions yield a non-linear boundary condition with an effective surface charge due to adsorption of ions from the bulk onto the interface. The calculation is done using the loop-expansion technique, where the zero-loop (mean field) corresponds of the non-linear Poisson-Boltzmann equation. The surface tension is obtained analytically to one-loop order, where the mean-field contribution is a modification of the Poisson-Boltzmann surface tension, and the one-loop contribution gives a generalization of the Onsager-Samaras result. Our theory fits well a wide range of different acids and salts, and is in accord with the reverse Hofmeister series for acids.
Trapping Horizons as inner boundary conditions for black hole spacetimes
Jaramillo, J L; Cordero-Carrion, I; Ibáñez, J M
2007-01-01
We present a set of inner boundary conditions for the numerical construction of dynamical black hole space-times, when employing a 3+1 constrained evolution scheme and an excision technique. These inner boundary conditions are heuristically motivated by the dynamical trapping horizon framework and are enforced in an elliptic subsystem of the full Einstein equation. In the stationary limit they reduce to existing isolated horizon boundary conditions. A characteristic analysis completes the discussion of inner boundary conditions for the radiative modes.
A Boundary Control Problem for the Viscous Cahn–Hilliard Equation with Dynamic Boundary Conditions
Energy Technology Data Exchange (ETDEWEB)
Colli, Pierluigi, E-mail: pierluigi.colli@unipv.it; Gilardi, Gianni, E-mail: gianni.gilardi@unipv.it [Universitá di Pavia and Research Associate at the IMATI – C.N.R. PAVIA, Dipartimento di Matematica “F. Casorati” (Italy); Sprekels, Jürgen, E-mail: juergen.sprekels@wias-berlin.de [Weierstrass Institute (Germany)
2016-04-15
A boundary control problem for the viscous Cahn–Hilliard equations with possibly singular potentials and dynamic boundary conditions is studied and first order necessary conditions for optimality are proved.
On Hydroelastic Body-Boundary Condition of Floating Structures
DEFF Research Database (Denmark)
Xia, Jinzhu
1996-01-01
A general linear body boundary condition of hydroelastic analysis of arbitrary shaped floating structures generalizes the classic kinematic rigid-body (Timman-Newman) boundary condition for seakeeping problems. The new boundary condition is consistent with the existing theories under certain assu...
Thermal momentum distribution from shifted boundary conditions
Giusti, Leonardo
2011-01-01
At finite temperature the distribution of the total momentum is an observable characterizing the thermal state of a field theory, and its cumulants are related to thermodynamic potentials. In a relativistic system at zero chemical potential, for instance, the thermal variance of the total momentum is a direct measure of the entropy. We relate the generating function of the cumulants to the ratio of a path integral with properly shifted boundary conditions in the compact direction over the ordinary partition function. In this form it is well suited for Monte-Carlo evaluation, and the cumulants can be extracted straightforwardly. We test the method in the SU(3) Yang--Mills theory, and obtain the entropy density at three different temperatures.
On reweighting for twisted boundary conditions
Bussone, Andrea; Hansen, Martin; Pica, Claudio
2016-01-01
We consider the possibility of using reweighting techniques in order to correct for the breaking of unitarity when twisted boundary conditions are imposed on valence fermions in simulations of lattice gauge theories. We start by studying the properties of reweighting factors and their variances at tree-level. That leads us to the introduction of a factorization for the fermionic reweighting determinant. In the numerical, stochastic, implementation of the method, we find that the effect of reweighting is negligible in the case of large volumes but it is sizeable when the volumes are small and the twisting angles are large. More importantly, we find that for un-improved Wilson fermions, and in small volumes, the dependence of the critical quark mass on the twisting angle is quite pronounced and results in large violations of the continuum dispersion relation.
An inhomogeneous wave equation and non-linear Diophantine approximation
DEFF Research Database (Denmark)
Beresnevich, V.; Dodson, M. M.; Kristensen, S.;
2008-01-01
A non-linear Diophantine condition involving perfect squares and arising from an inhomogeneous wave equation on the torus guarantees the existence of a smooth solution. The exceptional set associated with the failure of the Diophantine condition and hence of the existence of a smooth solution...... is studied. Both the Lebesgue and Hausdorff measures of this set are obtained....
Effects of Boundary Conditions on Single-File Pedestrian Flow
Zhang, Jun; Seyfried, Armin
2015-01-01
In this paper we investigate effects of boundary conditions on one dimensional pedestrian flow which involves purely longitudinal interactions. Qualitatively, stop-and-go waves are observed under closed boundary condition and dissolve when the boundary is open. To get more detailed information the fundamental diagrams of the open and closed systems are compared using Voronoi-based measurement method. Higher maximal specific flow is observed from the pedestrian movement at open boundary condition.
Surface free energy for systems with integrable boundary conditions
Energy Technology Data Exchange (ETDEWEB)
Goehmann, Frank [Fachbereich C-Physik, Bergische Universitaet Wuppertal, 42097 Wuppertal (Germany); Bortz, Michael [Department of Theoretical Physics, Australian National University, Canberra ACT 0200 (Australia); Frahm, Holger [Institut fuer Theoretische Physik, Universitaet Hannover, 30167 Hannover (Germany)
2005-12-16
The surface free energy is the difference between the free energies for a system with open boundary conditions and the same system with periodic boundary conditions. We use the quantum transfer matrix formalism to express the surface free energy in the thermodynamic limit of systems with integrable boundary conditions as a matrix element of certain projection operators. Specializing to the XXZ spin-1/2 chain we introduce a novel 'finite temperature boundary operator' which characterizes the thermodynamical properties of surfaces related to integrable boundary conditions.
Bucur, Dorin; Feireisl, Eduard; Nečasová, Šárka
2010-07-01
We consider a family of solutions to the evolutionary Navier-Stokes system supplemented with the complete slip boundary conditions on domains with rough boundaries. We give a complete description of the asymptotic limit by means of Γ-convergence arguments, and identify a general class of boundary conditions.
Directory of Open Access Journals (Sweden)
M.H. Tiwana
2017-04-01
Full Text Available This work investigates the fractional non linear reaction diffusion (FNRD system of Lotka-Volterra type. The system of equations together with the boundary conditions are solved by Homotopy perturbation transform method (HPTM. The series solutions are obtained for the two cases (homogeneous and non-homogeneous of FNRD system. The effect of fractional parameter on the mass concentration of two species are shown and discussed with the help of 3D graphs.
Measuring the entropy from shifted boundary conditions
Giusti, Leonardo
2013-01-01
We explore a new computational strategy for determining the equation of state of the SU(3) Yang-Mills theory. By imposing shifted boundary conditions, the entropy density is computed from the vacuum expectation value of the off-diagonal components T_{0k} of the energy-momentum tensor. A step-scaling function is introduced to span a wide range in temperature values. We present preliminary numerical results for the entropy density and its step-scaling function obtained at eight temperature values in the range T_c - 15 T_c. At each temperature, discretization effects are removed by simulating the theory at several lattice spacings and by extrapolating the results to the continuum limit. Finite-size effects are always kept below the statistical errors. The absence of ultraviolet power divergences and the remarkably small discretization effects allow for a precise determination of the step-scaling function in the explored temperature range. These findings establish this strategy as a viable solution for an accurat...
Positive solutions for the beam equation under certain boundary conditions
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Bo Yang
2005-07-01
Full Text Available We consider a boundary-value problem for the beam equation, in which the boundary conditions mean that the beam is embedded at one end and fastened with a sliding clamp at the other end. Some priori estimates to the positive solutions for the boundary-value problem are obtained. Sufficient conditions for the existence and nonexistence of positive solutions for the boundary-value problem are established.
Change-Of-Bases Abstractions for Non-Linear Systems
Sankaranarayanan, Sriram
2012-01-01
We present abstraction techniques that transform a given non-linear dynamical system into a linear system or an algebraic system described by polynomials of bounded degree, such that, invariant properties of the resulting abstraction can be used to infer invariants for the original system. The abstraction techniques rely on a change-of-basis transformation that associates each state variable of the abstract system with a function involving the state variables of the original system. We present conditions under which a given change of basis transformation for a non-linear system can define an abstraction. Furthermore, the techniques developed here apply to continuous systems defined by Ordinary Differential Equations (ODEs), discrete systems defined by transition systems and hybrid systems that combine continuous as well as discrete subsystems. The techniques presented here allow us to discover, given a non-linear system, if a change of bases transformation involving degree-bounded polynomials yielding an alge...
Non-linear growth and condensation in multiplex networks
Nicosia, Vincenzo; Latora, Vito; Barthelemy, Marc
2013-01-01
Different types of interactions coexist and coevolve to shape the structure and function of a multiplex network. We propose here a general class of growth models in which the various layers of a multiplex network coevolve through a set of non-linear preferential attachment rules. We show, both numerically and analytically, that by tuning the level of non-linearity these models allow to reproduce either homogeneous or heterogeneous degree distributions, together with positive or negative degree correlations across layers. In particular, we derive the condition for the appearance of a condensed state in which a single node connects to nearly all other nodes of a layer.
STOCHASTIC ANALYSIS OF GROUNDWATER FLOW SUBJECT TO RANDOM BOUNDARY CONDITIONS
Institute of Scientific and Technical Information of China (English)
SHI Liang-sheng; YANG Jin-zhong; CAI Shu-ying; LIN Lin
2008-01-01
A stochastic model was developed to simulate the flow in heterogeneous media subject to random boundary conditions.Approximate partial differential equations were derived based on the Karhunen-Loeve (KL) expansion and perturbation expansion. The effect of random boundary conditions on the two-dimensional flow was examined. It is shown that the proposed stochastic model is efficient to include the random boundary conditions. The random boundaries lead to the increase of head variance and velocity variance. The influence of the random boundary conditions on head uncertainty is exerted over the whole simulated region, while the randomness of the boundary conditions leads to the increase of the velocity variance in the vicinity of boundaries.
On the non-linearity of the subsidiary systems
Friedrich, H
2005-01-01
In hyperbolic reductions of the Einstein equations the evolution of gauge conditions or constraint quantities is controlled by subsidiary systems. We point out a class of non-linearities in these systems which may have the potential of generating catastrophic growth of gauge resp. constraint violations in numerical calculations.
Optimal boundary conditions at the staircase-shaped coastlines
Kazantsev, Eugene
2014-01-01
A 4D-Var data assimilation technique is applied to the rectangular-box configuration of the NEMO in order to identify the optimal parametrization of boundary conditions at lateral boundaries. The case of the staircase-shaped coastlines is studied by rotating the model grid around the center of the box. It is shown that, in some cases, the formulation of the boundary conditions at the exact boundary leads to appearance of exponentially growing modes while optimal boundary conditions allow to correct the errors induced by the staircase-like appriximation of the coastline.
Analysis of Boundary Conditions for Crystal Defect Atomistic Simulations
Ehrlacher, V.; Ortner, C.; Shapeev, A. V.
2016-12-01
Numerical simulations of crystal defects are necessarily restricted to finite computational domains, supplying artificial boundary conditions that emulate the effect of embedding the defect in an effectively infinite crystalline environment. This work develops a rigorous framework within which the accuracy of different types of boundary conditions can be precisely assessed. We formulate the equilibration of crystal defects as variational problems in a discrete energy space and establish qualitatively sharp regularity estimates for minimisers. Using this foundation we then present rigorous error estimates for (i) a truncation method (Dirichlet boundary conditions), (ii) periodic boundary conditions, (iii) boundary conditions from linear elasticity, and (iv) boundary conditions from nonlinear elasticity. Numerical results confirm the sharpness of the analysis.
Reconnection Rate in Collisionless Magnetic Reconnection under Open Boundary Conditions
Institute of Scientific and Technical Information of China (English)
HUANG Jun; MA Zhi-Wei
2008-01-01
Collisionless magnetic reconnection is studied by using two-dimensional Darwin particle-in-cell simulations with different types of open boundary conditions.The simulation results indicate that reconnection rates are strongly dependent on the imposed boundary conditions of the magnetic field Bx in the inward side. Under the zerogradient Bx boundary condition,the reconnection rate quickly decreases after reaching its maximum and no steady-state is found.Under both electromagnetic and magnetosonic boundary conditions,the system can reach a quasi-steady state.However,the reconnection rate Er≈ 0.08 under the electromagnetic boundary condition is weaker than Er≈ 0.13 under the magnetosonic boundary condition.
Non-linear analysis and calculation of the performance of a shelving protection system by FEM
García Nieto, P. J.; del Coz Díaz, J. J.; Vilán Vilán, J. A.; Suárez Sierra, J. L.
2012-12-01
The aim of this paper consists on the study, analysis and calculation of the efficiency of a shelving protection system by means of the finite element method (FEM). These shelving protection systems are intended to prevent the eventual damage due to the impacts of transport elements in motion, such as: forklifts, dumpers, hand pallet trucks, and so on. The impact loads may threaten the structural integrity of the shelving system. The present structural problem is highly non-linear, due to the simultaneous presence of the following nonlinearities: material non-linearity (plasticity in this case), geometrical non-linearity (large displacements) and contact-type boundary conditions (between the rigid body and the protection system). A total of forty eight different FEM models are built varying the thickness of the steel plate (4, 5 and 6 mm), the impact height (0.1, 0.2, 0.3 and 0.4 meters) and the impact direction (head-on collision and side impact). Once the models are solved, the stress distribution, the overall displacements and the absorbed impact energy were calculated. In order to determine the best shelving protection's candidate, some constraints must be taken into account: the maximum allowable stress (235 MPa), the maximum displacement (0.05 m) and the absorbed impact energy (400 J according to the European Standard Rule PREN-15512). Finally, the most important results are shown and conclusions of this study are exposed.
Phase modulated solitary waves controlled by bottom boundary condition
Mukherjee, Abhik
2014-01-01
A forced KdV equation is derived to describe weakly nonlinear, shallow water surface wave propagation over non trivial bottom boundary condition. We show that different functional forms of bottom boundary conditions self-consistently produce different forced kdV equations as the evolution equations for the free surface. Solitary wave solutions have been analytically obtained where phase gets modulated controlled by bottom boundary condition whereas amplitude remains constant.
Normal ordering and boundary conditions in open bosonic strings
Braga, N R F; Carrion, H L; Braga, Nelson R. F.; Godinho, Cresus F. L.; Carrion, Hector L.
2004-01-01
Boundary conditions play a non trivial role in string theory. For instance the rich structure of D-branes is generated by choosing appropriate combinations of Dirichlet and Neumann boundary conditions. Furthermore, when an antisymmetric background is present at the string end-points (corresponding to mixed boundary conditions) space time becomes non-commutative there. We show here how to build up normal ordered products for bosonic string position operators that satisfy both equations of motion and open string boundary conditions at quantum level. We also calculate the equal time commutator of these normal ordered products in the presence of antisymmetric tensor background.
Laganà, K; Dubini, G; Migliavacca, F; Pietrabissa, R; Pennati, G; Veneziani, A; Quarteroni, A
2002-01-01
This work was motivated by the problems of analysing detailed 3D models of vascular districts with complex anatomy. It suggests an approach to prescribing realistic boundary conditions to use in order to obtain information on local as well as global haemodynamics. A method was developed which simultaneously solves Navier-Stokes equations for local information and a non-linear system of ordinary differential equations for global information. This is based on the principle that an anatomically detailed 3D model of a cardiovascular district can be achieved by using the finite element method. In turn the finite element method requires a specific boundary condition set. The approach outlined in this work is to include the system of ordinary differential equations in the boundary condition set. Such a multiscale approach was first applied to two controls: (i) a 3D model of a straight tube in a simple hydraulic network and (ii) a 3D model of a straight coronary vessel in a lumped-parameter model of the cardiovascular system. The results obtained are very close to the solutions available for the pipe geometry. This paper also presents preliminary results from the application of the methodology to a particular haemodynamic problem: namely the fluid dynamics of a systemic-to-pulmonary shunt in paediatric cardiac surgery.
Quantum “violation” of Dirichlet boundary condition
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I.Y. Park
2017-02-01
Full Text Available Dirichlet boundary conditions have been widely used in general relativity. They seem at odds with the holographic property of gravity simply because a boundary configuration can be varying and dynamic instead of dying out as required by the conditions. In this work we report what should be a tension between the Dirichlet boundary conditions and quantum gravitational effects, and show that a quantum-corrected black hole solution of the 1PI action no longer obeys, in the naive manner one may expect, the Dirichlet boundary conditions imposed at the classical level. We attribute the ‘violation’ of the Dirichlet boundary conditions to a certain mechanism of the information storage on the boundary.
Non-Linear Relativity in Position Space
Kimberly, D; Medeiros-Neto, J F; Kimberly, Dagny; Magueijo, João; Medeiros, João
2003-01-01
We propose two methods for obtaining the dual of non-linear relativity as previously formulated in momentum space. In the first we allow for the (dual) position space to acquire a non-linear representation of the Lorentz group independently of the chosen representation in momentum space. This requires a non-linear definition for the invariant contraction between momentum and position spaces. The second approach, instead, respects the linearity of the invariant contraction. This fully fixes the dual of momentum space and dictates a set of energy-dependent space-time Lorentz transformations. We discuss a variety of physical implications that would distinguish these two strategies. We also show how they point to two rather distinct formulations of theories of gravity with an invariant energy and/or length scale.
Correlations and Non-Linear Probability Models
DEFF Research Database (Denmark)
Breen, Richard; Holm, Anders; Karlson, Kristian Bernt
2014-01-01
the dependent variable of the latent variable model and its predictor variables. We show how this correlation can be derived from the parameters of non-linear probability models, develop tests for the statistical significance of the derived correlation, and illustrate its usefulness in two applications. Under......Although the parameters of logit and probit and other non-linear probability models are often explained and interpreted in relation to the regression coefficients of an underlying linear latent variable model, we argue that they may also be usefully interpreted in terms of the correlations between...... certain circumstances, which we explain, the derived correlation provides a way of overcoming the problems inherent in cross-sample comparisons of the parameters of non-linear probability models....
Non-linear (loop) quantum cosmology
Bojowald, Martin; Dantas, Christine C; Jaffe, Matthew; Simpson, David
2012-01-01
Inhomogeneous quantum cosmology is modeled as a dynamical system of discrete patches, whose interacting many-body equations can be mapped to a non-linear minisuperspace equation by methods analogous to Bose-Einstein condensation. Complicated gravitational dynamics can therefore be described by more-manageable equations for finitely many degrees of freedom, for which powerful solution procedures are available, including effective equations. The specific form of non-linear and non-local equations suggests new questions for mathematical and computational investigations, and general properties of non-linear wave equations lead to several new options for physical effects and tests of the consistency of loop quantum gravity. In particular, our quantum cosmological methods show how sizeable quantum corrections in a low-curvature universe can arise from tiny local contributions adding up coherently in large regions.
Non-Linear Logging Parameters Inversion
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
The non-linear logging parameters inversion is based on the field theory, information optimization and predication theory. It uses seismic charaoters,geological model and logging data as a restriction to inverse 2D, 3D logging parameters data volume. Using this method,
Non linear system become linear system
Directory of Open Access Journals (Sweden)
Petre Bucur
2007-01-01
Full Text Available The present paper refers to the theory and the practice of the systems regarding non-linear systems and their applications. We aimed the integration of these systems to elaborate their response as well as to highlight some outstanding features.
Oscillatons formed by non linear gravity
Obregón, O; Schunck, F E; Obregon, Octavio; Schunck, Franz E.
2004-01-01
Oscillatons are solutions of the coupled Einstein-Klein-Gordon (EKG) equations that are globally regular and asymptotically flat. By means of a Legendre transformation we are able to visualize the behaviour of the corresponding objects in non-linear gravity where the scalar field has been absorbed by means of the conformal mapping.
Correlations and Non-Linear Probability Models
DEFF Research Database (Denmark)
Breen, Richard; Holm, Anders; Karlson, Kristian Bernt
2014-01-01
Although the parameters of logit and probit and other non-linear probability models are often explained and interpreted in relation to the regression coefficients of an underlying linear latent variable model, we argue that they may also be usefully interpreted in terms of the correlations betwee...... certain circumstances, which we explain, the derived correlation provides a way of overcoming the problems inherent in cross-sample comparisons of the parameters of non-linear probability models.......Although the parameters of logit and probit and other non-linear probability models are often explained and interpreted in relation to the regression coefficients of an underlying linear latent variable model, we argue that they may also be usefully interpreted in terms of the correlations between...... the dependent variable of the latent variable model and its predictor variables. We show how this correlation can be derived from the parameters of non-linear probability models, develop tests for the statistical significance of the derived correlation, and illustrate its usefulness in two applications. Under...
Parameter identification of stochastic diffusion systems with unknown boundary conditions
Aihara, Shin Ichi; Bagchi, Arunabha
2013-01-01
This paper treats the filtering and parameter identification for the stochastic diffusion systems with unknown boundary conditions. The physical situation of the unknown boundary conditions can be found in many industrial problems,i.g., the salt concentration model of the river Rhine is a typical ex
On domain wall boundary conditions for the XXZ spin Hamiltonian
DEFF Research Database (Denmark)
Orlando, Domenico; Reffert, Susanne; Reshetikhin, Nicolai
In this note, we derive the spectrum of the infinite quantum XXZ spin chain with domain wall boundary conditions. The eigenstates are constructed as limits of Bethe states for the finite XXZ spin chain with quantum sl(2) invariant boundary conditions....
Performance of Numerical Boundary Condition based on Active Wave Absorption
DEFF Research Database (Denmark)
Troch, Peter; De Rouck, Julien; Frigaard, Peter
2001-01-01
The performance of a new active wave generating-absorbing boundary condition for a numerical model based on the Volume Of Fluid (VOF) method for tracking free surfaces is presented.......The performance of a new active wave generating-absorbing boundary condition for a numerical model based on the Volume Of Fluid (VOF) method for tracking free surfaces is presented....
Periodic Boundary Conditions in the ALEGRA Finite Element Code
Energy Technology Data Exchange (ETDEWEB)
AIDUN,JOHN B.; ROBINSON,ALLEN C.; WEATHERBY,JOE R.
1999-11-01
This document describes the implementation of periodic boundary conditions in the ALEGRA finite element code. ALEGRA is an arbitrary Lagrangian-Eulerian multi-physics code with both explicit and implicit numerical algorithms. The periodic boundary implementation requires a consistent set of boundary input sets which are used to describe virtual periodic regions. The implementation is noninvasive to the majority of the ALEGRA coding and is based on the distributed memory parallel framework in ALEGRA. The technique involves extending the ghost element concept for interprocessor boundary communications in ALEGRA to additionally support on- and off-processor periodic boundary communications. The user interface, algorithmic details and sample computations are given.
Non-linear dendrites can tune neurons
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Romain Daniel Cazé
2014-03-01
Full Text Available A signature of visual, auditory, and motor cortices is the presence of neurons tuned to distinct features of the environment. While neuronal tuning can be observed in most brain areas, its origin remains enigmatic, and new calcium imaging data complicate this problem. Dendritic calcium signals, in a L2/3 neuron from the mouse visual cortex, display a wide range of tunings that could be different from the neuronal tuning (Jia et al 2010. To elucidate this observation we use multi-compartmental models of increasing complexity, from a binary to a realistic biophysical model of L2/3 neuron. These models possess non-linear dendritic subunits inside which the result of multiple excitatory inputs is smaller than their arithmetic sum. While dendritic non-linear subunits are ad-hoc in the binary model, non-linearities in the realistic model come from the passive saturation of synaptic currents. Because of these non-linearities our neuron models are scatter sensitive: the somatic membrane voltage is higher when presynaptic inputs target different dendrites than when they target a single dendrite. This spatial bias in synaptic integration is, in our models, the origin of neuronal tuning. Indeed, assemblies of presynaptic inputs encode the stimulus property through an increase in correlation or activity, and only the assembly that encodes the preferred stimulus targets different dendrites. Assemblies coding for the non-preferred stimuli target single dendrites, explaining the wide range of observed tunings and the possible difference between dendritic and somatic tuning. We thus propose, in accordance with the latest experimental observations, that non-linear integration in dendrites can generate neuronal tuning independently of the coding regime.
Conformal Boundary Conditions and what they teach us
Petkova, V B
2001-01-01
The question of boundary conditions in conformal field theories is discussed, in the light of recent progress. Two kinds of boundary conditions are examined, along open boundaries of the system, or along closed curves or ``seams''. Solving consistency conditions known as Cardy equation is shown to amount to the algebraic problem of finding integer valued representations of (one or two copies of) the fusion algebra. Graphs encode these boundary conditions in a natural way, but are also relevant in several aspects of physics ``in the bulk''. Quantum algebras attached to these graphs contain information on structure constants of the operator algebra, on the Boltzmann weights of the corresponding integrable lattice models etc. Thus the study of boundary conditions in Conformal Field Theory offers a new perspective on several old physical problems and offers an explicit realisation of recent mathematical concepts.
Gravitational instability on the brane: the role of boundary conditions
Shtanov, Y; Sahni, V; Shtanov, Yuri; Viznyuk, Alexander; Sahni, Varun
2007-01-01
An outstanding issue in braneworld theory concerns the setting up of proper boundary conditions for the brane-bulk system. Boundary conditions (BC's) employing regulatory branes or demanding that the bulk metric be nonsingular have yet to be implemented in full generality. In this paper, we take a different route and specify boundary conditions directly on the brane thereby arriving at a local and closed system of equations (on the brane). We consider a one-parameter family of boundary conditions involving the anisotropic stress of the projection of the bulk Weyl tensor on the brane and derive an exact system of equations describing scalar cosmological perturbations on a generic braneworld with induced gravity. Depending upon our choice of boundary conditions, perturbations on the brane either grow moderately (region of stability) or rapidly (instability). In the instability region, the evolution of perturbations usually depends upon the scale: small scale perturbations grow much more rapidly than those on la...
Poynting Flux-Conserving Boundary Conditions for Global MHD Models
Xi, S.; Lotko, W.; Zhang, B.; Brambles, O.; Lyon, J.; Merkin, V. G.; Wiltberger, M. J.
2014-12-01
Poynting Flux-conserving boundary conditions that conserve low-frequency, magnetic field-aligned, electromagnetic energy flux across the low-altitude (or inner) boundary in global magnetospheric magnetohydrodynamics (MHD) models is presented. This method involves the mapping of both the potential from the ionosphere and the perpendicular magnetic field from the inner magnetosphere to the ghost cells of the computational domain. The single fluid Lyon-Fedder-Mobarry (LFM) model is used to verify this method. The comparisons of simulations using the standard hardwall boundary conditions of the LFM model and the flux-conserving boundary conditions show that the method reported here improves the transparency of the boundary for the flow of low-frequency (essentially DC) electromagnetic energy flux along field lines. As a consequence, the field-aligned DC Poynting flux just above the boundary is very nearly equal to the ionospheric Joule heating, as it should be if electromagnetic energy is conserved.
Chiral boundary conditions for singletons and W-branes
Raeymaekers, Joris; Van den Bleeken, Dieter
2017-07-01
We revisit the holographic dictionary for a free massless scalar in AdS3, focusing on the `singleton' solutions for which the boundary profile is an arbitrary chiral function. We look for consistent boundary conditions which include this class of solutions. On one hand, we give a no-go argument that they cannot be interpreted within any boundary condition which preserves full conformal invariance. On the other hand, we show that such solutions fit naturally in a generalization of the Compère-Song-Strominger boundary conditions, which preserve a chiral Virasoro and current algebra. These observations have implications for the black hole deconstruction proposal, which proposes singleton solutions as candidate black hole microstate geometries. Our results suggest that the chiral boundary condition, which also contains the extremal BTZ black hole, is the natural setting for holographically interpreting the black hole deconstruction proposal.
Sinou, Jean-Jacques; Thouverez, Fabrice; Jezequel, Louis
2006-01-01
International audience; Herein, a novel non-linear procedure for producing non-linear behaviour and stable limit cycle amplitudes of non-linear systems subjected to super-critical Hopf bifurcation point is presented. This approach, called Complex Non-Linear Modal Analysis (CNLMA), makes use of the non-linear unstable mode which governs the non-linear dynamic of structural systems in unstable areas. In this study, the computational methodology of CNLMA is presented for the systematic estimatio...
Breakup of spiral wave under different boundary conditions
Institute of Scientific and Technical Information of China (English)
Zhao Ying-Kui; Wang Guang-Rui; Chen Shi-Gang
2007-01-01
In this paper, we investigate the breakup of spiral wave under no-flux, periodic and Dirichlet boundary conditions respectively. When the parameter ε is close to a critical value for Doppler-induced wave breakup, the instability of the system caused by the boundary effect occurs in the last two cases, resulting in the breakup of spiral wave near the boundary. With our defined average order measure of spiral wave (AOMSW), we quantify the degree of order of the system when the boundary-induced breakup of spiral wave happens. By analysing the AOMSW and outer diameter R of the spiral tip orbit, it is easy to find that this boundary effect is correlated with large values of R, especially under the Dirichlet boundary condition. This correlation is nonlinear, so the AOMSW sometimes oscillates with the variation of ε.
Boundary condition effects on maximum groundwater withdrawal in coastal aquifers.
Lu, Chunhui; Chen, Yiming; Luo, Jian
2012-01-01
Prevention of sea water intrusion in coastal aquifers subject to groundwater withdrawal requires optimization of well pumping rates to maximize the water supply while avoiding sea water intrusion. Boundary conditions and the aquifer domain size have significant influences on simulating flow and concentration fields and estimating maximum pumping rates. In this study, an analytical solution is derived based on the potential-flow theory for evaluating maximum groundwater pumping rates in a domain with a constant hydraulic head landward boundary. An empirical correction factor, which was introduced by Pool and Carrera (2011) to account for mixing in the case with a constant recharge rate boundary condition, is found also applicable for the case with a constant hydraulic head boundary condition, and therefore greatly improves the usefulness of the sharp-interface analytical solution. Comparing with the solution for a constant recharge rate boundary, we find that a constant hydraulic head boundary often yields larger estimations of the maximum pumping rate and when the domain size is five times greater than the distance between the well and the coastline, the effect of setting different landward boundary conditions becomes insignificant with a relative difference between two solutions less than 2.5%. These findings can serve as a preliminary guidance for conducting numerical simulations and designing tank-scale laboratory experiments for studying groundwater withdrawal problems in coastal aquifers with minimized boundary condition effects.
Heat-kernel coefficients for oblique boundary conditions
Dowker, John S; Kirsten, Klaus
1997-01-01
We calculate the heat-kernel coefficients, up to $a_2$, for a U(1) bundle on the 4-Ball for boundary conditions which are such that the normal derivative of the field at the boundary is related to a first-order operator in boundary derivatives acting on the field. The results are used to place restrictions on the general forms of the coefficients. In the specific case considered, there can be a breakdown of ellipticity.
Effective boundary condition at a rough surface starting from a slip condition
Dalibard, Anne-Laure
2010-01-01
We consider the homogenization of the Navier-Stokes equation, set in a channel with a rough boundary, of small amplitude and wavelength $\\epsilon$. It was shown recently that, for any non-degenerate roughness pattern, and for any reasonable condition imposed at the rough boundary, the homogenized boundary condition in the limit $\\epsilon = 0$ is always no-slip. We give in this paper error estimates for this homogenized no-slip condition, and provide a more accurate effective boundary condition, of Navier type. Our result extends those obtained in previous works, in which the special case of a Dirichlet condition at the rough boundary was examined.
HYCOM Initial and Boundary Conditions for Coupled COAMPS/NCOM
2016-06-07
conditions (BCs and ICs) into globally- relocatable coupled COAMPS/NCOM, (2) quantitatively evaluate HYCOM sources of ICs and BCs against other...HYCOM Initial and Boundary Conditions for Coupled COAMPS/NCOM Julie Pullen Naval Research Laboratory 7 Grace Hopper Ave. Stop 2 Monterey, CA...long-term goal of this effort is to evaluate HYbrid Coordinate Ocean Model (HYCOM) initial and boundary conditions supplied to the air-ocean coupled
Non-Linear Dynamics and Fundamental Interactions
Khanna, Faqir
2006-01-01
The book is directed to researchers and graduate students pursuing an advanced degree. It provides details of techniques directed towards solving problems in non-linear dynamics and chos that are, in general, not amenable to a perturbative treatment. The consideration of fundamental interactions is a prime example where non-perturbative techniques are needed. Extension of these techniques to finite temperature problems is considered. At present these ideas are primarily used in a perturbative context. However, non-perturbative techniques have been considered in some specific cases. Experts in the field on non-linear dynamics and chaos and fundamental interactions elaborate the techniques and provide a critical look at the present status and explore future directions that may be fruitful. The text of the main talks will be very useful to young graduate students who are starting their studies in these areas.
On the non-linear stability of scalar field cosmologies
Energy Technology Data Exchange (ETDEWEB)
Alho, Artur; Mena, Filipe C [Centro de Matematica, Universidade do Minho, 4710-057 Braga (Portugal); Kroon, Juan A Valiente, E-mail: aalho@math.uminho.pt, E-mail: fmena@math.uminho.pt, E-mail: jav@maths.qmul.ac.uk [School of Mathematical Sciences, Queen Mary, University of London, London E1 4NS (United Kingdom)
2011-09-22
We review recent work on the stability of flat spatially homogeneous and isotropic backgrounds with a self-interacting scalar field. We derive a first order quasi-linear symmetric hyperbolic system for the Einstein-nonlinear-scalar field system. Then, using the linearized system, we show how to obtain necessary and sufficient conditions which ensure the exponential decay to zero of small non-linear perturbations.
Yusop, Nur Syaza Mohd; Mohamed, Nurul Akmal
2017-05-01
Boundary Element Method (BEM) is a numerical way to approximate the solutions of a Boundary Value Problem (BVP). The potential problem which involves the Laplace's equation on the square shape domain will be considered where the boundary is divided into four sets of linear boundary elements. We study the derivation system of equation for mixed BVP with one Dirichlet Boundary Condition (BC) is prescribed on one element of the boundary and Neumann BC on the other three elements. The mixed BVP will be reduced to a Boundary Integral Equation (BIE) by using a direct method which involves Green's second identity representation formula. Then, linear interpolation is used where the boundary will be discretized into some linear elements. As the result, we then obtain the system of linear equations. In conclusion, the specific element in the mixed BVP will have the specific prescribe value depends on the type of boundary condition. For Dirichlet BC, it has only one value at each node but for the Neumann BC, there will be different values at the corner nodes due to outward normal. Therefore, the assembly process for the system of equations related to the mixed BVP may not be as straight forward as Dirichlet BVP and Neumann BVP. For the future research, we will consider the different shape domains for mixed BVP with different prescribed boundary conditions.
Fliess, Michel; Join, Cédric; Sira-Ramirez, Hebertt
2008-01-01
International audience; Non-linear state estimation and some related topics, like parametric estimation, fault diagnosis, and perturbation attenuation, are tackled here via a new methodology in numerical differentiation. The corresponding basic system theoretic definitions and properties are presented within the framework of differential algebra, which permits to handle system variables and their derivatives of any order. Several academic examples and their computer simulations, with on-line ...
Non-linear Loudspeaker Unit Modelling
DEFF Research Database (Denmark)
Pedersen, Bo Rohde; Agerkvist, Finn T.
2008-01-01
Simulations of a 6½-inch loudspeaker unit are performed and compared with a displacement measurement. The non-linear loudspeaker model is based on the major nonlinear functions and expanded with time-varying suspension behaviour and flux modulation. The results are presented with FFT plots of three...... frequencies and different displacement levels. The model errors are discussed and analysed including a test with loudspeaker unit where the diaphragm is removed....
Fliess, Michel; Sira-Ramirez, Hebertt
2007-01-01
Non-linear state estimation and some related topics, like parametric estimation, fault diagnosis, and perturbation attenuation, are tackled here via a new methodology in numerical differentiation. The corresponding basic system theoretic definitions and properties are presented within the framework of differential algebra, which permits to handle system variables and their derivatives of any order. Several academic examples and their computer simulations, with on-line estimations, are illustrating our viewpoint.
Boundary states and finite size effects in sine-Gordon model with Neumann boundary condition
Bajnok, Z; Takács, G
2001-01-01
The sine-Gordon model with Neumann boundary condition is investigated. Using the bootstrap principle the spectrum of boundary bound states is established. Somewhat surprisingly it is found that Coleman-Thun diagrams and bound state creation may coexist. A framework to describe finite size effects in boundary integrable theories is developed and used together with the truncated conformal space approach to confirm the bound states and reflection factors derived by bootstrap.
Exponential reduction of finite volume effects with twisted boundary conditions
Cherman, Aleksey; Wagman, Michael L; Yaffe, Laurence G
2016-01-01
Flavor-twisted boundary conditions can be used for exponential reduction of finite volume artifacts in flavor-averaged observables in lattice QCD calculations with $SU(N_f)$ light quark flavor symmetry. Finite volume artifact reduction arises from destructive interference effects in a manner closely related to the phase averaging which leads to large $N_c$ volume independence. With a particular choice of flavor-twisted boundary conditions, finite volume artifacts for flavor-singlet observables in a hypercubic spacetime volume are reduced to the size of finite volume artifacts in a spacetime volume with periodic boundary conditions that is four times larger.
Hydrodynamic Boundary Conditions and Dynamic Forces between Bubbles and Surfaces
Manor, Ofer; Vakarelski, Ivan U.; Tang, Xiaosong; O'Shea, Sean J.; Stevens, Geoffrey W.; Grieser, Franz; Dagastine, Raymond R.; Chan, Derek Y. C.
2008-07-01
Dynamic forces between a 50μm radius bubble driven towards and from a mica plate using an atomic force microscope in electrolyte and in surfactant exhibit different hydrodynamic boundary conditions at the bubble surface. In added surfactant, the forces are consistent with the no-slip boundary condition at the mica and bubble surfaces. With no surfactant, a new boundary condition that accounts for the transport of trace surface impurities explains variations of dynamic forces at different speeds and provides a direct connection between dynamic forces and surface transport effects at the air-water interface.
Extensions of diffusion processes on intervals and Feller's boundary conditions
Yano, Kouji
2012-01-01
For a minimal diffusion process on $ (a,b) $, any possible extension of it to a standard process on $ [a,b] $ is characterized by the characteristic measures of excursions away from the boundary points $ a $ and $ b $. The generator of the extension is proved to be characterized by Feller's boundary condition.
Facilitating conditions for boundary-spanning behaviour in governance networks
I.F. van Meerkerk (Ingmar); J. Edelenbos (Jurian)
2017-01-01
textabstractThis article examines the impact of two facilitating conditions for boundary-spanning behaviour in urban governance networks. While research on boundary spanning is growing, there is little attention for antecedents. Combining governance network literature on project management and
Facilitating conditions for boundary-spanning behavior in governance networks
I.F. van Meerkerk (Ingmar); J. Edelenbos (Jurian)
2017-01-01
textabstractThis article examines the impact of two facilitating conditions for boundary-spanning behaviour in urban governance networks. While research on boundary spanning is growing, there is little attention for antecedents. Combining governance network literature on project management and
Numerical Solution for the Helmholtz Equation with Mixed Boundary Condition
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
We consider the numerical solution for the Helmholtz equation in R2 with mixed boundary conditions. The solvability of this mixed boundary value problem is established by the boundary integral equation method. Based on the Green formula, we express the solution in terms of the boundary data. The key to the numerical realization of this method is the computation of weakly singular integrals. Numerical performances show the validity and feasibility of our method. The numerical schemes proposed in this paper have been applied in the realization of probe method for inverse scattering problems.
Boundary Conditions for Free Interfaces with the Lattice Boltzmann Method
Bogner, Simon; Rüde, Ulrich
2014-01-01
In this paper we analyze the boundary treatment of the Lattice Boltzmann method for simulating 3D flows with free surfaces. The widely used free surface boundary condition of K\\"orner et al. (2005) is shown to be first order accurate. The article presents new free surface boundary schemes that are suitable for the lattice Boltzmann method and that have second order spatial accuracy. The new method takes the free boundary position and orientation with respect to the computational lattice into account. Numerical experiments confirm the theoretical findings and illustrate the the difference between the old and the new method.
Integration of non-linear cellular mechanisms regulating microvascular perfusion.
Griffith, T M; Edwards, D H
1999-01-01
It is becoming increasingly evident that interactions between the different cell types present in the vessel wall and the physical forces that result from blood flow are highly complex. This short article will review evidence that irregular fluctuations in vascular resistance are generated by non-linearity in the control mechanisms intrinsic to the smooth muscle cell and can be classified as chaotic. Non-linear systems theory has provided insights into the mechanisms involved at the cellular level by allowing the identification of dominant control variables and the construction of one-dimensional iterative maps to model vascular dynamics. Experiments with novel peptide inhibitors of gap junctions have shown that the coordination of aggregate responses depends on direct intercellular communication. The sensitivity of chaotic trajectories to perturbation may nevertheless generate a high degree of variability in the response to pharmacological interventions and altered perfusion conditions.
Non-linear Dynamic Analysis of Steel Hollow I-core Sandwich Panel under Air Blast Loading
Directory of Open Access Journals (Sweden)
Asghar Vatani Oskouei
2015-12-01
Full Text Available In this paper, the non-linear dynamic response of novel steel sandwich panel with hollow I-core subjected to blast loading was studied. Special emphasis is placed on the evaluation of midpoint displacements and energy dissipation of the models. Several parameters such as boundary conditions, strain rate, mesh dependency and asymmetrical loading are considered in this study. The material and geometric non-linearities are also considered in the numerical simulation. The results obtained are compared with available experimental data to verify the developed FE model. Modeling techniques are described in detail. According to the results, sandwich panels with hollow I-core allowed more plastic deformation and energy dissipation and less midpoint displacement than conventional I-core sandwich panels and also equivalent solid plate with the same weight and material.
Topological boundary conditions in abelian Chern-Simons theory
Energy Technology Data Exchange (ETDEWEB)
Kapustin, Anton [California Institute of Technology, Pasadena, CA 91125 (United States); Saulina, Natalia, E-mail: saulina@theory.caltech.ed [Perimeter Institute, Waterloo (Canada)
2011-04-21
We study topological boundary conditions in abelian Chern-Simons theory and line operators confined to such boundaries. From the mathematical point of view, their relationships are described by a certain 2-category associated to an even integer-valued symmetric bilinear form (the matrix of Chern-Simons couplings). We argue that boundary conditions correspond to Lagrangian subgroups in the finite abelian group classifying bulk line operators (the discriminant group). We describe properties of boundary line operators; in particular we compute the boundary associator. We also study codimension one defects (surface operators) in abelian Chern-Simons theories. As an application, we obtain a classification of such theories up to isomorphism, in general agreement with the work of Belov and Moore.
A non-slip boundary condition for lattice Boltzmann simulations
Inamuro, T; Ogino, F; Inamuro, Takaji; Yoshino, Masato; Ogino, Fumimaru
1995-01-01
A non-slip boundary condition at a wall for the lattice Boltzmann method is presented. In the present method unknown distribution functions at the wall are assumed to be an equilibrium distribution function with a counter slip velocity which is determined so that fluid velocity at the wall is equal to the wall velocity. Poiseuille flow and Couette flow are calculated with the nine-velocity model to demonstrate the accuracy of the present boundary condition.
A generalized theory on the penetrating boundary conditions
Institute of Scientific and Technical Information of China (English)
邵振海; 洪伟; 周健义
2000-01-01
A generalized formula for penetrating boundary conditions is derived based on the Z-transform. The well-known absorbing boundary conditions (ABCs), such as the Mur’s ABC, and Liao’s ABC, can be deduced from the formula. Furthermore, some new ABCs can also be deduced from it. The stability of these ABCs are demonstrated via Von Neumann method and their validity is verified by numerical examples.
A generalized theory on the penetrating boundary conditions
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
A generalized formula for penetrating boundary conditions is derived based on the Z-transform. The well-known absorbing boundary conditions (ABCs), such as the Mur's ABC, and Liao's ABC, can be deduced from the formula. Furthermore, some new ABCs can also be deduced from it. The stability of these ABCs are demonstrated via Von Neumann method and their validity is verified by numerical examples.
A review of time domain impedance boundary conditions
Richter, Christoph
2012-01-01
International audience; Over the last 15 years, time domain impedance boundary conditions have been investigated by various authors. In a review, a general framework of time domain impedance boundary conditions is presented and then filled with a set of outstanding mathematical and numerical methods from literature. All of the authors struggled with an instability with grazing flow. Mainly this is linked to the Ingard or Myers model of the sound propagation through a sheared flow. This is rev...
Energy Technology Data Exchange (ETDEWEB)
Zhu, Z. W., E-mail: zhuzhiwen@tju.edu.cn [Department of Mechanics, Tianjin University, 300072, Tianjin (China); Tianjin Key Laboratory of Non-linear Dynamics and Chaos Control, 300072, Tianjin (China); Zhang, W. D., E-mail: zhangwenditju@126.com; Xu, J., E-mail: xujia-ld@163.com [Department of Mechanics, Tianjin University, 300072, Tianjin (China)
2014-03-15
The non-linear dynamic characteristics and optimal control of a giant magnetostrictive film (GMF) subjected to in-plane stochastic excitation were studied. Non-linear differential items were introduced to interpret the hysteretic phenomena of the GMF, and the non-linear dynamic model of the GMF subjected to in-plane stochastic excitation was developed. The stochastic stability was analysed, and the probability density function was obtained. The condition of stochastic Hopf bifurcation and noise-induced chaotic response were determined, and the fractal boundary of the system's safe basin was provided. The reliability function was solved from the backward Kolmogorov equation, and an optimal control strategy was proposed in the stochastic dynamic programming method. Numerical simulation shows that the system stability varies with the parameters, and stochastic Hopf bifurcation and chaos appear in the process; the area of the safe basin decreases when the noise intensifies, and the boundary of the safe basin becomes fractal; the system reliability improved through stochastic optimal control. Finally, the theoretical and numerical results were proved by experiments. The results are helpful in the engineering applications of GMF.
Two Baryons with Twisted Boundary Conditions
Energy Technology Data Exchange (ETDEWEB)
Briceno, Raul [Thomas Jefferson National Accelerator Facility, Newport News, VA (United States); Davoudi, Zohreh [Univ. of Washington, Seattle, WA (United States) and Institute for Nuclear Theory, Seattle, WA (United States); Luu, Thomas [Lawrence Livermore National Laboratory, Livermore, CA (United States); Savage, Martin [Univ. of Washington, Seattle, WA (United States) and Institute for Nuclear Theory, Seattle, WA (United States)
2014-04-01
The quantization condition for two particle systems with arbitrary number of two-body open coupled-channels, spin and masses in a finite cubic volume is presented. The condition presented is in agreement with all previous studies of two-body systems in a finite volume. The result is fully relativistic and holds for all momenta below inelastic thresholds and is exact up to exponential volume corrections that are governed by m{sub {pi}} L, where m{sub {pi}} is the pion mass and L is the spatial extent of my box. Its implication for the studies of coupled-channel baryon-baryon systems is discussed, and the necessary tools for implementing the formalism are review.
Coleman-Gurtin type equations with dynamic boundary conditions
Gal, Ciprian G.; Shomberg, Joseph L.
2015-02-01
We present a new formulation and generalization of the classical theory of heat conduction with or without fading memory. As a special case, we investigate the well-posedness of systems which consist of Coleman-Gurtin type equations subject to dynamic boundary conditions, also with memory. Nonlinear terms are defined on the interior of the domain and on the boundary and subject to either classical dissipation assumptions, or to a nonlinear balance condition in the sense of Gal (2012). Additionally, we do not assume that the interior and the boundary share the same memory kernel.
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.
On the wave equation with semilinear porous acoustic boundary conditions
Graber, Philip Jameson
2012-05-01
The goal of this work is to study a model of the wave equation with semilinear porous acoustic boundary conditions with nonlinear boundary/interior sources and a nonlinear boundary/interior damping. First, applying the nonlinear semigroup theory, we show the existence and uniqueness of local in time solutions. The main difficulty in proving the local existence result is that the Neumann boundary conditions experience loss of regularity due to boundary sources. Using an approximation method involving truncated sources and adapting the ideas in Lasiecka and Tataru (1993) [28], we show that the existence of solutions can still be obtained. Second, we prove that under some restrictions on the source terms, then the local solution can be extended to be global in time. In addition, it has been shown that the decay rates of the solution are given implicitly as solutions to a first order ODE and depends on the behavior of the damping terms. In several situations, the obtained ODE can be easily solved and the decay rates can be given explicitly. Third, we show that under some restrictions on the initial data and if the interior source dominates the interior damping term and if the boundary source dominates the boundary damping, then the solution ceases to exists and blows up in finite time. Moreover, in either the absence of the interior source or the boundary source, then we prove that the solution is unbounded and grows as an exponential function. © 2012 Elsevier Inc.
Non Linear Behaviour in Learning Processes
Manfredi, Paolo; Manfredi, Vicenzo Rosario
2003-01-01
This article is mainly based on R. E. Kahn's contribution to the book Non Linear Dynamics in Human Behavior. As stressed by Bronowski, both in art and in science, a person becomes creative by finding "a new unity" that is a link between things which were not thought alike before. Indeed the creative mind is a mind that looks for unexpected likeness finding a more profound unity, a pattern behind chaotic phenomena. In the context of scientific discovery, it can also be argued that creativi...
BRST structure of non-linear superalgebras
Asorey, M; Radchenko, O V; Sugamoto, A
2008-01-01
In this paper we analyse the structure of the BRST structure of nonlinear superalgebras. We consider quadratic non-linear superalgebras where a commutator (in terms of (super) Poisson brackets) of the generators is a quadratic polynomial of the generators. We find the explicit form of the BRST charge up to cubic order in Faddeev-Popov ghost fields for arbitrary quadratic nonlinear superalgebras. We point out the existence of constraints on structure constants of the superalgebra when the nilpotent BRST charge is quadratic in Faddeev-Popov ghost fields. The general results are illustrated by simple examples of superalgebras.
Limits on Non-Linear Electrodynamics
Fouché, M; Rizzo, C
2016-01-01
In this paper we set a framework in which experiments whose goal is to test QED predictions can be used in a more general way to test non-linear electrodynamics (NLED) which contains low-energy QED as a special case. We review some of these experiments and we establish limits on the different free parameters by generalizing QED predictions in the framework of NLED. We finally discuss the implications of these limits on bound systems and isolated charged particles for which QED has been widely and successfully tested.
Smirnov's Observable for Free Boundary Conditions, Interfaces and Crossing Probabilities
Izyurov, Konstantin
2015-07-01
We prove convergence results for variants of Smirnov's fermionic observable in the critical planar Ising model in the presence of free boundary conditions. One application of our analysis is a simple proof of a theorem by Hongler and Kytölä on convergence of critical Ising interfaces with plus-minus-free boundary conditions to dipolar SLE(3), and a generalization of this result to an arbitrary number of arcs carrying plus, minus or free boundary conditions. Another application is a computation of scaling limits of crossing probabilities in the critical FK-Ising model with an arbitrary number of alternating wired/free boundary arcs. We also deduce a new crossing formula for the spin Ising model.
Testing non-linear vacuum electrodynamics with Michelson interferometry
Schellstede, Gerold O; Lämmerzahl, Claus
2015-01-01
We discuss the theoretical foundations for testing non-linear vacuum electrodynamics with Michelson interferometry. Apart from some non-degeneracy conditions to be imposed, our discussion applies to all non-linear electrodynamical theories of the Pleba\\'nski class, i.e., to all Lagrangians that depend only on the two Lorentz-invariant scalars quadratic in the field strength. The main idea of the experiment proposed here is to use the fact that, according to non-linear electrodynamics, the phase velocity of light should depend on the strength and on the direction of an electromagnetic background field. There are two possible experimental set-ups for testing this prediction with Michelson interferometry. The first possibility is to apply a strong electromagnetic field to the beam in one arm of the interferometer and to compare the situation where the field is switched on with the situation where it is switched off. The second possibility is to place the whole interferometer in a strong electromagnetic field and...
Fabrication and characterization of non-linear parabolic microporous membranes.
Rajasekaran, Pradeep Ramiah; Sharifi, Payam; Wolff, Justin; Kohli, Punit
2015-01-01
Large scale fabrication of non-linear microporous membranes is of technological importance in many applications ranging from separation to microfluidics. However, their fabrication using traditional techniques is limited in scope. We report on fabrication and characterization of non-linear parabolic micropores (PMS) in polymer membranes by utilizing flow properties of fluids. The shape of the fabricated PMS corroborated well with simplified Navier-Stokes equation describing parabolic relationship of the form L - t(1/2). Here, L is a measure of the diameter of the fabricated micropores during flow time (t). The surface of PMS is smooth due to fluid surface tension at fluid-air interface. We demonstrate fabrication of PMS using curable polydimethylsiloxane (PDMS). The parabolic shape of micropores was a result of interplay between horizontal and vertical fluid movements due to capillary, viscoelastic, and gravitational forces. We also demonstrate fabrication of asymmetric "off-centered PMS" and an array of PMS membranes using this simple fabrication technique. PMS containing membranes with nanoscale dimensions are also possible by controlling the experimental conditions. The present method provides a simple, easy to adopt, and energy efficient way for fabricating non-linear parabolic shape pores at microscale. The prepared parabolic membranes may find applications in many areas including separation, parabolic optics, micro-nozzles / -valves / -pumps, and microfluidic and microelectronic delivery systems.
Climate model boundary conditions for four Cretaceous time slices
Directory of Open Access Journals (Sweden)
J. O. Sewall
2007-06-01
Full Text Available General circulation models (GCMs are useful tools for investigating the characteristics and dynamics of past climates. Understanding of past climates contributes significantly to our overall understanding of Earth's climate system. One of the most time consuming, and often daunting, tasks facing the paleoclimate modeler, particularly those without a geological background, is the production of surface boundary conditions for past time periods. These boundary conditions consist of, at a minimum, continental configurations derived from plate tectonic modeling, topography, bathymetry, and a vegetation distribution. Typically, each researcher develops a unique set of boundary conditions for use in their simulations. Thus, unlike simulations of modern climate, basic assumptions in paleo surface boundary conditions can vary from researcher to researcher. This makes comparisons between results from multiple researchers difficult and, thus, hinders the integration of studies across the broader community. Unless special changes to surface conditions are warranted, researcher dependent boundary conditions are not the most efficient way to proceed in paleoclimate investigations. Here we present surface boundary conditions (land-sea distribution, paleotopography, paleobathymetry, and paleovegetation distribution for four Cretaceous time slices (120 Ma, 110 Ma, 90 Ma, and 70 Ma. These boundary conditions are modified from base datasets to be appropriate for incorporation into numerical studies of Earth's climate and are available in NetCDF format upon request from the lead author. The land-sea distribution, bathymetry, and topography are based on the 1°×1° (latitude x longitude paleo Digital Elevation Models (paleoDEMs of Christopher Scotese. Those paleoDEMs were adjusted using the paleogeographical reconstructions of Ronald Blakey (Northern Arizona University and published literature and were then modified for use in GCMs. The paleovegetation
Climate model boundary conditions for four Cretaceous time slices
Directory of Open Access Journals (Sweden)
J. O. Sewall
2007-11-01
Full Text Available General circulation models (GCMs are useful tools for investigating the characteristics and dynamics of past climates. Understanding of past climates contributes significantly to our overall understanding of Earth's climate system. One of the most time consuming, and often daunting, tasks facing the paleoclimate modeler, particularly those without a geological background, is the production of surface boundary conditions for past time periods. These boundary conditions consist of, at a minimum, continental configurations derived from plate tectonic modeling, topography, bathymetry, and a vegetation distribution. Typically, each researcher develops a unique set of boundary conditions for use in their simulations. Thus, unlike simulations of modern climate, basic assumptions in paleo surface boundary conditions can vary from researcher to researcher. This makes comparisons between results from multiple researchers difficult and, thus, hinders the integration of studies across the broader community. Unless special changes to surface conditions are warranted, researcher dependent boundary conditions are not the most efficient way to proceed in paleoclimate investigations. Here we present surface boundary conditions (land-sea distribution, paleotopography, paleobathymetry, and paleovegetation distribution for four Cretaceous time slices (120 Ma, 110 Ma, 90 Ma, and 70 Ma. These boundary conditions are modified from base datasets to be appropriate for incorporation into numerical studies of Earth's climate and are available in NetCDF format upon request from the lead author. The land-sea distribution, bathymetry, and topography are based on the 1°×1° (latitude × longitude paleo Digital Elevation Models (paleoDEMs of Christopher Scotese. Those paleoDEMs were adjusted using the paleogeographical reconstructions of Ronald Blakey (Northern Arizona University and published literature and were then modified for use in GCMs. The paleovegetation
Khodayari, Arezoo; Olsen, Seth C.; Wuebbles, Donald J.; Phoenix, Daniel B.
2015-07-01
Atmospheric chemistry-climate models are often used to calculate the effect of aviation NOx emissions on atmospheric ozone (O3) and methane (CH4). Due to the long (∼10 yr) atmospheric lifetime of methane, model simulations must be run for long time periods, typically for more than 40 simulation years, to reach steady-state if using CH4 emission fluxes. Because of the computational expense of such long runs, studies have traditionally used specified CH4 mixing ratio lower boundary conditions (BCs) and then applied a simple parameterization based on the change in CH4 lifetime between the control and NOx-perturbed simulations to estimate the change in CH4 concentration induced by NOx emissions. In this parameterization a feedback factor (typically a value of 1.4) is used to account for the feedback of CH4 concentrations on its lifetime. Modeling studies comparing simulations using CH4 surface fluxes and fixed mixing ratio BCs are used to examine the validity of this parameterization. The latest version of the Community Earth System Model (CESM), with the CAM5 atmospheric model, was used for this study. Aviation NOx emissions for 2006 were obtained from the AEDT (Aviation Environmental Design Tool) global commercial aircraft emissions. Results show a 31.4 ppb change in CH4 concentration when estimated using the parameterization and a 1.4 feedback factor, and a 28.9 ppb change when the concentration was directly calculated in the CH4 flux simulations. The model calculated value for CH4 feedback on its own lifetime agrees well with the 1.4 feedback factor. Systematic comparisons between the separate runs indicated that the parameterization technique overestimates the CH4 concentration by 8.6%. Therefore, it is concluded that the estimation technique is good to within ∼10% and decreases the computational requirements in our simulations by nearly a factor of 8.
A parametric FE modeling of brake for non-linear analysis
Directory of Open Access Journals (Sweden)
Ibrahim Ahmed, Yasser Fatouh, Wael Aly
2014-01-01
Full Text Available A parametric modeling of a drum brake based on 3-D Finite Element Methods (FEM for non-contact analysis is presented. Many parameters are examined during this study such as the effect of drum-lining interface stiffness, coefficient of friction, and line pressure on the interface contact. Firstly, the modal analysis of the drum brake is also studied to get the natural frequency and instability of the drum to facilitate transforming the modal elements to non-contact elements. It is shown that the Unsymmetric solver of the modal analysis is efficient enough to solve this linear problem after transforming the non-linear behavior of the contact between the drum and the lining to a linear behavior. A SOLID45 which is a linear element is used in the modal analysis and then transferred to non-linear elements which are Targe170 and Conta173 that represent the drum and lining for contact analysis study. The contact analysis problems are highly non-linear and require significant computer resources to solve it, however, the contact problem give two significant difficulties. Firstly, the region of contact is not known based on the boundary conditions such as line pressure, and drum and friction material specs. Secondly, these contact problems need to take the friction into consideration. Finally, it showed a good distribution of the nodal reaction forces on the slotted lining contact surface and existing of the slot in the middle of the lining can help in wear removal due to the friction between the lining and the drum. Accurate contact stiffness can give a good representation for the pressure distribution between the lining and the drum. However, a full contact of the front part of the slotted lining could occur in case of 20, 40, 60 and 80 bar of piston pressure and a partially contact between the drum and lining can occur in the rear part of the slotted lining.
PROBLEM WITH INTEGRAL BOUNDARY CONDITIONS INVOLVING PETTIS INTEGRAL
Institute of Scientific and Technical Information of China (English)
Hussein A.H. Salem
2011-01-01
In this article, we investigate the existence of Pseudo solutions for some frac- tional order boundary value problem with integral boundary conditions in the Banach space of continuous function equipped with its weak topology. The class of such problems constitute a very interesting and important class of problems. They include two, three, multi-point and nonlocal boundary-value problems as special cases. In our investigation, the right hand side of the above problem is assumed to be Pettis integrable function. To encompass the full scope of this article, we give an example illustrating the main result.
Determination of optical properties by variation of boundary conditions
Nickell, Stephan; Essenpreis, Matthias; Kraemer, U.; Kohl-Bareis, Matthias; Boecker, Dirk
1998-01-01
Propagation of photons in multiple scattering media depends on absorbing and scattering properties as well as the boundary conditions of the semi-infinite medium. A new method is shown that makes use of differences in boundary conditions to determine the optical properties. Induced are these different conditions by varying the reflectivity of a sensor head. We describe the influence of the change in reflectivity with the common diffusion theory. By building a ratio between the spatially-resolved diffuse reflectance under different boundary conditions it is possible to calculate the optical properties of homogeneous phantoms. Due to optical heterogeneities in living tissue, limitations of the method was observed, which restricts the application to in vivo measurements.
Experimental studies of pedestrian flows under different boundary conditions
Zhang, Jun
2015-01-01
In this article the dynamics of pedestrian streams in four different scenarios are compared empirically to investigate the influence of boundary conditions on it. The Voronoi method, which allows high resolution and small fluctuations of measured density in time and space, is used to analyze the experiments. It is found that pedestrian movement in systems with different boundary conditions (open, periodic boundary conditions and outflow restrained) presents various characteristics especially when the density is larger than 2 m-2. In open corridor systems the specific flow increases continuously with increasing density till 4 m-2. The specific flow keeps constant in systems with restrained outflow, whereas it decreases from 1 (m.s)-1 to zero in system with closed periodical condition.
Approximate open boundary conditions for a class of hyperbolic equations
Maikov, A. R.
2006-06-01
Initial-boundary value problems formulated in spatially unbounded domains can be sometimes reduced to problems in their bounded subdomains by using the so-called open boundary conditions. These conditions are set on the surface separating the subdomain from the rest of the domain. One of the approaches to obtaining such a kind of conditions is based on an approximation of the kernels of the time convolution operators in the relations connecting the exact solution of the original problem and its derivatives on the open boundary. In this case, it is possible to considerably reduce the requirements for system resources required to solve numerically for a wide range of physical and engineering problems. Estimates of the perturbations of the exact solution due to the approximate conditions are obtained for a model problem with one space variable.
A unified slip boundary condition for flow over a surface
Thalakkottor, Joseph John
2015-01-01
Interface between two phases of matter are ubiquitous in nature and technology. Determining the correct velocity condition at an interface is essential for understanding and designing of flows over a surface. We demonstrate that both the widely used no-slip and the Navier and Maxwell slip boundary conditions do not capture the complete physics associated with complex problems, such as spreading of liquids or corner flows. Hence, we present a unified boundary condition that is applicable to a wide-range of flow problems.
Normal ordering and boundary conditions for fermionic string coordinates
Braga, N R F; Godinho, C F L; Braga, Nelson R. F.; Carrion, Hector L.; Godinho, Cresus F. L.
2006-01-01
We build up normal ordered products for fermionic open string coordinates consistent with boundary conditions. The results are obtained considering the presence of antisymmetric tensor fields. We find a discontinuity of the normal ordered products at string endpoints even in the absence of the background. We discuss how the energy momentum tensor also changes at the world-sheet boundary in such a way that the central charge keeps the standard value at string end points.
Normal ordering and boundary conditions for fermionic string coordinates
Energy Technology Data Exchange (ETDEWEB)
Braga, Nelson R.F. [Instituto de Fisica, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, 21941-972 Rio de Janeiro, RJ (Brazil)]. E-mail: braga@if.ufrj.br; Carrion, Hector L. [Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318, 05315-970, Sao Paulo, SP (Brazil)]. E-mail: hlc@fma.if.usp.br; Godinho, Cresus F.L. [Centro Brasileiro de Pesquisas Fisicas, Rua Dr Xavier Sigaud 150, 22290-180, Rio de Janeiro, RJ (Brazil)]. E-mail: godinho@cbpf.br
2006-07-06
We build up normal ordered products for fermionic open string coordinates consistent with boundary conditions. The results are obtained considering the presence of antisymmetric tensor fields. We find a discontinuity of the normal ordered products at string endpoints even in the absence of the background. We discuss how the energy-momentum tensor also changes at the world-sheet boundary in such a way that central charge keeps the standard value at string end points.
STURM-LIOUVILLE PROBLEMS WITH EIGENDEPENDENT BOUNDARY AND TRANSMISSIONS CONDITIONS
Institute of Scientific and Technical Information of China (English)
Z. Akdo(g)an; M. Demirci; O.Sh. Mukhtarov
2005-01-01
The purpose of this paper is to extend some fundamental spectral properties of regular Sturm-Liouville problems to special kind discontinuous boundary value problem,which consist of a Sturm-Liouville equation with piecewise continuous potential together with eigenvalue parameter on the boundary and transmission conditions. The authors suggest their own approach for finding asymptotic approximations formulas for eigenvalues and eigenfunctions of such discontinuous problems.
Variational Data Assimilation for Optimizing Boundary Conditions in Ocean Models
Kazantsev, Christine; Tolstykh, Mikhail
2016-01-01
The review describes the development of ideas Gury Ivanovich Marchuk in the field of variational data assimilation for ocean models applied in particular in coupled models for long-range weather forecasts. Particular attention is paid to the optimization of boundary conditions on rigid boundaries. As idealized and realistic model configurations are considered. It is shown that the optimization allows us to determine the most sensitive model operators and bring the model solution closer to the assimilated data.
Comment on the uncertainty relation with periodic boundary conditions
Fujikawa, Kazuo
2010-01-01
The Kennard-type uncertainty relation $\\Delta x\\Delta p >\\frac{\\hbar}{2}$ is formulated for a free particle with given momentum $ inside a box with periodic boundary conditions in the large box limit. Our construction of a free particle state is analogous to that of the Bloch wave in a periodic potential. A simple Robertson-type relation, which minimizes the effect of the box boundary and may be useful in some practical applications, is also presented.
Current leakage performance of dielectric elastomers under different boundary conditions
Lu, Tongqing; Shi, Zhibao; Chen, Zhiqiang; Huang, He; Wang, T. J.
2015-10-01
In the past decade, dielectric elastomers have become promising candidates in the applications of soft electromechanical transducers due to their outstanding properties of large deformation and high energy density. Current leakage of dielectric elastomer is one of the important dissipative mechanisms affecting the energy conversion efficiency. In this work, we experimentally investigate the current leakage performance of dielectric elastomers with different boundary conditions. We find that for displacement-type boundary conditions, the transition from Ohmic conduction to non-Ohmic conduction is abrupt near the critical electric field. By comparison, for force-type boundary conditions, the current leakage density versus electric field curve is smooth and is fit well by an exponential function. The equivalent resistivity of dielectric elastomers under force-type boundary conditions is approximately an order of magnitude smaller than that under displacement-type boundary conditions. The difference is qualitatively explained by a microscopic physical model. These results will help to design and optimize dielectric elastomer transducers to improve their energy conversion efficiency.
A two-dimensional mathematical model of non-linear dual-sorption of percutaneous drug absorption
Directory of Open Access Journals (Sweden)
George K
2005-07-01
the direction parallel to the skin surface must be examined, as well as in the direction into the skin, examined in one-dimensional models. The dual-sorption model is an initial/boundary value problem which consists of (1 one non-linear, two-dimensional, second-order parabolic equation, (2 boundary conditions, (3 one initial condition. Note that, the number of boundary conditions are, six and four, respectively, if the permeation process under consideration is, during the application of the vehicle and during the removal of the vehicle. Adopting the approach of method of lines, the initial/boundary value problem is transformed into an initial-value problem, which consists of (1 a system of non-linear ordinary differential equations, (2 one initial condition. The system of non-linear ordinary differential equations contains time-dependent non-homogeneous terms, if the permeation process under consideration is, during the application of the vehicle. To solve this initial-value problem, an eight-stage sequential algorithm which is second-order accurate, and requires only tri-diagonal solvers, is developed. Results Simulation of the numerical methods described is carried out with various values of the parameter C. The illustrations are given in the form of figures. The concentration profiles are viewed as parabolas along the mesh lines parallel to x-axis or y-axis. The flow rates in different subregions of the skin-region are studied. The shapes of the concentration profiles are examined before and after the steady-state concentration is reached. The concentration reaches steady-state when the flux reaches the steady state. The plots of flux versus time and cumulative amount of drug eliminated into the receptor cell versus time are given. Conclusion Based on the various values of the parameter, C, conclusions are drawn about (1 flow rate of the drug in different regions of the skin, (2 shape of the concentration profiles, (3 the time required to reach the steady
Non-Linear Dynamics of Saturn’s Rings
Esposito, Larry W.
2015-11-01
Non-linear processes can explain why Saturn’s rings are so active and dynamic. Ring systems differ from simple linear systems in two significant ways: 1. They are systems of granular material: where particle-to-particle collisions dominate; thus a kinetic, not a fluid description needed. We find that stresses are strikingly inhomogeneous and fluctuations are large compared to equilibrium. 2. They are strongly forced by resonances: which drive a non-linear response, pushing the system across thresholds that lead to persistent states.Some of this non-linearity is captured in a simple Predator-Prey Model: Periodic forcing from the moon causes streamline crowding; This damps the relative velocity, and allows aggregates to grow. About a quarter phase later, the aggregates stir the system to higher relative velocity and the limit cycle repeats each orbit.Summary of Halo Results: A predator-prey model for ring dynamics produces transient structures like ‘straw’ that can explain the halo structure and spectroscopy: This requires energetic collisions (v ≈ 10m/sec, with throw distances about 200km, implying objects of scale R ≈ 20km).Transform to Duffing Eqn : With the coordinate transformation, z = M2/3, the Predator-Prey equations can be combined to form a single second-order differential equation with harmonic resonance forcing.Ring dynamics and history implications: Moon-triggered clumping at perturbed regions in Saturn’s rings creates both high velocity dispersion and large aggregates at these distances, explaining both small and large particles observed there. We calculate the stationary size distribution using a cell-to-cell mapping procedure that converts the phase-plane trajectories to a Markov chain. Approximating the Markov chain as an asymmetric random walk with reflecting boundaries allows us to determine the power law index from results of numerical simulations in the tidal environment surrounding Saturn. Aggregates can explain many dynamic aspects
Optimal non-linear health insurance.
Blomqvist, A
1997-06-01
Most theoretical and empirical work on efficient health insurance has been based on models with linear insurance schedules (a constant co-insurance parameter). In this paper, dynamic optimization techniques are used to analyse the properties of optimal non-linear insurance schedules in a model similar to one originally considered by Spence and Zeckhauser (American Economic Review, 1971, 61, 380-387) and reminiscent of those that have been used in the literature on optimal income taxation. The results of a preliminary numerical example suggest that the welfare losses from the implicit subsidy to employer-financed health insurance under US tax law may be a good deal smaller than previously estimated using linear models.
Chaotic Discrimination and Non-Linear Dynamics
Directory of Open Access Journals (Sweden)
Partha Gangopadhyay
2005-01-01
Full Text Available This study examines a particular form of price discrimination, known as chaotic discrimination, which has the following features: sellers quote a common price but, in reality, they engage in secret and apparently unsystematic price discounts. It is widely held that such forms of price discrimination are seriously inconsistent with profit maximization by sellers.. However, there is no theoretical salience to support this kind of price discrimination. By straining the logic of non-linear dynamics this study explains why such secret discounts are chaotic in the sense that sellers fail to adopt profit-maximising price discounts. A model is developed to argue that such forms of discrimination may derive from the regions of instability of a dynamic model of price discounts.
Symmetries in Non-Linear Mechanics
Aldaya, Victor; López-Ruiz, Francisco F; Cossío, Francisco
2014-01-01
In this paper we exploit the use of symmetries of a physical system so as to characterize the corresponding solution manifold by means of Noether invariants. This constitutes a necessary preliminary step towards the correct quantisation in non-linear cases, where the success of Canonical Quantisation is not guaranteed in general. To achieve this task "point symmetries" of the Lagrangian are generally not enough, and the notion of contact transformations is in order. The use of the Poincar\\'e-Cartan form permits finding both the symplectic structure on the solution manifold, through the Hamilton-Jacobi transformation, and the required symmetries, realized as Hamiltonian vector fields, associated with functions on the solution manifold (thus constituting an inverse of the Noether Theorem), lifted back to the evolution space through the inverse of this Hamilton-Jacobi mapping. In this framework, solutions and symmetries are somehow identified and this correspondence is also kept at a perturbative level. We prese...
Non-linear Vibrations of Deep Cylindrical Shells by the p-Version Finite Element Method
Directory of Open Access Journals (Sweden)
Pedro Ribeiro
2010-01-01
Full Text Available A p-version shell finite element based on the so-called shallow shell theory is for the first time employed to study vibrations of deep cylindrical shells. The finite element formulation for deep shells is presented and the linear natural frequencies of different shells, with various boundary conditions, are computed. These linear natural frequencies are compared with published results and with results obtained using a commercial software finite element package; good agreement is found. External forces are applied and the displacements in the geometrically non-linear regime computed with the p-model are found to be close to the ones computed using a commercial FE package. In all numerical tests the p-FE model requires far fewer degrees of freedom than the regular FE models. A numerical study on the dynamic behaviour of deep shells is finally carried out.
Risks of non-linear climate change
Energy Technology Data Exchange (ETDEWEB)
Van Ham, J.; Van Beers, R.J.; Builtjes, P.J.H.; Koennen, G.P.; Oerlemans, J.; Roemer, M.G.M. [TNO-SCMO, Delft (Netherlands)
1995-12-31
Climate forcing as a result of increased concentrations of greenhouse gases has been primarily addressed as a problem of a possibly warmer climate. So far, such change has been obscured in observations, possibly as a result of natural climate variability and masking by aerosols. Consequently, projections of the effect of climate forcing have to be based on modelling, more specifically by applying Global Circulation Models GCMs. These GCMs do not cover all possible feedbacks; neither do they address all specific possible effects of climate forcing. The investigation reviews possible non-linear climate change which does not fall within the coverage of present GCMs. The review includes the potential relevance of changes in biogeochemical cycles, aerosol and cloud feedback, albedo instability, ice-flow instability, changes in the thermohaline circulation and changes resulting from stratospheric cooling. It is noted that these changes may have different time horizons. Three from the investigated issues provide indications for a possible non-linear change. On the decadal scale stratospheric cooling, which is the result of the enhanced greenhouse effect, in combination with a depleted ozone layer, could provide a positive feedback to further ozone depletion, in particular in the Arctic. Decreasing albedo on the Greenland ice sheet may enhance the runoff from this ice sheet significantly in case of warming on a timescale of a few centuries. Changes in ocean circulation in the North Atlantic could seasonally more than compensate a global warming of 3C in North-West Europe on a timescale of centuries to a millennium. 263 refs.
Transport synthetic acceleration with opposing reflecting boundary conditions
Energy Technology Data Exchange (ETDEWEB)
Zika, M.R.; Adams, M.L.
2000-02-01
The transport synthetic acceleration (TSA) scheme is extended to problems with opposing reflecting boundary conditions. This synthetic method employs a simplified transport operator as its low-order approximation. A procedure is developed that allows the use of the conjugate gradient (CG) method to solve the resulting low-order system of equations. Several well-known transport iteration algorithms are cast in a linear algebraic form to show their equivalence to standard iterative techniques. Source iteration in the presence of opposing reflecting boundary conditions is shown to be equivalent to a (poorly) preconditioned stationary Richardson iteration, with the preconditioner defined by the method of iterating on the incident fluxes on the reflecting boundaries. The TSA method (and any synthetic method) amounts to a further preconditioning of the Richardson iteration. The presence of opposing reflecting boundary conditions requires special consideration when developing a procedure to realize the CG method for the proposed system of equations. The CG iteration may be applied only to symmetric positive definite matrices; this condition requires the algebraic elimination of the boundary angular corrections from the low-order equations. As a consequence of this elimination, evaluating the action of the resulting matrix on an arbitrary vector involves two transport sweeps and a transmission iteration. Results of applying the acceleration scheme to a simple test problem are presented.
Vibration Analysis of Annular Sector Plates under Different Boundary Conditions
Directory of Open Access Journals (Sweden)
Dongyan Shi
2014-01-01
Full Text Available An analytical framework is developed for the vibration analysis of annular sector plates with general elastic restraints along each edge of plates. Regardless of boundary conditions, the displacement solution is invariably expressed as a new form of trigonometric expansion with accelerated convergence. The expansion coefficients are treated as the generalized coordinates and determined using the Rayleigh-Ritz technique. This work allows a capability of modeling annular sector plates under a variety of boundary conditions and changing the boundary conditions as easily as modifying the material properties or dimensions of the plates. Of equal importance, the proposed approach is universally applicable to annular sector plates of any inclusion angles up to 2π. The reliability and accuracy of the current method are adequately validated through numerical examples.
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.
Boundary conditions on internal three-body wave functions
Energy Technology Data Exchange (ETDEWEB)
Mitchell, Kevin A.; Littlejohn, Robert G.
1999-10-01
For a three-body system, a quantum wave function {Psi}{sub m}{sup {ell}} with definite {ell} and m quantum numbers may be expressed in terms of an internal wave function {chi}{sub k}{sup {ell}} which is a function of three internal coordinates. This article provides necessary and sufficient constraints on {chi}{sub k}{sup {ell}} to ensure that the external wave function {Psi}{sub k}{sup {ell}} is analytic. These constraints effectively amount to boundary conditions on {chi}{sub k}{sup {ell}} and its derivatives at the boundary of the internal space. Such conditions find similarities in the (planar) two-body problem where the wave function (to lowest order) has the form r{sup |m|} at the origin. We expect the boundary conditions to prove useful for constructing singularity free three-body basis sets for the case of nonvanishing angular momentum.
Quarks with Twisted Boundary Conditions in the Epsilon Regime
Energy Technology Data Exchange (ETDEWEB)
Thomas Mehen; Brian C. Tiburzi
2005-05-01
We study the effects of twisted boundary conditions on the quark fields in the epsilon regime of chiral perturbation theory. We consider the SU(2){sub L} x SU(2){sub R} chiral theory with non-degenerate quarks and the SU(3){sub L} x SU(3){sub R} chiral theory with massless up and down quarks and massive strange quarks. The partition function and condensate are derived for each theory. Because flavor-neutral Goldstone bosons are unaffected by twisted boundary conditions chiral symmetry is still restored in finite volumes. The dependence of the condensate on the twisting parameters can be used to extract the pion decay constant from simulations in the epsilon regime. The relative contribution to the partition function from sectors of different topological charge is numerically insensitive to twisted boundary conditions.
Role of the basin boundary conditions in gravity wave turbulence
Deike, Luc; Gutiérrez-Matus, Pablo; Jamin, Timothée; Semin, Benoit; Aumaitre, Sébastien; Berhanu, Michael; Falcon, Eric; BONNEFOY, Félicien
2014-01-01
Gravity wave turbulence is studied experimentally in a large wave basin where irregular waves are generated unidirectionally. The role of the basin boundary conditions (absorbing or reflecting) and of the forcing properties are investigated. To that purpose, an absorbing sloping beach opposite to the wavemaker can be replaced by a reflecting vertical wall. We observe that the wave field properties depend strongly on these boundary conditions. Quasi-one dimensional field of nonlinear waves propagate before to be damped by the beach whereas a more multidirectional wave field is observed with the wall. In both cases, the wave spectrum scales as a frequency-power law with an exponent that increases continuously with the forcing amplitude up to a value close to -4, which is the value predicted by the weak turbulence theory. The physical mechanisms involved are probably different according to the boundary condition used, but cannot be easily discriminated with only temporal measurements. We have also studied freely...
Technique for observation derived boundary conditions for Space Weather
Pagano, Paolo; Mackay, Duncan; Yeates, Anthony
2017-04-01
We propose a new efficient and accurate modelling technique suitable for the next generation of Space Weather predictive tools. Specifically, we put forward an approach that can provide interplanetary Space Weather forecasting models with an accurate time dependent boundary condition of erupting flux ropes in the upper Solar Corona. The unique strength of this technique is that it follows the time evolution of coronal magnetic fields directly driven from observations and captures the full life span of magnetic flux ropes from formation to ejection. To produce accurate and effective boundary conditions we couple two different modelling techniques, MHD simulations with quasi-static non-potential modelling. Our modelling approach uses a time series of observed synoptic magnetograms to drive the non-potential evolution model of the coronal magnetic field to follow the formation and loss of equilibrium of magnetic flux ropes. Following this a MHD simulation captures the dynamic evolution of the ejection phase of the flux rope into interplanetary space. We focus here on the MHD simulation that describes the ejection of two magnetic flux ropes through the solar corona to the outer boundary. At this boundary we then produce time dependent boundary conditions for the magnetic field and plasma that in the future may be applied to interplanetary space weather prediction models. We illustrate that the coupling of observationally derived quasi-static non-potential magnetic field modelling and MHD simulations can significantly reduce the computational time for producing realistic observationally derived boundary conditions at the boundary between the corona and interplanetary space.
Dirichlet-to-Neumann boundary conditions for multiple scattering problems
Grote, Marcus J.; Kirsch, Christoph
2004-12-01
A Dirichlet-to-Neumann (DtN) condition is derived for the numerical solution of time-harmonic multiple scattering problems, where the scatterer consists of several disjoint components. It is obtained by combining contributions from multiple purely outgoing wave fields. The DtN condition yields an exact non-reflecting boundary condition for the situation, where the computational domain and its exterior artificial boundary consist of several disjoint components. Because each sub-scatterer can be enclosed by a separate artificial boundary, the computational effort is greatly reduced and becomes independent of the relative distances between the different sub-domains. The DtN condition naturally fits into a variational formulation of the boundary-value problem for use with the finite element method. Moreover, it immediately yields as a by-product an exact formula for the far-field pattern of the scattered field. Numerical examples show that the DtN condition for multiple scattering is as accurate as the well-known DtN condition for single scattering problems [J. Comput. Phys. 82 (1989) 172; Numerical Methods for Problems in Infinite Domains, Elsevier, Amsterdam, 1992], while being more efficient due to the reduced size of the computational domain.
Function Substitution in Partial Differential Equations: Nonhomogeneous Boundary Conditions
Directory of Open Access Journals (Sweden)
T. V. Oblakova
2017-01-01
Full Text Available In this paper we consider a mixed initial-boundary value problem for a parabolic equation with nonhomogeneous boundary conditions. The classical methods of searching for an analytical solution of such problems in the first stage involve variable substitution , leading to a problem with homogeneous boundary conditions. In the reference literature ([1], as a rule, the simplest types of variable substitutions are given, under which the new and old unknown functions differ by a term linear in the spatial variable. The form of this additional term depends on the type of the boundary conditions, but is in no way connected with the equation under consideration. Moreover, in the case of the second boundary-value problem, it is necessary to use quadratic additives, since a linear replacement for this type of conditions may not exist. In the educational literature ([2] - [4], it is usually limited to considering only the first boundary-value problem in the general formulation.In this paper, we consider a substitution that takes into account in principle the form of a linear differential operator. Namely, as an additive term, it is proposed to use the parametrically time-dependent solution of the boundary value problem for an ordinary differential equation obtained from the original partial differential equation by the method of separation of the Fourier variables.The existence of the proposed replacement for boundary conditions of any type is proved on the example of a nonstationary heat equation in the presence of heat exchange with the surrounding medium. In this case, the additional term is a linear combination of hyperbolic functions. It is shown that in addition to the "insensitivity" to the type of boundary conditions, the advantages of a new replacement in comparison with the traditional linear (or quadratic substitution include a much simpler structure of the resulting solution. Namely, the described approach allows one to obtain a solution
Long-term cavity closure in non-linear rocks
Cornet, Jan; Dabrowski, Marcin; Schmid, Daniel Walter
2017-08-01
-field deformation rate. The solution remains valid in the limit of ideal power-law fluid when \\overline M_s = 1/n. The solution is based on an approximation which transforms the non-linear isotropic constitutive law into a linear anisotropic one in the far field. The proposed approximate solution for closure velocity for general far-field load is based on the two end-member analytical solutions. They are additively combined after replacing the material threshold viscosity μ0 by the apparent background viscosity due to the far-field shear. Benchmarking the solution shows that there is a 50 per cent misfit at most between the analytical and the numerical solution for closure rate. Comparing the closure velocities obtained with a Carreau viscosity model with the ones from a power-law material shows an increase of several orders of magnitude for pressure loads smaller than 2{μ _0}D_{II}^*. Far field shear can also increase hole closure rate by several orders of magnitude. Compared with other available solutions, the approximate solution presented here ensures that both speed ups are taken into account making it well suited for actual underground conditions where both diffusion creep and shear stresses occur. The additional closure mechanisms considered here can potentially explain the fast closure rates observed underground without referring to transient mechanisms.
The non-linear evolution of edge localized modes
Energy Technology Data Exchange (ETDEWEB)
Wenninger, Ronald
2013-01-09
Edge localized modes (ELMs) are instabilities in the edge of tokamak plasmas in the high confinement regime (H-mode). Without them the edge transport in ordinary H-mode plasmas is too low to establish a stationary situation. However in a future device large unmitigated ELMs are believed to cause divertor power flux densities far in excess of tolerable material limits. Hence the size of energy loss per ELM and the resulting ELM frequency must be controlled. To proceed in understanding how the ELM size is determined and how ELM mitigation methods work it is necessary to characterize the non-linear evolution of pedestal erosion. In order to achieve this experimental data is compared to the results of ELM simulations with the code JOREK (reduced MHD, non-linear) applying a specially developed synthetic magnetic diagnostic. The experimental data are acquired by several fast sampling diagnostics at the experiments ASDEX Upgrade and TCV at a large number of toroidal/poloidal positions. A central element of the presented work is the detailed characterization of dominant magnetic perturbations during ELMs. These footprints of the instability can be observed most intensely in close temporal vicinity to the onset of pedestal erosion. Dominant magnetic perturbations are caused by current perturbations located at or inside the last closed flux surface. In ASDEX Upgrade under certain conditions dominant magnetic perturbations like other H-mode edge instabilities display a similarity to solitons. Furthermore - as expected - they are often observed to be correlated to a perturbation of electron temperature. In TCV it is possible to characterize the evolution of the toroidal structure of dominant magnetic perturbations. Between growing above the level of background fluctuations and the maximum perturbation level for all time instance a similar toroidal structure is observed. This rigid mode-structure is an indication for non-linear coupling. Most frequently the dominant toroidal
Optimal control problems for impulsive systems with integral boundary conditions
Directory of Open Access Journals (Sweden)
Allaberen Ashyralyev
2013-03-01
Full Text Available In this article, the optimal control problem is considered when the state of the system is described by the impulsive differential equations with integral boundary conditions. Applying the Banach contraction principle the existence and uniqueness of the solution is proved for the corresponding boundary problem by the fixed admissible control. The first and second variation of the functional is calculated. Various necessary conditions of optimality of the first and second order are obtained by the help of the variation of the controls.
Thermodynamically admissible boundary conditions for the regularized 13 moment equations
Energy Technology Data Exchange (ETDEWEB)
Rana, Anirudh Singh, E-mail: anirudh@uvic.ca [Department of Mechanical and Aerospace Engineering, Gyeongsang National University, Jinju, Gyeongnam 52828 (Korea, Republic of); Struchtrup, Henning, E-mail: struchtr@uvic.ca [Department of Mechanical Engineering, University of Victoria, Victoria, British Columbia V8W 2Y2 (Canada)
2016-02-15
A phenomenological approach to the boundary conditions for linearized R13 equations is derived using the second law of thermodynamics. The phenomenological coefficients appearing in the boundary conditions are calculated by comparing the slip, jump, and thermal creep coefficients with linearized Boltzmann solutions for Maxwell’s accommodation model for different values of the accommodation coefficient. For this, the linearized R13 equations are solved for viscous slip, thermal creep, and temperature jump problems and the results are compared to the solutions of the linearized Boltzmann equation. The influence of different collision models (hard-sphere, Bhatnagar–Gross–Krook, and Maxwell molecules) and accommodation coefficients on the phenomenological coefficients is studied.
Modeling magnetized star-planet interactions: boundary conditions effects
Strugarek, Antoine; Matt, Sean P; Reville, Victor
2013-01-01
We model the magnetized interaction between a star and a close-in planet (SPMIs), using global, magnetohydrodynamic numerical simulations. In this proceedings, we study the effects of the numerical boundary conditions at the stellar surface, where the stellar wind is driven, and in the planetary interior. We show that is it possible to design boundary conditions that are adequate to obtain physically realistic, steady-state solutions for cases with both magnetized and unmagnetized planets. This encourages further development of numerical studies, in order to better constrain and understand SPMIs, as well as their effects on the star-planet rotational evolution.
Studies for an alternative LHC non-linear collimation system
Lari, L; Boccone, V; Cerutti, F; Versaci, R; Vlachoudis, V; Mereghetti, A; Faus-Golfe, A; Resta-Lopez, J
2012-01-01
A LHC non-linear betatron cleaning collimation system would allow larger gap for the mechanical jaws, reducing as a consequence the collimator-induced impedance, which may limit the LHC beam intensity. In this paper, the performance of the proposed system is analyzed in terms of beam losses distribution around the LHC ring and cleaning efficiency in stable physics condition at 7TeV for Beam1. Moreover, the energy deposition distribution on the machine elements is compared to the present LHC Betatron cleaning collimation system in the Point 7 Insertion Region (IR).
Non-linear Bayesian update of PCE coefficients
Litvinenko, Alexander
2014-01-06
Given: a physical system modeled by a PDE or ODE with uncertain coefficient q(?), a measurement operator Y (u(q), q), where u(q, ?) uncertain solution. Aim: to identify q(?). The mapping from parameters to observations is usually not invertible, hence this inverse identification problem is generally ill-posed. To identify q(!) we derived non-linear Bayesian update from the variational problem associated with conditional expectation. To reduce cost of the Bayesian update we offer a unctional approximation, e.g. polynomial chaos expansion (PCE). New: We apply Bayesian update to the PCE coefficients of the random coefficient q(?) (not to the probability density function of q).
Directory of Open Access Journals (Sweden)
Masood Khan
Full Text Available In the present investigation we analyze the impact of magnetic field on the stagnation-point flow of a generalized Newtonian Carreau fluid. The convective surface boundary conditions are considered to investigate the thermal boundary layer. The leading partial differential equations of the current problem are altered to a set of ordinary differential equations by picking local similarity transformations. The developed non-linear ordinary differential equations are then numerically integrated via Runge-Kutta Fehlberg method after changing into initial value problems. This investigation explores that the momentum and thermal boundary layers are significantly influenced by various pertinent parameters like the Hartmann number M, velocity shear ratio parameter α, Weissenberg number We, power law index n, Biot number γ and Prandtl number Pr. The analysis further reveals that the fluid velocity as well as the skin friction is raised by the velocity shear ratio parameter. Moreover, strong values of the Hartmann number correspond to thinning of the momentum boundary layer thickness while quite the opposite is true for the thermal boundary layer thickness. Additionally, it is seen that the numerical computations are in splendid consent with previously reported studies.
Khan, Masood; Hashim; Alshomrani, Ali Saleh
2016-01-01
In the present investigation we analyze the impact of magnetic field on the stagnation-point flow of a generalized Newtonian Carreau fluid. The convective surface boundary conditions are considered to investigate the thermal boundary layer. The leading partial differential equations of the current problem are altered to a set of ordinary differential equations by picking local similarity transformations. The developed non-linear ordinary differential equations are then numerically integrated via Runge-Kutta Fehlberg method after changing into initial value problems. This investigation explores that the momentum and thermal boundary layers are significantly influenced by various pertinent parameters like the Hartmann number M, velocity shear ratio parameter α, Weissenberg number We, power law index n, Biot number γ and Prandtl number Pr. The analysis further reveals that the fluid velocity as well as the skin friction is raised by the velocity shear ratio parameter. Moreover, strong values of the Hartmann number correspond to thinning of the momentum boundary layer thickness while quite the opposite is true for the thermal boundary layer thickness. Additionally, it is seen that the numerical computations are in splendid consent with previously reported studies.
Sub-Alfvenic inlet boundary conditions for axisymmetric MHD nozzles
Energy Technology Data Exchange (ETDEWEB)
Cassibry, J T [Propulsion Research Center, University of Alabama in Huntsville, Huntsville, AL 35899 (United States); Wu, S T [Center for Space Plasma and Aeronomy Research, University of Alabama in Huntsville, Huntsville, AL 35899 (United States)
2007-09-07
There are numerous electromagnetic accelerator concepts which require plasma expansion through a magnetic nozzle. If the inlet flow is slower than one or all of the outgoing characteristics, namely, the Alfven, slow and fast magnetosonic speeds, then the number of inlet conditions which could be arbitrarily specified are reduced by the number of outgoing characteristics (up to three). We derive the axisymmetric compatibility equations using the method of projected characteristics for the inlet conditions in the z-plane to assure the boundary conditions being consistent with flow properties. We make simplifications to the equations assuming that the inlet Alfven speed is much faster than the sonic and slow magnetosonic speeds. We compare results for various inlet boundary conditions, including a modified Lax-Wendroff implementation of the compatibility equations, first order extrapolation and arbitrarily specifying the inlet conditions, in order to assess the stability and accuracy of various approaches.
Influence of imperfect end boundary condition on the nonlocal dynamics of CNTs
Fathi, Reza; Lotfan, Saeed; Sadeghi, Morteza H.
2017-03-01
Imperfections that unavoidably occur during the fabrication process of carbon nanotubes (CNTs) have a significant influence on the vibration behavior of CNTs. Among these imperfections, the boundary condition defect is studied in this investigation based on the nonlocal elasticity theory. To this end, a mathematical model of the non-ideal end condition in a cantilever CNT is developed by a strongly non-linear spring to study its effect on the vibration behavior. The weak form equation of motion is derived via Hamilton's principle and solved based on Rayleigh-Ritz approach. Once the frequency response function (FRF) of the CNT is simulated, it is found that the defect parameter injects noise to the FRF in the range of lower frequencies and as a result the small scale effect on the FRF remains undisturbed in high frequency ranges. Besides, in this work a process is introduced to estimate the nonlocal and defect parameters for establishing the mathematical model of the CNT based on FRF, which can be competitive because of its lower instrumentation and data analysis costs. The estimation process relies on the resonance frequencies and the magnitude of noise in the frequency response function of the CNT. The results show that the constructed dynamic response of the system based on estimated parameters is in good agreement with the original response of the CNT.
Optimal Control of a Parabolic Equation with Dynamic Boundary Condition
Energy Technology Data Exchange (ETDEWEB)
Hoemberg, D., E-mail: hoemberg@wias-berlin.de; Krumbiegel, K., E-mail: krumbieg@wias-berlin.de [Weierstrass Institute for Applied Mathematics and Stochastics, Nonlinear Optimization and Inverse Problems (Germany); Rehberg, J., E-mail: rehberg@wias-berlin.de [Weierstrass Institute for Applied Mathematics and Stochastics, Partial Differential Equations (Germany)
2013-02-15
We investigate a control problem for the heat equation. The goal is to find an optimal heat transfer coefficient in the dynamic boundary condition such that a desired temperature distribution at the boundary is adhered. To this end we consider a function space setting in which the heat flux across the boundary is forced to be an L{sup p} function with respect to the surface measure, which in turn implies higher regularity for the time derivative of temperature. We show that the corresponding elliptic operator generates a strongly continuous semigroup of contractions and apply the concept of maximal parabolic regularity. This allows to show the existence of an optimal control and the derivation of necessary and sufficient optimality conditions.
Interpolated lattice Boltzmann boundary conditions for surface reaction kinetics.
Walsh, S D C; Saar, M O
2010-12-01
This paper describes a method for implementing surface reaction kinetics in lattice Boltzmann simulations. The interpolated boundary conditions are capable of simulating surface reactions and dissolution at both stationary and moving solid-fluid and fluid-fluid interfaces. Results obtained with the boundary conditions are compared to analytical solutions for first-order and constant-flux kinetic surface reactions in a one-dimensional half space, as well as to the analytical solution for evaporation from the surface of a cylinder. Excellent agreement between analytical and simulated results is obtained for a wide range of diffusivities, lattice velocities, and surface reaction rates. The boundary model's ability to represent dissolution in binary fluid mixtures is demonstrated by modeling diffusion from a rising bubble and dissolution of a droplet near a flat plate.
Jiwari, Ram
2015-08-01
In this article, the author proposed two differential quadrature methods to find the approximate solution of one and two dimensional hyperbolic partial differential equations with Dirichlet and Neumann's boundary conditions. The methods are based on Lagrange interpolation and modified cubic B-splines respectively. The proposed methods reduced the hyperbolic problem into a system of second order ordinary differential equations in time variable. Then, the obtained system is changed into a system of first order ordinary differential equations and finally, SSP-RK3 scheme is used to solve the obtained system. The well known hyperbolic equations such as telegraph, Klein-Gordon, sine-Gordon, Dissipative non-linear wave, and Vander Pol type non-linear wave equations are solved to check the accuracy and efficiency of the proposed methods. The numerical results are shown in L∞ , RMS andL2 errors form.
Institute of Scientific and Technical Information of China (English)
Gui-Qiang Chen; Dan Osborne; Zhongmin Qian
2009-01-01
We study the initial-boundary value problem of the Navier-Stokes equations for incompressible fluids in a general domain in RN with compact and smooth boundary, subject to the kinematic and vorticity boundary conditions on the non-fiat boundary. We observe that, under the nonhomogeneons boundary conditions, the pressure p can be still recovered by solving the Neumann problem for the Poisson equation. Then we establish the well-posedness of the unsteady Stokes equations and employ the solution to reduce our initial-boundary value problem into an initial-boundary value problem with absolute boundary conditions. Based on this, we first establish the well-posedness for an appropriate local linearized problem with the absolute boundary conditions and the initial condition (without the incompressibility condition), which establishes a velocity mapping. Then we develop apriori estimates for the velocity mapping, especially involving the Sobolev norm for the time-derivative of the mapping to deal with the complicated boundary conditions, which leads to the existence of the fixed point of the mapping and the existence of solutions to our initial-boundary value problem. Finally, we establish that, when the viscosity coefficient tends zero, the strong solutions of the initial-boundary value problem in RN(n≥3) with nonhomogeneous vorticity boundary condition converge in L2 to the corresponding Euler equations satisfying the kinematic condition.
On a stochastic Burgers equation with Dirichlet boundary conditions
Directory of Open Access Journals (Sweden)
Ekaterina T. Kolkovska
2003-01-01
Full Text Available We consider the one-dimensional Burgers equation perturbed by a white noise term with Dirichlet boundary conditions and a non-Lipschitz coefficient. We obtain existence of a weak solution proving tightness for a sequence of polygonal approximations for the equation and solving a martingale problem for the weak limit.
Seawall Boundary Condition in Numerical Models of Shoreline Evolution.
1986-04-01
o _ 11111 41 11u MICROCOPY RESOLUTION TESI CHART A NATIONAL BUREAU OF STANDARDS 196, A i TECHNICAL REPORT CERC-86-3 SEAWALL BOUNDARY CONDITION IN...numerical accu- racy. Engineering judgment must be exercised on a case-by-case basis to de- cide if a 24-hr time step will give acceptable physical
New approach to streaming semigroups with multiplying boundary conditions
Directory of Open Access Journals (Sweden)
Mohamed Boulanouar
2008-11-01
Full Text Available This paper concerns the generation of a C_0-semigroup by the streaming operator with general multiplying boundary conditions. A first approach, presented in [2], is based on the Hille-Yosida's Theorem. Here, we present a second approach based on the construction of the generated semigroup, without using the Hille-Yosida's Theorem.
Gravitational wave extraction and outer boundary conditions by perturbative matching
Abrahams, A M; Rupright, M E; Anderson, A; Anninos, P; Baumgarte, T W; Bishop, N T; Brandt, S R; Browne, J C; Camarda, K; Choptuik, M W; Cook, G B; Evans, C R; Finn, L S; Fox, G; Gómez, R; Haupt, T; Huq, M F; Kidder, L E; Klasky, S; Laguna, P; Landry, W; Lehner, L; Lenaghan, J T; Marsa, R L L; Massó, J; Matzner, R A; Mitra, S; Papadopoulos, P P; Parashar, M; Saied, F; Saylor, P E; Scheel, M A; Seidel, E; Shapiro, S L; Shoemaker, D M; Smarr, L L; Szilágyi, B; Teukolsky, S A; Van Putten, M H P M; Walker, P; Winicour, J; York, J W
1998-01-01
We present a method for extracting gravitational radiation from a three-dimensional numerical relativity simulation and, using the extracted data, to provide outer boundary conditions. The method treats dynamical gravitational variables as nonspherical perturbations of Schwarzschild geometry. We discuss a code which implements this method and present results of tests which have been performed with a three dimensional numerical relativity code.
Carleman Estimates for Parabolic Equations with Nonhomogeneous Boundary Conditions
Institute of Scientific and Technical Information of China (English)
Oleg Yu IMANUVILOV; Jean Pierre PUEL; Masahiro YAMAMOTO
2009-01-01
The authors prove a new Carleman estimate for general linear second order parabolic equation with nonhomogeneous boundary conditions.On the basis of this estimate,improved Carleman estimates for the Stokes system and for a system of parabolic equations with a penalty term are obtained.This system can be viewed as an approximation of the Stokes system.
Heat Flow for the Minimal Surface with Plateau Boundary Condition
Institute of Scientific and Technical Information of China (English)
Kung Ching CHANG; Jia Quan LIU
2003-01-01
The heat flow for the minimal surface under Plateau boundary condition is defined to be aparabolic variational inequality, and then the existence, uniqueness, regularity, continuous dependenceon the initial data and the asymptotics are studied. It is applied as a deformation of the level sets inthe critical point theory.
BPS Monopole in the Space of Boundary Conditions
Ohya, Satoshi
2015-01-01
The space of all possible boundary conditions that respect self-adjointness of Hamiltonian operator is known to be given by the group manifold $U(2)$ in one-dimensional quantum mechanics. In this paper we study non-Abelian Berry's connections in the space of boundary conditions in a simple quantum mechanical system. We consider a system for a free spinless particle on a circle with two point-like interactions described by the $U(2) \\times U(2)$ family of boundary conditions. We show that, for a certain $SU(2) \\subset U(2) \\times U(2)$ subfamily of boundary conditions, all the energy levels become doubly-degenerate thanks to the so-called higher-derivative supersymmetry, and non-Abelian Berry's connection in the ground-state sector is given by the Bogomolny-Prasad-Sommerfield (BPS) monopole of $SU(2)$ Yang-Mills-Higgs theory. We also show that, in the ground-state sector of this quantum mechanical model, matrix elements of position operator give the adjoint Higgs field that satisfies the BPS equation. It is al...
Poroelastic modeling of seismic boundary conditions across a fracture.
Nakagawa, Seiji; Schoenberg, Michael A
2007-08-01
Permeability of a fracture can affect how the fracture interacts with seismic waves. To examine this effect, a simple mathematical model that describes the poroelastic nature of wave-fracture interaction is useful. In this paper, a set of boundary conditions is presented which relate wave-induced particle velocity (or displacement) and stress including fluid pressure across a compliant, fluid-bearing fracture. These conditions are derived by modeling a fracture as a thin porous layer with increased compliance and finite permeability. Assuming a small layer thickness, the boundary conditions can be derived by integrating the governing equations of poroelastic wave propagation. A finite jump in the stress and velocity across a fracture is expressed as a function of the stress and velocity at the boundaries. Further simplification for a thin fracture yields a set of characteristic parameters that control the seismic response of single fractures with a wide range of mechanical and hydraulic properties. These boundary conditions have potential applications in simplifying numerical models such as finite-difference and finite-element methods to compute seismic wave scattering off nonplanar (e.g., curved and intersecting) fractures.
Validation of Boundary Conditions for CFD Simulations on Ventilated Rooms
DEFF Research Database (Denmark)
Topp, Claus; Jensen, Rasmus Lund; Pedersen, D.N.
2001-01-01
The application of Computational Fluid Dynamics (CFD) for ventilation research and design of ventilation systems has increased during the recent years. This paper provides an investigation of direct description of boundary conditions for a complex inlet diffuser and a heated surface. A series of ...
Directory of Open Access Journals (Sweden)
Jeffrey W. Lyons
2017-01-01
Full Text Available For \\(\\alpha\\in(1,2]\\, the singular fractional boundary value problem \\[D^{\\alpha}_{0^+}x+f\\left(t,x,D^{\\mu}_{0^+}x\\right=0,\\quad 0\\lt t\\lt 1,\\] satisfying the boundary conditions \\(x(0=D^{\\beta}_{0^+}x(1=0\\, where \\(\\beta\\in(0,\\alpha-1]\\, \\(\\mu\\in(0,\\alpha-1]\\, and \\(D^{\\alpha}_{0^+}\\, \\(D^{\\beta}_{0^+}\\ and \\(D^{\\mu}_{0^+}\\ are Riemann-Liouville derivatives of order \\(\\alpha\\, \\(\\beta\\ and \\(\\mu\\ respectively, is considered. Here \\(f\\ satisfies a local Carathéodory condition, and \\(f(t,x,y\\ may be singular at the value 0 in its space variable \\(x\\. Using regularization and sequential techniques and Krasnosel'skii's fixed point theorem, it is shown this boundary value problem has a positive solution. An example is given.
Numerical Simulation of Seabed Response and Liquefaction due to Non-linear Waves
Institute of Scientific and Technical Information of China (English)
ZHANG Jin-feng; ZHANG Qing-he; HAN Tao; QIN Chong-ren
2005-01-01
Based on Biot's consolidation theory, a two-dimensional model for computation of the seabed response to waves is presented with the finite element method. Numerical results for different wave conditions are obtained, and the effects of wave non-linearity on the wave-induced seabed response are examined. Moreover, the wave-induced momentary liquefaction in uniform and inhomogeneous seabeds is investigated. It is shown that the wave non-linearity affects the distribution of the wave-induced pore pressure and effective stresses, while the influence of wave non-linearity on the seabed liquefaction potential is not so significant.
SOME PROBLEMS CONCERNING FREE NON-LINEAR VIBRATIONS OF BEAM STRUCTURES
Directory of Open Access Journals (Sweden)
S. V. Bosakov
2008-01-01
Full Text Available The paper analyzes an influence of physical non-linearity material account on vibrations of single beams with various support fixing. The authors also analyze power criteria for existing stable periodic vibrations and dependence of vibration period on initial power is determined in the paper. Accurate values of an amplitude and non-linear bending vibration period of beams have been also determined as a conservative system with due account of initial conditions. A number of examples are given that clearly illustrate the obtained solutions and show an influence rate of the mentioned effects on amplitude-frequency characteristics of non-linear systems.
On accurate boundary conditions for a shape sensitivity equation method
Duvigneau, R.; Pelletier, D.
2006-01-01
This paper studies the application of the continuous sensitivity equation method (CSEM) for the Navier-Stokes equations in the particular case of shape parameters. Boundary conditions for shape parameters involve flow derivatives at the boundary. Thus, accurate flow gradients are critical to the success of the CSEM. A new approach is presented to extract accurate flow derivatives at the boundary. High order Taylor series expansions are used on layered patches in conjunction with a constrained least-squares procedure to evaluate accurate first and second derivatives of the flow variables at the boundary, required for Dirichlet and Neumann sensitivity boundary conditions. The flow and sensitivity fields are solved using an adaptive finite-element method. The proposed methodology is first verified on a problem with a closed form solution obtained by the Method of Manufactured Solutions. The ability of the proposed method to provide accurate sensitivity fields for realistic problems is then demonstrated. The flow and sensitivity fields for a NACA 0012 airfoil are used for fast evaluation of the nearby flow over an airfoil of different thickness (NACA 0015).
Non-Linear Sigma Model on Conifolds
Parthasarathy, R
2002-01-01
Explicit solutions to the conifold equations with complex dimension $n=3,4$ in terms of {\\it{complex coordinates (fields)}} are employed to construct the Ricci-flat K\\"{a}hler metrics on these manifolds. The K\\"{a}hler 2-forms are found to be closed. The complex realization of these conifold metrics are used in the construction of 2-dimensional non-linear sigma model with the conifolds as target spaces. The action for the sigma model is shown to be bounded from below. By a suitable choice of the 'integration constants', arising in the solution of Ricci flatness requirement, the metric and the equations of motion are found to be {\\it{non-singular}}. As the target space is Ricci flat, the perturbative 1-loop counter terms being absent, the model becomes topological. The inherent U(1) fibre over the base of the conifolds is shown to correspond to a gauge connection in the sigma model. The same procedure is employed to construct the metric for the resolved conifold, in terms of complex coordinates and the action ...
Non-Linear Electrohydrodynamics in Microfluidic Devices
Directory of Open Access Journals (Sweden)
Jun Zeng
2011-03-01
Full Text Available Since the inception of microfluidics, the electric force has been exploited as one of the leading mechanisms for driving and controlling the movement of the operating fluid and the charged suspensions. Electric force has an intrinsic advantage in miniaturized devices. Because the electrodes are placed over a small distance, from sub-millimeter to a few microns, a very high electric field is easy to obtain. The electric force can be highly localized as its strength rapidly decays away from the peak. This makes the electric force an ideal candidate for precise spatial control. The geometry and placement of the electrodes can be used to design electric fields of varying distributions, which can be readily realized by Micro-Electro-Mechanical Systems (MEMS fabrication methods. In this paper, we examine several electrically driven liquid handling operations. The emphasis is given to non-linear electrohydrodynamic effects. We discuss the theoretical treatment and related numerical methods. Modeling and simulations are used to unveil the associated electrohydrodynamic phenomena. The modeling based investigation is interwoven with examples of microfluidic devices to illustrate the applications.
Global non-linear effect of temperature on economic production.
Burke, Marshall; Hsiang, Solomon M; Miguel, Edward
2015-11-12
Growing evidence demonstrates that climatic conditions can have a profound impact on the functioning of modern human societies, but effects on economic activity appear inconsistent. Fundamental productive elements of modern economies, such as workers and crops, exhibit highly non-linear responses to local temperature even in wealthy countries. In contrast, aggregate macroeconomic productivity of entire wealthy countries is reported not to respond to temperature, while poor countries respond only linearly. Resolving this conflict between micro and macro observations is critical to understanding the role of wealth in coupled human-natural systems and to anticipating the global impact of climate change. Here we unify these seemingly contradictory results by accounting for non-linearity at the macro scale. We show that overall economic productivity is non-linear in temperature for all countries, with productivity peaking at an annual average temperature of 13 °C and declining strongly at higher temperatures. The relationship is globally generalizable, unchanged since 1960, and apparent for agricultural and non-agricultural activity in both rich and poor countries. These results provide the first evidence that economic activity in all regions is coupled to the global climate and establish a new empirical foundation for modelling economic loss in response to climate change, with important implications. If future adaptation mimics past adaptation, unmitigated warming is expected to reshape the global economy by reducing average global incomes roughly 23% by 2100 and widening global income inequality, relative to scenarios without climate change. In contrast to prior estimates, expected global losses are approximately linear in global mean temperature, with median losses many times larger than leading models indicate.
Global non-linear effect of temperature on economic production
Burke, Marshall; Hsiang, Solomon M.; Miguel, Edward
2015-11-01
Growing evidence demonstrates that climatic conditions can have a profound impact on the functioning of modern human societies, but effects on economic activity appear inconsistent. Fundamental productive elements of modern economies, such as workers and crops, exhibit highly non-linear responses to local temperature even in wealthy countries. In contrast, aggregate macroeconomic productivity of entire wealthy countries is reported not to respond to temperature, while poor countries respond only linearly. Resolving this conflict between micro and macro observations is critical to understanding the role of wealth in coupled human-natural systems and to anticipating the global impact of climate change. Here we unify these seemingly contradictory results by accounting for non-linearity at the macro scale. We show that overall economic productivity is non-linear in temperature for all countries, with productivity peaking at an annual average temperature of 13 °C and declining strongly at higher temperatures. The relationship is globally generalizable, unchanged since 1960, and apparent for agricultural and non-agricultural activity in both rich and poor countries. These results provide the first evidence that economic activity in all regions is coupled to the global climate and establish a new empirical foundation for modelling economic loss in response to climate change, with important implications. If future adaptation mimics past adaptation, unmitigated warming is expected to reshape the global economy by reducing average global incomes roughly 23% by 2100 and widening global income inequality, relative to scenarios without climate change. In contrast to prior estimates, expected global losses are approximately linear in global mean temperature, with median losses many times larger than leading models indicate.
The spectrum of boundary states in sine-Gordon model with integrable boundary conditions
Bajnok, Z; Takács, G; Tóth, G
2002-01-01
The bound state spectrum and the associated reflection factors are determined for the sine-Gordon model with arbitrary integrable boundary condition by closing the bootstrap. Comparing the symmetries of the bound state spectrum with that of the Lagrangian it is shown how one can "derive" the relationship between the UV and IR parameters conjectured earlier.
Institute of Scientific and Technical Information of China (English)
Xiang Li; Serge Cescotto; Barbara Rossi
2009-01-01
The natural neighbour method can be considered as one of many variants of the meshless methods. In the present paper, a new approach based on the Fraeijs de Veubeke (FdV) functional, which is initially developed for linear elasticity, is extended to the case of geometrically linear but materially non-linear solids. The new approach provides an original treatment to two classical problems: the numerical evaluation of the integrals over the domain A and the enforcement of boundary conditions of the type ui = uion Su. In the absence of body forces (Fi = 0), it will be shown that the calculation of integrals of the type fA .dA can be avoided and that boundary conditions of the type ui = ui on Su can be imposed in the average sense in general and exactly if ui is linear between two contour nodes, which is obviously the case for ui = 0.
The boundary conditions for point transformed electromagnetic invisibility cloaks
Energy Technology Data Exchange (ETDEWEB)
Weder, Ricardo [Departamento de Metodos Matematicos y Numericos, Instituto de Investigaciones en Matematicas Aplicadas y en Sistemas, Universidad Nacional Autonoma de Mexico, Apartado Postal 20-726, Mexico DF 01000 (Mexico)], E-mail: weder@servidor.unam.mx
2008-10-17
In this paper we study point transformed electromagnetic invisibility cloaks in transformation media that are obtained by transformation from general anisotropic media. We assume that there are several point transformed electromagnetic cloaks located in different points in space. Our results apply in particular to the first-order invisibility cloaks introduced by Pendry et al and to the high-order invisibility cloaks introduced by Hendi et al and by Cai et al. We identify the appropriate cloaking boundary conditions that the solutions of Maxwell equations have to satisfy at the outside, {partial_derivative}K{sub +}, and at the inside, {partial_derivative}K{sub -}, of the boundary of the cloaked object K in the case where the permittivity and the permeability are bounded below and above in K. Namely, that the tangential components of the electric and the magnetic fields have to vanish at {partial_derivative}K{sub +}-which is always true-and that the normal components of the curl of the electric and the magnetic fields have to vanish at {partial_derivative}K{sub -}. These results are proven requiring that energy be conserved. In the case of one spherical cloak with a spherically stratified K and a radial current at {partial_derivative}K we verify by an explicit calculation that our cloaking boundary conditions are satisfied and that cloaking of active devices holds, even if the current is at the boundary of the cloaked object. As we prove our results for media that are obtained by transformation from general anisotropic media, our results apply to the cloaking of objects with passive and active devices contained in general anisotropic media, in particular to objects with passive and active devices contained inside general crystals. Our results suggest a method to enhance cloaking in the approximate transformation media that are used in practice. Namely, to coat the boundary of the cloaked object (the inner boundary of the cloak) with a material that imposes the
Free, transverse vibrations of thin plates with discontinuous boundary conditions
Febbo, M.; Vera, S. A.; Laura, P. A. A.
2005-03-01
Vibrations of circular and rectangular plates clamped on part of the boundary and simply supported along the remainder are analyzed by means of a method of perturbation of boundary conditions. This approach appears to be simple and straightforward, giving excellent results for the first mode and its versatility permits to extend it to higher modes of vibration without difficulty. Furthermore, it is shown that the fundamental frequency coefficient can also be determined using a modified Galerkin approach and very simple polynomial coordinate functions which yield good engineering accuracy.
Boundary Conditions for NHEK through Effective Action Approach
Institute of Scientific and Technical Information of China (English)
CHEN Bin; NING Bo; ZHANG Jia-Ju
2012-01-01
We study the asymptotic symmetry group (ASG) of the near horizon geometry of extreme Kerr black hole through the effective action approach developed by Porfyriadis and Wilczek (arXiv:1007.1031v1[gr qc]).By requiring a finite boundary effective action,we derive a new set of asymptotic Killing vectors and boundary conditions,which are much more relaxed than the ones proposed by Matsuo Y et al.[Nucl.Phys.B 825 (2010) 231],and still allow a copy of a conformal group as its ASG.In the covariant formalism,the asymptotic charges are finite,with the corresponding central charge vanishing.By using the quasi-local charge and introducing a plausible cut-off,we find that the higher order terms of the asymptotic Killing vectors,which could not be determined through the effective action approach,contribute to the central charge as well.We also show that the boundary conditions suggested by Guica et al.[Phys.Rev.D 80 (2009)124008] lead to a divergent first-order boundary effective action.%We study the asymptotic symmetry group (ASG) of the near horizon geometry of extreme Kerr black hole through the effective action approach developed by Porfyriadis and Wilczek (arXiv:1007.1031vl[gr qc]). By requiring a finite boundary effective action, we derive a new set of asymptotic Killing vectors and boundary conditions, which are much more relaxed than the ones proposed by Matsuo Y et al. [Nucl. Phys. B 825 (2010) 231], and still allow a copy of a conformal group as its ASG. In the covariant formalism, the asymptotic charges are finite, with the corresponding central charge vanishing. By using the quasi-local charge and introducing a plausible cut-off, we find that the higher order terms of the asymptotic Killing vectors, which could not be determined through the effective action approach, contribute to the central charge as well. We also show that the boundary conditions suggested by Guica et al. [Phys. Rev. D 80 (2009) 124008] lead to a divergent first-order boundary effective action.
Most general AdS_3 boundary conditions
Grumiller, Daniel
2016-01-01
We consider the most general asymptotically anti-de Sitter boundary conditions in three-dimensional Einstein gravity with negative cosmological constant. The metric contains in total twelve independent functions, six of which are interpreted as chemical potentials (or non-normalizable fluctuations) and the other half as canonical boundary charges (or normalizable fluctuations). Their presence modifies the usual Fefferman-Graham expansion. The asymptotic symmetry algebra consists of two sl(2)_k current algebras, the levels of which are given by k=l/(4G_N), where l is the AdS radius and G_N the three-dimensional Newton constant.
Most general AdS{sub 3} boundary conditions
Energy Technology Data Exchange (ETDEWEB)
Grumiller, Daniel; Riegler, Max [Institute for Theoretical Physics, TU Wien,Wiedner Hauptstr. 8-10/136, A-1040 Vienna (Austria)
2016-10-06
We consider the most general asymptotically anti-de Sitter boundary conditions in three-dimensional Einstein gravity with negative cosmological constant. The metric contains in total twelve independent functions, six of which are interpreted as chemical potentials (or non-normalizable fluctuations) and the other half as canonical boundary charges (or normalizable fluctuations). Their presence modifies the usual Fefferman-Graham expansion. The asymptotic symmetry algebra consists of two sl(2){sub k} current algebras, the levels of which are given by k=ℓ/(4G{sub N}), where ℓ is the AdS radius and G{sub N} the three-dimensional Newton constant.
Stretched flow of Carreau nanofluid with convective boundary condition
Indian Academy of Sciences (India)
T Hayat; M Waqas; S A Shehzad; A Alsaedi
2016-01-01
The steady laminar boundary layer flow of Carreau nanofluid over a stretching sheet is investigated. Effects of Brownian motion and thermophoresis are present. Heat transfer is characterized using convective boundary condition at the sheet. The governing partial differential equations are reduced into a set of nonlinear ordinary differential equations through suitable transformations. Results of velocity, temperature and concentration fields are computed via homotopic procedure. Numerical values of skin-friction coefficient, local Nusselt and Sherwood numbers are computed and discussed. A comparative study with existing solutions in a limiting sense is made.
Application of non-linear discretetime feedback regulators with assignable closed-loop dynamics
Directory of Open Access Journals (Sweden)
Dubljević Stevan
2003-01-01
Full Text Available In the present work the application of a new approach is demonstrated to a discrete-time state feedback regulator synthesis with feedback linearization and pole-placement for non-linear discrete-time systems. Under the simultaneous implementation of a non-linear coordinate transformation and a non-linear state feedback law computed through the solution of a system of non-linear functional equations, both the feedback linearization and pole-placement design objectives were accomplished. The non-linear state feedback regulator synthesis method was applied to a continuous stirred tank reactor (CSTR under non-isothermal operating conditions that exhibits steady-state multiplicity. The control objective was to regulate the reactor at the middle unstable steady state by manipulating the rate of input heat in the reactor. Simulation studies were performed to evaluate the performance of the proposed non-linear state feedback regulator, as it was shown a non-linear state feedback regulator clearly outperformed a standard linear one, especially in the presence of adverse disturbance under which linear regulation at the unstable steady state was not feasible.
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.
Diffusion processes, Feller semigroups and Wentzell boundary conditions.
Romanelli, S
2001-01-01
Different approaches to the study of many diffusion processes in Genetics involve Probability, Functional Analysis and Partial Differential Equations, as in the case of changes in gene frequency due only to random sampling or under random fluctuation of selective advantages. In the one-dimensional case, a unified treatment of them was given by Feller. For particular classes of Markov processes, Taira showed that these different approaches are equivalent even in the N-dimensional case. It follows that the generator of a Feller semigroup on the space of real-valued continuous functions C(D), where D is a bounded domain of RN with smooth boundary, can be identified with a particular Markov transition function. Under suitable assumptions, Taira, Favini and the author proved that some classes of degenerate elliptic operators with Wentzell boundary condition generate Feller semigroups on C(D), in such a way that the diffusion phenomenon of viscosity occurs at each point of the boundary.
DYNA3D Non-reflecting Boundary Conditions - Test Problems
Energy Technology Data Exchange (ETDEWEB)
Zywicz, E
2006-09-28
Two verification problems were developed to test non-reflecting boundary segments in DYNA3D (Whirley and Engelmann, 1993). The problems simulate 1-D wave propagation in a semi-infinite rod using a finite length rod and non-reflecting boundary conditions. One problem examines pure pressure wave propagation, and the other problem explores pure shear wave propagation. In both problems the non-reflecting boundary segments yield results that differ only slightly (less than 6%) during a short duration from their corresponding theoretical solutions. The errors appear to be due to the inability to generate a true step-function compressive wave in the pressure wave propagation problem and due to segment integration inaccuracies in the shear wave propagation problem. These problems serve as verification problems and as regression test problems for DYNA3D.
Flow and heat transfer in Sisko fluid with convective boundary condition.
Malik, Rabia; Khan, Masood; Munir, Asif; Khan, Waqar Azeem
2014-01-01
In this article, we have studied the flow and heat transfer in Sisko fluid with convective boundary condition over a nonisothermal stretching sheet. The flow is influenced by non-linearly stretching sheet in the presence of a uniform transverse magnetic field. The partial differential equations governing the problem have been reduced by similarity transformations into the ordinary differential equations. The transformed coupled ordinary differential equations are then solved analytically by using the homotopy analysis method (HAM) and numerically by the shooting method. Effects of different parameters like power-law index n, magnetic parameter M, stretching parameter s, generalized Prandtl number Pr and generalized Biot number γ are presented graphically. It is found that temperature profile increases with the increasing value of M and γ whereas it decreases for Pr. Numerical values of the skin-friction coefficient and local Nusselt number are tabulated at various physical situations. In addition, a comparison between the HAM and exact solutions is also made as a special case and excellent agreement between results enhance a confidence in the HAM results.
Non - linear laminar flow of fluid into an open bottom well
Directory of Open Access Journals (Sweden)
S. K. JAIN
1982-06-01
Full Text Available In steady state condition, non - linear laminar flow of fluid into an open
bottom well just penetrating the semi-infinite porous aquifer is considered. The
influence of non-linear laminar flow on discharge and its dependance on related
physical quantities is examined. It is found that an open bottom well actually
behaves like a hemispherical well, which is an obvious practical phenomenon.
Flux change in viscous laminar flow under oscillating boundary condition
Ueda, R.; Mikada, H.; Goto, T.; Takekawa, J.
2012-12-01
The behavior of interstitial fluid is one of major interest in earth sciences in terms of the exploitation of water resources, the initiation of earthquakes, enhanced oil recovery (EOR), etc. Seismic waves are often known to increase the flux of interstitial fluid but the relationship between the flux and propagating seismic waves have not been well investigated in the past, although seismic stimulation has been applied in the oil industry for enhanced oil recovery (EOR). Many observations indicated that seismic waves could stimulate the oil production due to lowering of apparent viscosity coefficient, to the coalescence and/or the dispersion of droplets of a phase in multiphase fluids. However, the detailed mechanism of seismic stimulation has not been fully understood, either. In this study, We attempt to understand the mechanism of the flux change in viscous laminar flow under oscillating boundary condition for the simulation of interstitial flow. Here, we analyze a monophase flow in a pore throat. We first assume a Hagen-Poiseuille flow of incompressible fluid through a pore-throat in a porous medium. We adopt the Lattice Boltzmann method (LBM) in which the motion of fluid is simulated through the variation of velocity distribution function representing the distribution of discrete particle velocities. We use an improved incompressible LBKG model (d2q9i) proposed in Zou et. al. (1995) to accurately accommodate the boundary conditions of pressure and velocity in the Hagen-Poiseuille flow. We also use an half-way bounce back boundary condition as the velocity boundary condition. Also, we assume a uniform pressure (density) difference between inlet and outlet flow, and the density difference could initiate the flow in our simulation. The oscillating boundary condition is given by the body force acting on fluid particles. In this simulation, we found that the flux change is negligible under small amplitude of oscillation in both horizontal and vertical directions
Parameter Scaling in Non-Linear Microwave Tomography
DEFF Research Database (Denmark)
Jensen, Peter Damsgaard; Rubæk, Tonny; Talcoth, Oskar;
2012-01-01
Non-linear microwave tomographic imaging of the breast is a challenging computational problem. The breast is heterogeneous and contains several high-contrast and lossy regions, resulting in large differences in the measured signal levels. This implies that special care must be taken when the imag......Non-linear microwave tomographic imaging of the breast is a challenging computational problem. The breast is heterogeneous and contains several high-contrast and lossy regions, resulting in large differences in the measured signal levels. This implies that special care must be taken when...... the imaging problem is formulated. Under such conditions, microwave imaging systems will most often be considerably more sensitive to changes in the electromagnetic properties in certain regions of the breast. The result is that the parameters might not be reconstructed correctly in the less sensitive regions...... introduced as a measure of the sensitivity. The scaling of the parameters is shown to improve performance of the microwave imaging system when applied to reconstruction of images from 2-D simulated data and measurement data....
Primordial black holes in linear and non-linear regimes
Allahyari, Alireza; Abolhasani, Ali Akbar
2016-01-01
Using the concept of apparent horizon for dynamical black holes, we revisit the formation of primordial black holes (PBH) in the early universe for both linear and non-linear regimes. First, we develop the perturbation theory for spherically symmetric spacetimes to study the formation of spherical PBHs in linear regime and we fix two gauges. We also introduce a well defined gauge invariant quantity for the expansion. Using this quantity, we argue that PBHs do not form in the linear regime. Finally, we study the non-linear regime. We adopt the spherical collapse picture by taking a closed FRW model in the radiation dominated era to investigate PBH formation. Taking the initial condition of the spherical collapse from the linear theory of perturbations, we allow for both density and velocity perturbations. Our model gives a constraint on the velocity perturbation. This model also predicts that the apparent horizon of PBHs forms when $\\delta > 3$. Applying the sound horizon constraint, we have shown the threshol...
Non-linear leak currents affect mammalian neuron physiology
Directory of Open Access Journals (Sweden)
Shiwei eHuang
2015-11-01
Full Text Available In their seminal works on squid giant axons, Hodgkin and Huxley approximated the membrane leak current as Ohmic, i.e. linear, since in their preparation, sub-threshold current rectification due to the influence of ionic concentration is negligible. Most studies on mammalian neurons have made the same, largely untested, assumption. Here we show that the membrane time constant and input resistance of mammalian neurons (when other major voltage-sensitive and ligand-gated ionic currents are discounted varies non-linearly with membrane voltage, following the prediction of a Goldman-Hodgkin-Katz-based passive membrane model. The model predicts that under such conditions, the time constant/input resistance-voltage relationship will linearize if the concentration differences across the cell membrane are reduced. These properties were observed in patch-clamp recordings of cerebellar Purkinje neurons (in the presence of pharmacological blockers of other background ionic currents and were more prominent in the sub-threshold region of the membrane potential. Model simulations showed that the non-linear leak affects voltage-clamp recordings and reduces temporal summation of excitatory synaptic input. Together, our results demonstrate the importance of trans-membrane ionic concentration in defining the functional properties of the passive membrane in mammalian neurons as well as other excitable cells.
Parameter Scaling in Non-Linear Microwave Tomography
DEFF Research Database (Denmark)
Jensen, Peter Damsgaard; Rubæk, Tonny; Talcoth, Oskar
2012-01-01
Non-linear microwave tomographic imaging of the breast is a challenging computational problem. The breast is heterogeneous and contains several high-contrast and lossy regions, resulting in large differences in the measured signal levels. This implies that special care must be taken when the imag......Non-linear microwave tomographic imaging of the breast is a challenging computational problem. The breast is heterogeneous and contains several high-contrast and lossy regions, resulting in large differences in the measured signal levels. This implies that special care must be taken when...... the imaging problem is formulated. Under such conditions, microwave imaging systems will most often be considerably more sensitive to changes in the electromagnetic properties in certain regions of the breast. The result is that the parameters might not be reconstructed correctly in the less sensitive regions...... introduced as a measure of the sensitivity. The scaling of the parameters is shown to improve performance of the microwave imaging system when applied to reconstruction of images from 2-D simulated data and measurement data....
Zhao, Shan; Wei, G W
2009-03-19
High-order central finite difference schemes encounter great difficulties in implementing complex boundary conditions. This paper introduces the matched interface and boundary (MIB) method as a novel boundary scheme to treat various general boundary conditions in arbitrarily high-order central finite difference schemes. To attain arbitrarily high order, the MIB method accurately extends the solution beyond the boundary by repeatedly enforcing only the original set of boundary conditions. The proposed approach is extensively validated via boundary value problems, initial-boundary value problems, eigenvalue problems, and high-order differential equations. Successful implementations are given to not only Dirichlet, Neumann, and Robin boundary conditions, but also more general ones, such as multiple boundary conditions in high-order differential equations and time-dependent boundary conditions in evolution equations. Detailed stability analysis of the MIB method is carried out. The MIB method is shown to be able to deliver high-order accuracy, while maintaining the same or similar stability conditions of the standard high-order central difference approximations. The application of the proposed MIB method to the boundary treatment of other non-standard high-order methods is also considered.
Second-order schemes for a boundary value problem with Neumann's boundary conditions
Dehghan, Mehdi
2002-01-01
A new second-order finite difference scheme based on the (3, 3) alternating direction implicit method and a new second-order finite difference technique based on the (5, 5) implicit formula are discussed for solving a nonlocal boundary value problem for the two-dimensional diffusion equation with Neumann's boundary conditions. While sharing some common features with the one-dimensional models, the solution of two-dimensional equations are substantially more difficult, thus some considerations are taken to be able to extend some ideas of the one-dimensional case. Using a suitable transformation the solution of this problem is equivalent to the solution of two other problems. The former, which is a one-dimensional nonlocal boundary value problem giving the value of [mu] through using the unconditionally stable standard implicit (3, 1) backward time-centred space (denoted BTCS) scheme. Using this result the second problem will be changed to a classical two-dimensional diffusion equation with Neumann's boundary conditions which will be solved numerically by using the unconditionally stable alternating direction implicit (3, 3) technique or the fully implicit finite difference scheme. The results of a numerical example are given and computation times are presented. Error estimates derived in the maximum norm are also tabulated.
Vibration suppression for laminated composite plates with arbitrary boundary conditions
Li, J.; Narita, Y.
2013-11-01
An analysis of vibration suppression for laminated composite plates subject to active constrained layer damping under various boundary conditions is presented. Piezoelectric-fiber-reinforced composites (PFRCs) are used as active actuators, and the effect of PFRC patches on vibration control is reported here. An analytical approach is expanded to analyze the vibration of laminated composites with arbitrary boundary conditions. By using Hamilton's principle and the Rayleigh-Ritz method, the equation of motion for the resulting electromechanical coupling system is derived. A velocity feedback control rule is employed to obtain an effective active damping in the vibration control. The orientation effect of piezoelectric fibers in the PFRC patches on the suppression of forced vibrations is also investigated.
Revisiting Johnson and Jackson boundary conditions for granular flows
Energy Technology Data Exchange (ETDEWEB)
Li, Tingwen; Benyahia, Sofiane
2012-07-01
In this article, we revisit Johnson and Jackson boundary conditions for granular flows. The oblique collision between a particle and a flat wall is analyzed by adopting the classic rigid-body theory and a more realistic semianalytical model. Based on the kinetic granular theory, the input parameter for the partial-slip boundary conditions, specularity coefficient, which is not measurable in experiments, is then interpreted as a function of the particle-wall restitution coefficient, the frictional coefficient, and the normalized slip velocity at the wall. An analytical expression for the specularity coefficient is suggested for a flat, frictional surface with a low frictional coefficient. The procedure for determining the specularity coefficient for a more general problem is outlined, and a working approximation is provided.
A Boundary Condition for Simulation of Flow Over Porous Surfaces
Frink, Neal T.; Bonhaus, Daryl L.; Vatsa, Veer N.; Bauer, Steven X. S.; Tinetti, Ana F.
2001-01-01
A new boundary condition is presented.for simulating the flow over passively porous surfaces. The model builds on the prior work of R.H. Bush to eliminate the need for constructing grid within an underlying plenum, thereby simplifying the numerical modeling of passively porous flow control systems and reducing computation cost. Code experts.for two structured-grid.flow solvers, TLNS3D and CFL3D. and one unstructured solver, USM3Dns, collaborated with an experimental porosity expert to develop the model and implement it into their respective codes. Results presented,for the three codes on a slender forebody with circumferential porosity and a wing with leading-edge porosity demonstrate a good agreement with experimental data and a remarkable ability to predict the aggregate aerodynamic effects of surface porosity with a simple boundary condition.
Finite-time H∞ filtering for non-linear stochastic systems
Hou, Mingzhe; Deng, Zongquan; Duan, Guangren
2016-09-01
This paper describes the robust H∞ filtering analysis and the synthesis of general non-linear stochastic systems with finite settling time. We assume that the system dynamic is modelled by Itô-type stochastic differential equations of which the state and the measurement are corrupted by state-dependent noises and exogenous disturbances. A sufficient condition for non-linear stochastic systems to have the finite-time H∞ performance with gain less than or equal to a prescribed positive number is established in terms of a certain Hamilton-Jacobi inequality. Based on this result, the existence of a finite-time H∞ filter is given for the general non-linear stochastic system by a second-order non-linear partial differential inequality, and the filter can be obtained by solving this inequality. The effectiveness of the obtained result is illustrated by a numerical example.
Non-Linearity in Wide Dynamic Range CMOS Image Sensors Utilizing a Partial Charge Transfer Technique
Directory of Open Access Journals (Sweden)
Izhal Abdul Halin
2009-11-01
Full Text Available The partial charge transfer technique can expand the dynamic range of a CMOS image sensor by synthesizing two types of signal, namely the long and short accumulation time signals. However the short accumulation time signal obtained from partial transfer operation suffers of non-linearity with respect to the incident light. In this paper, an analysis of the non-linearity in partial charge transfer technique has been carried, and the relationship between dynamic range and the non-linearity is studied. The results show that the non-linearity is caused by two factors, namely the current diffusion, which has an exponential relation with the potential barrier, and the initial condition of photodiodes in which it shows that the error in the high illumination region increases as the ratio of the long to the short accumulation time raises. Moreover, the increment of the saturation level of photodiodes also increases the error in the high illumination region.
Non-Linearity in Wide Dynamic Range CMOS Image Sensors Utilizing a Partial Charge Transfer Technique
Shafie, Suhaidi; Kawahito, Shoji; Halin, Izhal Abdul; Hasan, Wan Zuha Wan
2009-01-01
The partial charge transfer technique can expand the dynamic range of a CMOS image sensor by synthesizing two types of signal, namely the long and short accumulation time signals. However the short accumulation time signal obtained from partial transfer operation suffers of non-linearity with respect to the incident light. In this paper, an analysis of the non-linearity in partial charge transfer technique has been carried, and the relationship between dynamic range and the non-linearity is studied. The results show that the non-linearity is caused by two factors, namely the current diffusion, which has an exponential relation with the potential barrier, and the initial condition of photodiodes in which it shows that the error in the high illumination region increases as the ratio of the long to the short accumulation time raises. Moreover, the increment of the saturation level of photodiodes also increases the error in the high illumination region. PMID:22303133
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 ...
Slarti: A boundary condition editor for a coupled climate model
Mickelson, S. A.; Jacob, R. L.; Pierrehumbert, R.
2006-12-01
One of the largest barriers to making climate models more flexible is the difficulty in creating new boundary conditions, especially for "deep time" paleoclimate cases where continents are in different positions. Climate models consist of several mutually-interacting component models and the boundary conditions must be consistent between them. We have developed a program called Slarti which uses a Graphical User Interface and a set of consistency rules to aid researchers in creating new, consistent, boundary condition files for the Fast Ocean Atmosphere Model (FOAM). Users can start from existing mask, topography, or bathymetry data or can build a "world" entirely from scratch (e.g. a single island continent). Once a case has been started, users can modify mask, vegetation, bathymetry, topography, and river flow fields by drawing new data through a "paint" interface. Users activate a synchronization button which goes through the fields to eliminate inconsistencies. When the changes are complete and save is selected, Slarti creates all the necessary files for an initial run of FOAM. The data is edited at the highest resolution (the ocean-land surface in FOAM) and then interpolated to the atmosphere resolution. Slarti was implemented in Java to maintain portability across platforms. We also relied heavily on Java Swing components to create the interface. This allowed us to create an object-oriented interface that could be used on many different systems. Since Slarti allows users to visualize their changes, they are able to see areas that may cause problems when the model is ran. Some examples would be lakes from the river flow field and narrow trenches within the bathymetry. Through different checks and options available through its interface, Slarti makes the process of creating new boundary conditions for FOAM easier and faster while reducing the chance for user errors.
Scattering of wedges and cones with impedance boundary conditions
Lyalinov, Mikhail
2012-01-01
This book is a systematic and detailed exposition of different analytical techniques used in studying two of the canonical problems, the wave scattering by wedges or cones with impedance boundary conditions. It is the first reference on novel, highly efficient analytical-numerical approaches for wave diffraction by impedance wedges or cones. The applicability of the reported solution procedures and formulae to existing software packages designed for real-world high-frequency problems encountered in antenna, wave propagation, and radar cross section.
The XXZ model with anti-periodic twisted boundary conditions
Niekamp, Sönke; Frahm, Holger
2009-01-01
We derive functional equations for the eigenvalues of the XXZ model subject to anti-diagonal twisted boundary conditions by means of fusion of transfer matrices and by Sklyanin's method of separation of variables. Our findings coincide with those obtained using Baxter's method and are compared to the recent solution of Galleas. As an application we study the finite size scaling of the ground state energy of the model in the critical regime.
The XXZ model with anti-periodic twisted boundary conditions
Energy Technology Data Exchange (ETDEWEB)
Niekamp, Soenke; Wirth, Tobias; Frahm, Holger [Institut fuer Theoretische Physik, Leibniz Universitaet Hannover, Appelstrasse 2, 30167 Hannover (Germany)
2009-05-15
We derive functional equations for the eigenvalues of the XXZ model subject to anti-diagonal twisted boundary conditions by means of fusion of transfer matrices and by Sklyanin's method of separation of variables. Our findings coincide with those obtained using Baxter's method and are compared to the recent solution of Galleas. As an application we study the finite size scaling of the ground-state energy of the model in the critical regime.
Asymptotic stability of the Boltzmann equation with Maxwell boundary conditions
Briant, Marc; Guo, Yan
2016-12-01
In a general C1 domain, we study the perturbative Cauchy theory for the Boltzmann equation with Maxwell boundary conditions with an accommodation coefficient α in (√{ 2 / 3 } , 1 ], and discuss this threshold. We consider polynomial or stretched exponential weights m (v) and prove existence, uniqueness and exponential trend to equilibrium around a global Maxwellian in Lx,v∞ (m). Of important note is the fact that the methods do not involve contradiction arguments.
On the extraction of spectral quantities with open boundary conditions
Bruno, Mattia; Korzec, Tomasz; Lottini, Stefano; Schaefer, Stefan
2014-01-01
We discuss methods to extract decay constants, meson masses and gluonic observables in the presence of open boundary conditions. The ensembles have been generated by the CLS effort and have 2+1 flavors of O(a)-improved Wilson fermions with a small twisted-mass term as proposed by L\\"uscher and Palombi. We analyse the effect of the associated reweighting factors on the computation of different observables.
On Vector Helmholtz Equation with a Coupling Boundary Condition
Institute of Scientific and Technical Information of China (English)
Gang Li; Jiangsong Zhang; Jiang Zhu; Danping Yang
2007-01-01
The Helmholtz equation is sometimes supplemented by conditions that include the specification of the boundary value of the divergence of the unknown. In this paper,we study the vector Helmholtz problem in domains of both C1,1 and Lipschitz. We establish a rigorous variational analysis such as equivalence, existence and uniqueness.And we propose finite element approximations based on the uncoupled solutions. Finally we present a convergence analysis and error estimates.
Hydrodynamic boundary condition of water on hydrophobic surfaces.
Schaeffel, David; Yordanov, Stoyan; Schmelzeisen, Marcus; Yamamoto, Tetsuya; Kappl, Michael; Schmitz, Roman; Dünweg, Burkhard; Butt, Hans-Jürgen; Koynov, Kaloian
2013-05-01
By combining total internal reflection fluorescence cross-correlation spectroscopy with Brownian dynamics simulations, we were able to measure the hydrodynamic boundary condition of water flowing over a smooth solid surface with exceptional accuracy. We analyzed the flow of aqueous electrolytes over glass coated with a layer of poly(dimethylsiloxane) (advancing contact angle Θ = 108°) or perfluorosilane (Θ = 113°). Within an error of better than 10 nm the slip length was indistinguishable from zero on all surfaces.
Maxwell boundary conditions impose non-Lindblad master equation
Bamba, Motoaki
2016-01-01
From the Hamiltonian connecting the inside and outside of an Fabry-Perot cavity, which is derived from the Maxwell boundary conditions at a mirror of the cavity, a master equation of a non-Lindblad form is derived when the cavity embeds matters, although we can transform it to the Lindblad form by performing the rotating-wave approximation to that Hamiltonian. We calculate absorption spectra by these Lindblad and non-Lindblad master equations and also by the Maxwell boundary conditions in framework of the classical electrodynamics, which we consider the most reliable approach. We found that, compared to the Lindblad master equation, the absorption spectra by the non-Lindblad one agree better with those by the Maxwell boundary conditions. Although the discrepancy is highlighted only in the ultra-strong light-matter interaction regime with a relatively large broadening, the master equation of the non-Lindblad form is preferable rather than of the Lindblad one for pursuing the consistency with the classical elec...
Maxwell boundary conditions imply non-Lindblad master equation
Bamba, Motoaki; Imoto, Nobuyuki
2016-09-01
From the Hamiltonian connecting the inside and outside of a Fabry-Pérot cavity, which is derived from the Maxwell boundary conditions at a mirror of the cavity, a master equation of a non-Lindblad form is derived when the cavity embeds matters, although we can transform it to the Lindblad form by performing the rotating-wave approximation to the connecting Hamiltonian. We calculate absorption spectra by these Lindblad and non-Lindblad master equations and also by the Maxwell boundary conditions in the framework of the classical electrodynamics, which we consider the most reliable approach. We found that, compared to the Lindblad master equation, the absorption spectra by the non-Lindblad one agree better with those by the Maxwell boundary conditions. Although the discrepancy is highlighted only in the ultrastrong light-matter interaction regime with a relatively large broadening, the master equation of the non-Lindblad form is preferable rather than of the Lindblad one for pursuing the consistency with the classical electrodynamics.
Outer boundary conditions for evolving cool white dwarfs
Rohrmann, R D; García-Berro, E; Córsico, A H; Bertolami, M M Miller
2012-01-01
White dwarf evolution is essentially a gravothermal cooling process, which,for cool white dwarfs, sensitively depends on the treatment of the outer boundary conditions. We provide detailed outer boundary conditions appropriate for computing the evolution of cool white dwarfs employing detailed non-gray model atmospheres for pure H composition. We also explore the impact on the white dwarf cooling times of different assumptions for energy transfer in the atmosphere of cool white dwarfs. Detailed non-gray model atmospheres are computed taken into account non-ideal effects in the gas equation of state and chemical equilibrium, collision-induced absorption from molecules, and the Lyman alpha quasi-molecular opacity. Our results show that the use of detailed outer boundary conditions becomes relevant for effective temperatures lower than 5800 and 6100K for sequences with 0.60 and 0.90 M_sun, respectively. Detailed model atmospheres predict ages that are up to approx 10% shorter at log L/L_sun=-4 when compared with...
New boundary conditions for oil reservoirs with fracture
Andriyanova, Elena; Astafev, Vladimir
2017-06-01
Based on the fact that most of oil fields are on the late stage of field development, it becomes necessary to produce hard-to-extract oil, which can be obtained only by use of enhance oil recovery methods. For example many low permeable or shale formations can be developed only with application of massive hydraulic fracturing technique. In addition, modern geophysical researches show that mostly oil bearing formations are complicated with tectonic faults of different shape and permeability. These discontinuities exert essential influence on the field development process and on the well performance. For the modeling of fluid flow in the reservoir with some area of different permeability, we should determine the boundary conditions. In this article for the first time the boundary conditions for the problem of fluid filtration in the reservoir with some discontinuity are considered. This discontinuity represents thin but long area, which can be hydraulic fracturing of tectonic fault. The obtained boundary condition equations allow us to take into account pressure difference above and below the section and different values of permeability.
Non-Linear Unit Root Properties of Crude Oil Production
Svetlana Maslyuk; Russell Smyth
2007-01-01
While there is good reason to expect crude oil production to be non-linear, previous studies that have examined the stochastic properties of crude oil production have assumed that crude oil production follows a linear process. If crude oil production is a non-linear process, conventional unit root tests, which assume linear and systematic adjustment, could interpret departure from linearity as permanent stochastic disturbances. The objective of this paper is to test for non-linearities and un...
Pan, Wenxiao; Bao, Jie; Tartakovsky, Alexandre M.
2014-02-01
A Robin boundary condition for the Navier-Stokes equations is used to model slip conditions at the fluid-solid boundaries. A novel continuous boundary force (CBF) method is proposed for solving the Navier-Stokes equations subject to the Robin boundary condition. In the CBF method, the Robin boundary condition is replaced by the homogeneous Neumann boundary condition and a volumetric force term added to the momentum conservation equation. Smoothed particle hydrodynamics (SPH) method is used to solve the resulting Navier-Stokes equations. We present solutions for two- and three-dimensional flows subject to various forms of the Robin boundary condition in domains bounded by flat and curved boundaries. The numerical accuracy and convergence are examined through comparison of the SPH-CBF results with the solutions of finite difference or finite-element method. Considering the no-slip boundary condition as a special case of the slip boundary condition, we demonstrate that the SPH-CBF method accurately describes both the no-slip and slip conditions.
High Energy Boundary Conditions for a Cartesian Mesh Euler Solver
Pandya, Shishir A.; Murman, Scott M.; Aftosmis, Michael J.
2004-01-01
Inlets and exhaust nozzles are often omitted or fared over in aerodynamic simulations of aircraft due to the complexities involving in the modeling of engine details such as complex geometry and flow physics. However, the assumption is often improper as inlet or plume flows have a substantial effect on vehicle aerodynamics. A tool for specifying inlet and exhaust plume conditions through the use of high-energy boundary conditions in an established inviscid flow solver is presented. The effects of the plume on the flow fields near the inlet and plume are discussed.
Solitons induced by boundary conditions from the Boussinesq equation
Chou, Ru Ling; Chu, C. K.
1990-01-01
The behavior of solitons induced by boundary excitation is investigated at various time-dependent conditions and different unperturbed water depths, using the Korteweg-de Vries (KdV) equation. Then, solitons induced from Boussinesq equations under similar conditions were studied, making it possible to remove the restriction in the KdV equation and to treat soliton head-on collisions (as well as overtaking collisions) and reflections. It is found that the results obtained from the KdV and the Boussinesq equations are in good agreement.
Non-linear finite element analysis in structural mechanics
Rust, Wilhelm
2015-01-01
This monograph describes the numerical analysis of non-linearities in structural mechanics, i.e. large rotations, large strain (geometric non-linearities), non-linear material behaviour, in particular elasto-plasticity as well as time-dependent behaviour, and contact. Based on that, the book treats stability problems and limit-load analyses, as well as non-linear equations of a large number of variables. Moreover, the author presents a wide range of problem sets and their solutions. The target audience primarily comprises advanced undergraduate and graduate students of mechanical and civil engineering, but the book may also be beneficial for practising engineers in industry.
Repulsive Casimir force from fractional Neumann boundary conditions
Energy Technology Data Exchange (ETDEWEB)
Lim, S.C. [Faculty of Engineering, Multimedia University, Jalan Multimedia, 63100 Cyberjaya, Selangor (Malaysia)], E-mail: sclim@mmu.edu.my; Teo, L.P. [Faculty of Information Technology, Multimedia University, Jalan Multimedia, 63100 Cyberjaya, Selangor (Malaysia); Department of Applied Mathematics, Faculty of Engineering, University of Nottingham Malaysia Campus, Jalan Broga, 43500 Semenyih, Selangor Darul Ehsan (Malaysia)], E-mail: lpteo@mmu.edu.my
2009-08-17
This Letter studies the finite temperature Casimir force acting on a rectangular piston associated with a massless fractional Klein-Gordon field at finite temperature. Dirichlet boundary conditions are imposed on the walls of a d-dimensional rectangular cavity, and a fractional Neumann condition is imposed on the piston that moves freely inside the cavity. The fractional Neumann condition gives an interpolation between the Dirichlet and Neumann conditions, where the Casimir force is known to be always attractive and always repulsive respectively. For the fractional Neumann boundary condition, the attractive or repulsive nature of the Casimir force is governed by the fractional order which takes values from zero (Dirichlet) to one (Neumann). When the fractional order is larger than 1/2, the Casimir force is always repulsive. For some fractional orders that are less than but close to 1/2, it is shown that the Casimir force can be either attractive or repulsive depending on the aspect ratio of the cavity and the temperature.
Askari, Amir R.; Tahani, Masoud
2017-02-01
This paper focuses on the size-dependent dynamic pull-in instability in rectangular micro-plates actuated by step-input DC voltage. The present model accounts for the effects of in-plane displacements and their non-classical higher-order boundary conditions, von Kármán geometric non-linearity, non-classical couple stress components and the inherent non-linearity of distributed electrostatic pressure on the micro-plate motion. The governing equations of motion, which are clearly derived using Hamilton's principle, are solved through a novel computationally very efficient Galerkin-based reduced order model (ROM) in which all higher-order non-classical boundary conditions are completely satisfied. The present findings are compared and successfully validated by available results in the literature as well as those obtained by three-dimensional finite element simulations carried out using COMSOL Multyphysics. A detailed parametric study is also conducted to illustrate the effects of in-plane displacements, plate aspect ratio, couple stress components and geometric non-linearity on the dynamic instability threshold of the system.
Non-linear dimensionality reduction of signaling networks
Directory of Open Access Journals (Sweden)
Ivakhno Sergii
2007-06-01
Full Text Available Abstract Background Systems wide modeling and analysis of signaling networks is essential for understanding complex cellular behaviors, such as the biphasic responses to different combinations of cytokines and growth factors. For example, tumor necrosis factor (TNF can act as a proapoptotic or prosurvival factor depending on its concentration, the current state of signaling network and the presence of other cytokines. To understand combinatorial regulation in such systems, new computational approaches are required that can take into account non-linear interactions in signaling networks and provide tools for clustering, visualization and predictive modeling. Results Here we extended and applied an unsupervised non-linear dimensionality reduction approach, Isomap, to find clusters of similar treatment conditions in two cell signaling networks: (I apoptosis signaling network in human epithelial cancer cells treated with different combinations of TNF, epidermal growth factor (EGF and insulin and (II combination of signal transduction pathways stimulated by 21 different ligands based on AfCS double ligand screen data. For the analysis of the apoptosis signaling network we used the Cytokine compendium dataset where activity and concentration of 19 intracellular signaling molecules were measured to characterise apoptotic response to TNF, EGF and insulin. By projecting the original 19-dimensional space of intracellular signals into a low-dimensional space, Isomap was able to reconstruct clusters corresponding to different cytokine treatments that were identified with graph-based clustering. In comparison, Principal Component Analysis (PCA and Partial Least Squares – Discriminant analysis (PLS-DA were unable to find biologically meaningful clusters. We also showed that by using Isomap components for supervised classification with k-nearest neighbor (k-NN and quadratic discriminant analysis (QDA, apoptosis intensity can be predicted for different
Nonstationary Stokes System in Cylindrical Domains Under Boundary Slip Conditions
Zaja¸czkowski, Wojciech M.
2017-03-01
Existence and uniqueness of solutions to the nonstationary Stokes system in a cylindrical domain {Ωsubset{R}^3} and under boundary slip conditions are proved in anisotropic Sobolev spaces. Assuming that the external force belong to {L_r(Ω×(0,T))} and initial velocity to {W_r^{2-2/r}(Ω)} there exists a solution such that velocity belongs to {W_r^{2,1}(Ω×(0,T))} and gradient of pressure to {L_r(Ω×(0,T))}, {rin(1,∞)}, {T > 0}. Thanks to the slip boundary conditions and a partition of unity the Stokes system is transformed to the Poisson equation for pressure and the heat equation for velocity. The existence of solutions to these equations is proved by applying local considerations. In this case we have to consider neighborhoods near the edges which by local mapping can be transformed to dihedral angle {π/2}. Hence solvability of the problem bases on construction local Green functions (near an interior point, near a point of a smooth part of the boundary, near a point of the edge) and their appropriate estimates. The technique presented in this paper can also work in other functional spaces: Sobolev-Slobodetskii, Besov, Nikolskii, Hölder and so on.
Boundary conditions towards realistic simulation of jet engine noise
Dhamankar, Nitin S.
Strict noise regulations at major airports and increasing environmental concerns have made prediction and attenuation of jet noise an active research topic. Large eddy simulation coupled with computational aeroacoustics has the potential to be a significant research tool for this problem. With the emergence of petascale computer clusters, it is now computationally feasible to include the nozzle geometry in jet noise simulations. In high Reynolds number experiments on jet noise, the turbulent boundary layer on the inner surface of the nozzle separates into a turbulent free shear layer. Inclusion of a nozzle with turbulent inlet conditions is necessary to simulate this phenomenon realistically. This will allow a reasonable comparison of numerically computed noise levels with the experimental results. Two viscous wall boundary conditions are implemented for modeling the nozzle walls. A characteristic-based approach is compared with a computationally cheaper, extrapolation-based formulation. In viscous flow over a circular cylinder under two different regimes, excellent agreement is observed between the results of the two approaches. The results agree reasonably well with reference experimental and numerical results. Both the boundary conditions are thus found to be appropriate, the extrapolation-based formulation having an edge with its low cost. This is followed with the crucial step of generation of a turbulent boundary layer inside the nozzle. A digital filter-based turbulent inflow condition, extended in a new way to non-uniform curvilinear grids is implemented to achieve this. A zero pressure gradient flat plate turbulent boundary layer is simulated at a high Reynolds number to show that the method is capable of producing sustained turbulence. The length of the adjustment region necessary for synthetic inlet turbulence to recover from modeling errors is estimated. A low Reynolds number jet simulation including a round nozzle geometry is performed and the method
Negative bending mode curvature via Robin boundary conditions
Adams, Samuel D. M.; Craster, Richard V.; Guenneau, Sébastien
2009-06-01
We examine the band spectrum, and associated Floquet-Bloch eigensolutions, arising in straight walled acoustic waveguides that have periodic structure along the guide. Homogeneous impedance (Robin) conditions are imposed along the guide walls and we find that in certain circumstances, negative curvature of the lowest (bending) mode can be achieved. This is unexpected, and has not been observed in a variety of physical situations examined by other authors. Further unexpected properties include the existence of the bending mode only on a subset of the Brillouin zone, as well as permitting otherwise unobtainable velocities of energy transmission. We conclude with a discussion of how such boundary conditions might be physically reproduced using effective conditions and homogenization theory, although the methodology to achieve these effective conditions is an open problem. To cite this article: S.D.M. Adams et al., C. R. Physique 10 (2009).
Non-Gaussianity vs. non-linearity of cosmological perturbations
Verde, L
2001-01-01
Following the discovery of the CMB, the hot big-bang model has become the standard cosmological model. In this theory, small primordial fluctuations are subsequently amplified by gravity to form the large-scale structure seen today. Different theories for unified models of particle physics, lead to different predictions for the statistical properties of the primordial fluctuations, that can be divided in two classes: gaussian and non-gaussian. Convincing evidence against or for gaussian initial conditions would rule out many scenarios and point us towards a physical theory for the origin of structures. The statistical distribution of cosmological perturbations, as we observe them, can deviate from the gaussian distribution in several different ways. Even if perturbations start off gaussian, non-linear gravitational evolution can introduce non-gaussian features. Additionally, our knowledge of the Universe comes principally from the study of luminous material such as galaxies, but these might not be faithful tr...
Non-linear Kalman filters for calibration in radio interferometry
Tasse, Cyril
2014-01-01
We present a new calibration scheme based on a non-linear version of Kalman filter that aims at estimating the physical terms appearing in the Radio Interferometry Measurement Equation (RIME). We enrich the filter's structure with a tunable data representation model, together with an augmented measurement model for regularization. We show using simulations that it can properly estimate the physical effects appearing in the RIME. We found that this approach is particularly useful in the most extreme cases such as when ionospheric and clock effects are simultaneously present. Combined with the ability to provide prior knowledge on the expected structure of the physical instrumental effects (expected physical state and dynamics), we obtain a fairly cheap algorithm that we believe to be robust, especially in low signal-to-noise regime. Potentially the use of filters and other similar methods can represent an improvement for calibration in radio interferometry, under the condition that the effects corrupting visib...
Applying Twisted Boundary Conditions for Few-body Nuclear Systems
Körber, Christopher
2015-01-01
We describe and implement twisted boundary conditions for the deuteron and triton systems within finite-volumes using the nuclear lattice EFT formalism. We investigate the finite-volume dependence of these systems with different twists angles. We demonstrate how various finite-volume information can be used to improve calculations of binding energies in such a framework. Our results suggests that with appropriate twisting of boundaries, infinite-volume binding energies can be reliably extracted from calculations using modest volume sizes with cubic length $L\\approx8-14$ fm. Of particular importance is our derivation and numerical verification of three-body analogue of `i-periodic' twist angles that eliminate the leading order finite-volume effects to the three-body binding energy.
Non-linear dynamics of a spur gear pair
Kahraman, A.; Singh, R.
1990-10-01
Non-linear frequency response characteristics of a spur gear pair with backlash are examined in this paper for both external and internal excitations. The internal excitation is of importance from the high frequency noise and vibration control viewpoint and it represents the overall kinematic or static transmission error. Such problems may be significantly different from the rattle problems associated with external, low frequency torque excitation. Two solution methods, namely the digital simulation technique and the method of harmonic balance, have been used to develop the steady state solutions for the internal sinusoidal excitation. Difficulties associated with the determination of the multiple solutions at a given frequency in the digital simulation technique have been resolved, as one must search the entire initial conditions map. Such solutions and the transition frequencies for various impact situations are easily found by the method of harmonic balance. Further, the principle of superposition can be employed to analyze the periodic transmission error excitation and/or combined excitation problems provided that the excitation frequencies are sufficiently apart from each other. Our analytical predictions match satisfactorily with the limited experimental data available in the literature. Using the digital simulation, we have also observed that the chaotic and subharmonic resonances may exist in a gear pair depending upon the mean or design load, mean to alternating force ratio, damping and backlash. Specifically, the mean load determines the conditions for no impacts, single-sided impacts and double-sided impacts. Our results are different from the frequency response characteristics of the conventional, single-degree-of-freedom, clearance type non-linear system. Our formulation should form the basis of further analytical and experimental work in the geared rotor dynamics area.
Boundary Condition Effects on Taylor States in SSX
Han, Jeremy; Shrock, Jaron; Kaur, Manjit; Brown, Michael; Schaffner, David
2016-10-01
Three different boundary conditions are applied to the SSX 0.15 m diameter plasma wind tunnel and the resultant Taylor states are characterized. The glass walls of the wind tunnel act as an insulating boundary condition. For the second condition, a flux conserver is wrapped around the tunnel to trap magnetic field lines inside the SSX. For the last condition, the flux conserver is segmented to add theta pinch coils, which will accelerate the plasma. We used resistive stainless steel and copper mesh for the flux conservers, which have soak times of 3 μs and 250 μs , respectively. The goal is to increase the speed, temperature, and density of the plasma plume by adding magnetic energy into the system using the coils and compressing the plasma into small volumes by stagnation. The time of flight is measured by using a linear array of magnetic pick-up loops, which track the plasma plume's location as a function of time. The density is measured by precision quadrature He-Ne laser interferometry, and the temperature is measured by ion Doppler spectroscopy. Speed and density without the coils are 30km /s and 1015cm-3 . We will reach a speed of 100km /s and density of 1016cm-3 by adding the coil. Work supported by DOE OFES and ARPA-E ALPHA program.
Acoustic boundary conditions at an impedance lining in inviscid shear flow
Khamis, Doran; Brambley, Edward James
2016-01-01
This is the author accepted manuscript. It is currently under an indefinite embargo pending publication by Cambridge University Press. The accuracy of existing impedance boundary conditions is investigated, and new impedance boundary conditions are derived, for lined ducts with inviscid shear flow. The accuracy of the Ingard–Myers boundary condition is found to be poor. Matched asymptotic expansions are used to derive a boundary condition accurate to second order in the boundary layer thic...
A non-Linear transport model for determining shale rock characteristics
Ali, Iftikhar; Malik, Nadeem
2016-04-01
Unconventional hydrocarbon reservoirs consist of tight porous rocks which are characterised by nano-scale size porous networks with ultra-low permeability [1,2]. Transport of gas through them is not well understood at the present time, and realistic transport models are needed in order to determine rock properties and for estimating future gas pressure distribution in the reservoirs. Here, we consider a recently developed non-linear gas transport equation [3], ∂p-+ U ∂p- = D ∂2p-, t > 0, (1) ∂t ∂x ∂x2 complimented with suitable initial and boundary conditions, in order to determine shale rock properties such as the permeability K, the porosity φ and the tortuosity, τ. In our new model, the apparent convection velocity, U = U(p,px), and the apparent diffusivity D = D(p), are both highly non-linear functions of the pressure. The model incorporate various flow regimes (slip, surface diffusion, transition, continuum) based upon the Knudsen number Kn, and also includes Forchchiemers turbulence correction terms. In application, the model parameters and associated compressibility factors are fully pressure dependent, giving the model more realism than previous models. See [4]. Rock properties are determined by solving an inverse problem, with model parameters adjustment to minimise the error between the model simulation and available data. It is has been found that the proposed model performs better than previous models. Results and details of the model will be presented at the conference. Corresponding author: namalik@kfupm.edu.sa and nadeem_malik@cantab.net References [1] Cui, X., Bustin, A.M. and Bustin, R., "Measurements of gas permeability and diffusivity of tight reservoir rocks: different approaches and their applications", Geofluids 9, 208-223 (2009). [2] Chiba R., Fomin S., Chugunov V., Niibori Y. and Hashida T., "Numerical Simulation of Non Fickian Diffusion and Advection in a Fractured Porous Aquifer", AIP Conference Proceedings 898, 75 (2007
Numerical modelling in non linear fracture mechanics
Directory of Open Access Journals (Sweden)
Viggo Tvergaard
2007-07-01
Full Text Available Some numerical studies of crack propagation are based on using constitutive models that accountfor damage evolution in the material. When a critical damage value has been reached in a materialpoint, it is natural to assume that this point has no more carrying capacity, as is done numerically in the elementvanish technique. In the present review this procedure is illustrated for micromechanically based materialmodels, such as a ductile failure model that accounts for the nucleation and growth of voids to coalescence, and a model for intergranular creep failure with diffusive growth of grain boundary cavities leading to micro-crack formation. The procedure is also illustrated for low cycle fatigue, based on continuum damage mechanics. In addition, the possibility of crack growth predictions for elastic-plastic solids using cohesive zone models to represent the fracture process is discussed.
Graphical and Analytical Analysis of the Non-Linear PLL
de Boer, Bjorn; Radovanovic, S.; Annema, Anne J.; Nauta, Bram
The fixed width control pulses from the Bang-Bang Phase Detector in non-linear PLLs allow for operation at higher data rates than the linear PLL. The high non-linearity of the Bang- Bang Phase Detector gives rise to unwanted effects, such as limit-cycles, not yet fully described. This paper
Non-linear stochastic response of a shallow cable
DEFF Research Database (Denmark)
Larsen, Jesper Winther; Nielsen, Søren R.K.
2004-01-01
The paper considers the stochastic response of geometrical non-linear shallow cables. Large rain-wind induced cable oscillations with non-linear interactions have been observed in many large cable stayed bridges during the last decades. The response of the cable is investigated for a reduced two-degrees-of-freedom...
Non-linear Frequency Scaling Algorithm for FMCW SAR Data
Meta, A.; Hoogeboom, P.; Ligthart, L.P.
2006-01-01
This paper presents a novel approach for processing data acquired with Frequency Modulated Continuous Wave (FMCW) dechirp-on-receive systems by using a non-linear frequency scaling algorithm. The range frequency non-linearity correction, the Doppler shift induced by the continuous motion and the ran
Non Linear Gauge Fixing for FeynArts
Gajdosik, Thomas
2007-01-01
We review the non-linear gauge-fixing for the Standard Model, proposed by F. Boudjema and E. Chopin, and present our implementation of this non-linear gauge-fixing to the Standard Model and to the minimal supersymmetric Standard Model in FeynArts.
Identification of Non-Linear Structures using Recurrent Neural Networks
DEFF Research Database (Denmark)
Kirkegaard, Poul Henning; Nielsen, Søren R. K.; Hansen, H. I.
1995-01-01
Two different partially recurrent neural networks structured as Multi Layer Perceptrons (MLP) are investigated for time domain identification of a non-linear structure.......Two different partially recurrent neural networks structured as Multi Layer Perceptrons (MLP) are investigated for time domain identification of a non-linear structure....
Identification of Non-Linear Structures using Recurrent Neural Networks
DEFF Research Database (Denmark)
Kirkegaard, Poul Henning; Nielsen, Søren R. K.; Hansen, H. I.
Two different partially recurrent neural networks structured as Multi Layer Perceptrons (MLP) are investigated for time domain identification of a non-linear structure.......Two different partially recurrent neural networks structured as Multi Layer Perceptrons (MLP) are investigated for time domain identification of a non-linear structure....
Identification of Non-Linear Structures using Recurrent Neural Networks
DEFF Research Database (Denmark)
Kirkegaard, Poul Henning; Nielsen, Søren R. K.; Hansen, H. I.
1995-01-01
Two different partially recurrent neural networks structured as Multi Layer Perceptrons (MLP) are investigated for time domain identification of a non-linear structure.......Two different partially recurrent neural networks structured as Multi Layer Perceptrons (MLP) are investigated for time domain identification of a non-linear structure....
Non-linear wave packet dynamics of coherent states
Indian Academy of Sciences (India)
J Banerji
2001-02-01
We have compared the non-linear wave packet dynamics of coherent states of various symmetry groups and found that certain generic features of non-linear evolution are present in each case. Thus the initial coherent structures are quickly destroyed but are followed by Schrödinger cat formation and revival. We also report important differences in their evolution.
Bayesian Inference for Linear Parabolic PDEs with Noisy Boundary Conditions
Ruggeri, Fabrizio
2015-01-07
In this work we develop a hierarchical Bayesian setting to infer unknown parameters in initial-boundary value problems (IBVPs) for one-dimensional linear parabolic partial differential equations. Noisy boundary data and known initial condition are assumed. We derive the likelihood function associated with the forward problem, given some measurements of the solution field subject to Gaussian noise. Such function is then analytically marginalized using the linearity of the equation. Gaussian priors have been assumed for the time-dependent Dirichlet boundary values. Our approach is applied to synthetic data for the one-dimensional heat equation model, where the thermal diffusivity is the unknown parameter. We show how to infer the thermal diffusivity parameter when its prior distribution is lognormal or modeled by means of a space-dependent stationary lognormal random field. We use the Laplace method to provide approximated Gaussian posterior distributions for the thermal diffusivity. Expected information gains and predictive posterior densities for observable quantities are numerically estimated for different experimental setups.
Bayesian Inference for Linear Parabolic PDEs with Noisy Boundary Conditions
Ruggeri, Fabrizio
2016-01-06
In this work we develop a hierarchical Bayesian setting to infer unknown parameters in initial-boundary value problems (IBVPs) for one-dimensional linear parabolic partial differential equations. Noisy boundary data and known initial condition are assumed. We derive the likelihood function associated with the forward problem, given some measurements of the solution field subject to Gaussian noise. Such function is then analytically marginalized using the linearity of the equation. Gaussian priors have been assumed for the time-dependent Dirichlet boundary values. Our approach is applied to synthetic data for the one-dimensional heat equation model, where the thermal diffusivity is the unknown parameter. We show how to infer the thermal diffusivity parameter when its prior distribution is lognormal or modeled by means of a space-dependent stationary lognormal random field. We use the Laplace method to provide approximated Gaussian posterior distributions for the thermal diffusivity. Expected information gains and predictive posterior densities for observable quantities are numerically estimated for different experimental setups.
Non-linear vorticity upsurge in Burgers flow
Lam, F
2016-01-01
We demonstrate that numerical solutions of Burgers' equation can be obtained by a scale-totality algorithm for fluids of small viscosity (down to one billionth). Two sets of initial data, modelling simple shears and wall boundary layers, are chosen for our computations. Most of the solutions are carried out well into the fully turbulent regime over finely-resolved scales in space and in time. It is found that an abrupt spatio-temporal concentration in shear constitutes an essential part during the flow evolution. The vorticity surge has been instigated by the non-linearity complying with instantaneous enstrophy production while ad hoc disturbances play no role in the process. In particular, the present method predicts the precipitous vorticity re-distribution and accumulation, predominantly over localised regions of minute dimension. The growth rate depends on viscosity and is a strong function of initial data. Nevertheless, the long-time energy decay is history-independent and is inversely proportional to ti...
Boundary conditions for soft glassy flows: slippage and surface fluidization.
Mansard, Vincent; Bocquet, Lydéric; Colin, Annie
2014-09-28
We explore the question of surface boundary conditions for the flow of a dense emulsion. We make use of microlithographic tools to create surfaces with well controlled roughness patterns and measure using dynamic confocal microscopy both the slip velocity and the shear rate close to the wall, which we relate to the notion of surface fluidization. Both slippage and wall fluidization depend non-monotonously on the roughness. We interpret this behavior within a simple model in terms of the building of a stratified layer and the activation of plastic events by the surface roughness.
Stokes Flow with Slip and Kuwabara Boundary Conditions
Indian Academy of Sciences (India)
Sunil Datta; Satya Deo
2002-08-01
The forces experienced by randomly and homogeneously distributed parallel circular cylinder or spheres in uniform viscous flow are investigated with slip boundary condition under Stokes approximation using particle-in-cell model technique and the result compared with the no-slip case. The corresponding problem of streaming flow past spheroidal particles departing but little in shape from a sphere is also investigated. The explicit expression for the stream function is obtained to the first order in the small parameter characterizing the deformation. As a particular case of this we considered an oblate spheroid and evaluate the drag on it.
Cauchy-perturbative matching and outer boundary conditions computational studies
Rezzolla, L; Matzner, R A; Rupright, M E; Shapiro, S L; Rezzolla, Luciano; Abrahams, Andrew M; Matzner, Richard A.; Rupright, Mark E.; Shapiro, Stuart L.
1999-01-01
We present results from a new technique which allows extraction of gravitational radiation information from a generic three-dimensional numerical relativity code and provides stable outer boundary conditions. In our approach we match the solution of a Cauchy evolution of the nonlinear Einstein field equations to a set of one-dimensional linear equations obtained through perturbation techniques over a curved background. We discuss the validity of this approach in the case of linear and mildly nonlinear gravitational waves and show how a numerical module developed for this purpose is able to provide an accurate and numerically convergent description of the gravitational wave propagation and a stable numerical evolution.
Quantum Nuclear Pasta Calculations with Twisted Angular Boundary Conditions
Schuetrumpf, Bastian; Nazarewicz, Witold
2015-10-01
Nuclear pasta, expected to be present in the inner crust of neutron stars and core collapse supernovae, can contain a wide spectrum of different exotic shapes such as nuclear rods and slabs. There are also more complicated, network-like structures, the triply periodic minimal surfaces, already known e.g. in biological systems. These shapes are studied with the Hartree-Fock method using modern Skyrme forces. Furthermore twisted angular boundary conditions are utilized to reduce finite size effects in the rectangular simulation boxes. It is shown, that this improves the accuracy of the calculations drastically and additionally more insights into the mechanism of forming minimal surfaces can be gained.
On the trigonometric Felderhof model with domain wall boundary conditions
Caradoc, A; Wheeler, M; Zuparic, M; 10.1088/1742-5468/2007/03/P03010
2008-01-01
We consider the trigonometric Felderhof model, of free fermions in an external field, on a finite lattice with domain wall boundary conditions. The vertex weights are functions of rapidities and external fields. We obtain a determinant expression for the partition function in the special case where the dependence on the rapidities is eliminated, but for general external field variables. This determinant can be evaluated in product form. In the homogeneous limit, it is proportional to a 2-Toda tau function. Next, we use the algebraic Bethe ansatz factorized basis to obtain a product expression for the partition function in the general case with dependence on all variables.
Boundary conditions and generalized functions in a transition radiation problem
Villavicencio, M.; Jiménez, J. L.
2017-03-01
The aim of this work is to show how all the components of the electromagnetic field involved in the transition radiation problem can be obtained using distribution functions. The handling of the products and derivatives of distributions appearing in the differential equations governing transition radiation, allows to obtain the necessary boundary conditions, additional to those implied by Maxwell's equations, in order to exactly determine the longitudinal components of the electromagnetic field. It is shown that this method is not only useful but it is really convenient to achieve a full analysis of the problem.
Non-linear dynamics of wind turbine wings
DEFF Research Database (Denmark)
Larsen, Jesper Winther; Nielsen, Søren R.K.
2006-01-01
by the rotation of the aerodynamic load and the curvature, as well as inertial induced non-linearities caused by the support point motion. The non-linear partial differential equations of motion in the moving frame of reference have been discretized, using the fixed base eigenmodes as a functional basis......The paper deals with the formulation of non-linear vibrations of a wind turbine wing described in a wing fixed moving coordinate system. The considered structural model is a Bernoulli-Euler beam with due consideration to axial twist. The theory includes geometrical non-linearities induced....... Important non-linear couplings between the fundamental blade mode and edgewise modes have been identified based on a resonance excitation of the wing, caused by a harmonically varying support point motion with the circular frequency omega. Assuming that the fundamental blade and edgewise eigenfrequencies...
Employment of CB models for non-linear dynamic analysis
Klein, M. R. M.; Deloo, P.; Fournier-Sicre, A.
1990-01-01
The non-linear dynamic analysis of large structures is always very time, effort and CPU consuming. Whenever possible the reduction of the size of the mathematical model involved is of main importance to speed up the computational procedures. Such reduction can be performed for the part of the structure which perform linearly. Most of the time, the classical Guyan reduction process is used. For non-linear dynamic process where the non-linearity is present at interfaces between different structures, Craig-Bampton models can provide a very rich information, and allow easy selection of the relevant modes with respect to the phenomenon driving the non-linearity. The paper presents the employment of Craig-Bampton models combined with Newmark direct integration for solving non-linear friction problems appearing at the interface between the Hubble Space Telescope and its solar arrays during in-orbit maneuvers. Theory, implementation in the FEM code ASKA, and practical results are shown.
Non-linear dielectric monitoring of biological suspensions
Energy Technology Data Exchange (ETDEWEB)
Treo, E F; Felice, C J [Departamento de BioingenierIa, Universidad Nacional de Tucuman and Consejo Nacional de Investigaciones Cientificas y Tecnicas. CC327, CP4000, San Miguel de Tucuman (Argentina)
2007-11-15
Non-linear dielectric spectroscopy as a tool for in situ monitoring of enzyme assumes a non-linear behavior of the sample when a sinusoidal voltage is applied to it. Even many attempts have been made to improve the original experiments, all of them had limited success. In this paper we present upgrades made to a non-linear dielectric spectrometer developed and the results obtained when using different cells. We emphasized on the electrode surface, characterizing the grinding and polishing procedure. We found that the biological medium does not behave as expected, and the non-linear response is generated in the electrode-electrolyte interface. The electrochemistry of this interface can bias unpredictably the measured non-linear response.
The effects of external conditions in turbulent boundary layers
Brzek, Brian G.
The effects of multiple external conditions on turbulent boundary layers were studied in detail. These external conditions include: surface roughness, upstream turbulence intensity, and pressure gradient. Furthermore, the combined effects of these conditions show the complicated nature of many realistic flow conditions. It was found that the effects of surface roughness are difficult to generalize, given the importance of so many parameters. These parameters include: roughness geometry, roughness regime, roughness height to boundary layer thickness, (k/delta), roughness parameter, ( k+), Reynolds number, and roughness function (Delta B+). A further complication, is the difficulty in computing the wall shear stress, tauw/rho. For the sand grain type roughness, the mean velocity and Reynolds stresses were studied in inner and outer variables, as well as, boundary layer parameters, anisotropy tensor, production term, and viscous stress and form drag contributions. To explore the effects of roughness and Reynolds number dependence in the boundary layer, a new experiment was carefully designed to properly capture the x-dependence of the single-point statistics. It was found that roughness destroys the viscous layer near the wall, thus, reducing the contribution of the viscous stress in the wall region. As a result, the contribution in the skin friction due to form drag increases, while the viscous stress decreases. This yields Reynolds number invariance in the skin friction, near-wall roughness parameters, and inner velocity profiles as k + increases into the fully rough regime. However, in the transitionally rough regime, (i.e., 5 component shows the largest influence of roughness, where the high peak near the wall was decreased and became nearly flat for the fully rough regime profiles. In addition, the Reynolds stresses in outer variables show self-similarity for fixed experimental conditions. However, as the roughness parameter, k +, increases, all Reynolds stress
STABILITY, BIFURCATIONS AND CHAOS IN UNEMPLOYMENT NON-LINEAR DYNAMICS
Directory of Open Access Journals (Sweden)
Pagliari Carmen
2013-07-01
Full Text Available The traditional analysis of unemployment in relation to real output dynamics is based on some empirical evidences deducted from Okun’s studies. In particular the so called Okun’s Law is expressed in a linear mathematical formulation, which cannot explain the fluctuation of the variables involved. Linearity is an heavy limit for macroeconomic analysis and especially for every economic growth study which would consider the unemployment rate among the endogenous variables. This paper deals with an introductive study about the role of non-linearity in the investigation of unemployment dynamics. The main idea is the existence of a non-linear relation between the unemployment rate and the gap of GDP growth rate from its trend. The macroeconomic motivation of this idea moves from the consideration of two concatenate effects caused by a variation of the unemployment rate on the real output growth rate. These two effects are concatenate because there is a first effect that generates a secondary one on the same variable. When the unemployment rate changes, the first effect is the variation in the level of production in consequence of the variation in the level of such an important factor as labour force; the secondary effect is a consecutive variation in the level of production caused by the variation in the aggregate demand in consequence of the change of the individual disposal income originated by the previous variation of production itself. In this paper the analysis of unemployment dynamics is carried out by the use of the logistic map and the conditions for the existence of bifurcations (cycles are determined. The study also allows to find the range of variability of some characteristic parameters that might be avoided for not having an absolute unpredictability of unemployment dynamics (deterministic chaos: unpredictability is equivalent to uncontrollability because of the total absence of information about the future value of the variable to
PLASTICITY AND NON-LINEAR ELASTIC STRAINS
conditions existing in plane waves in an extended medium to give the time rate of change of stress as a function of the time rate of change of strain, the stress invariants, the total strain and the plastic strain. (Author)
Directory of Open Access Journals (Sweden)
Darae Jeong
2015-01-01
Full Text Available We briefly review and investigate the performance of various boundary conditions such as Dirichlet, Neumann, linear, and partial differential equation boundary conditions for the numerical solutions of the Black-Scholes partial differential equation. We use a finite difference method to numerically solve the equation. To show the efficiency of the given boundary condition, several numerical examples are presented. In numerical test, we investigate the effect of the domain sizes and compare the effect of various boundary conditions with pointwise error and root mean square error. Numerical results show that linear boundary condition is accurate and efficient among the other boundary conditions.
Boundary conditions and phase transitions in neural networks. Simulation results.
Demongeot, Jacques; Sené, Sylvain
2008-09-01
This paper gives new simulation results on the asymptotic behaviour of theoretical neural networks on Z and Z(2) following an extended Hopfield law. It specifically focuses on the influence of fixed boundary conditions on such networks. First, we will generalise the theoretical results already obtained for attractive networks in one dimension to more complicated neural networks. Then, we will focus on two-dimensional neural networks. Theoretical results have already been found for the nearest neighbours Ising model in 2D with translation-invariant local isotropic interactions. We will detail what happens for this kind of interaction in neural networks and we will also focus on more complicated interactions, i.e., interactions that are not local, neither isotropic, nor translation-invariant. For all these kinds of interactions, we will show that fixed boundary conditions have significant impacts on the asymptotic behaviour of such networks. These impacts result in the emergence of phase transitions whose geometric shape will be numerically characterised.
Nonlinear Vibrations of Multiwalled Carbon Nanotubes under Various Boundary Conditions
Directory of Open Access Journals (Sweden)
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.
Spatial heterogeneity of ocean surface boundary conditions under sea ice
Barthélemy, Antoine; Fichefet, Thierry; Goosse, Hugues
2016-06-01
The high heterogeneity of sea ice properties implies that its effects on the ocean are spatially variable at horizontal scales as small as a few meters. Previous studies have shown that taking this variability into account in models could be required to simulate adequately mixed layer processes and the upper ocean temperature and salinity structures. Although many advanced sea ice models include a subgrid-scale ice thickness distribution, potentially providing heterogeneous surface boundary conditions, the information is lost in the coupling with a unique ocean grid cell underneath. The present paper provides a thorough examination of boundary conditions at the ocean surface in the NEMO-LIM model, which can be used as a guideline for studies implementing subgrid-scale ocean vertical mixing schemes. Freshwater, salt, solar heat and non-solar heat fluxes are examined, as well as the norm of the surface stress. All of the thermohaline fluxes vary considerably between the open water and ice fractions of grid cells. To a lesser extent, this is also the case for the surface stress. Moreover, the salt fluxes in both hemispheres and the solar heat fluxes in the Arctic show a dependence on the ice thickness category, with more intense fluxes for thinner ice, which promotes further subgrid-scale heterogeneity. Our analysis also points out biases in the simulated open water fraction and in the ice thickness distribution, which should be investigated in more details in order to ensure that the latter is used to the best advantage.
Boundary conditions for NLTE polarized radiative transfer with incident radiation
Faurobert, Marianne; Atanackovic, Olga
2013-01-01
Polarized NLTE radiative transfer in the presence of scattering in spectral lines and/or in continua may be cast in a so-called reduced form for six reduced components of the radiation field. In this formalism the six components of the reduced source function are angle-independent quantities. It thus reduces drastically the storage requirement of numerical codes. This approach encounters a fundamental problem when the medium is illuminated by a polarized incident radiation, because there is a priori no way of relating the known (and measurable) Stokes parameters of the incident radiation to boundary conditions for the reduced equations. The origin of this problem is that there is no unique way of deriving the radiation reduced components from its Stokes parameters (only the inverse operation is clearly defined). The method proposed here aims at enabling to work with arbitrary incident radiation field (polarized or unpolarized). In previous works an ad-hoc treatment of the boundary conditions, applying to case...
Complex Wall Boundary Conditions for Modeling Combustion in Catalytic Channels
Zhu, Huayang; Jackson, Gregory
2000-11-01
Monolith catalytic reactors for exothermic oxidation are being used in automobile exhaust clean-up and ultra-low emissions combustion systems. The reactors present a unique coupling between mass, heat, and momentum transport in a channel flow configuration. The use of porous catalytic coatings along the channel wall presents a complex boundary condition when modeled with the two-dimensional channel flow. This current work presents a 2-D transient model for predicting the performance of catalytic combustion systems for methane oxidation on Pd catalysts. The model solves the 2-D compressible transport equations for momentum, species, and energy, which are solved with a porous washcoat model for the wall boundary conditions. A time-splitting algorithm is used to separate the stiff chemical reactions from the convective/diffusive equations for the channel flow. A detailed surface chemistry mechanism is incorporated for the catalytic wall model and is used to predict transient ignition and steady-state conversion of CH4-air flows in the catalytic reactor.
Comparative Quantum Cosmology: Causality, Singularity, and Boundary Conditions
Fellman, Philip V; Carmichael, Christine M; Post, Andrew Carmichael
2007-01-01
In this review article we compare the recent work of Peter Lynds, "On a finite universe with no beginning or end", with that of Stephen Hawking, primarily "Quantum Cosmology, M-Theory, and the Anthropic Principle", and two foundational works by Sean M. Carroll and Jennifer Chen, "Does Inflation Provide Natural Conditions for the Universe" and "Spontaneous Inflation and the Origin of the Arrow of Time", in order to evaluate their comparative treatments of the nature and role of causality, time ordering, thermodynamic reversibility, singularities and boundary conditions in the formation of the early universe. We briefly reference Smolin and Kauffman's recent arguments with respect to possible processes of "evolutionary selection" in early universe formation as an alternative explanation to key elements of Hawking's earlier "M-Theory", and its attendant anthropic principle. We also briefly excerpt a short section of Smolin's recent work on topology in quantum loop gravity, simply as an illustrative example of th...
Estimation of saturation and coherence effects in the KGBJS equation - a non-linear CCFM equation
Deak, Michal
2012-01-01
We solve the modified non-linear extension of the CCFM equation - KGBJS equation - numerically for certain initial conditions and compare the resulting gluon Green functions with those obtained from solving the original CCFM equation and the BFKL and BK equations for the same initial conditions. We improve the low transversal momentum behaviour of the KGBJS equation by a small modification.
Influence of Spanwise Boundary Conditions on Slat Noise Simulations
Lockard, David P.; Choudhari, Meelan M.; Buning, Pieter G.
2015-01-01
The slat noise from the 30P/30N high-lift system is being investigated through computational fluid dynamics simulations with the OVERFLOW code in conjunction with a Ffowcs Williams-Hawkings acoustics solver. In the present study, two different spanwise grids are being used to investigate the effect of the spanwise extent and periodicity on the near-field unsteady structures and radiated noise. The baseline grid with periodic boundary conditions has a short span equal to 1/9th of the stowed chord, whereas the other, longer span grid adds stretched grids on both sides of the core, baseline grid to allow inviscid surface boundary conditions at both ends. The results indicate that the near-field mean statistics obtained using the two grids are similar to each other, as are the directivity and spectral shapes of the radiated noise. However, periodicity forces all acoustic waves with less than one wavelength across the span to be two-dimensional, without any variation in the span. The spanwise coherence of the acoustic waves is what is needed to make estimates of the noise that would be radiated from realistic span lengths. Simulations with periodic conditions need spans of at least six slat chords to allow spanwise variation in the low-frequencies associated with the peak of broadband slat noise. Even then, the full influence of the periodicity is unclear, so employing grids with a fine, central region and highly stretched meshes that go to slip walls may be a more efficient means of capturing the spanwise decorrelation of low-frequency acoustic phenomena.
Superdiffusions and positive solutions of non-linear partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Dynkin, E B [Cornell University, New York (United States)
2004-02-28
By using super-Brownian motion, all positive solutions of the non-linear differential equation {delta}u=u{sup {alpha}} with 1<{alpha}{<=}2 in a bounded smooth domain E are characterized by their (fine) traces on the boundary. This solves a problem posed by the author a few years ago. The special case {alpha}=2 was treated by B. Mselati in 2002.
Theory of a curved planar waveguide with Robin boundary conditions
Olendski, O.; Mikhailovska, L.
2010-03-01
A model of a thin straight strip with a uniformly curved section and with boundary requirements zeroing at the edges a linear superposition of the wave function and its normal derivative (Robin boundary condition) is analyzed theoretically within the framework of the linear Schrödinger equation and is applied to the study of the processes in the bent magnetic multilayers, superconducting films and metallic ferrite-filled waveguides. In particular, subband thresholds of the straight and curved parts of the film are calculated and analyzed as a function of the Robin parameter 1/Λ , with Λ being an extrapolation length entering Robin boundary condition. For the arbitrary Robin coefficients which are equal on the opposite interfaces of the strip and for all bend parameters the lowest-mode energy of the continuously curved duct is always smaller than its straight counterpart. Accordingly, the bound state below the fundamental propagation threshold of the straight arms always exists as a result of the bend. In terms of the superconductivity language it means an increased critical temperature of the curved film compared to its straight counterpart. Localized-level dependence on the parameters of the curve is investigated with its energy decreasing with increasing bend angle and decreasing bend radius. Conditions of the bound-state existence for the different Robin parameters on the opposite edges are analyzed too; in particular, it is shown that the bound state below the first transverse threshold of the straight arm always exists if the inner extrapolation length is not larger than the outer one. In the opposite case there is a range of the bend parameters where the curved film cannot trap the wave and form the localized mode; for example, for the fixed bend radius the bound state emerges from the continuum at some nonzero bend angle that depends on the difference of the two lengths Λ at the opposite interfaces. Various transport properties of the film such as
Topological susceptibility in lattice Yang-Mills theory with open boundary condition
Energy Technology Data Exchange (ETDEWEB)
Chowdhury, Abhishek; Harindranath, A. [Theory Division, Saha Institute of Nuclear Physics,1/AF Bidhan Nagar, Kolkata 700064 (India); Maiti, Jyotirmoy [Department of Physics, Barasat Government College,10 KNC Road, Barasat, Kolkata 700124 (India); Majumdar, Pushan [Department of Theoretical Physics, Indian Association for the Cultivation of Science,Kolkata 700032 (India)
2014-02-11
We find that using open boundary condition in the temporal direction can yield the expected value of the topological susceptibility in lattice SU(3) Yang-Mills theory. As a further check, we show that the result agrees with numerical simulations employing the periodic boundary condition. Our results support the preferability of the open boundary condition over the periodic boundary condition as the former allows for computation at smaller lattice spacings needed for continuum extrapolation at a lower computational cost.
Non Linear Seismic Analysis of Masonry Structures
Directory of Open Access Journals (Sweden)
Sirajuddin, M
2011-12-01
Full Text Available Nowadays, even though many new construction techniques have been introduced, masonry has got its own importance in building industry. Masonry structures fail miserably under lateral loading conditions like earth quakes and impact loads. The occurrence of recent earthquakes in India and in different parts of the world have highlighted that most of the loss of human lives and damage to property have been due to the collapse of masonry structures. Though an earthquake could not be prevented, the loss of life and property could be minimized, if necessary steps could be taken to reduce the damages on the existing masonry structures. This paper investigates the application ofNonlinear Seismic Analysis of a masonry building using ANSYS software and check the efficacy of retrofit measuresto protect the existing building.
Homogenized boundary conditions and resonance effects in Faraday cages
Hewett, D. P.; Hewitt, I. J.
2016-05-01
We present a mathematical study of two-dimensional electrostatic and electromagnetic shielding by a cage of conducting wires (the so-called `Faraday cage effect'). Taking the limit as the number of wires in the cage tends to infinity, we use the asymptotic method of multiple scales to derive continuum models for the shielding, involving homogenized boundary conditions on an effective cage boundary. We show how the resulting models depend on key cage parameters such as the size and shape of the wires, and, in the electromagnetic case, on the frequency and polarization of the incident field. In the electromagnetic case, there are resonance effects, whereby at frequencies close to the natural frequencies of the equivalent solid shell, the presence of the cage actually amplifies the incident field, rather than shielding it. By appropriately modifying the continuum model, we calculate the modified resonant frequencies, and their associated peak amplitudes. We discuss applications to radiation containment in microwave ovens and acoustic scattering by perforated shells.
Theoretical Foundations of Incorporating Local Boundary Conditions into Nonlocal Problems
Aksoylu, Burak; Beyer, Horst Reinhard; Celiker, Fatih
2017-08-01
We study nonlocal equations from the area of peridynamics on bounded domains. We present four main results. In our recent paper, we have discovered that, on R, the governing operator in peridynamics, which involves a convolution, is a bounded function of the classical (local) governing operator. Building on this, as main result 1, we construct an abstract convolution operator on bounded domains which is a generalization of the standard convolution based on integrals. The abstract convolution operator is a function of the classical operator, defined by a Hilbert basis available due to the purely discrete spectrum of the latter. As governing operator of the nonlocal equation we use a function of the classical operator, this allows us to incorporate local boundary conditions into nonlocal theories. As main result 2, we prove that the solution operator can be uniquely decomposed into a Hilbert-Schmidt operator and a multiple of the identity operator. As main result 3, we prove that Hilbert-Schmidt operators provide a smoothing of the input data in the sense a square integrable function is mapped into a function that is smooth up to boundary of the domain. As main result 4, for the homogeneous nonlocal wave equation, we prove that continuity is preserved by time evolution. Namely, the solution is discontinuous if and only if the initial data is discontinuous. As a consequence, discontinuities remain stationary.
Homogenized boundary conditions and resonance effects in Faraday cages.
Hewett, D P; Hewitt, I J
2016-05-01
We present a mathematical study of two-dimensional electrostatic and electromagnetic shielding by a cage of conducting wires (the so-called 'Faraday cage effect'). Taking the limit as the number of wires in the cage tends to infinity, we use the asymptotic method of multiple scales to derive continuum models for the shielding, involving homogenized boundary conditions on an effective cage boundary. We show how the resulting models depend on key cage parameters such as the size and shape of the wires, and, in the electromagnetic case, on the frequency and polarization of the incident field. In the electromagnetic case, there are resonance effects, whereby at frequencies close to the natural frequencies of the equivalent solid shell, the presence of the cage actually amplifies the incident field, rather than shielding it. By appropriately modifying the continuum model, we calculate the modified resonant frequencies, and their associated peak amplitudes. We discuss applications to radiation containment in microwave ovens and acoustic scattering by perforated shells.
DEFF Research Database (Denmark)
Johannessen, Kim
2014-01-01
The exact solution to the one-dimensional Poisson–Boltzmann equation with asymmetric boundary conditions can be expressed in terms of the Jacobi elliptic functions. The boundary conditions determine the modulus of the Jacobi elliptic functions. The boundary conditions can not be solved analytically...
`Gas cushion' model and hydrodynamic boundary conditions for superhydrophobic textures
Nizkaya, Tatiana V; Vinogradova, Olga I
2014-01-01
Superhydrophobic Cassie textures with trapped gas bubbles reduce drag, by generating large effective slip, which is important for a variety of applications that involve a manipulation of liquids at the small scale. Here we discuss how the dissipation in the gas phase of textures modifies their friction properties and effective slip. We propose an operator method, which allows us the mapping of the flow in the gas subphase to a local slip boundary condition at the liquid/gas interface. The determined uniquely local slip length depends on the viscosity contrast and underlying topography, and can be immediately used to evaluate an effective slip of the texture. Beside Cassie surfaces our approach is valid for Wenzel textures, where a liquid follows the surface relief, as well as for rough surfaces impregnated by a low-viscosity `lubricant'. These results provide a framework for the rational design of textured surfaces for numerous applications.
Boundary conditions for free surface inlet and outlet problems
Taroni, M.
2012-08-10
We investigate and compare the boundary conditions that are to be applied to free-surface problems involving inlet and outlets of Newtonian fluid, typically found in coating processes. The flux of fluid is a priori known at an inlet, but unknown at an outlet, where it is governed by the local behaviour near the film-forming meniscus. In the limit of vanishing capillary number Ca it is well known that the flux scales with Ca 2/3, but this classical result is non-uniform as the contact angle approaches π. By examining this limit we find a solution that is uniformly valid for all contact angles. Furthermore, by considering the far-field behaviour of the free surface we show that there exists a critical capillary number above which the problem at an inlet becomes over-determined. The implications of this result for the modelling of coating flows are discussed. © 2012 Cambridge University Press.
Thermal momentum distribution from path integrals with shifted boundary conditions
Giusti, Leonardo
2011-01-01
For a thermal field theory formulated in the grand canonical ensemble, the distribution of the total momentum is an observable characterizing the thermal state. We show that its cumulants are related to thermodynamic potentials. In a relativistic system for instance, the thermal variance of the total momentum is a direct measure of the enthalpy. We relate the generating function of the cumulants to the ratio of (a) a partition function expressed as a Matsubara path integral with shifted boundary conditions in the compact direction, and (b) the ordinary partition function. In this form the generating function is well suited for Monte-Carlo evaluation, and the cumulants can be extracted straightforwardly. We test the method in the SU(3) Yang-Mills theory and obtain the entropy density at three different temperatures.
Physiologically structured populations with diffusion and dynamic boundary conditions.
Farkas, József Z; Hinow, Peter
2011-04-01
We consider a linear size-structured population model with diffusion in the size-space. Individuals are recruited into the population at arbitrary sizes. We equip the model with generalized Wentzell-Robin (or dynamic) boundary conditions. This approach allows the modelling of populations in which individuals may have distinguished physiological states. We establish existence and positivity of solutions by showing that solutions are governed by a positive quasicontractive semigroup of linear operators on the biologically relevant state space. These results are obtained by establishing dissipativity of a suitably perturbed semigroup generator. We also show that solutions of the model exhibit balanced exponential growth, that is, our model admits a finite-dimensional global attractor. In case of strictly positive fertility we are able to establish that solutions in fact exhibit asynchronous exponential growth.
Boundary Conditions for a New Type of Design Task
DEFF Research Database (Denmark)
McAloone, Tim C.
2011-01-01
object and research paradigm, studying service‐oriented approaches to product development and seeking to understand how to spell the systematic development of these so-called Product/Service‐Systems (PSS). When considering the shift towards PSS in the domain of engineering, it is in......-teresting to understand the shifting focus and identification of boundary conditions that manufacturing organisations must undergo, in order to develop just as systematic an approach to the service-related aspects of their business development, as they have in place for their product development. This chapter......Manufacturing companies have traditionally focused their efforts on developing and producing physical products for the market. Currently, however, many companies are rethinking their business strategies, from selling products to providing services. In place of the product alone, the activity...
Steady-State Axisymmetric MHD Solutions with Various Boundary Conditions
Wang, Lile
2014-01-01
Axisymmetric magnetohydrodynamics (MHD) can be invoked for describing astrophysical magnetized flows and formulated to model stellar magnetospheres including main sequence stars (e.g. the Sun), compact stellar objects [e.g. magnetic white dwarfs (MWDs), radio pulsars, anomalous X-ray pulsars (AXPs), magnetars, isolated neutron stars etc.], and planets as a major step forward towards a full three-dimensional model construction. Using powerful and reliable numerical solvers based on two distinct finite-difference method (FDM) and finite-element method (FEM) schemes of algorithm, we examine axisymmetric steady-state or stationary MHD models in Throumoulopoulos & Tasso (2001), finding that their separable semi-analytic nonlinear solutions are actually not unique given their specific selection of several free functionals and chosen boundary conditions. The multiplicity of nonlinear steady MHD solutions gives rise to differences in the total energies contained in the magnetic fields and flow velocity fields as ...
Solution of MHD problems with mixed-type boundary conditions
Energy Technology Data Exchange (ETDEWEB)
Antimirov, M.IA.
1985-06-01
The introduction of artificial anisotropy of the dynamic viscosity in one of the subregions in which the solution is sought is utilized to derive an approximation method for MHD problems with mixed-type boundary conditions. The method is demonstrated through two problems: slow rotation of a disk and motion of a finite-width infinitely long plate in an infinite volume of a conducting fluid. The velocity and magnetic field solutions are obtained in the form of integrals of Bessel functions, and the torque is found. It is shown that when the Hartmann number approaches infinity the torque of a convex body of revolution in a longitudinal magnetic field is equal to that of a disk lying at the centerline section of the body.
Sprlak, M.; Novak, P.; Pitonak, M.; Hamackova, E.
2015-12-01
Values of scalar, vectorial and second-order tensorial parameters of the Earth's gravitational field have been collected by various sensors in geodesy and geophysics. Such observables have been widely exploited in different parametrization methods for the gravitational field modelling. Moreover, theoretical aspects of these quantities have extensively been studied and are well understood. On the other hand, new sensors for observing gravitational curvatures, i.e., components of the third-order gravitational tensor, are currently under development. This fact may be documented by the terrestrial experiments Dulkyn and Magia, as well as by the proposal of the gravity-dedicated satellite mission called OPTIMA. As the gravitational curvatures represent new types of observables, their exploitation for modelling of the Earth's gravitational field is a subject of this study. Firstly, we derive integral transforms between the gravitational potential and gravitational curvatures, i.e., we find analytical solutions of the boundary value problems with gravitational curvatures as boundary conditions. Secondly, properties of the corresponding Green kernel functions are studied in the spatial and spectral domains. Thirdly, the correctness of the new analytical solutions is tested in a simulation study. The presented mathematical apparatus reveal important properties of the gravitational curvatures. It also extends the Meissl scheme, i.e., an important theoretical paradigm that relates various parameters of the Earth's gravitational field.
Behavior of the reversed field pinch with nonideal boundary conditions
Ho, Yung-Lung
1988-11-01
The linear and nonlinear magnetohydrodynamic stability of current-driven modes are studied for a reversed field pinch with nonideal boundary conditions. The plasma is bounded by a thin resistive shell surrounded by a vacuum region out to a radius at which a perfectly conducting wall is situated. The distant wall and the thin shell problems are studied by removing either the resistive shell or the conducting wall. Linearly, growth rates of tearing modes and kink modes are calculated by analytical solutions based on the modified Bessel function model for the equilibrium. The effects of variation of the shell resistivity and wall proximity on the growth rates are investigated. The modes that may be important in different parameter regimes and with different boundary conditions are identified. The nonlinear behaviors are studied with a three-dimensional magnetohydrodynamics code. The fluctuations generally rise with increasing distance between the conducting wall and the plasma. The enhanced fluctuation induced v x b electric field primarily oppose toroidal current; hence, loop voltage must increase to sustain the constant. Quasilinear interaction between modes typically associated with the dynamo action is identified as the most probable nonlinear destabilization mechanism. The helicity and energy balance properties of the simulation results are discussed. The interruption of current density along field lines intersecting the resistive shell is shown to lead to surface helicity leakage. This effect is intimately tied to stability, as fluctuation induced v x b electric field is necessary to transport the helicity to the surface. In this manner, all aspects of helicity balance, i.e., injection, transport, and dissipation, are considered self-consistently. The importance of the helicity and energy dissipation by the mean components of the magnetic field and current density is discussed.
Non-linear controls on the persistence of La Nina
Di Nezio, P. N.; Deser, C.
2013-12-01
Non-linear controls on the persistence of La Nina Pedro DiNezio and Clara Deser Up to half of the observed La Nina events last for two years or more. Most El Nino events, in contrast, last no longer than one year. The physical processes causing this asymmetry in the duration of warm and cold ENSO events is unknown. The persistence of La Nina, not only exacerbates the climate impacts, especially in regions prone to drought, but also is highly unpredictable. In this talk we will explore the nonlinear processes that generate the persistence of La Nina in observations and in CCSM4 - a coupled climate model that simulates this feature realistically. First, we develop a non-linear delayed-oscillator model (nonlinDO) based on CCSM4's heat budget. All positive and negative feedbacks of nonlinDO capture the nonlinear and seasonal dependence exhibited by CCSM4. The nonlinear behavior is due to: 1) weaker atmospheric damping of cold events with respect to warm events, 2) stronger wind response for large warm events, and 3) weaker coupling between thermocline and sea-surface temperature anomalies when the thermocline deepens. We force the simple model with white Gaussian noise resulting in seasonal modulation of variance and skewness, and a spectral peak, that are in agreement with CCSM4. Sensitivity experiments with nonlinDO show that the thermocline nonlinearity (3) is the sole process controlling the duration of La Nina events. Linear ENSO theory indicates that La Nina events drive a delayed thermocline deepening that leads to their demise. However, the thermocline nonlinearity (3) renders this response ineffective as La Nina events become stronger. This diminishing of the delayed-thermocline feedback prevents the equatorial Pacific from returning to neutral or warm conditions and cold conditions persist for a second year. Observations show evidence for this thermocline nonlinearity suggesting that this process could be at work in the real world. Last, we show evidence that
Burau, Viola; Vrangbaek, Karsten
2008-01-01
The paper aims to account for the substance of non-linear governance change by analysing the importance of sector-specific institutions and the pathways of governing they create. The analysis uses recent reforms of the governance of medical performance in four European countries as a case, adopting an inductively oriented approach to comparison. The governance of medical performance is a good case as it is both, closely related to redistributive policies, where the influence of institutions tends to be pertinent, and is subject to considerable policy pressures. The overall thrust of reforms is similar across countries, while there are important differences in relation to how individual forms of governance and the balance between different forms of governance are changing. More specifically, sector-specific institutions can account for the specific ways in which reforms redefine hierarchy and professional self-regulation and for the extent to which reforms strengthen hierarchy and affect the balance with other forms of governance. The recent literature on governance mainly focuses on mapping out the substance of non-linear change, whereas the development of explanations of the substance of governance change is less systematic. In the present paper, therefore, it is suggested coupling the notion of non-linear change with an analysis of sector specific institutions inspired by the historical institutionalist tradition to better account for the substance of non-linear governance change. Further, the analysis offers interesting insights into the complexity of redrawing boundaries between the public and the private in health care.
Non-Linear Stability of an Electrified Plane Interface in Porous Media
El-Dib, Yusry O.; Moatimid, Galal M.
2004-03-01
The non-linear electrohydrodynamic stability of capillary-gravity waves on the interface between two semi-infinite dielectric fluids is investigated. The system is stressed by a vertical electric field in the presence of surface charges. The work examines a few representative porous media configurations. The analysis includes Rayleigh-Taylor and Kelvin-Helmholtz instabilities. The boundary - value problem leads to a non-linear equation governing the surface evolution. Taylor theory is adopted to expand this equation, in the light of multiple scales, in order to obtain a non-linear Schr¨odinger equation describing the behavior of the perturbed interface. The latter equation, representing the amplitude of the quasi-monochromatic traveling wave, is used to describe the stability criteria. These criteria are discussed both analytically and numerically. In order to identifiy regions of stability and instability, the electric field intensity is plotted versus the wave number. Through a linear stability approach it is found that Darcy's coefficients have a destabilizing influence, while in the non-linear scope these coefficients as well as the electric field intensity play a dual role on the stability.
Two Degrees of Freedom Non-linear Model to Study the Automobile’s Vibrations
Nicolae–Doru Stănescu
2010-01-01
In this paper we present a non-linear model for the study of an automobile's vibrations. The model has two degrees of freedom and it is highly non-linear. The forces in the springs are considered to be given by a polynomial potential. The equations of motion are obtained using the Lagrange second order equations. We determined the equilibrium positions. We proved the conditions for the uniqueness of the equilibrium. In our paper we studied the stability of the equilibrium and the stability of...
Two Degrees of Freedom Non-linear Model to Study the Automobile’s Vibrations
Directory of Open Access Journals (Sweden)
Nicolae–Doru Stănescu
2010-01-01
Full Text Available In this paper we present a non-linear model for the study of an automobile's vibrations. The model has two degrees of freedom and it is highly non-linear. The forces in the springs are considered to be given by a polynomial potential. The equations of motion are obtained using the Lagrange second order equations. We determined the equilibrium positions. We proved the conditions for the uniqueness of the equilibrium. In our paper we studied the stability of the equilibrium and the stability of the motion. Finally a numerical application is presented.
Lipschitz Operators and the Solvability of Non-linear Operator Equations
Institute of Scientific and Technical Information of China (English)
Huai Xin CAO; Zong Ben XU
2004-01-01
Let U and V be Banach spaces, L and N be non-linear operators from U into V. L is some basic properties of Lipschitz operators and then discuss the unique solvability, exact solvability,approximate solvability of the operator equations Lx = y and Lx + Nx = y. Under some conditions we prove the equivalence of these solvabilities. We also give an estimation for the relative-errors of the solutions of these two systems and an application of our method to a non-linear control system.
The height of the atmospheric boundary layer during unstable conditions
Energy Technology Data Exchange (ETDEWEB)
Gryning, S.E.
2005-11-01
The height of the convective atmospheric boundary layer, also called the mixed-layer, is one of the fundamental parameters that characterise the structure of the atmosphere near the ground. It has many theoretical and practical applications such as the prediction of air pollution concentrations, surface temperature and the scaling of turbulence. However, as pointed out by Builtjes (2001) in a review paper on Major Twentieth Century Milestones in Air Pollution Modelling and Its Application, the weakest point in meteorology data is still the determination of the height of the mixed-layer, the so-called mixing height. A simple applied model for the height of the mixed-layer over homogeneous terrain is suggested in chapter 2. It is based on a parameterised budget for the turbulent kinetic energy. In the model basically three terms - the spin-up term and the production of mechanical and convective turbulent kinetic energy - control the growth of the mixed layer. The interplay between the three terms is related to the meteorological conditions and the height of the mixed layer. A stable layer, the so-called entrainment zone, which is confined between the mixed layer and the free air above, caps the mixed layer. A parameterisation of the depth of the entrainment zone is also suggested, and used to devise a combined model for the height of the mixed layer and the entrainment zone. Another important aspect of the mixed layer development exists in coastal areas where an internal boundary layer forms downwind from the coastline. A model for the growth of the internal boundary layer is developed in analogy with the model for mixed layer development over homogeneous terrain. The strength of this model is that it can operate on a very fine spatial resolution with minor computer resources. Chapter 3 deals with the validation of the models. It is based in parts on data from the literature, and on own measurements. For the validation of the formation of the internal boundary layer
DYNAMIC SURFACE BOUNDARY-CONDITIONS - A SIMPLE BOUNDARY MODEL FOR MOLECULAR-DYNAMICS SIMULATIONS
JUFFER, AH; BERENDSEN, HJC
1993-01-01
A simple model for the treatment of boundaries in molecular dynamics simulations is presented. The method involves the positioning of boundary atoms on a surface that surrounds a system of interest. The boundary atoms interact with the inner region and represent the effect of atoms outside the surfa
DEFF Research Database (Denmark)
Larsen, Jon Steffen; Santos, Ilmar
2015-01-01
An efficient finite element scheme for solving the non-linear Reynolds equation for compressible fluid coupled to compliant structures is presented. The method is general and fast and can be used in the analysis of airfoil bearings with simplified or complex foil structure models. To illustrate...... the computational performance, it is applied to the analysis of a compliant foil bearing modelled using the simple elastic foundation model. The model is derived and perturbed using complex notation. Top foil sagging effect is added to the bump foil compliance in terms of a close-form periodic function. For a foil...... bearing utilized in an industrial turbo compressor, the influence of boundary conditions and sagging on the pressure profile, shaft equilibrium position and dynamic coefficients is numerically simulated. The proposed scheme is faster, leading to the conclusion that it is suitable, not only for steady...
Sensitivity of African easterly waves to boundary layer conditions
Directory of Open Access Journals (Sweden)
A. Lenouo
2008-06-01
Full Text Available A linearized version of the quasi-geostrophic model (QGM with an explicit Ekman layer and observed static stability parameter and profile of the African easterly jet (AEJ, is used to study the instability properties of the environment of the West African wave disturbances. It is found that the growth rate, the propagation velocity and the structure of the African easterly waves (AEW can be well simulated. Two different lower boundary conditions are applied. One assumes a lack of vertical gradient of perturbation stream function and the other assumes zero wind perturbation at the surface. The first case gives more realistic results since in the absence of horizontal diffusion, growth rate, phase speed and period have values of 0.5 day^{−1}, 10.83 m s^{−1} and 3.1 day, respectively. The zero wind perturbation at the surface case leads to values of these parameters that are 50 percent lower. The analysis of the sensitivity to diffusion shows that the magnitude of the growth rate decreases with this parameter. Modelled total relative vorticity has its low level maximum around 900 hPa under no-slip, and 700 hPa under free slip condition.
Effects of Boundary Conditions on Near Field Plasma Plume Simulations
Boyd, Iain
2004-11-01
The successful development of various types of electric propulsion devices is providing the need for accurate assessment of integration effects generated by the interaction of the plasma plumes of these thrusters with the host spacecraft. Assessment of spacecraft interaction effects in ground based laboratory facilities is inadequate due to the technical difficulties involved in accurately recreating the near vacuum ambient conditions experienced in space. This situation therefore places a heavy demand on computational modeling of plasma plume phenomena. Recently (Boyd and Yim, Journal of Applied Physics, Vol. 95, 2004, pp. 4575-5484) a hybrid model of the near field of the plume of a Hall thruster was reported in which the heavy species are modeled using particles and the electrons are modeled using a detailed fluid description. The present study continues the model development and assessment by considering the sensitivity of computed results to different types of boundary conditions that must be formulated for the thruster exit, for the cathode exit, for the thruster walls, and for the plume far field. The model is assessed through comparison of its predictions with several sets of experimental data measured in the plume of the BHT-200 Hall thruster.
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
This paper presents a method on non-linear correction of broadband LFMCW signal utilizing its relativenonlinear error. The deriving procedure and the results simulated by a computer and tested by a practical system arealso introduced. The method has two obvious advantages compared with the previous methods: (1) Correction has norelation with delay time td and sweep bandwidth B; (2) The inherent non-linear error of VCO has no influence on thecorrection and its last results.
Few-photon Non-linearities in Nanophotonic Devices for Quantum Information Technology
DEFF Research Database (Denmark)
Nysteen, Anders
In this thesis we investigate few-photon non-linearities in all-optical, on-chip circuits, and we discuss their possible applications in devices of interest for quantum information technology, such as conditional two-photon gates and single-photon sources. In order to propose efficient devices...
Are oil markets chaotic? A non-linear dynamic analysis
Energy Technology Data Exchange (ETDEWEB)
Panas, E.; Ninni, V. [Athens University of Economics and Business, Athens (Greece)
2000-10-01
The analysis of products' price behaviour continues to be an important empirical issue. This study contributes to the current literature on price dynamics of products by examining for the presence of chaos and non-linear dynamics in daily oil products for the Rotterdam and Mediterranean petroleum markets. Previous studies using only one invariant, such as the correlation dimension may not effectively determine the chaotic structure of the underlying time series. To obtain better information on the time series structure, a framework is developed, where both invariant and non-invariant quantities were also examined. In this paper various invariants for detecting a chaotic time series were analysed along with the associated Brock's theorem and Eckman-Ruelle condition, to return series for the prices of oil products. An additional non-invariant quantity, the BDS statistic, was also examined. The correlation dimension, entropies and Lyapunov exponents show strong evidence of chaos in a number of oil products considered. 30 refs.
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.
A Note on Fractional Differential Equations with Fractional Separated Boundary Conditions
Directory of Open Access Journals (Sweden)
Bashir Ahmad
2012-01-01
Full Text Available We consider a new class of boundary value problems of nonlinear fractional differential equations with fractional separated boundary conditions. A connection between classical separated and fractional separated boundary conditions is developed. Some new existence and uniqueness results are obtained for this class of problems by using standard fixed point theorems. Some illustrative examples are also discussed.
An Artificial Boundary Condition for the Vortex Movements in Two Dimensions
Institute of Scientific and Technical Information of China (English)
Qiyuan Cheng
2006-01-01
An approximate artificial boundary condition based on a boundary integral equation is designed for the vortex movements. Point vortex and cloud in cell methods are used in numerical simulation of vortex motions. The numerical experiments show that the approximate artificial boundary condition is useful and sufficiently accurate in hydrodynamics.
Directory of Open Access Journals (Sweden)
Nahed S. Hussein
2014-01-01
Full Text Available A numerical boundary integral scheme is proposed for the solution to the system of eld equations of plane. The stresses are prescribed on one-half of the circle, while the displacements are given. The considered problem with mixed boundary conditions in the circle is replaced by two problems with homogeneous boundary conditions, one of each type, having a common solution. The equations are reduced to a system of boundary integral equations, which is then discretized in the usual way, and the problem at this stage is reduced to the solution to a rectangular linear system of algebraic equations. The unknowns in this system of equations are the boundary values of four harmonic functions which define the full elastic solution and the unknown boundary values of stresses or displacements on proper parts of the boundary. On the basis of the obtained results, it is inferred that a stress component has a singularity at each of the two separation points, thought to be of logarithmic type. The results are discussed and boundary plots are given. We have also calculated the unknown functions in the bulk directly from the given boundary conditions using the boundary collocation method. The obtained results in the bulk are discussed and three-dimensional plots are given. A tentative form for the singular solution is proposed and the corresponding singular stresses and displacements are plotted in the bulk. The form of the singular tangential stress is seen to be compatible with the boundary values obtained earlier. The efficiency of the used numerical schemes is discussed.
Mirror-type Boundary Condition in Smoothed Particle Hydrodynamics
Marjani, A.; Edge, B. L.
2013-12-01
The main purpose of this study is to enhance the Smoothed Particle Hydrodynamics (SPH) method that can accurately simulate the hydrodynamic forces on a structure and can be used for determining efficient designs for wave energy devices. Smoothed particle hydrodynamics is a method used in various fields of study. Unlike the finite difference method (FDM), SPH is a Lagrangian mesh-free method in which each particle moves according to the property of the surrounding flow and governing conservation equations, and carries the properties of water such as density, pressure and mass. Smoothed Particle Hydrodynamics is recently applied to a wide range of fluid mechanics problems. Although it is known as a highly accurate model, slow performance in 3D interface is one of its drawbacks. Not only the computational time becomes very long but also the number of processors and required memory are not easily available. Practical applications deal with high Reynolds numbers that requires high resolution to achieve adequate accuracy. A large number of coastal engineering problems are geometrically symmetric; hence, as a solution, mirror boundary condition is introduced and applied to two different tests in this paper, one is the impact of solitary wave on a large circular cylinder and the other is the interaction of dam break wave and structure. Mirror boundary condition can either produce a remarkable speedup with the same number of processors or the same running time with less number of processors. Regarding the fact that SPH algorithm yields Np log(Np) particle interactions at each time step, reducing the number of particles by a factor of 2 decreases the total number of interactions by a factor greater than 2. In other words, the relation between computational time and the number of particles does not behave like a linear function. Results show that smaller number of particles results in fewer particle interactions and less communications between processors. We believe that this
Reconstructing geographical boundary conditions for palaeoclimate modelling during the Cenozoic
Baatsen, Michiel; van Hinsbergen, Douwe J. J.; von der Heydt, Anna S.; Dijkstra, Henk A.; Sluijs, Appy; Abels, Hemmo A.; Bijl, Peter K.
2016-08-01
Studies on the palaeoclimate and palaeoceanography using numerical model simulations may be considerably dependent on the implemented geographical reconstruction. Because building the palaeogeographic datasets for these models is often a time-consuming and elaborate exercise, palaeoclimate models frequently use reconstructions in which the latest state-of-the-art plate tectonic reconstructions, palaeotopography and -bathymetry, or vegetation have not yet been incorporated. In this paper, we therefore provide a new method to efficiently generate a global geographical reconstruction for the middle-late Eocene. The generalised procedure is also reusable to create reconstructions for other time slices within the Cenozoic, suitable for palaeoclimate modelling. We use a plate-tectonic model to make global masks containing the distribution of land, continental shelves, shallow basins and deep ocean. The use of depth-age relationships for oceanic crust together with adjusted present-day topography gives a first estimate of the global geography at a chosen time frame. This estimate subsequently needs manual editing of areas where existing geological data indicate that the altimetry has changed significantly over time. Certain generic changes (e.g. lowering mountain ranges) can be made relatively easily by defining a set of masks while other features may require a more specific treatment. Since the discussion regarding many of these regions is still ongoing, it is crucial to make it easy for changes to be incorporated without having to redo the entire procedure. In this manner, a complete reconstruction can be made that suffices as a boundary condition for numerical models with a limited effort. This facilitates the interaction between experts in geology and palaeoclimate modelling, keeping reconstructions up to date and improving the consistency between different studies. Moreover, it facilitates model inter-comparison studies and sensitivity tests regarding certain
Eigenmode Analysis of Boundary Conditions for One-Dimensional Preconditioned Euler Equations
Darmofal, David L.
1998-01-01
An analysis of the effect of local preconditioning on boundary conditions for the subsonic, one-dimensional Euler equations is presented. Decay rates for the eigenmodes of the initial boundary value problem are determined for different boundary conditions. Riemann invariant boundary conditions based on the unpreconditioned Euler equations are shown to be reflective with preconditioning, and, at low Mach numbers, disturbances do not decay. Other boundary conditions are investigated which are non-reflective with preconditioning and numerical results are presented confirming the analysis.
Vu, The Manh; Sulem, Jean; Subrin, Didier; Monin, Nathalie
2013-03-01
A semi-analytical solution based on the transfer matrix technique is proposed to analyze the stresses and displacements in a two-dimensional circular opening excavated in transversely isotropic formation with non-linear behavior. A non-isotropic far field can be accounted for and the process of excavation is simulated by progressive reduction of the internal radial stress. A hyperbolic stress-strain law is proposed to take into account the non-linear behavior of the rock. The model contains seven independent parameters corresponding to the five elastic constants of an elastic material with transverse isotropy and to the friction coefficient and cohesion along the parallel joints (weakness planes). This approach is based on the discretization of the space into concentric rings. It requires the establishment of elementary solutions corresponding to the stress and displacement fields inside each ring for given conditions at its boundaries. These solutions, based on complex variable theory, are obtained in the form of infinite series. The appropriate number of terms to be kept for acceptable approximation is discussed. This non-linear model is applied to back analyze the convergence measurements of Saint-Martin-la-Porte access gallery. Short-term and long-term ground parameters are evaluated.
Non-linear dynamics of a geared rotor-bearing system with multiple clearances
Kahraman, A.; Singh, R.
1991-02-01
Non-linear frequency response characteristics of a geared rotor-bearing system are examined in this paper. A three-degree-of-freedom dynamic model is developed which includes non-linearities associated with radial clearances in the radial rolling element bearings and backlash between a spur gear pair; linear time-invariant gear meshing stiffness is assumed. The corresponding linear system problem is also solved, and predicted natural frequencies and modes match with finite element method results. The bearing non-linear stiffness function is approximated for the sake of convenience by a simple model which is identical to that used for the gear mesh. This approximate bearing model has been verified by comparing steady state frequency spectra. Applicability of both analytical and numerical solution techniques to the multi-degree-of-freedom non-linear problem is investigated. Satisfactory agreement has been found between our theory and available experimental data. Several key issues such as non-linear modal interactions and differences between internal static transmission error excitation and external torque excitation are discussed. Additionally, parametric studies are performed to understand the effect of system parameters such as bearing stiffness to gear mesh stiffness ratio, alternating to mean force ratio and radial bearing preload to mean force ratio on the non-linear dynamic behavior. A criterion used to classify the steady state solutions is presented, and the conditions for chaotic, quasi-periodic and subharmonic steady state solutions are determined. Two typical routes to chaos observed in this geared system are also identified.
Massive Neutrinos and the Non-linear Matter Power Spectrum
Bird, Simeon; Haehnelt, Martin G
2011-01-01
We perform an extensive suite of N-body simulations of the matter power spectrum, incorporating massive neutrinos in the range M = 0.15-0.6 eV, probing the non-linear regime at scales k < 10 hMpc-1 at z < 3. We extend the widely used HALOFIT approximation (Smith et al. 2003) to account for the effect of massive neutrinos on the power spectrum. In the strongly non-linear regime HALOFIT systematically over-predicts the suppression due to the free-streaming of the neutrinos. The maximal discrepancy occurs at k \\sim 1hMpc-1, and is at the level of 10% of the total suppression. Most published constraints on neutrino masses based on HALOFIT are not affected, as they rely on data probing the matter power spectrum in the linear or mildly non-linear regime. However, predictions for future galaxy, Lyman-alpha forest and weak lensing surveys extending to more non-linear scales will benefit from the improved approximation to the non-linear matter power spectrum we provide. Our approximation reproduces the induced n...
Analytical exact solution of the non-linear Schroedinger equation
Energy Technology Data Exchange (ETDEWEB)
Martins, Alisson Xavier; Rocha Filho, Tarcisio Marciano da [Universidade de Brasilia (UnB), DF (Brazil). Inst. de Fisica. Grupo de Fisica e Matematica
2011-07-01
Full text: In this work we present how to classify and obtain analytical solutions of the Schroedinger equation with a generic non-linearity in 1+1 dimensions. Our approach is based on the determination of Lie symmetry transformation mapping solutions into solutions, and non-classical symmetry transformations, mapping a given solution into itself. From these symmetries it is then possible to reduce the equation to a system of ordinary differential equations which can then be solved using standard methods. The generic non-linearity is handled by considering it as an additional unknown in the determining equations for the symmetry transformations. This results in an over-determined system of non-linear partial differential equations. Its solution can then be determined in some cases by reducing it to the so called involutive (triangular) form, and then solved. This reduction is very tedious and can only performed using a computer algebra system. Once the determining system is solved, we obtain the explicit form for the non-linearity admitting a Lie or non-classical symmetry. The analytical solutions are then derived by solving the reduced ordinary differential equations. The non-linear determining system for the non-classical symmetry transformations and Lie symmetry generators are obtaining using the computer algebra package SADE (symmetry analysis of differential equations), developed at our group. (author)
The Importance of Non-Linearity on Turbulent Fluxes
DEFF Research Database (Denmark)
Rokni, Masoud
2007-01-01
Two new non-linear models for the turbulent heat fluxes are derived and developed from the transport equation of the scalar passive flux. These models are called as non-linear eddy diffusivity and non-linear scalar flux. The structure of these models is compared with the exact solution which...... is derived from the Cayley-Hamilton theorem and contains a three term-basis plus a non-linear term due to scalar fluxes. In order to study the performance of the model itself, all other turbulent quantities are taken from a DNS channel flow data-base and thus the error source has been minimized. The results...... are compared with the DNS channel flow and good agreement is achieved. It has been shown that the non-linearity parts of the models are important to capture the true path of the streamwise scalar fluxes. It has also been shown that one of model constant should have negative sign rather than positive, which had...
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.
Positive solutions of quasilinear parabolic systems with Dirichlet boundary condition
Pao, C. V.; Ruan, W. H.
Coupled systems for a class of quasilinear parabolic equations and the corresponding elliptic systems, including systems of parabolic and ordinary differential equations are investigated. The aim of this paper is to show the existence, uniqueness, and asymptotic behavior of time-dependent solutions. Also investigated is the existence of positive maximal and minimal solutions of the corresponding quasilinear elliptic system. The elliptic operators in both systems are allowed to be degenerate in the sense that the density-dependent diffusion coefficients D(u) may have the property D(0)=0 for some or all i=1,…,N, and the boundary condition is u=0. Using the method of upper and lower solutions, we show that a unique global classical time-dependent solution exists and 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 scalar polynomial growth problem, a coupled system of polynomial growth problem, and a two component competition model in ecology.
Stability of a flexible structure with destabilizing boundary conditions
Shubov, M.; Shubov, V.
2016-07-01
The Euler-Bernoulli beam model with non-dissipative boundary conditions of feedback control type is investigated. Components of the two-dimensional input vector are shear and moment at the right end, and components of the observation vector are time derivatives of displacement and slope at the right end. The codiagonal matrix depending on two control parameters relates input and observation. The paper contains five results. First, asymptotic approximation for eigenmodes is derived. Second, `the main identity' is established. It provides a relation between mode shapes of two systems: one with non-zero control parameters and the other one with zero control parameters. Third, when one control parameter is positive and the other one is zero, `the main identity' yields stability of all eigenmodes (though the system is non-dissipative). Fourth, the stability of eigenmodes is extended to the case when one control parameter is positive, and the other one is sufficiently small. Finally, existence and properties of `deadbeat' modes are investigated.
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.
CT image segmentation using FEM with optimized boundary condition.
Directory of Open Access Journals (Sweden)
Hiroyuki Hishida
Full Text Available The authors propose a CT image segmentation method using structural analysis that is useful for objects with structural dynamic characteristics. Motivation of our research is from the area of genetic activity. In order to reveal the roles of genes, it is necessary to create mutant mice and measure differences among them by scanning their skeletons with an X-ray CT scanner. The CT image needs to be manually segmented into pieces of the bones. It is a very time consuming to manually segment many mutant mouse models in order to reveal the roles of genes. It is desirable to make this segmentation procedure automatic. Although numerous papers in the past have proposed segmentation techniques, no general segmentation method for skeletons of living creatures has been established. Against this background, the authors propose a segmentation method based on the concept of destruction analogy. To realize this concept, structural analysis is performed using the finite element method (FEM, as structurally weak areas can be expected to break under conditions of stress. The contribution of the method is its novelty, as no studies have so far used structural analysis for image segmentation. The method's implementation involves three steps. First, finite elements are created directly from the pixels of a CT image, and then candidates are also selected in areas where segmentation is thought to be appropriate. The second step involves destruction analogy to find a single candidate with high strain chosen as the segmentation target. The boundary conditions for FEM are also set automatically. Then, destruction analogy is implemented by replacing pixels with high strain as background ones, and this process is iterated until object is decomposed into two parts. Here, CT image segmentation is demonstrated using various types of CT imagery.
Generalized non-linear strength theory and transformed stress space
Institute of Scientific and Technical Information of China (English)
YAO Yangping; LU Dechun; ZHOU Annan; ZOU Bo
2004-01-01
Based on the test data of frictional materials and previous research achievements in this field, a generalized non-linear strength theory (GNST) is proposed. It describes non-linear strength properties on the π-plane and the meridian plane using a unified formula, and it includes almost all the present non-linear strength theories, which can be used in just one material. The shape of failure function of the GNST is a smooth curve between the SMP criterion and the Mises criterion on the π-plane, and an exponential curve on the meridian plane. Through the transformed stress space based on the GNST, the combination of the GNST and various constitutive models using p and q as stress parameters can be realized simply and rationally in three-dimensional stress state.
Controlling ultrafast currents by the non-linear photogalvanic effect
Wachter, Georg; Lemell, Christoph; Tong, Xiao-Min; Yabana, Kazuhiro; Burgdörfer, Joachim
2015-01-01
We theoretically investigate the effect of broken inversion symmetry on the generation and control of ultrafast currents in a transparent dielectric (SiO2) by strong femto-second optical laser pulses. Ab-initio simulations based on time-dependent density functional theory predict ultrafast DC currents that can be viewed as a non-linear photogalvanic effect. Most surprisingly, the direction of the current undergoes a sudden reversal above a critical threshold value of laser intensity I_c ~ 3.8*10^13 W/cm2. We trace this switching to the transition from non-linear polarization currents to the tunneling excitation regime. We demonstrate control of the ultrafast currents by the time delay between two laser pulses. We find the ultrafast current control by the non-linear photogalvanic effect to be remarkably robust and insensitive to laser-pulse shape and carrier-envelope phase.
An algorithm for earthwork allocation considering non-linear factors
Institute of Scientific and Technical Information of China (English)
WANG Ren-chao; LIU Jin-fei
2008-01-01
For solving the optimization model of earthwork allocation considering non-linear factors, a hybrid al-gorithm combined with the ant algorithm (AA) and particle swarm optimization (PSO) is proposed in this pa-per. Then the proposed method and the LP method are used respectively in solving a linear allocation model of a high rockfill dam project. Results obtained by these two methods are compared each other. It can be conclu-ded that the solution got by the proposed method is extremely approximate to the analytic solution of LP method. The superiority of the proposed method over the LP method in solving a non-linear allocation model is illustrated by a non-linear case. Moreover, further researches on improvement of the algorithm and the allocation model are addressed.
Non-linear behaviour of large-area avalanche photodiodes
Fernandes, L M P; Monteiro, C M B; Santos, J M; Morgado, R E
2002-01-01
The characterisation of photodiodes used as photosensors requires a determination of the number of electron-hole pairs produced by scintillation light. One method involves comparing signals produced by X-ray absorptions occurring directly in the avalanche photodiode with the light signals. When the light is derived from light-emitting diodes in the 400-600 nm range, significant non-linear behaviour is reported. In the present work, we extend the study of the linear behaviour to large-area avalanche photodiodes, of Advanced Photonix, used as photosensors of the vacuum ultraviolet (VUV) scintillation light produced by argon (128 nm) and xenon (173 nm). We observed greater non-linearities in the avalanche photodiodes for the VUV scintillation light than reported previously for visible light, but considerably less than the non-linearities observed in other commercially available avalanche photodiodes.
Pattern formation due to non-linear vortex diffusion
Wijngaarden, Rinke J.; Surdeanu, R.; Huijbregtse, J. M.; Rector, J. H.; Dam, B.; Einfeld, J.; Wördenweber, R.; Griessen, R.
Penetration of magnetic flux in YBa 2Cu 3O 7 superconducting thin films in an external magnetic field is visualized using a magneto-optic technique. A variety of flux patterns due to non-linear vortex diffusion is observed: (1) Roughening of the flux front with scaling exponents identical to those observed in burning paper including two distinct regimes where respectively spatial disorder and temporal disorder dominate. In the latter regime Kardar-Parisi-Zhang behavior is found. (2) Fractal penetration of flux with Hausdorff dimension depending on the critical current anisotropy. (3) Penetration as ‘flux-rivers’. (4) The occurrence of commensurate and incommensurate channels in films with anti-dots as predicted in numerical simulations by Reichhardt, Olson and Nori. It is shown that most of the observed behavior is related to the non-linear diffusion of vortices by comparison with simulations of the non-linear diffusion equation appropriate for vortices.
Non-linear system identification in flow-induced vibration
Energy Technology Data Exchange (ETDEWEB)
Spanos, P.D.; Zeldin, B.A. [Rice Univ., Houston, TX (United States); Lu, R. [Hudson Engineering Corp., Houston, TX (United States)
1996-12-31
The paper introduces a method of identification of non-linear systems encountered in marine engineering applications. The non-linearity is accounted for by a combination of linear subsystems and known zero-memory non-linear transformations; an equivalent linear multi-input-single-output (MISO) system is developed for the identification problem. The unknown transfer functions of the MISO system are identified by assembling a system of linear equations in the frequency domain. This system is solved by performing the Cholesky decomposition of a related matrix. It is shown that the proposed identification method can be interpreted as a {open_quotes}Gram-Schmidt{close_quotes} type of orthogonal decomposition of the input-output quantities of the equivalent MISO system. A numerical example involving the identification of unknown parameters of flow (ocean wave) induced forces on offshore structures elucidates the applicability of the proposed method.
Non-linear Growth Models in Mplus and SAS.
Grimm, Kevin J; Ram, Nilam
2009-10-01
Non-linear growth curves or growth curves that follow a specified non-linear function in time enable researchers to model complex developmental patterns with parameters that are easily interpretable. In this paper we describe how a variety of sigmoid curves can be fit using the Mplus structural modeling program and the non-linear mixed-effects modeling procedure NLMIXED in SAS. Using longitudinal achievement data collected as part of a study examining the effects of preschool instruction on academic gain we illustrate the procedures for fitting growth models of logistic, Gompertz, and Richards functions. Brief notes regarding the practical benefits, limitations, and choices faced in the fitting and estimation of such models are included.
Reactive Boundary Conditions as Limits of Interaction Potentials for Brownian and Langevin Dynamics
Chapman, S Jonathan; Isaacson, Samuel A
2015-01-01
A popular approach to modeling bimolecular reactions between diffusing molecules is through the use of reactive boundary conditions. One common model is the Smoluchowski partial absorption condition, which uses a Robin boundary condition in the separation coordinate between two possible reactants. This boundary condition can be interpreted as an idealization of a reactive interaction potential model, in which a potential barrier must be surmounted before reactions can occur. In this work we show how the reactive boundary condition arises as the limit of an interaction potential encoding a steep barrier within a shrinking region in the particle separation, where molecules react instantly upon reaching the peak of the barrier. The limiting boundary condition is derived by the method of matched asymptotic expansions, and shown to depend critically on the relative rate of increase of the barrier height as the width of the potential is decreased. Limiting boundary conditions for the same interaction potential in b...
Coupling the Gaussian free fields with free and with zero boundary conditions via common level lines
Qian, Wei; Werner, Wendelin
2017-01-01
We describe level-line decompositions of the two-dimensional Gaussian Free Field (GFF) with free boundary conditions. In particular, we point out a simple way to couple the GFF with free boundary conditions in a domain with the GFF with zero boundary conditions in the same domain: Starting from the latter, one just has to sample at random all the signs of the height gaps on its boundary touching 0-level lines (these signs are alternating for the zero-boundary GFF) in order to obtain a free bo...
Realization of non-linear coherent states by photonic lattices
Directory of Open Access Journals (Sweden)
Shahram Dehdashti
2015-06-01
Full Text Available In this paper, first, by introducing Holstein-Primakoff representation of α-deformed algebra, we achieve the associated non-linear coherent states, including su(2 and su(1, 1 coherent states. Second, by using waveguide lattices with specific coupling coefficients between neighbouring channels, we generate these non-linear coherent states. In the case of positive values of α, we indicate that the Hilbert size space is finite; therefore, we construct this coherent state with finite channels of waveguide lattices. Finally, we study the field distribution behaviours of these coherent states, by using Mandel Q parameter.
Comparison of Simulated and Measured Non-linear Ultrasound Fields
DEFF Research Database (Denmark)
Du, Yigang; Jensen, Henrik; Jensen, Jørgen Arendt
2011-01-01
In this paper results from a non-linear AS (angular spectrum) based ultrasound simulation program are compared to water-tank measurements. A circular concave transducer with a diameter of 1 inch (25.4 mm) is used as the emitting source. The measured pulses are rst compared with the linear...... simulation program Field II, which will be used to generate the source for the AS simulation. The generated non-linear ultrasound eld is measured by a hydrophone in the focal plane. The second harmonic component from the measurement is compared with the AS simulation, which is used to calculate both...
Non-linear effects in bunch compressor of TARLA
Yildiz, Hüseyin; Aksoy, Avni; Arikan, Pervin
2016-03-01
Transport of a beam through an accelerator beamline is affected by high order and non-linear effects such as space charge, coherent synchrotron radiation, wakefield, etc. These effects damage form of the beam, and they lead particle loss, emittance growth, bunch length variation, beam halo formation, etc. One of the known non-linear effects on low energy machine is space charge effect. In this study we focus on space charge effect for Turkish Accelerator and Radiation Laboratory in Ankara (TARLA) machine which is designed to drive InfraRed Free Electron Laser covering the range of 3-250 µm. Moreover, we discuss second order effects on bunch compressor of TARLA.
Foundations of the non-linear mechanics of continua
Sedov, L I
1966-01-01
International Series of Monographs on Interdisciplinary and Advanced Topics in Science and Engineering, Volume 1: Foundations of the Non-Linear Mechanics of Continua deals with the theoretical apparatus, principal concepts, and principles used in the construction of models of material bodies that fill space continuously. This book consists of three chapters. Chapters 1 and 2 are devoted to the theory of tensors and kinematic applications, focusing on the little-known theory of non-linear tensor functions. The laws of dynamics and thermodynamics are covered in Chapter 3.This volume is suitable
Realization of non-linear coherent states by photonic lattices
Energy Technology Data Exchange (ETDEWEB)
Dehdashti, Shahram, E-mail: shdehdashti@zju.edu.cn; Li, Rujiang; Chen, Hongsheng, E-mail: hansomchen@zju.edu.cn [State Key Laboratory of Modern Optical Instrumentations, Zhejiang University, Hangzhou 310027 (China); The Electromagnetics Academy at Zhejiang University, Zhejiang University, Hangzhou 310027 (China); Liu, Jiarui, E-mail: jrliu@zju.edu.cn; Yu, Faxin [School of Aeronautics and Astronautics, Zhejiang University, Hangzhou 310027 (China)
2015-06-15
In this paper, first, by introducing Holstein-Primakoff representation of α-deformed algebra, we achieve the associated non-linear coherent states, including su(2) and su(1, 1) coherent states. Second, by using waveguide lattices with specific coupling coefficients between neighbouring channels, we generate these non-linear coherent states. In the case of positive values of α, we indicate that the Hilbert size space is finite; therefore, we construct this coherent state with finite channels of waveguide lattices. Finally, we study the field distribution behaviours of these coherent states, by using Mandel Q parameter.
Hejranfar, Kazem; Parseh, Kaveh
2017-09-01
The preconditioned characteristic boundary conditions based on the artificial compressibility (AC) method are implemented at artificial boundaries for the solution of two- and three-dimensional incompressible viscous flows in the generalized curvilinear coordinates. The compatibility equations and the corresponding characteristic variables (or the Riemann invariants) are mathematically derived and then applied as suitable boundary conditions in a high-order accurate incompressible flow solver. The spatial discretization of the resulting system of equations is carried out by the fourth-order compact finite-difference (FD) scheme. In the preconditioning applied here, the value of AC parameter in the flow field and also at the far-field boundary is automatically calculated based on the local flow conditions to enhance the robustness and performance of the solution algorithm. The code is fully parallelized using the Concurrency Runtime standard and Parallel Patterns Library (PPL) and its performance on a multi-core CPU is analyzed. The incompressible viscous flows around a 2-D circular cylinder, a 2-D NACA0012 airfoil and also a 3-D wavy cylinder are simulated and the accuracy and performance of the preconditioned characteristic boundary conditions applied at the far-field boundaries are evaluated in comparison to the simplified boundary conditions and the non-preconditioned characteristic boundary conditions. It is indicated that the preconditioned characteristic boundary conditions considerably improve the convergence rate of the solution of incompressible flows compared to the other boundary conditions and the computational costs are significantly decreased.
A Convective-like Energy-Stable Open Boundary Condition for Simulations of Incompressible Flows
Dong, Suchuan
2015-01-01
We present a new energy-stable open boundary condition, and an associated numerical algorithm, for simulating incompressible flows with outflow/open boundaries. This open boundary condition ensures the energy stability of the system, even when strong vortices or backflows occur at the outflow boundary. Under certain situations it can be reduced to a form that can be analogized to the usual convective boundary condition. One prominent feature of this boundary condition is that it provides a control over the velocity on the outflow/open boundary. This is not available with the other energy-stable open boundary conditions from previous works. Our numerical algorithm treats the proposed open boundary condition based on a rotational velocity-correction type strategy. It gives rise to a Robin-type condition for the discrete pressure and a Robin-type condition for the discrete velocity on the outflow/open boundary, respectively at the pressure and the velocity sub-steps. We present extensive numerical experiments on...
Error transport equation boundary conditions for the Euler and Navier-Stokes equations
Phillips, Tyrone S.; Derlaga, Joseph M.; Roy, Christopher J.; Borggaard, Jeff
2017-02-01
Discretization error is usually the largest and most difficult numerical error source to estimate for computational fluid dynamics, and boundary conditions often contribute a significant source of error. Boundary conditions are described with a governing equation to prescribe particular behavior at the boundary of a computational domain. Boundary condition implementations are considered sufficient when discretized with the same order of accuracy as the primary governing equations; however, careless implementations of boundary conditions can result in significantly larger numerical error. Investigations into different numerical implementations of Dirichlet and Neumann boundary conditions for Burgers' equation show a significant impact on the accuracy of Richardson extrapolation and error transport equation discretization error estimates. The development of boundary conditions for Burgers' equation shows significant improvements in discretization error estimates in general and a significant improvement in truncation error estimation. The latter of which is key to accurate residual-based discretization error estimation. This research investigates scheme consistent and scheme inconsistent implementations of inflow and outflow boundary conditions up to fourth order accurate and a formulation for a slip wall boundary condition for truncation error estimation are developed for the Navier-Stokes and Euler equations. The scheme consistent implementation resulted in much smoother truncation error near the boundaries and more accurate discretization error estimates.
Impact of the kinetic boundary condition on porous media flow in the lattice Boltzmann formulation
Singh, Shiwani; Jiang, Fei; Tsuji, Takeshi
2017-07-01
To emphasize the importance of the kinetic boundary condition for micro- to nanoscale flow, we present an ad hoc kinetic boundary condition suitable for torturous geological porous media. We found that the kinetic boundary condition is one of the essential features which should be supplemented to the standard lattice Boltzmann scheme in order to obtain accurate continuum observables. The claim is validated using a channel flow setup by showing the agreement of mass flux with analytical value. Further, using a homogeneous porous structure, the importance of the kinetic boundary condition is shown by comparing the permeability correction factor with the analytical value. Finally, the proposed alternate to the kinetic boundary condition is validated by showing its capability to capture the basic feature of the kinetic boundary condition.
RADIATION BOUNDARY CONDITIONS FOR MAXWELL'S EQUATIONS: A REVIEW OF ACCURATE TIME-DOMAIN FORMULATIONS
Institute of Scientific and Technical Information of China (English)
Thomas Hagstrom; Stephen Lau
2007-01-01
We review time-domain formulations of radiation boundary conditions for Maxwell's equations, focusing on methods which can deliver arbitrary accuracy at acceptable computational cost. Examples include fast evaluations of nonlocal conditions on symmetric and general boundaries, methods based on identifying and evaluating equivalent sources, and local approximations such as the perfectly matched layer and sequences of local boundary conditions. Complexity estimates are derived to assess work and storage requirements as a function of wavelength and simulation time.
Supersymmetry Breaking through Boundary Conditions Associated with the $U(1)_{R}$
Takenaga, K
1998-01-01
The effects of boundary conditions imposed on the fields for the compactified space directions to the supersymmetric theories are discussed. The boundary conditions can be taken to be periodic up to the degrees of freedom of localized $U(1)_{R}$ transformations. The boundary condition breaks the supersymmetry to yield universal soft supersymmetry breaking terms. The 4-dimensional supersymmetric QED with one flavour and the pure supersymmetric QCD are studied as toy models when one of the space coordinates is compactified on $S^1$.
Revisit boundary conditions for the self-adjoint angular flux formulation
Energy Technology Data Exchange (ETDEWEB)
Wang, Yaqi [Idaho National Lab. (INL), Idaho Falls, ID (United States); Gleicher, Frederick N. [Idaho National Lab. (INL), Idaho Falls, ID (United States)
2015-03-01
We revisit the boundary conditions for SAAF. We derived the equivalent parity variational form ready for coding up. The more rigorous approach of evaluating odd parity should be solving the odd parity equation coupled with the even parity. We proposed a symmetric reflecting boundary condition although neither positive definiteness nor even-odd decoupling is achieved. A simple numerical test verifies the validity of these boundary conditions.
Analysis of boundary conditions for SSME subsonic internal viscous flow analysis
Baker, A. J.
1986-01-01
A study was completed of mathematically proper boundary conditions for unique numerical solution of internal, viscous, subsonic flows in the space shuttle main engine. The study has concentrated on well posed considerations, with emphasis on computational efficiency and numerically stable boundary condition statements. The method of implementing the established boundary conditions is applicable to a wide variety of finite difference and finite element codes, as demonstrated.
A method for solving systems of non-linear differential equations with moving singularities
Gousheh, S S; Ghafoori-Tabrizi, K
2003-01-01
We present a method for solving a class of initial valued, coupled, non-linear differential equations with `moving singularities' subject to some subsidiary conditions. We show that this type of singularities can be adequately treated by establishing certain `moving' jump conditions across them. We show how a first integral of the differential equations, if available, can also be used for checking the accuracy of the numerical solution.
Directory of Open Access Journals (Sweden)
Ćosić Mladen
2015-01-01
Full Text Available The paper deals with methodology developed and presented for analyzing the damage on structures exposed to accidental and seismic actions. The procedure is based on non-linear numerical analysis, taking into account the principles of Performance-Based Seismic Design (PBSD. The stiffness matrix of the effects of vertical action is used as the initial stiffness matrix in non-linear analysis which simulates the collapse of individual ground-floor columns, forming thereby a number of possible scenarios. By the end of the analysis that simulates the collapse of individual columns, the stiffness matrix is used as the initial stiffness matrix for Non-linear Static Pushover Analysis (NSPA of bi-directional seismic action (X and Y directions. Target displacement analyses were conducted using the Capacity Spectrum Method (CSM. The structure's conditions/state was assessed based on the calculated global and inter-storey drifts and the damage coefficient developed. The damage level to the building was established using an integrated approach based on global and inter-storey drifts, so that, depending on the level of displacements for which the drifts are identified, a more reliable answer can be obtained. Applying the damage coefficient, a prompt, reliable and accurate indication can be obtained on the damage level to the entire structure in the capacitive domain, from elastic and non-linear to collapse state.
Characteristics of the Main Journal Bearings of an Engine Based on Non-linear Dynamics
Institute of Scientific and Technical Information of China (English)
NI Guangjian; ZHANG Junhong; CHENG Xiaoming
2009-01-01
Many simple nonlinear main journal bearing models have been studied theoretically, but the connection to existing engineering system has not been equally investigated. The consideration of the characteristics of engine main journal bearings may provide a prediction of the bearing load and lubrication. Due to the strong non-linear features in bearing lubrication procedure, it is difficult to predict those characteristics. A non-linear dynamic model is described for analyzing the characteristics of engine main journal bearings. Components such as crankshaft, main journals and con rods are found by applying the finite element method. Non-linear spring/dampers are introduced to imitate the constraint and supporting functions provided by the main bearing and oil film. The engine gas pressure is imposed as excitation on the model via the engine piston, con rod, etc. The bearing reaction force is calculated over one engine cycle, and meanwhile, the oil film thickness and pressure distribution are obtained based on Reynolds differential equation. It can be found that the maximum bearing reaction force always occurs when the maximum cylinder pressure arises in the cylinder adjacent to that bearing. The simulated minimum oil film thickness, which is 3 μm, demonstrates the reliability of the main journal bearings. This non-linear dynamic analysis may save computing efforts of engine main bearing design and also is of good precision and close connection to actual engine main journal bearing conditions.
Numerical simulation of non-linear phenomena in geotechnical engineering
DEFF Research Database (Denmark)
Sørensen, Emil Smed
Geotechnical problems are often characterized by the non-linear behavior of soils and rock which are strongly linked to the inherent properties of the porous structure of the material as well as the presence and possible flow of any surrounding fluids. Dynamic problems involving such soil-fluid i...
Implementation of neural network based non-linear predictive control
DEFF Research Database (Denmark)
Sørensen, Paul Haase; Nørgård, Peter Magnus; Ravn, Ole
1999-01-01
of non-linear systems. GPC is model based and in this paper we propose the use of a neural network for the modeling of the system. Based on the neural network model, a controller with extended control horizon is developed and the implementation issues are discussed, with particular emphasis...
Algorithms for non-linear M-estimation
DEFF Research Database (Denmark)
Madsen, Kaj; Edlund, O; Ekblom, H
1997-01-01
a sequence of estimation problems for linearized models is solved. In the testing we apply four estimators to ten non-linear data fitting problems. The test problems are also solved by the Generalized Levenberg-Marquardt method and standard optimization BFGS method. It turns out that the new method...
Non-Linear Vibration of Euler-Bernoulli Beams
DEFF Research Database (Denmark)
Barari, Amin; Kaliji, H. D.; Domairry, G.
2011-01-01
In this paper, variational iteration (VIM) and parametrized perturbation (PPM)methods have been used to investigate non-linear vibration of Euler-Bernoulli beams subjected to the axial loads. The proposed methods do not require small parameter in the equation which is difficult to be found...
Range non-linearities correction in FMCW SAR
Meta, A.; Hoogeboom, P.; Ligthart, L.P.
2006-01-01
The limiting factor to the use of Frequency Modulated Continuous Wave (FMCW) technology with Synthetic Aperture Radar (SAR) techniques to produce lightweight, cost effective, low power consuming imaging sensors with high resolution, is the well known presence of non-linearities in the transmitted si
Non-Linear Langmuir Wave Modulation in Collisionless Plasmas
DEFF Research Database (Denmark)
Dysthe, K. B.; Pécseli, Hans
1977-01-01
A non-linear Schrodinger equation for Langmuir waves is presented. The equation is derived by using a fluid model for the electrons, while both a fluid and a Vlasov formulation are considered for the ion dynamics. The two formulations lead to significant differences in the final results, especially...
Non-Linear Interactive Stories in Computer Games
DEFF Research Database (Denmark)
Bangsø, Olav; Jensen, Ole Guttorm; Kocka, Tomas
2003-01-01
The paper introduces non-linear interactive stories (NOLIST) as a means to generate varied and interesting stories for computer games automatically. We give a compact representation of a NOLIST based on the specification of atomic stories, and show how to build an object-oriented Bayesian network...
Quantum-dot-based integrated non-linear sources
DEFF Research Database (Denmark)
Bernard, Alice; Mariani, Silvia; Andronico, Alessio
2015-01-01
The authors report on the design and the preliminary characterisation of two active non-linear sources in the terahertz and near-infrared range. The former is associated to difference-frequency generation between whispering gallery modes of an AlGaAs microring resonator, whereas the latter is gra...
Note About Hamiltonian Structure of Non-Linear Massive Gravity
Kluson, J
2011-01-01
We perform the Hamiltonian analysis of non-linear massive gravity action studied recently in arXiv:1106.3344 [hep-th]. We show that the Hamiltonian constraint is the second class constraint. As a result the theory possesses an odd number of the second class constraints and hence all non physical degrees of freedom cannot be eliminated.
Locally supersymmetric D=3 non-linear sigma models
Wit, B. de; Tollsten, A. K.; Nicolai, H.
1992-01-01
We study non-linear sigma models with N local supersymmetries in three space-time dimensions. For N=1 and 2 the target space of these models is Riemannian or Kahler, respectively. All N>2 theories are associated with Einstein spaces. For N=3 the target space is quaternionic, while for N=4 it general
Non-linear magnetorheological behaviour of an inverse ferrofluid
de Gans, B.J.; Hoekstra, Hans; Mellema, J.
1999-01-01
The non-linear magnetorheological behaviour is studied of a model system consisting of monodisperse silica particles suspended in a ferrofluid. The stress/strain curve as well as the flow curve was measured as a function of volume fraction silica particles and field strength, using a home-made
Development and Control of a Non Linear Magnetic Levitation System
Directory of Open Access Journals (Sweden)
A Sanjeevi Gandhi
2013-06-01
Full Text Available Nowadays, studies to develop and control non linear systems is of great significance. Magnetic Levitation System has gained considerable interests due to its great practical importance in different engineering fields In this paper an electromagnetic levitation system was developed and mathematical model for the system was derived. The developed system was controlled manually.
S-AMP for non-linear observation models
DEFF Research Database (Denmark)
Cakmak, Burak; Winther, Ole; Fleury, Bernard H.
2015-01-01
Recently we presented the S-AMP approach, an extension of approximate message passing (AMP), to be able to handle general invariant matrix ensembles. In this contribution we extend S-AMP to non-linear observation models. We obtain generalized AMP (GAMP) as the special case when the measurement...
Applications of non-linear methods in astronomy
Martens, P.C.H.
1984-01-01
In this review I discuss catastrophes, bifurcations and strange attractors in a non-mathematical manner by giving very simple examples that st ill contain the essence of the phenomenon. The salientresults of the applications of these non-linear methods in astrophysics are reviewed and include such d
Neural Generalized Predictive Control of a non-linear Process
DEFF Research Database (Denmark)
Sørensen, Paul Haase; Nørgård, Peter Magnus; Ravn, Ole
1998-01-01
qualities. The controller is a non-linear version of the well-known generalized predictive controller developed in linear control theory. It involves minimization of a cost function which in the present case has to be done numerically. Therefore, we develop the numerical algorithms necessary in substantial...
The DtN nonreflecting boundary condition for multiple scattering problems in the half-plane
Acosta, Sebastian; Malone, Bruce
2013-01-01
The multiple-Dirichlet-to-Neumann (multiple-DtN) non-reflecting boundary condition is adapted to acoustic scattering from obstacles embedded in the half-plane. The multiple-DtN map is coupled with the method of images as an alternative model for multiple acoustic scattering in the presence of acoustically soft and hard plane boundaries. As opposed to the current practice of enclosing all obstacles with a large semicircular artificial boundary that contains portion of the plane boundary, the proposed technique uses small artificial circular boundaries that only enclose the immediate vicinity of each obstacle in the half-plane. The adapted multiple-DtN condition is simultaneously imposed in each of the artificial circular boundaries. As a result the computational effort is significantly reduced. A computationally advantageous boundary value problem is numerically solved with a finite difference method supported on boundary-fitted grids. Approximate solutions to problems involving two scatterers of arbitrary geo...
An Explicit Time-Domain Hybrid Formulation Based on the Unified Boundary Condition
Energy Technology Data Exchange (ETDEWEB)
Madsen, N; Fasenfest, B J; White, D; Stowell, M; Jandhyala, V; Pingenot, J; Champagne, N J; Rockway, J D
2007-02-28
An approach to stabilize the two-surface, time domain FEM/BI hybrid by means of a unified boundary condition is presented. The first-order symplectic finite element formulation [1] is used along with a version of the unified boundary condition of Jin [2] reformulated for Maxwell's first-order equations in time to provide both stability and accuracy over the first-order ABC. Several results are presented to validate the numerical solutions. In particular the dipole in a free-space box is analyzed and compared to the Dirchlet boundary condition of Ziolkowski and Madsen [3] and to a Neuman boundary condition approach.
S-duality of boundary conditions and the Geometric Langlands program
Gaiotto, Davide
2016-01-01
Maximally supersymmetric gauge theory in four dimensions admits local boundary conditions which preserve half of the bulk supersymmetries. The S-duality of the bulk gauge theory can be extended in a natural fashion to act on such half-BPS boundary conditions. The purpose of this note is to explain the role these boundary conditions can play in the Geometric Langlands program. In particular, we describe how to obtain pairs of Geometric Langland dual objects from S-dual pairs of half-BPS boundary conditions.
Pekker, Leonid
2015-01-01
In this paper we propose new boundary conditions at the hot walls with thermionic electron emission for two-temperature thermal arc models. In the derived boundary conditions the walls are assumed to be made from refractory metals and that the erosion of the wall is small and, therefore, is not taken into account in the model. In these boundary conditions the plasma sheath formed at the electrode is considered as the interface between the plasma and the wall. The derived boundary conditions allow the calculation of the heat flux to the walls from the plasma and consequently the thermionic electron current that makes the two temperature thermal model self consistent.
Solitonic sectors, conformal boundary conditions and three-dimensional topological field theory
Schweigert, C
2000-01-01
The correlation functions of a two-dimensional rational conformal field theory, for an arbitrary number of bulk and boundary fields and arbitrary world sheets can be expressed in terms of Wilson graphs in appropriate three-manifolds. We present a systematic approach to boundary conditions that break bulk symmetries. It is based on the construction, by `alpha-induction', of a fusion ring for the boundary fields. Its structure constants are the annulus coefficients and its 6j-symbols give the OPE of boundary fields. Symmetry breaking boundary conditions correspond to solitonic sectors.
Borjan, Z.
2016-09-01
We consider critical Casimir force in the Ising strips with boundary conditions defined by standard normal and ordinary surface universality classes containing also the internal grain boundary. Using exact variational approach of Mikheev and Fisher we have elaborated on behaviors of Casimir amplitudes Δ++(g) , ΔOO(g) and Δ+O(g) , corresponding to normal-normal, ordinary-ordinary and mixed normal-ordinary boundary conditions, respectively, with g as a strength of the grain boundary. Closed analytic results describe Casimir amplitudes Δ++(g) and ΔOO(g) as continuous functions of the grain boundary's strength g, changing the character of the Casimir force from repulsive to attractive and vice versa for certain domains of g. Present results reveal a new type of symmetry between Casimir amplitudes Δ++(g) and ΔOO(g) . Unexpectedly simple constant result for the Casimir amplitude Δ+O(g) = π/12 we have comprehensively interpreted in terms of equilibrium states of the present Ising strip as a complex interacting system comprising two sub-systems. Short-distance expansions of energy density profiles in the vicinity of the grain boundary reveal new distant-wall correction amplitudes that we examined in detail. Analogy of present considerations with earlier more usual short-distance expansions near one of the (N), (O) and (SB) boundaries, as well as close to surfaces with variable boundary conditions refers to the set of scaling dimensions appearing in the present calculations but also to the discovery of the de Gennes-Fisher distant wall correction amplitudes.
Oscillations of a Beam on a Non-Linear Elastic Foundation under Periodic Loads
Directory of Open Access Journals (Sweden)
Donald Mark Santee
2006-01-01
Full Text Available The complexity of the response of a beam resting on a nonlinear elastic foundation makes the design of this structural element rather challenging. Particularly because, apparently, there is no algebraic relation for its load bearing capacity as a function of the problem parameters. Such an algebraic relation would be desirable for design purposes. Our aim is to obtain this relation explicitly. Initially, a mathematical model of a flexible beam resting on a non-linear elastic foundation is presented, and its non-linear vibrations and instabilities are investigated using several numerical methods. At a second stage, a parametric study is carried out, using analytical and semi-analytical perturbation methods. So, the influence of the various physical and geometrical parameters of the mathematical model on the non-linear response of the beam is evaluated, in particular, the relation between the natural frequency and the vibration amplitude and the first period doubling and saddle-node bifurcations. These two instability phenomena are the two basic mechanisms associated with the loss of stability of the beam. Finally Melnikov's method is used to determine an algebraic expression for the boundary that separates a safe from an unsafe region in the force parameters space. It is shown that this can be used as a basis for a reliable engineering design criterion.
Boundary conditions control for a Shallow-Water model
Kazantsev, Eugene
2012-01-01
A variational data assimilation technique was used to estimate optimal discretization of interpolation operators and derivatives in the nodes adjacent to the rigid boundary. Assimilation of artificially generated observational data in the shallow-water model in a square box and assimilation of real observations in the model of the Black sea are discussed. It is shown in both experiments that controlling the discretization of operators near a rigid boundary can bring the model solution closer to observations as in the assimilation window and beyond the window. This type of control allows also to improve climatic variability of the model.
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.
Directory of Open Access Journals (Sweden)
A. D. Pataraya
Full Text Available Non-linear α-ω; dynamo waves existing in an incompressible medium with the turbulence dissipative coefficients depending on temperature are studied in this paper. We investigate of α-ω solar non-linear dynamo waves when only the first harmonics of magnetic induction components are included. If we ignore the second harmonics in the non-linear equation, the turbulent magnetic diffusion coefficient increases together with the temperature, the coefficient of turbulent viscosity decreases, and for an interval of time the value of dynamo number is greater than 1. In these conditions a stationary solution of the non-linear equation for the dynamo wave's amplitude exists; meaning that the magnetic field is sufficiently excited. The amplitude of the dynamo waves oscillates and becomes stationary. Using these results we can explain the existence of Maunder's minimum.
Integral Invariance and Non-linearity Reduction for Proliferating Vorticity Scales in Fluid Dynamics
Lam, F
2013-01-01
A vorticity theory for incompressible fluid flows in the absence of solid boundaries is proposed. Some apriori bounds are established. They are used in an interpolation theory to show the well-posedness of the vorticity Cauchy problem. A non-linear integral equation for vorticity is derived and its solution is expressed in an expansion. Interpretations of flow evolutions starting from given initial data are given and elaborated. The kinetic theory for Maxwellian molecules with cut-off is revisited in order to link microscopic properties to flow characters on the continuum.
Conformal field theory, boundary conditions and applications to string theory
Schweigert, C.; Fuchs, J.; Walcher, J.
2000-01-01
This is an introduction to two-dimensional conformal field theory and its applications in string theory. Modern concepts of conformal field theory are explained, and it is outlined how they are used in recent studies of D-branes in the strong curvature regime by means of CFT on surfaces with boundary.
Modelling female fertility traits in beef cattle using linear and non-linear models.
Naya, H; Peñagaricano, F; Urioste, J I
2017-06-01
Female fertility traits are key components of the profitability of beef cattle production. However, these traits are difficult and expensive to measure, particularly under extensive pastoral conditions, and consequently, fertility records are in general scarce and somehow incomplete. Moreover, fertility traits are usually dominated by the effects of herd-year environment, and it is generally assumed that relatively small margins are kept for genetic improvement. New ways of modelling genetic variation in these traits are needed. Inspired in the methodological developments made by Prof. Daniel Gianola and co-workers, we assayed linear (Gaussian), Poisson, probit (threshold), censored Poisson and censored Gaussian models to three different kinds of endpoints, namely calving success (CS), number of days from first calving (CD) and number of failed oestrus (FE). For models involving FE and CS, non-linear models overperformed their linear counterparts. For models derived from CD, linear versions displayed better adjustment than the non-linear counterparts. Non-linear models showed consistently higher estimates of heritability and repeatability in all cases (h(2 ) 0.23 and r > 0.24, for non-linear models). While additive and permanent environment effects showed highly favourable correlations between all models (>0.789), consistency in selecting the 10% best sires showed important differences, mainly amongst the considered endpoints (FE, CS and CD). In consequence, endpoints should be considered as modelling different underlying genetic effects, with linear models more appropriate to describe CD and non-linear models better for FE and CS. © 2017 Blackwell Verlag GmbH.
Green's function of a heat problem with a periodic boundary condition
Erzhanov, Nurzhan E.
2016-08-01
In the paper, a nonlocal initial-boundary value problem for a non-homogeneous one-dimensional heat equation is considered. The domain under consideration is a rectangle. The classical initial condition with respect to t is put. A nonlocal periodic boundary condition by a spatial variable x is put. It is well-known that a solution of problem can be constructed in the form of convergent orthonormal series according to eigenfunctions of a spectral problem for an operator of multiple differentiation with periodic boundary conditions. Therefore Green's function can be also written in the form of an infinite series with respect to trigonometric functions (Fourier series). For classical first and second initial-boundary value problems there also exists a second representation of the Green's function by Jacobi function. In this paper we find the representation of the Green's function of the nonlocal initial-boundary value problem with periodic boundary conditions in the form of series according to exponents.
Absorption and impedance boundary conditions for phased geometrical-acoustics methods
DEFF Research Database (Denmark)
Jeong, Cheol-Ho
2012-01-01
developed on which boundary condition produces accurate results. In this study, various boundary conditions in terms of normal, random, and field incidence absorption coefficients and normal incidence surface impedance are used in a phased beam tracing model, and the simulated results are validated...... with boundary element solutions. Two rectangular rooms with uniform and non-uniform absorption distributions are tested. Effects of the neglect of reflection phase shift are also investigated. It is concluded that the impedance, random incidence, and field incidence absorption boundary conditions produce......Defining accurate acoustical boundary conditions is of crucial importance for room acoustic simulations. In predicting sound fields using phased geometrical acoustics methods, both absorption coefficients and surface impedances of the boundary surfaces can be used, but no guideline has been...
Absorption and impedance boundary conditions for phased geometrical-acoustics methods.
Jeong, Cheol-Ho
2012-10-01
Defining accurate acoustical boundary conditions is of crucial importance for room acoustic simulations. In predicting sound fields using phased geometrical acoustics methods, both absorption coefficients and surface impedances of the boundary surfaces can be used, but no guideline has been developed on which boundary condition produces accurate results. In this study, various boundary conditions in terms of normal, random, and field incidence absorption coefficients and normal incidence surface impedance are used in a phased beam tracing model, and the simulated results are validated with boundary element solutions. Two rectangular rooms with uniform and non-uniform absorption distributions are tested. Effects of the neglect of reflection phase shift are also investigated. It is concluded that the impedance, random incidence, and field incidence absorption boundary conditions produce reasonable results with some exceptions at low frequencies for acoustically soft materials.
An Implicit Method for Solving Fuzzy Partial Differential Equation with Nonlocal Boundary Conditions
Directory of Open Access Journals (Sweden)
B. Orouji
2015-06-01
Full Text Available In this paper we introduce a numerical solution for the fuzzy heat equation with nonlocal boundary conditions. The main purpose is finding a difference scheme for the one dimensional heat equation with nonlocal boundary conditions. In these types of problems, an integral equation is appeared in the boundary conditions. We first express the necessary materials and definitions, and then consider our difference scheme and next the integrals in the boundary equations are approximated by the composite trapezoid rule. In the final part, we present an example for checking the numerical results. In this example we obtain the Hausdorff distance between exact solution and approximate solution.
Nested Bethe Ansatz for Spin Ladder Model with Open Boundary Conditions
Institute of Scientific and Technical Information of China (English)
WU Jun-Fang; ZHANG Chun-Min; YUE Rui-Hong; LI Run-Ling
2005-01-01
The nested Bethe ansatz (BA) method is applied to find the eigenvalues and the eigenvectors of the transfer matrix for spin-ladder model with open boundary conditions. Based on the reflection equation, we find the general diagonal solution, which determines the generalboundary interaction in the Hamiltonian. We introduce the spin-ladder model with open boundary conditions. By finding the solution K± of the reflection equation which determines the nontrivial boundary terms in the Hamiltonian, we diagonalize the transfer matrix of the spin-ladder model with open boundary conditions in the framework of nested BA.
Boundary conditions for the Einstein-Christoffel formulation of Einstein's equations
Directory of Open Access Journals (Sweden)
Douglas N. Arnold
2007-02-01
Full Text Available Specifying boundary conditions continues to be a challenge in numerical relativity in order to obtain a long time convergent numerical simulation of Einstein's equations in domains with artificial boundaries. In this paper, we address this problem for the Einstein-Christoffel (EC symmetric hyperbolic formulation of Einstein's equations linearized around flat spacetime. First, we prescribe simple boundary conditions that make the problem well posed and preserve the constraints. Next, we indicate boundary conditions for a system that extends the linearized EC system by including the momentum constraints and whose solution solves Einstein's equations in a bounded domain.
Moist turbulent Rayleigh-Benard convection with Neumann and Dirichlet boundary conditions
Weidauer, Thomas
2012-01-01
Turbulent Rayleigh-Benard convection with phase changes in an extended layer between two parallel impermeable planes is studied by means of three-dimensional direct numerical simulations for Rayleigh numbers between 10^4 and 1.5\\times 10^7 and for Prandtl number Pr=0.7. Two different sets of boundary conditions of temperature and total water content are compared: imposed constant amplitudes which translate into Dirichlet boundary conditions for the scalar field fluctuations about the quiescent diffusive equilibrium and constant imposed flux boundary conditions that result in Neumann boundary conditions. Moist turbulent convection is in the conditionally unstable regime throughout this study for which unsaturated air parcels are stably and saturated air parcels unstably stratified. A direct comparison of both sets of boundary conditions with the same parameters requires to start the turbulence simulations out of differently saturated equilibrium states. Similar to dry Rayleigh-Benard convection the differences...
Directory of Open Access Journals (Sweden)
A. Malvandi
2015-01-01
Full Text Available The objective of this paper is to consider both effects of slip and convective heat boundary conditions on steady two-dimensional boundary layer flow of a nanofluid over a stretching sheet in the presence of blowing/suction simultaneously. Flow meets the Navier's slip condition at the surface and Biot number is also used to consider the effects of convective heat transfer. The employed model for nanofluid includes two-component four-equation nonhomogeneous equilibrium model that incorporates the effects of nanoparticle migration owing to Brownian motion and thermophoresis. The basic partial boundary layer equations have been transformed into a two-point boundary value problem via similarity variables. Results for impermeable isothermal surface and also no-slip boundary condition were in best agreements with those existing in literatures. Effects of governing parameters such as Biot number (Bi, slip parameter (λ, thermophoresis (Nt, Prandtl number (Pr, Lewis number (Le, Brownian motion (Nb and blowing/suction (S on reduced Nusselt and Sherwood numbers are analyzed and discussed in details. The obtained results indicate that unlike heat transfer rate, concentration rate is very sensitive to all parameters among which Le, S and Pr are the most effective ones.
Non-Linear Second-Order Periodic Systems with Non-Smooth Potential
Indian Academy of Sciences (India)
Evgenia H Papageorgiou; Nikolaos S, Papageorgiou
2004-08-01
In this paper we study second order non-linear periodic systems driven by the ordinary vector -Laplacian with a non-smooth, locally Lipschitz potential function. Our approach is variational and it is based on the non-smooth critical point theory. We prove existence and multiplicity results under general growth conditions on the potential function. Then we establish the existence of non-trivial homoclinic (to zero) solutions. Our theorem appears to be the first such result (even for smooth problems) for systems monitored by the -Laplacian. In the last section of the paper we examine the scalar non-linear and semilinear problem. Our approach uses a generalized Landesman–Lazer type condition which generalizes previous ones used in the literature. Also for the semilinear case the problem is at resonance at any eigenvalue.
Fully non-linear cosmological perturbations of multicomponent fluid and field systems
Hwang, Jai-chan; Noh, Hyerim; Park, Chan-Gyung
2016-09-01
We present fully non-linear and exact cosmological perturbation equations in the presence of multiple components of fluids and minimally coupled scalar fields. We ignore the tensor-type perturbation. The equations are presented without taking the temporal gauge condition in the Friedmann background with general curvature and the cosmological constant. We include the anisotropic stress. Even in the absence of anisotropic stress of individual component, the multiple component nature introduces the anisotropic stress in the collective fluid quantities. We prove the Newtonian limit of multiple fluids in the zero-shear gauge and the uniform-expansion gauge conditions, present the Newtonian hydrodynamic equations in the presence of general relativistic pressure in the zero-shear gauge, and present the fully non-linear equations and the third-order perturbation equations of the non-relativistic pressure fluids in the CDM-comoving gauge.
Non-linear aeroelastic prediction for aircraft applications
de C. Henshaw, M. J.; Badcock, K. J.; Vio, G. A.; Allen, C. B.; Chamberlain, J.; Kaynes, I.; Dimitriadis, G.; Cooper, J. E.; Woodgate, M. A.; Rampurawala, A. M.; Jones, D.; Fenwick, C.; Gaitonde, A. L.; Taylor, N. V.; Amor, D. S.; Eccles, T. A.; Denley, C. J.
2007-05-01
Current industrial practice for the prediction and analysis of flutter relies heavily on linear methods and this has led to overly conservative design and envelope restrictions for aircraft. Although the methods have served the industry well, it is clear that for a number of reasons the inclusion of non-linearity in the mathematical and computational aeroelastic prediction tools is highly desirable. The increase in available and affordable computational resources, together with major advances in algorithms, mean that non-linear aeroelastic tools are now viable within the aircraft design and qualification environment. The Partnership for Unsteady Methods in Aerodynamics (PUMA) Defence and Aerospace Research Partnership (DARP) was sponsored in 2002 to conduct research into non-linear aeroelastic prediction methods and an academic, industry, and government consortium collaborated to address the following objectives: To develop useable methodologies to model and predict non-linear aeroelastic behaviour of complete aircraft. To evaluate the methodologies on real aircraft problems. To investigate the effect of non-linearities on aeroelastic behaviour and to determine which have the greatest effect on the flutter qualification process. These aims have been very effectively met during the course of the programme and the research outputs include: New methods available to industry for use in the flutter prediction process, together with the appropriate coaching of industry engineers. Interesting results in both linear and non-linear aeroelastics, with comprehensive comparison of methods and approaches for challenging problems. Additional embryonic techniques that, with further research, will further improve aeroelastics capability. This paper describes the methods that have been developed and how they are deployable within the industrial environment. We present a thorough review of the PUMA aeroelastics programme together with a comprehensive review of the relevant research
Poynting flux-conserving low-altitude boundary conditions for global magnetospheric models
Xi, S.; Lotko, W.; Zhang, B.; Brambles, O. J.; Lyon, J. G.; Merkin, V. G.; Wiltberger, M.
2015-01-01
A method for specifying low-altitude or inner boundary conditions that conserve low-frequency, magnetic field-aligned, electromagnetic energy flux across the boundary in global magnetospheric magnetohydrodynamics (MHD) models is presented. The single-fluid Lyon-Fedder-Mobarry (LFM) model is used to verify this method, with comparisons between simulations using LFM's standard hardwall boundary conditions and the new flux-conserving boundary conditions. Identical idealized upstream solar wind and interplanetary magnetic field conditions and the same constant ionospheric conductance are used in both runs. The results show that, compared to LFM's standard hardwall boundary conditions, the flux-conserving method improves the transparency of the boundary for the flow of low-frequency (essentially DC) electromagnetic energy flux along field lines. As a consequence, the hemispheric integrated field-aligned DC Poynting flux just above the boundary is close to the hemispheric total Joule heating of the ionosphere, as it should be if electromagnetic energy is conserved. The MHD velocity and perpendicular currents are well-behaved near the inner boundary for the flux conserving boundary conditions.
General Considerations of the Electrostatic Boundary Conditions in Oxide Heterostructures
Energy Technology Data Exchange (ETDEWEB)
Higuchi, Takuya
2011-08-19
When the size of materials is comparable to the characteristic length scale of their physical properties, novel functionalities can emerge. For semiconductors, this is exemplified by the 'superlattice' concept of Esaki and Tsu, where the width of the repeated stacking of different semiconductors is comparable to the 'size' of the electrons, resulting in novel confined states now routinely used in opto-electronics. For metals, a good example is magnetic/non-magnetic multilayer films that are thinner than the spin-scattering length, from which giant magnetoresistance (GMR) emerged, used in the read heads of hard disk drives. For transition metal oxides, a similar research program is currently underway, broadly motivated by the vast array of physical properties that they host. This long-standing notion has been recently invigorated by the development of atomic-scale growth and probe techniques, which enables the study of complex oxide heterostructures approaching the precision idealized in Fig. 1(a). Taking the subset of oxides derived from the perovskite crystal structure, the close lattice match across many transition metal oxides presents the opportunity, in principle, to develop a 'universal' heteroepitaxial materials system. Hand-in-hand with the continual improvements in materials control, an increasingly relevant challenge is to understand the consequences of the electrostatic boundary conditions which arise in these structures. The essence of this issue can be seen in Fig. 1(b), where the charge sequence of the sublayer 'stacks' for various representative perovskites is shown in the ionic limit, in the (001) direction. To truly 'universally' incorporate different properties using different materials components, be it magnetism, ferroelectricity, superconductivity, etc., it is necessary to access and join different charge sequences, labelled here in analogy to the designations 'group IV, III-V, II
Institute of Scientific and Technical Information of China (English)
马西奎; 韩社教
2002-01-01
Based on the multipole expansion theory of the potential, a satisfactory interpretation is put forward of the exact nature of the approximations of asymptotic boundary condition (called the ABC) techniques for the numerical solutions of open-boundary static electromagnetic-field problems, and a definite physical meaning is bestowed on ABC, which provide a powerful theoretical background for laying down the operating rules and the key to the derivation of asymptotic boundary conditions. This paper is also intended to reveal the shortcomings of the conventional higher-order ABC, and at the same time to give the concept of a new type of higher-order ABC, and to present a somewhat different formulation of the new nth-order ABC. In order to test its feasibility, several simple problems of electrostatic potentials are analyzed. The results are found to be much better than those of conventional higher-order ABCs.
Vibrations of stretched damped beams under non-ideal boundary conditions
Indian Academy of Sciences (India)
Hakan Boyaci
2006-02-01
A simply supported damped Euler–Bernoulli beam with immovable end conditions are considered. The concept of non-ideal boundary conditions is applied to the beam problem. In accordance, the boundaries are assumed to allow small deﬂections and moments. Approximate analytical solution of the problem is found using the method of multiple scales, a perturbation technique.
Eigenstates of a particle in an array of hexagons with periodic boundary condition
Directory of Open Access Journals (Sweden)
A Nemati
2013-10-01
Full Text Available In this paper the problem of a particle in an array of hexagons with periodic boundary condition is solved. Using the projection operators, we categorize eigenfunctions corresponding to each of the irreducible representations of the symmetry group . Based on these results, the Dirichlet and Neumann boundary conditions are discussed.
Daalen, van Edwin F.G.; Broeze, Jan; Groesen, van Embrecht
1992-01-01
Radiation boundary conditions are derived for partial differential equations which describe wave phenomena. Assuming the evolution of the system to be governed by a Lagrangian variational principle, boundary conditions are obtained with Noether's theorem from the requirement that they transmit some
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.
The effect of external boundary conditions on condensation heat transfer in rotating heat pipes
Daniels, T. C.; Williams, R. J.
1979-01-01
Experimental evidence shows the importance of external boundary conditions on the overall performance of a rotating heat pipe condenser. Data are presented for the boundary conditions of constant heat flux and constant wall temperature for rotating heat pipes containing either pure vapor or a mixture of vapor and noncondensable gas as working fluid.
Question of consistent boundary conditions when simulating reversed field pinch dynamics. Revision 1
Energy Technology Data Exchange (ETDEWEB)
Mirin, A.A.
1986-03-01
The issue of proper boundary conditions when performing magnetohydrodynamic simulations of the reversed field pinch is examined. Of particular concern is the choice of constant current, which when combined with other commonly used boundary conditions, may, under careless implementation, lead to an inconsistency. It is shown that this may cause erroneous results. Cases both with and without Hall terms are presented.
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 the Boundary Condition Between Two Multiplying Media
Friedman, F. L.; Wigner, E. P.
1944-04-19
The transition region between two parts of a pile which have different compositions is investigated. In the case where the moderator is the same in both parts of the pile, it is found that the diffusion constant times thermal neutron density plus diffusion constant times fast neutron density satisfies the usual pile equations everywhere, right to the boundary. More complicated formulae apply in a more general case.
Conformal Boundary Conditions and Three-Dimensional Topological Field Theory
Felder, Giovanni; Fröhlich, Jürg; Fuchs, Jürgen; Schweigert, Christoph
2000-02-01
We present a general construction of all correlation functions of a two-dimensional rational conformal field theory, for an arbitrary number of bulk and boundary fields and arbitrary topologies. The correlators are expressed in terms of Wilson graphs in a certain three-manifold, the connecting manifold. The amplitudes constructed this way can be shown to be modular invariant and to obey the correct factorization rules.
Conformal boundary conditions and three-dimensional topological field theory
Felder, G; Fuchs, J; Schweigert, C
2000-01-01
We present a general construction of all correlation functions of a two-dimensional rational conformal field theory, for an arbitrary number of bulk and boundary fields and arbitrary topologies. The correlators are expressed in terms of Wilson graphs in a certain three-manifold, the connecting manifold. The amplitudes constructed this way can be shown to be modular invariant and to obey the correct factorization rules.
Modes and exceptional points in waveguides with impedance boundary conditions
Midya, Bikashkali
2016-01-01
A planar waveguide with impedance boundary, composed of non-perfect metallic plates, and with passive or active dielectric filling is considered. We show the possibility of selective mode guiding and amplification when homogeneous pump is added to the dielectric, and analyze differences in TE and TM mode propagation. Such a non-conservative system is also shown to feature exceptional points, for specific and experimentally tunable parameters, which are described for a particular case of transparent dielectric.
Non-linear effects for cylindrical gravitational two-soliton
Tomizawa, Shinya
2015-01-01
Using a cylindrical soliton solution to the four-dimensional vacuum Einstein equation, we study non-linear effects of gravitational waves such as Faraday rotation and time shift phenomenon. In the previous work, we analyzed the single-soliton solution constructed by the Pomeransky's improved inverse scattering method. In this work, we construct a new two-soliton solution with complex conjugate poles, by which we can avoid light-cone singularities unavoidable in a single soliton case. In particular, we compute amplitudes of such non-linear gravitational waves and time-dependence of the polarizations. Furthermore, we consider the time shift phenomenon for soliton waves, which means that a wave packet can propagate at slower velocity than light.
NON-LINEAR FINITE ELEMENT MODELING OF DEEP DRAWING PROCESS
Directory of Open Access Journals (Sweden)
Hasan YILDIZ
2004-03-01
Full Text Available Deep drawing process is one of the main procedures used in different branches of industry. Finding numerical solutions for determination of the mechanical behaviour of this process will save time and money. In die surfaces, which have complex geometries, it is hard to determine the effects of parameters of sheet metal forming. Some of these parameters are wrinkling, tearing, and determination of the flow of the thin sheet metal in the die and thickness change. However, the most difficult one is determination of material properties during plastic deformation. In this study, the effects of all these parameters are analyzed before producing the dies. The explicit non-linear finite element method is chosen to be used in the analysis. The numerical results obtained for non-linear material and contact models are also compared with the experiments. A good agreement between the numerical and the experimental results is obtained. The results obtained for the models are given in detail.
Non-linear irreversible thermodynamics of single-molecule experiments
Santamaria-Holek, I; Hidalgo-Soria, M; Perez-Madrid, A
2015-01-01
Irreversible thermodynamics of single-molecule experiments subject to external constraining forces of a mechanical nature is presented. Extending Onsager's formalism to the non-linear case of systems under non-equilibrium external constraints, we are able to calculate the entropy production and the general non-linear kinetic equations for the variables involved. In particular, we analyze the case of RNA stretching protocols obtaining critical oscillations between di?erent con?gurational states when forced by external means to remain in the unstable region of its free-energy landscape, as observed in experiments. We also calculate the entropy produced during these hopping events, and show how resonant phenomena in stretching experiments of single RNA macromolecules may arise. We also calculate the hopping rates using Kramer's approach obtaining a good comparison with experiments.
The linear-non-linear frontier for the Goldstone Higgs
Gavela, M B; Machado, P A N; Saa, S
2016-01-01
The minimal $SO(5)/SO(4)$ sigma model is used as a template for the ultraviolet completion of scenarios in which the Higgs particle is a low-energy remnant of some high-energy dynamics, enjoying a (pseudo) Nambu-Goldstone boson ancestry. Varying the $\\sigma$ mass allows to sweep from the perturbative regime to the customary non-linear implementations. The low-energy benchmark effective non-linear Lagrangian for bosons and fermions is obtained, determining as well the operator coefficients including linear corrections. At first order in the latter, three effective bosonic operators emerge which are independent of the explicit soft breaking assumed. The Higgs couplings to vector bosons and fermions turn out to be quite universal: the linear corrections are proportional to the explicit symmetry breaking parameters. Furthermore, we define an effective Yukawa operator which allows a simple parametrization and comparison of different heavy fermion ultraviolet completions. In addition, one particular fermionic compl...
Non-linear Young's double-slit experiment.
San Roman, Julio; Ruiz, Camilo; Perez, Jose Antonio; Delgado, Diego; Mendez, Cruz; Plaja, Luis; Roso, Luis
2006-04-01
The Young's double slit experiment is recreated using intense and short laser pulses. Our experiment evidences the role of the non-linear Kerr effect in the formation of interference patterns. In particular, our results evidence a mixed mechanism in which the zeroth diffraction order of each slit are mainly affected by self-focusing and self-phase modulation, while the higher orders propagate linearly. Despite of the complexity of the general problem of non-linear propagation, we demonstrate that this experiment retains its simplicity and allows for a geometrical interpretation in terms of simple optical paths. In consequence, our results may provide key ideas on experiments on the formation of interference patterns with intense laser fields in Kerr media.
SSNN toolbox for non-linear system identification
Luzar, Marcel; Czajkowski, Andrzej
2015-11-01
The aim of this paper is to develop and design a State Space Neural Network toolbox for a non-linear system identification with an artificial state-space neural networks, which can be used in a model-based robust fault diagnosis and control. Such toolbox is implemented in the MATLAB environment and it uses some of its predefined functions. It is designed in the way that any non-linear multi-input multi-output system is identified and represented in the classical state-space form. The novelty of the proposed approach is that the final result of the identification process is the state, input and output matrices, not only the neural network parameters. Moreover, the toolbox is equipped with the graphical user interface, which makes it useful for the users not familiar with the neural networks theory.
A non-linear model of economic production processes
Ponzi, A.; Yasutomi, A.; Kaneko, K.
2003-06-01
We present a new two phase model of economic production processes which is a non-linear dynamical version of von Neumann's neoclassical model of production, including a market price-setting phase as well as a production phase. The rate of an economic production process is observed, for the first time, to depend on the minimum of its input supplies. This creates highly non-linear supply and demand dynamics. By numerical simulation, production networks are shown to become unstable when the ratio of different products to total processes increases. This provides some insight into observed stability of competitive capitalist economies in comparison to monopolistic economies. Capitalist economies are also shown to have low unemployment.
Parametric Analysis of Fiber Non-Linearity in Optical systems
Directory of Open Access Journals (Sweden)
Abhishek Anand
2013-06-01
Full Text Available With the advent of technology Wavelength Division Multiplexing (WDM is always an area of interest in the field of optical communication. When combined with Erbium Doped Fiber Amplifier (EDFA, it provides high data transmission rate and low attenuation. But due to fiber non-linearity such as Self Phase Modulation (SPM and Cross Phase Modulation (XPM the system performance has degraded. This non-linearity depends on different parameters of an optical system such as channel spacing, power of the channel and length of the fiber section. The degradation can be seen in terms of phase deviation and Bit Error Rate (BER performance. Even after dispersion compensation at the fiber end, residual pulse broadening still exists due to cross talk penalty.
Non-linear Behavior of Curved Sandwich Panels
DEFF Research Database (Denmark)
Berggreen, Carl Christian; Jolma, P.; Karjalainen, J. P.;
2003-01-01
In this paper the non-linear behavior of curved sandwich panels is investigated both numerically and experimentally. Focus is on various aspects of finite element modeling and calculation procedures. A simply supported, singly curved, CFRP/PVC sandwich panel is analyzed under uniform pressure load...... and results are compared to test data. A novel test arrangement utilizing a water filled cushion to create the uniform pressure load on curved panel specimen is used to obtain the experimental data. The panel is modeled with three different commercial finite element codes. Two implicit and one explicit code...... are used with various element types, modeling approaches and material models. The results show that the theoretical and experimental methods generally show fair agreement in panel non-linear behavior before collapse. It is also shown that special attention to detail has to be taken, because the predicted...
Non-Linear Aeroelastic Stability of Wind Turbines
DEFF Research Database (Denmark)
Zhang, Zili; Sichani, Mahdi Teimouri; Li, Jie;
2013-01-01
As wind turbines increase in magnitude without a proportional increase in stiffness, the risk of dynamic instability is believed to increase. Wind turbines are time dependent systems due to the coupling between degrees of freedom defined in the fixed and moving frames of reference, which may...... trigger off internal resonances. Further, the rotational speed of the rotor is not constant due to the stochastic turbulence, which may also influence the stability. In this paper, a robust measure of the dynamic stability of wind turbines is suggested, which takes the collective blade pitch control...... and non-linear aero-elasticity into consideration. The stability of the wind turbine is determined by the maximum Lyapunov exponent of the system, which is operated directly on the non-linear state vector differential equations. Numerical examples show that this approach is promising for stability...
On the non-linear scale of cosmological perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Blas, Diego [Theory Division, CERN, 1211 Geneva (Switzerland); Garny, Mathias; Konstandin, Thomas, E-mail: diego.blas@cern.ch, E-mail: mathias.garny@desy.de, E-mail: Thomas.Konstandin@desy.de [DESY, Notkestr. 85, 22607 Hamburg (Germany)
2013-09-01
We discuss the convergence of cosmological perturbation theory. We prove that the polynomial enhancement of the non-linear corrections expected from the effects of soft modes is absent in equal-time correlators like the power or bispectrum. We first show this at leading order by resumming the most important corrections of soft modes to an arbitrary skeleton of hard fluctuations. We derive the same result in the eikonal approximation, which also allows us to show the absence of enhancement at any order. We complement the proof by an explicit calculation of the power spectrum at two-loop order, and by further numerical checks at higher orders. Using these insights, we argue that the modification of the power spectrum from soft modes corresponds at most to logarithmic corrections at any order in perturbation theory. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.
On the non-linear scale of cosmological perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Blas, Diego [European Organization for Nuclear Research (CERN), Geneva (Switzerland); Garny, Mathias; Konstandin, Thomas [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2013-04-15
We discuss the convergence of cosmological perturbation theory. We prove that the polynomial enhancement of the non-linear corrections expected from the effects of soft modes is absent in equal-time correlators like the power or bispectrum. We first show this at leading order by resumming the most important corrections of soft modes to an arbitrary skeleton of hard fluctuations. We derive the same result in the eikonal approximation, which also allows us to show the absence of enhancement at any order. We complement the proof by an explicit calculation of the power spectrum at two-loop order, and by further numerical checks at higher orders. Using these insights, we argue that the modification of the power spectrum from soft modes corresponds at most to logarithmic corrections. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.
Non-linear shape functions over time in the space-time finite element method
Directory of Open Access Journals (Sweden)
Kacprzyk Zbigniew
2017-01-01
Full Text Available This work presents a generalisation of the space-time finite element method proposed by Kączkowski in his seminal of 1970’s and early 1980’s works. Kączkowski used linear shape functions in time. The recurrence formula obtained by Kączkowski was conditionally stable. In this paper, non-linear shape functions in time are proposed.
Field computation in non-linear magnetic media using particle swarm optimization
Energy Technology Data Exchange (ETDEWEB)
Adly, A.A. E-mail: amradlya@intouch.com; Abd-El-Hafiz, S.K
2004-05-01
This paper presents an automated particle swarm optimization approach using which field computations may be carried out in devices involving non-linear magnetic media. Among the advantages of the proposed approach are its ability to handle complex geometries and its computational efficiency. The proposed approach has been implemented and computations were carried out for an electromagnet subject to different DC excitation conditions. These computations showed good agreement with the results obtained by the finite-element approach.
THE ARTIFICIAL BOUNDARY CONDITION FOR EXTERIOR OSEEN EQUATION IN 2-D SPACE
Institute of Scientific and Technical Information of China (English)
Chun-xiong Zheng; Hou-de Han
2002-01-01
A finite element method for the solution of Oseen equation in exterior domain is proposed. In this method, a circular artificial boundary is introduced to make the computational domain finite. Then, the exact relation between the normal stress and the prescribed velocity field on the artificial boundary can be obtained analytically. This relation can serve as an boundary condition for the boundary value problem defined on the finite domain bounded by the artificial boundary. Numerical experiment is presented to demonstrate the performance of the method.
Mogilevskii, Vadim
2011-01-01
We investigate in the paper general (not necessarily definite) canonical systems of differential equation in the framework of extension theory of symmetric linear relations. For this aim we first introduce the new notion of a boundary relation $\\G:\\gH^2\\to\\HH$ for $A^*$, where $\\gH$ is a Hilbert space, $A$ is a symmetric linear relation in $\\gH, \\cH_0$ is a boundary Hilbert space and $\\cH_1$ is a subspace in $\\cH_0$. Unlike known concept of a boundary relation (boundary triplet) for $A^*$ our definition of $\\G$ is applicable to relations $A$ with possibly unequal deficiency indices $n_\\pm(A)$. Next we develop the known results on minimal and maximal relations induced by the general canonical system $ J y'(t)-B(t)y(t)=\\D (t)f(t)$ on an interval $\\cI=(a,b),\\; -\\infty\\leq aboundary relation for $\\Tma$ we describe in terms of boundary conditions proper extensions of $\\Tmi$ in the case of the regular endpoint $a$ and arbitrary (possibly unequal)...
Defects in the discrete non-linear Schroedinger model
Energy Technology Data Exchange (ETDEWEB)
Doikou, Anastasia, E-mail: adoikou@upatras.gr [University of Patras, Department of Engineering Sciences, Physics Division, GR-26500 Patras (Greece)
2012-01-01
The discrete non-linear Schroedinger (NLS) model in the presence of an integrable defect is examined. The problem is viewed from a purely algebraic point of view, starting from the fundamental algebraic relations that rule the model. The first charges in involution are explicitly constructed, as well as the corresponding Lax pairs. These lead to sets of difference equations, which include particular terms corresponding to the impurity point. A first glimpse regarding the corresponding continuum limit is also provided.
Neural Generalized Predictive Control of a non-linear Process
DEFF Research Database (Denmark)
Sørensen, Paul Haase; Nørgård, Peter Magnus; Ravn, Ole
1998-01-01
The use of neural network in non-linear control is made difficult by the fact the stability and robustness is not guaranteed and that the implementation in real time is non-trivial. In this paper we introduce a predictive controller based on a neural network model which has promising stability...... detail and discuss the implementation difficulties. The neural generalized predictive controller is tested on a pneumatic servo sys-tem....
Measuring the Non-Linear Effects of Monetary Policy
Christian Matthes; Regis Barnichon
2015-01-01
This paper proposes a method to identify the non-linear effects of structural shocks by using Gaussian basis functions to parametrize impulse response functions. We apply our approach to monetary policy and find that the effect of a monetary intervention depends strongly on (i) the sign of the intervention, (ii) the size of the intervention, and (iii) the state of the business cycle at the time of the intervention. A contractionary policy has a strong adverse effect on output, much stronger t...
The coupling of non-linear supersymmetry to supergravity
Energy Technology Data Exchange (ETDEWEB)
Antoniadis, Ignatios [Sorbonne Universites, UPMC Paris 6, LPTHE, UMR CNRS 7589, Paris (France); University of Bern, Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, Bern (Switzerland); Markou, Chrysoula [Sorbonne Universites, UPMC Paris 6, LPTHE, UMR CNRS 7589, Paris (France)
2015-12-15
We study the coupling of non-linear supersymmetry to supergravity. The goldstino nilpotent superfield of global supersymmetry coupled to supergravity is described by a geometric action of the chiral curvature superfield R subject to the constraint (R - λ){sup 2} = 0 with an appropriate constant λ. This constraint can be found as the decoupling limit of the scalar partner of the goldstino in a class of f(R) supergravity theories. (orig.)
The coupling of non-linear supersymmetry to supergravity
Energy Technology Data Exchange (ETDEWEB)
Antoniadis, Ignatios, E-mail: antoniad@lpthe.jussieu.fr [LPTHE, UMR CNRS 7589, Sorbonne Universités, UPMC Paris 6, 75005, Paris (France); Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, Sidlestrasse 5, 3012, Bern (Switzerland); Markou, Chrysoula, E-mail: chrysoula@lpthe.jussieu.fr [LPTHE, UMR CNRS 7589, Sorbonne Universités, UPMC Paris 6, 75005, Paris (France)
2015-12-09
We study the coupling of non-linear supersymmetry to supergravity. The goldstino nilpotent superfield of global supersymmetry coupled to supergravity is described by a geometric action of the chiral curvature superfield R subject to the constraint (R-λ){sup 2}=0 with an appropriate constant λ. This constraint can be found as the decoupling limit of the scalar partner of the goldstino in a class of f(R) supergravity theories.
Non-linear high-frequency waves in the magnetosphere
Indian Academy of Sciences (India)
S Moolla; R Bharuthram; S V Singh; G S Lakhina
2003-12-01
Using ﬂuid theory, a set of equations is derived for non-linear high-frequency waves propagating oblique to an external magnetic ﬁeld in a three-component plasma consisting of hot electrons, cold electrons and cold ions. For parameters typical of the Earth’s magnetosphere, numerical solutions of the governing equations yield sinusoidal, sawtooth or bipolar wave-forms for the electric ﬁeld.
Linear Algebraic Method for Non-Linear Map Analysis
Energy Technology Data Exchange (ETDEWEB)
Yu,L.; Nash, B.
2009-05-04
We present a newly developed method to analyze some non-linear dynamics problems such as the Henon map using a matrix analysis method from linear algebra. Choosing the Henon map as an example, we analyze the spectral structure, the tune-amplitude dependence, the variation of tune and amplitude during the particle motion, etc., using the method of Jordan decomposition which is widely used in conventional linear algebra.
Non-Linear Vibration of Euler-Bernoulli Beams
DEFF Research Database (Denmark)
Barari, Amin; Kaliji, H. D.; Domairry, G.
2011-01-01
In this paper, variational iteration (VIM) and parametrized perturbation (PPM)methods have been used to investigate non-linear vibration of Euler-Bernoulli beams subjected to the axial loads. The proposed methods do not require small parameter in the equation which is difficult to be found for no...... for nonlinear problems. Comparison of VIM and PPM with Runge-Kutta 4th leads to highly accurate solutions....
Control of Non-linear Marine Cooling System
DEFF Research Database (Denmark)
Hansen, Michael; Stoustrup, Jakob; Bendtsen, Jan Dimon
2011-01-01
We consider the problem of designing control laws for a marine cooling system used for cooling the main engine and auxiliary components aboard several classes of container vessels. We focus on achieving simple set point control for the system and do not consider compensation of the non......-linearities, closed circuit flow dynamics or transport delays that are present in the system. Control laws are therefore designed using classical control theory and the performance of the design is illustrated through two simulation examples....
Adaptive spectral identification techniques in presence of undetected non linearities
Cella, G; Guidi, G M
2002-01-01
The standard procedure for detection of gravitational wave coalescing binaries signals is based on Wiener filtering with an appropriate bank of template filters. This is the optimal procedure in the hypothesis of addictive Gaussian and stationary noise. We study the possibility of improving the detection efficiency with a class of adaptive spectral identification techniques, analyzing their effect in presence of non stationarities and undetected non linearities in the noise
Likelihood inference for discretely observed non-linear diffusions
1998-01-01
This paper is concerned with the Bayesian estimation of non-linear stochastic differential equations when observations are discretely sampled. The estimation framework relies on the introduction of latent auxiliary data to complete the missing diffusion between each pair of measurements. Tuned Markov chain Monte Carlo (MCMC) methods based on the Metropolis-Hastings algorithm, in conjunction with the Euler-Maruyama discretization scheme, are used to sample the posterior distribution of the lat...